S4 – 03: LIVE from NCTM with Bethany and Dan

Hosts Bethany and Dan, both smiling, in a promotional image for the "Math Teacher Lounge" podcast, Season 4 Episode 3, titled "Live from NCTM!" with an

In this episode, co-hosts Bethany Lockhart Johnson and Dan Meyer are LIVE with more than one hundred Math Teacher Lounge listeners at the recent National Council of Teachers of Mathematics conference. Listen in as they answer the pressing question: Who is the best teacher in film or television?

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Presenter (00:00):
Ladies and gentlemen, from Math Teacher Lounge, we have Bethany Lockhart Johnson and Dan Meyer! <cheering>

Bethany Lockhart Johnson (00:08):
Doesn’t go well that the door was locked. Like, I could not get in! <Laugh>

Dan Meyer (00:12):
Yeah. Gotcha. All right. We’re gonna sit a little bit. Let’s see how that works—

Bethany Lockhart Johnson (00:16):
Hi!

Dan Meyer (00:16):
Yeah. I think we’ll stand up? Or whaddaya think, sit…?

Bethany Lockhart Johnson (00:19):
Should we stand? Hi.

Dan Meyer (00:22):
Hello. Great to see you folks. Yeah, I can hear you.

Bethany Lockhart Johnson (00:25):
Can you hear me? That’s—I know YOU can me. Can you hear me OK? OK! We’re here. Hello. Thank you for like, lining up and coming out and being here. Thank you!

Dan Meyer (00:35):
Means so much to me that you could be here for me, on my show, with Bethany Lockhart Johnson, my co-host. <Audience laughs>

Bethany Lockhart Johnson (00:40):
The hour has just started.

Dan Meyer (00:42):
We’re just getting going. Yeah. If you folks have heard the podcast, you don’t know how much gets cut out. And it’s like, mostly me just having, you know, anxious nerves and saying something silly and then we cut it out and we can’t do that here today. So it should be real fun for all of us, I think. Yeah.

Bethany Lockhart Johnson (00:55):
It’s not true. It’s mostly dancing. “Bethany, can you stop talking? Bethany?” Cause it’s mostly—

Dan Meyer (00:59):
“It’s my turn. It’s my turn! Bethany <laugh>! I haven’t been heard for a while.”

Bethany Lockhart Johnson (01:02):
Dan. We’re at an in-person conference.

Dan Meyer (01:05):
In-person BIG conference, I would say. I’d say a big conference. Yeah.

Bethany Lockhart Johnson (01:08):
And have you been to the Amplify booth?

Dan Meyer (01:11):
I have! Have these people? There’s a claw machine with free socks.

Bethany Lockhart Johnson (01:16):
Yeah. You’re saving me socks, right? That’s what you’re saying. <Laugh> I mean, it’s exciting. How has your conference been so far?

Dan Meyer (01:21):
So far it’s been a blast. I feel fed. I feel like the community’s been awesome. How are you feeling about it?

Bethany Lockhart Johnson (01:29):
OK. Let’s talk about me for just a second.

Dan Meyer (01:31):
Yeah. Talk about you.

Bethany Lockhart Johnson (01:31):
Last night, Dan, was the very first night that I was away from my toddler. <Audience: Aw!>

Dan Meyer (01:38):
Big commitment being here. Thank you.

Bethany Lockhart Johnson (01:40):
I got super-emotional walking back to the hotel after dinner, and then I got in my room, <laugh> I put on pajamas, and I turned on music. I slept so good!

Dan Meyer (01:50):
Yeah. <Audience laughs> Give it up for no kids! <Audience laughs> Hey!

Bethany Lockhart Johnson (01:55):
I love him so much. But I slept all the way through the night. Oh, by the way, I ordered room service in the morning.

Dan Meyer (02:01):
On Amplify.

Bethany Lockhart Johnson (02:01):
That bill’s coming. But it’s been a great conference and I’m so delighted to be here in person and to get to share energy…and hopefully that’s all we’re sharing today. Y’all got your tests, right? Yep. Sharing energy and community today. Because we know it’s been hard. Hardness. Hard.

Dan Meyer (02:25):
Yeah.

Bethany Lockhart Johnson (02:26):
Years. Hard. And to be in person, I know conferences reinvigorate me and I go back into my educational spaces feeling revitalized with new connections and new ideas to try. So yeah, I’ve been excited to be here. And thank you all for being here.

Dan Meyer (02:40):
Yep. I don’t care if I get six different strains of Covid here. I’m just thrilled to be here. <Audience laughs> I don’t know if you’ve had the same feeling, though, Bethany, you folks…I’m a little bit confused to some degree about what we’re doing. I just wanna be really transparent. This is my sarcastic voice but I’m being sincere here. It kind of feels like we’re in a little bit of a time capsule. Like we all got in a time capsule in 2019 and, you know, you open it back up and it’s like, OK, so we’re still, you know, talking about X, Y, or Z protocol for establishing classroom routines or whatever. And I’m like, OK! Like, I loved that in 2019! But I do admit, I’m still trying to figure out a little bit like, what are we doing now? What’s our relationship to the world out there? Things are very different. I have had some great sessions that I’ve enjoyed. I’m also like, still waiting for a session to draw a little blood. Do you know what I mean? Like there’s been sessions…no? OK. You’ve been in these sessions where it’s like, “Oh, ow.” Like, and you look down and there’s and there’s blood there. It’s like, I thought I knew what we were up to. Like, I thought I knew what teaching was and how we relate to the world. I dunno, like in any Danny Martin session in 2019, “Take a Knee” was one, where I was like, “Oh, OK. Like, I’m not as hot as I think I am here. Like, I’m part of a system.” That kind of thing for me draws blood. And I haven’t been in one of those yet. Been some great sessions. I’m a little hopeful that today we draw a little blood and think about what we’re doing here, is my hope here, if that’s OK. So Bethany’s gonna moderate that impulse and she’ll be the fun one and I’ll be the blood-drawing one.

Bethany Lockhart Johnson (04:05):
No, I don’t…that metaphor doesn’t speak to me personally. But what I will say is, I get what you’re saying about really wanting to be in that room where there’s like this synergy happening. No promises about that today other than—

Dan Meyer (04:18):
I promise. <Audience laughs> Go on.

Bethany Lockhart Johnson (04:20):
Other than I get what you’re saying. I’ll find my own metaphor that does not involve bloodshed, but.

Dan Meyer (04:25):
Sure. There’s a lot of ways we we could go about this today. And the one that I’m excited about is, you know, we could like, you know, analyze some results from students, and talk about what went into that. Look at classroom video. Lots of possibilities. But here’s what we’re up to today. Hope you’re into it. Which is, we are here in the heart of the entertainment industry. You know, Tinseltown! Um, the Big Apple! Uh…

Bethany Lockhart Johnson (04:47):
No!

Dan Meyer (04:47):
Come on. What do you got here? Um…

Bethany Lockhart Johnson (04:51):
It was daytime at night. Like the lights were so bright.

Dan Meyer (04:54):
The City of Lights.

Bethany Lockhart Johnson (04:55):
There was a movie premiere outside my hotel room, which I was not invited to, unfortunately. But so what are we doing today?

Dan Meyer (05:01):
So here’s what we’re doing. We are gonna settle, once and for all, a question you have not asked yourself yet, perhaps, but will want to know the answer to in a moment. Which is: Who is the best teacher in all of film or television? OK? We’re gonna do that. It’ll be fun. But I hope that in debating this a little bit with a special guest we’ll bring up in a moment, that we will start to uncover some truths about what makes good teaching. How that’s different from teaching as we see it in movies and tv. Why middle-class America wants teachers to look a certain way in movies and tv. What all that means. And it’ll be awesome. I think. I’m hopeful it’ll be awesome. So what we did here is we’ve invited eight people. Eight folks you people may have known. You’ve been in their sessions today, in this conference, perhaps. And asked them: Who’s your fave? Like, we might have our favorites, but we wanted to democratize it a bit. So asked some cool people who you folks like, who are very smart and thoughtful about teaching: Who’s your favorite teacher?

Bethany Lockhart Johnson (05:58):
A few of whom are in this room. Thank you for your submission.

Dan Meyer (06:00):
Thank so much. Yeah. We’ll see what happens here. <laugh>

Bethany Lockhart Johnson (06:03):
As they shrink down.

Dan Meyer (06:03):
Yeah. Might draw some blood that I don’t mean to right now. We’ll see. OK.

Bethany Lockhart Johnson (06:06):
That metaphor, what IS that??

Dan Meyer (06:07):
Yeah. Yeah. I love it. I’m still going with it. <laugh> And you folks will be a huge part of this. THE part of this, really. So what will happen is I’ll share with you our first nominees. A few of us will make a case for our favorites, or least favorites, as the case may be sometimes. And then by applause, by acclamation, you folks will decide who wins and advances to the next round. Start with eight, move to four. You folks know math.You know where this goes. OK.

Bethany Lockhart Johnson (06:34):
No, keep going. Keep going.

Dan Meyer (06:36):
Two, then one.

Bethany Lockhart Johnson (06:36):
Yeah. Got it.

Dan Meyer (06:37):
Then a half of it. No?

Bethany Lockhart Johnson (06:38):
He had to school me on the making of brackets. But we got it. Yeah.

Dan Meyer (06:41):
How brackets work.

Bethany Lockhart Johnson (06:41):
But we got it. March Madness, what?

Dan Meyer (06:44):
Yeah, in order to do this right, we had to bring up—all the folks that you’ll see are also former Math Teacher Lounge guests, or like, just fan favorites. And we’re also bringing up a former Math Teacher Lounge guest to help us decide this and debate this in a respectful manner.

Bethany Lockhart Johnson (06:59):
New dad.

Dan Meyer (07:00):
New dad.

Bethany Lockhart Johnson (07:01):
You see where my brain’s still at? I miss him. <Laughs>

Dan Meyer (07:03):
Friend from San Diego. Really cool teacher.

Bethany Lockhart Johnson (07:06):
Incredible teacher.

Dan Meyer (07:06):
Works at Desmos and Amplify. And I just want you to welcome up your friend and mine. Chris Nho!

Bethany Lockhart Johnson (07:11):
Chris Nho!

Dan Meyer (07:13):
Come up, Chris. Let’s go, buddy. We didn’t talk about it, but did you want to do the cornball stuff too?

Chris Nho (07:22):
Wow. Would I love to do—

Bethany Lockhart Johnson (07:23):
And then the door could be locked! And then you have to wait and like, just—

Chris Nho (07:27):
Yeah, I’ll skip that part.

Bethany Lockhart Johnson (07:28):
Hi. Welcome. You’re here. We’re here in person.

Chris Nho (07:30):
Very glad to be here. Thank you all for having me.

Dan Meyer (07:33):
Tell me who you are.

Chris Nho (07:34):
My name is Chris Nho. I live in San Diego. I’m a new dad. A three month old, just had. Yeah, she’s actually here at the conference with us in the hotel room. And I promise you she is not by herself. She is with…come on. I was like, “Hey, just gimme one hour. I’ll be right back. I have to do very important work.” But yeah, I think I got invited here because I have opinions and I’m willing to draw…some…blood.

Dan Meyer (08:02):
There we go! Two outta three! We’re good on the metaphor now.

Bethany Lockhart Johnson (08:06):
We’re so glad you’re here. If you haven’t listened to the episode where Chris and Molly and some other public math folks share their ideas and ideas of how to take math out into the world, please listen, because we had a blast.

Dan Meyer (08:19):
Inspiring work. Really inspiring work. Very cool. Cool. OK. Right on. OK.

Bethany Lockhart Johnson (08:23):
Let’s do this!

Dan Meyer (08:24):
Let’s get started here. Yeah! <Audience cheers> Yeah. And we might ask you who your favorite teacher is, who’s missing from our list of eight? We might have forgotten some people. Anyway. All right. So here’s our first two. Our first two are nominated by way of, let’s see, um, Mandy Jansen is a professor at the University of Delaware. Got some awesome talks here this week, a Shadow Con talk last night. She’ll be nominating one. And also, um, Lani Horn is a professor at Vanderbilt, also extremely cool, prolific author and speaker, just all-around great human and friend of teachers everywhere. And she’ll nominate another in this bracket, which is the Northeastern Comedy bracket, Northeastern comedy bracket.

Bethany Lockhart Johnson (09:06):
It just worked out that way.

Dan Meyer (09:07):
Yeah. Here it is. Here is Tina Fey in Mean Girls.

Tina Fey in Mean Girls (09:12):
“OK. Everybody close your eyes. All right. I want you to raise your hand if you have ever had a girl say something bad about you behind your back. Open your eyes. Now close your eyes again. And this time I want you to raise your hand if you have ever said anything about a friend behind her back. Open up. It’s been some girl-on-girl crime here.”

Lani Horn (09:52):
I am nominating Sharon Norbury from Mean Girls as the best movie math teacher. She is an awesome teacher who is always there for her kids. She always sees the best in them. She shows that she can forgive even some pretty bad behavior, if she sees that kids are trying. She’s a strong feminist who makes sure that smart girls don’t dumb themselves down just to impress boys.

Tina Fey in Mean Girls (10:22):
“Katie, I know that having a boyfriend may seem like the most important thing in the world right now, but you don’t have to dumb yourself down to get guys to like you.”

Lani Horn (10:30):
She’s also super hard-working. She works three jobs. She’s always there for the kids. She plays piano in the talent show and takes them to Mathlete competitions. And she’s also socially aware. And when things go really badly among the girls, she does some pretty creative things to try to get them to be kinder to each other.

Dan Meyer (10:54):
OK. That’s one.

Bethany Lockhart Johnson (10:55):
Helen Case.

Dan Meyer (10:57):
All right. Settle down. Settle down. Settle down. All right.

Bethany Lockhart Johnson (10:59):
Piano too!

Dan Meyer (11:00):
Bethany’s already trying to bias people here. All right. Chill out. Hold on. So next one is Mandy Jansen with Jack Black from School of Rock. Uh-oh. Uh-oh.

Jack Black in School of Rock (11:09):
“What was your name?”

Kid in School of Rock (11:10):
“Katie.”

Jack Black in School of Rock (11:11):
“Katie. What was that thing you were playing today? The big thing.”

Kid in School of Rock (11:14):
“Cello.”

Jack Black in School of Rock (11:15):
“OK. This is a bass guitar and it’s the exact same thing, but instead of playing like this, you tip it on the side. Chellooooo! You’ve got a bass! <Laugh> Try it on.”

Mandy Jansen (11:25):
And I’m nominating for best teacher in a film Jack Black as Dewey Finn playing Mr. Ned Schneebly in the film School of Rock. So why this portrayal? First of all, playing a longterm sub. Those are so hard to find right now. <Audience laughs> Really hard. And then he teaches using class projects. That’s brilliant. Integrated learning. And then love this. He gives students roles and tasks that are differentiated and align to the specific strengths that each student has.

Kid 2 in School of Rock (12:05):
“I can also play clarinet, you know!”

Jack Black in School of Rock (12:06):
“I’ll find something for you when we get back from lunch. I’ll assign the rest of you killer positions.”

Mandy Jansen (12:13):
And the film culminates in a performance of a collaborative song that they all wrote and performed together. And the students experience that collaboration and teamwork and creating something beautiful is much more important than winning first place. And finally, one of the songs that the character sings in the film is “Math is a Wonderful Thing.” Can’t beat that.

Dan Meyer (12:40):
All right. That’s tough. That’s tough. So here’s the deal. What we have right now is just a quick minute—so Bethany, you ranked, we all ranked our own faves here outta the list of eight. And Bethany put Jack Black in School of Rock a bit higher than Tina Fey in Mean Girls.

Bethany Lockhart Johnson (12:54):
Missed the piano part though.

Dan Meyer (12:55):
And Chris, vice versa here. So Bethany, would you start us off and just make a quick case here for Jack Black versus Tina Fey?

Bethany Lockhart Johnson (13:01):
OK. So here’s what I’m thinking. There’s been rumor that maybe they’re putting less than credentialed people into classrooms to fill teaching gaps. I mean, just rumor. And so here’s this guy who is a rocker. He is not a substitute. He has no teaching training. And yet he goes in there and it turns out that he has the ability to see students’ potential and to recognize their unique abilities. And like Mandy said, he really tapped into, like, he saw them and said, “No, more is possible for you than what you think is possible.” And there’s like real sub anxiety. When you walk in, you can either be like, happy there’s a sub, but I was usually really nervous. Right? And he goes in and he makes that classroom into a home.

Dan Meyer (13:53):
Wow.

Chris Nho (13:54):
Wow.

Dan Meyer (13:56):
Chris, speak on it. Tina Fey needs you. Chris.

Chris Nho (13:59):
Tina Fey. Here we go. I’m gonna argue here that—when was that movie made?

Dan Meyer (14:03):
T is for terrific. I is for Interesting.

Chris Nho (14:06):
Decades ago. And I’m gonna argue that Tina Fey was very progressive for her time. OK, let’s talk about social emotional learning. Hello. <Audience laughs> Love that. Right? Stand up if, I mean, she’s getting people to talk about their emotions. And there’s a curriculum. But let’s just pause, because that’s not what’s really happening in the classroom right now. So social emotional learning, I think she’s, she’s got that a lot. And then number two, you know, if you remember the plot of Mean Girls a little bit, she gets her name written in that Burn Book. Like she sees what they say about her. Restorative justice. Let’s go. <Audience laughs>.

Dan Meyer (14:38):
Whom amongst us. Yes.

Chris Nho (14:40):
You write Mr. Nho in the Burn Book?? Well, your grade book is gonna look like a Burn Book! OK? <Audience laughs> Tina Fey, Tina Fey, she was like, “No, you know, know what? I’m actually gonna spend more time with you. You’re gonna become a mathlete.” And Lindsay Lohan discovers—she drops the most iconic line in all of math education. “The limit does not exist.” Thank you, Tina Fey, for that. For that gift.

Dan Meyer (15:04):
Bless. Bless you. Tina Fey. Wow.

Bethany Lockhart Johnson (15:05):
Oh, man. Wow.

Dan Meyer (15:09):
Let’s see what the people say here. I do wanna just add one quick thing about—it’s interesting to me how often in these movies—just kind of go in a little bit, zoom out just a minute—how often it’s a teacher who has no training as a teacher. <Bethany laughs> I am kind of curious why it is. Like, those are the movies that get hot, that get made. Again, these are all kind of a mirror of the taste of the moviegoing public. You know what I’m saying? Like, these, these are not movies—I wanna believe they are made for me and for us as teachers. But they are not. There’s not enough of us to justify, you know, Jack Black’s, you know, M&M budget or whatever he’s got going on in his trailer or whatever. That needs to be for everybody in middle-class America. So what is it about middle-class America that wants to see teaching as something that anybody can do? Just like, you know, just, just run up there in your van and make it happen.

Bethany Lockhart Johnson (15:54):
Magic magically manifests.

Dan Meyer (15:56):
Yeah. Manifest. Yeah. That’s just interesting to me. I just toss that out there as some red meat. Let’s see what the people say here. All right, OK, so you’re ready. Let’s get the bracket going here. The question is Tina Fey versus Jack Black. You had a moment here. Just whisper to someone real fast who you’re going for here real quick. What are you thinking here? <Crowd murmuring> All right. Crowd’s buzzing. Crowd’s buzzing. Would you folks…? All right. Bring it back. Go ahead and make some noise for Tina Fey. <Crowd cheers> OK. OK. Make some noise for Jack Black! <Crowd cheers> Judges say Tina Fey. Tina Fey moves on. All right. All right.

Chris Nho (16:44):
Stunned. I’m stunned. I’m speechless.

Bethany Lockhart Johnson (16:46):
Tina Fey moves on. Wow.

Dan Meyer (16:48):
This has exceeded my expectations in terms of having some fun, but also getting deep, getting deep and real about teaching. I’m into this right here. Yeah. What’s up?

Bethany Lockhart Johnson (16:54):
That’s the goal. That’s the goal. OK. You wanted blood? Oooh, this next matchup might just be where that blood comes forth! OK. Stretch. Warm up. Dan Meyer, who’s up next?

Dan Meyer (17:11):
We’ve got the animated/animatronic round here in the Southeast. And repping the two contestants here, who do we have? We have Allison Hintz, professor, author outta Washington, as one of the two nominators. And the other nominator is one of my heroes, though we’ll find out very wrong about this nomination, Jenna Laib, who’s in the crowd, and I’m trying not to make eye contact here. <Laugh> And here are the two nominations. A couple minutes each. And then we’ll chat about it. And one of us will probably die. But we’ll see how it goes.

Allison Hintz (17:50):
A long, long time ago, in a galaxy far, far away, MTL, we began learning from the Jedi Master of Teaching. With the Socratic and experiential approach. With unparalleled mindfulness, compassion, and humility. The best teacher in TV and film, Yoda is. <Audience laughs> Yoda lives the values we share as teachers and learners. He humbly comes alongside us as we construct new knowledge.

Yoda (18:29):
“You must unlearn what you have learned.”

Allison Hintz (18:32):
Yoda allows us to struggle and sees mistakes as critical to learning.

Yoda (18:39):
“The greatest teacher, failure is.”

Allison Hintz (18:43):
Yoda values curiosity and reminds us of the beauty and joy of teachers learning from children.

Yoda (18:52):
“Truly wonderful, the mind of a child is.”

Allison Hintz (18:59):
MTL! Join the Resistance! Let the force flow through you in declaring, the best teacher in TV and film, Yoda is.

Dan Meyer (19:18):
Give it up for Allison Hintz! All right! <Audience applauds>

Bethany Lockhart Johnson (19:20):
Alison! And to have that on hand too, which Is kind of perfect.

Bethany Lockhart Johnson (19:26):
Just to be clear, the helmet is not a part of a Zoom background.

Dan Meyer (19:29):
You may evaluate the quality of the nomination based on the costumes of the nominator. That is acceptable. That’s acceptable.

Bethany Lockhart Johnson (19:35):
That is a REAL HELMET.

Dan Meyer (19:35):
All right. The next nominator here, this one is from Jenna Laib, math coach, all-around stellar human. Here we go. This is Ms. Frizzle.

Ms. Frizzle (19:42):
“Single file, class. Our rotten field trip has only just begun.”

Jenna Laib (19:47):
And I think that the best teacher from TV or movies is Ms .Valerie Frizzle from The Magic School Bus. First and foremost, Ms. Frizzle believes in her students. She encourages them to take an active role in their learning, and also to advocate for change in their local community. For example, there’s an episode where there is a logger who’s gonna cut down a rotting log that would benefit the local ecosystem. And the students figure out a way to convince him to leave the log so that all of the animals and the plant life can benefit. She orchestrates really challenging situations for these students, and she allows them the space to ask questions and engage in problem-solving and puzzle their way out of these really, really difficult scenarios. Ms. Frizzle has unmatched pedagogy. She’s bold, she’s innovative, and she’s a major proponent of experiential learning. So these students are heading straight into a storm to learn about weather systems. <Audience laughs> These students are heading into the human body to learn about digestion and disease. They literally get baked into a cake to learn about some chemistry and reactions.

Children in The Magic School Bus (20:54):
“What’s happening?” <Audience laughs> “Why is it suddenly getting so hot?” “Maybe it’s because the floor is on fire!” <Audience laughs>

Jenna Laib (21:02):
This pedagogy is all led by her outstanding catchphrase, which is:

Ms. Frizzle (21:06):
“Take chances; make mistakes; get messy!”

Jenna Laib (21:14):
From her pedagogy to the classroom community that she creates, Ms. Frizzle is an inspiration, and that is why I think that she is the best teacher from TV or film. <Audience applauds>

Dan Meyer (21:25):
Right on! Give it up for Jenna. Give it up for Jenna. All right. I’m gonna take first pass at this. Chris knows my argument already, so I’m gonna take this here. I see some of you are feeling how I’m feeling on this one. OK, so I don’t have tons to say in favor of Yoda. I think it was all true what Allison said. I think the costume was banging. It was awesome. So there’s all that, but I have more to say against Ms. Frizzle than for Yoda.

Bethany Lockhart Johnson (21:48):
No, no, no. Wait a second!

Bethany Lockhart Johnson (21:49):
Let’s let it happen. Bethany, I’ve come prepared.

Dan Meyer (21:54):
I may have made a misstep here, I realize.

Bethany Lockhart Johnson (21:56):
I’ve come prepared.

Dan Meyer (21:56):
So I think Jenna is all correct. I think those clips spoke for themselves. I think that what they add up to, to me, is not “great teacher,” but more “someone who should be locked up.” <Audience laughs> Or at the very minimum, “someone who should be kept away from children.” <Audience laughs> Do not let that woman around children. I mean, check it out. Look, I don’t wanna throw down credentials. I’ve been to grad school, though. I know how this works. When your brain is stressed, you get these—all the cortisol happens. Your working memory shrinks up. You cannot learn when you’re stressed. And those kids, like whatever lesson Ms. Frizzle is teaching by sending them into an oven, I repeat, an oven <audience laughs>, like, they’re not gonna learn anything ’cause their brains are freaking out with stress and fear. OK?

Bethany Lockhart Johnson (22:41):
“What’s happening??”

Dan Meyer (22:43):
“What’s happening? Am I on fire? Well…I’m learning lots, though! Sure is magical!” <Audience laughs> It’s like, “No. Get that woman out of a classroom.” That’s my opening and closing argument. Right? There’s all it is.

Chris Nho (23:01):
All right. All right. All right.

Bethany Lockhart Johnson (23:02):
Chris knows.

Chris Nho (23:03):
I’ve got, I’ve got lots to say. First off, I think Dan was in charge of the editing of those video clips. So let’s let that be—you know, let the record stand. <Audience laughs>

Dan Meyer (23:11):
Where’s the lie though? Where’s the lie?

Chris Nho (23:14):
And, you know, second, I think, um—this is the guy up here saying, “I wanna see blood.” You know? And then he has a teacher who literally takes the students into a blood cell and, and you get a little scared! You get a little worried for the students, you know? So I just don’t get it, Dan. This or that. OK? I think Ms. Frizzle—so I actually went to a project-based learning school. I taught at a project-based learning school. And the best thing about it is like, your learning, it doesn’t just stay in this box of math lesson or writing lesson, history lesson. And I think with Ms. Frizzle, like you can’t help but learn things because you are getting baked in a cake. <Audience laughs> Yeah, it is a little scary. And I imagine there’s cortisol and things happening, but guess what? Probably the next episode, they go into their own brains and explore what’s happening. That kind of thing. You know?

Dan Meyer (24:07):
The kids that survived, just be clear. <Audience laughs>

Chris Nho (24:10):
Yeah. OK. Would I want Nora, my three-month-old, to be babysat by Ms. Frizzle? Maybe not. <Audience laughs> But what I have to say about Yoda is Yoda maybe wins the best tutor award. Give it up for Yoda’s Best Tutor Award.

Bethany Lockhart Johnson (24:24):
Oh, yeah…

Chris Nho (24:25):
That ratio’s looking really nice. I could teach the heck outta Luke Skywalker. OK? But 20 little Luke Skywalkers running around. I’m not sure. OK?

Dan Meyer (24:34):
Luke did survive the training, though. <Audience laughs> So that’s awfully nice to say about it. All right, Great words from Chris here. I’m still not convinced. We’ll see how you’re convinced here. Would you whisper to someone where you’re leaning here? Frizzle or Yoda? <Audience buzzing>

Chris Nho (24:47):
I tried. I tried.

Dan Meyer (24:53):
All right. That’s enough of that. Let’s hear it folks. Give it up for Yoda. <Audience cheers> Give it up. Give it up. You. Give. It. Up.

Chris Nho (25:05):
Hey, next. Next.

Dan Meyer (25:06):
All right. All right, all right. <Mutters> Give it up for Ms. Frizzle. <Audience cheers louder> I dunno, it’s pretty close. Call a tie. Maybe Yoda? Yoda by nose? <Audience laughs> All right. All right. Let’s…let me see who’s it. Let’s get the people advancing here. I’ll keep on moving here.

Chris Nho (25:26):
As you’re doing that. Um, Dan ranked Ms. Frizzle last in his personal ranking. And I ranked Ms. Frizzle very high, so we knew this one would be spicy,

Bethany Lockhart Johnson (25:36):
<laugh> Spicy it was. Are you having a good time so far? <Audience cheers> So while we love seeing these images and we love seeing these video clips, at the core, what are these things about how teachers are portrayed? And how accurate is that to our real lives? I mean, besides the cake part, right? That my chemistry class did often feel like I was on fire. I was so stressed in it. Um, we’re ready?

Dan Meyer (26:05):
Yep. Great. We’re ready, we’re up here. So the next two nominees are coming to you folks from Tracy Zager, who is the editor of my book, forthcoming in 2027 at the earliest and 2032 at the latest. And also your very own Zak Champagne from Florida, here in the room. Hey, Zak. Zak, let’s see who the nominations are. I’m gonna skip past that, didn’t work out so well for me. Here it is. This is Marshall Kane from the TV show Community.

Michael K. Williams in Community (26:32):
“You two complete your case to the class and let them decide your grades.”

Joel McHale in Community (26:37):
“Professor, thank you.”

Michael K. Williams in Community (26:40):
“It’s not a favor, Mr. Winger. Man’s gotta have a code.”

Joel McHale in Community (26:44):
“Awesome.”

Zak Champagne (26:46):
This is a pitch for an underdog. This teacher didn’t stand on desks or encourage his students to follow their musical passions. In fact, this teacher was seen only in a few episodes of my favorite TV show of all time, Community, Community has set at Greendale Community College in Colorado. And in season three, we get to meet Dr. Marshall Kane, a biology professor whose story is an inspiration to anyone who just takes the time to look and listen. Dr. Marshall Kane slowly earned his PhD while in prison, serving a sentence of 25 to life. In his classroom, he inspires students to love biology, question why LEGO has become so complicated, and randomly pairs his students for group projects to ensure no one feels left out. His greatest performance comes when a group of students believe their yam project was intentionally sabotaged. Dr. Kane took this as an opportunity for some trans-disciplinary real-world learning. So yes, at community college, he felt that a middle-school mock trial was the best way to determine who killed the yam. So let’s all pick the underdog and vote for Dr. Marshall Kane. After all, man’s gotta have a code. <Audience goes “oh!” and applauds>

Dan Meyer (27:53):
Thank you, Zak.

Bethany Lockhart Johnson (27:54):
I have a code.

Dan Meyer (27:56):
Next up is Tracy Zager, nominating an unusual nomination, not a single person, but an ensemble performance. A bunch of people from a movie called Searching for Bobby Fisher. Here we go.

Rapid-fire movie dialogue (28:11):
“What’s that?” “Schleimann attack.” “Schleimann attack? Where’d you learn that from, a book?” “No, my teacher taught me.” “Aw, your teacher. Well, forget it. Play like you used to, from the gut. Get your pawns rolling on the queen’s side.”

Tracy Zager (28:26):
Hey, Math Teacher Lounge. This is Tracy Zager. I’m excited to share my nominee for the best movie teacher. But I have to admit that when I first got the email, I thought, oh, who am I gonna nominate? Because most movies about teachers are highly problematic. They usually have like a saviorism thing, usually white saviors. And I just felt like I couldn’t suggest any of those. So rather than nominate a movie about a single teacher, I wanted to nominate a movie that taught me something about teaching. And that movie is a deep cut. It’s Searching for Bobby Fischer. It’s a movie about a chess prodigy. And what I love about it is that all of the different adults in the movie are in teacher roles in some way. And the student, Josh, the chess player, is a fully realized character, not an empty pail, who pulls from the strengths of each one of those adults while also dealing with their flaws and humanity. And there’s just beautiful synergy in the way he gets the best out of everybody, but also has to overcome some of the barriers that they put in front of him. So I feel like it’s a much more authentic and humbling, but also inspiring, movie about the power of teaching. So if you haven’t ever seen it, check it out. And I can’t wait to see who the other nominees are. Thanks so much.

Dan Meyer (29:53):
Right on. Thank you, Tracy. Wherever you are. <Applause> We’ll move a little quicker here. I’m curious, Bethany, you put Marshall Kane pretty high. I put Bobby Fischer pretty high. What do you have to say about Marshall Kane for us here?

Bethany Lockhart Johnson (30:04):
Well, I just wanna say two things. One is that, like Zak said, he has this code of conduct that he brings in. And he stays true to it no matter what happens. If you saw him in in Community, you know that he held himself up to such high esteem, but not just himself, his students as well. And he took accountability when he felt he had done wrong, even though, well, that’s controversy. But first—oh, the other thing, rest in peace, Michael K. Williams. Oh my gosh. The actor who plays Marshall K. And the thing that I wanna say most of all about it is that he brings his whole self to the classroom. He was in prison for decades. He brings his whole self and says, “This is who I was. This is who I am today. And this is how we can work together as a community.”

Dan Meyer (30:58):
That’s big. I love your comments about code of conduct too. It makes me wish that Ms. Frizzle had a code of conduct also.

Bethany Lockhart Johnson (31:05):
I knew that was coming back!

Chris Nho (31:06):
Two slides ago, Dan. That was two slides ago.

Dan Meyer (31:08):
Can’t let it go. So yeah, I love what you said there. I have no strong beef here either way. Bobby Fischer’s a movie I have loved dearly and can’t be objective about it. I love that the kid in that movie, more than any other movie here, the kid teaches the adults so much through his innocence and how he challenges them and how they’re treating him. Dig all that so much. Will not, will not begrudge anyone any vote either way here. I do begrudge many of you your vote in previous rounds. <Audience laughs> So let’s just, let’s hear. We’re not gonna ask you folks at all to chitchat. We’re gonna move on this one. So would you folks make some noise here for Marshall Kane in Community? OK. OK. And would you make some noise here for Bobby Fischer, the kid in Bobby Fischer, the ensemble? <Audience cheers, applauds>

Bethany Lockhart Johnson (31:56):
Marshall Kane.

Dan Meyer (31:57):
Marshall Kane takes it. All right. Good job, Marshall Kane! All right. Zak’s feeling good. Moving on to the final four here, Zak, right on. OK. Our last—the Northwest Division here is also the large urban district division here. We have a couple different teachers in sets of large urban schools. They’re nominated, they’re advanced by a couple people here. One is past president of NCTM, Robert Berry. And another is Fawn Nguyen, Southern California phenom. Great teacher and friend of lots of us. Um, let’s see who they nominated here. First from Robert Berry, let’s see, who is it here? Janine Teagues from Abbott Elementary.

Abbott Elementary dialogue (32:37):
“Hey, you know what? I’m probably probably gonna be Kenny’s second-grade teacher. Why don’t you just let him get a head start with me today?” “That’d be great.” “Yeah? OK. Hey, Kenny, would you like to be in my group today?” “Not really.” “That’s the spirit.”

Robert Berry (32:54):
My nomination is gonna be Quinta Brunson, the Emmy Award-winning Quinta Brunson from Abbott Elementary. Janine Teagues is the character. She exemplifies care not only from an affect way, but she also exemplifies care in the things that she does for her students. While the scenes in the show are entertaining, they do represent the challenges that teachers experience when they’re trying to meet the needs of her students. So she goes, goes all out for her students and finding resources. She accesses other people to get resources for her students. But the care shows up in the way that she is mindful of their needs. And so, for me, when I think about teachers and teaching, sometimes we can talk about pedagogy, but sometimes we also can talk about those kind of intangibles that makes a teacher a great teacher. It is apparent from her students that she cares about them, she supports them, and she goes all out 100% for her students. Janine Teagues, Quinta Brunson is, I think, is my choice of the best teacher on television because of the realism and the representation that she brings to this character of what teaching is about. <Applause>

Dan Meyer (34:28):
Right on. Right on. OK. OK. Next up, we’ve got, Fawn Nguyen is nominating Erin Gruwell from Freedom Writers. Here we go.

Hilary Swank in Freedom Writers movie (34:39):
“Look, you can either sit in your seats reading those workbooks or you can play a game. Either way, you’re in here till the bell rings. OK? This is called the Line Game. I’m gonna ask you a question. If that question applies to you, you step onto the line and then step back away for the next question. Easy, right? The first question. How many of you have the new Snoop Dog album? <kids move around> OK, back away. Next question. How many of you have seen Boys in the Hood?”

Fawn Nguyen (35:26):
We all learn about Miss G and her 150 students in the movie Freedom Writers starring Hilary Swank. All great teachers share a common set of traits. They care deeply about their students, have high expectations of them, and always believing wholeheartedly that they will succeed. Great teachers go above and beyond, not because they extraordinary—as Anne Gruwell would always refer to herself as an ordinary teacher—but because extraordinary things happen to people when we believe in them, give them hope, help them write their own story with a different ending. So what stood out for me with Miss G is the scope of her reach, the ever-expanding sphere of her humanity. The red tape she had placed on the classroom floor for the line game shows just how much we all have in common despite our differences. Her students didn’t just learn from her; they learned from one another. If you’d like to be part of this expanding sphere to give voice and hope, please check out Freedom Writers Foundation dot org.

Dan Meyer (36:38):
OK. This right here is a tough one for us. Thank you, Fawn. We collectively ranked—that’s our number one seed and number eight seed, which I hasten to say does not have to do with Erin Gruwell, a person, but the portrayal and the movie. So we don’t have like a whole lot of…there’s not a lot of defense we have to offer here of our eighth seed. And I heard like a kind of a little bit of a murmur over the crowd on Erin Gruwell. So I’m more interested than having a defense back and forth. I’d be curious what you, Bethany, think about what, like, what both movies have to say about like, what teaching is, especially teaching urban schools with black and brown kids and lower-class kids, for instance. They both have, I think, very different things to say about them. Do you have thoughts about that?

Bethany Lockhart Johnson (37:19):
Well, it’s interesting because there is some overlap in the sense that the arguments that both Fawn and Robert Berry put out, they both care deeply about their students, right? We’re not gonna argue that. They care deeply. And something that I would say about Miss Teagues is there’s something about the way that she sees not only her classroom, her students, but she sees all of the students in the school as her students. And her idea of resource generation is really helping the teachers to generate resources from their community themselves, and to also realize that the students see themselves reflected in the teachers. And I think that—you know, again, this is not about the real person—but the movie portrayal, and we often see kind of this, for Freedom Writers, we often see this like, Great Last Hope whisked in and her personal sacrifices are what makes these students, these brown and black students’ transformation possible. Because of her sacrifices. Including her marriage. Including, you know, three jobs. And it’s just portrayed in a way that I think really celebrates her sacrifices rather than what the students have already brought—they already come into the room bringing so much as they are, already, without her intervention.

Dan Meyer (38:38):
I love the portrayal of the teacher as part of a community of teachers. Versus in so many of these movies, it’s the teacher as the only person who gets it, you know, oftentimes coming from outside of the world of teaching and everyone’s against them and wants ’em just to fall in line and do the thing we always do, and they’re the outlier. But in Abbott Elementary, it’s like we all rise and we fall together. And teachers are investing in each other’s success, especially with Gregory the longterm sub. We’re all rooting for his, you know, his flourishing. I love that. And yeah. That’s bigtime.

Chris Nho (39:09):
Yeah, I think one interesting thing is that Freedom Writers, when it came out, I think it was like a commercial success.

Bethany Lockhart Johnson (39:17):
Oh, big time. Yeah. It was.

Chris Nho (39:18):
It probably influenced a lot of people to try teaching out. So I do wonder what it says about us, right? Like that we want teaching to fit this narrative, and we wanna be those people who could go into a classroom and <puts on “cool voice”> “Y’all listen to Snoop Dog?” and just have that question HIT. <laughter> And you know, I’ve taught in a large urban school district, and I’ve been that person and I’ve seen other people try and be that person. And I think stepping away from it a little bit, just—it’s a reflection of what people want out of teaching and what they think better education looks like.

Dan Meyer (39:57):
Yeah, yeah. This idea that, so I’m a middle-class person, let’s say, and like, there’s this idea, like, “I know what I would do if I was going into circumstances of impoverishment.” Like I have—

Bethany Lockhart Johnson (40:06):
“All they really need is…”

Dan Meyer (40:07):
…for me to give ’em some real talk and tell ’em, you know, pull their pants up or whatever, listen to Snoop Dog, that kind of thing. And that will be the key. And that’s not how it is in, you know, in Jack Black in School of Rock or Tina Fey school, which are, you know, coded as largely like upper-class or largely white schools. And in those movies, it’s interesting, like how it’s about students discovering themselves, oftentimes. And the central figures are often students. And the students need to reject an oppressive parent figure or something and find themselves. But no, in Freedom Writers, it’s like, “You need to become more like the middle-class teachers who are coming in here to give you this wisdom.” It’s just interesting. I do find it—a pet peeve of mine is when movies portray teachers as only successful if you endure, for instance, the failure of your marriage, or even in Stand and Deliver, for instance, like Jaime Escalante, they depict him having a heart attack. And, like, the job oughta be…easier. <Audience laughs>

Chris Nho (41:04):
Truth.

Bethany Lockhart Johnson (41:05):
That’s the barometer for how much….

Dan Meyer (41:09):
Like, no heart attacks and no divorces related to the job, that kind of thing. I do love how in Abbott—one last thing and we’ll vote and Abbott will win <audience laughs>—is like how, like there, there is a lot of degradation in Abbott, but it’s not a divorce or a heart attack—it’s the petty indignities of asking a student, “Do you wanna hang with me?” And a student says, “Nah, not really.” And that just spoke to me like how it’s not cinematic, but teaching, successful teaching, is like a collection of developing an immunity to students saying, “You’re not hot.” <Laugh> You know? And so I love that. I do wish that there was more depiction of students in Abbott Elementary. It’s a lot of adult stuff. Whatever. Give it up for Abbott, if you would, please. Let’s just get this done here. All right. That’s plenty. That’s plenty. Not gonna ask folks about Freedom Writers. OK, let’s move on to— all right, let’s hear it for Freedom Writers! Yeah. OK, cool. We go, yep.

Chris Nho (42:05):
Plot twist!

Bethany Lockhart Johnson (42:07):
OK, let’s see our final four. Cut and paste. Real time. Real time.

Audience member (42:12):
Where’s Dolores Umbridge?

Dan Meyer (42:14):
Oh….

Bethany Lockhart Johnson (42:16):
Hey, did you hear that? He said, “Where’s Dolores Umbridge?”

Dan Meyer (42:20):
All right. OK.

Bethany Lockhart Johnson (42:20):
See, we missed so many. We could…

Dan Meyer (42:21):
So coming up here, we’ve got in the Eastern Conference, Tina Fey and Ms. Frizzle. Y’all know how I feel about that one. Let’s just get this one done. OK, let’s give it up for Tina Fey. Let’s hear it. <Audience cheers> OK. All right. Yes! Let’s give it up for menace to children everywhere, the terror, the Ms. Frizzle. <Audience cheers> One more time for Tina Fey. Let’s hear it. <Audience cheers> One more time for Ms. Frizzle. Let’s hear it. <Audience cheers>

Bethany Lockhart Johnson (42:59):
Yeah. OK.

Dan Meyer (43:00):
It took ’em one round, but they made the right call in the end. <Laugh>

Chris Nho (43:04):
All it took was 10 minutes of constant Ms. Frizzle-bashing. <Laugh>

Dan Meyer (43:09):
Persevering and problem-solving, that’s my game. Yes. All right. So, do either of you want to influence the audience one way or the other?

Bethany Lockhart Johnson (43:16):
That’s not how I play, Dan.

Dan Meyer (43:18):
Oh, OK. Yeah, that’s true. That’s true. You’re good. On Abbott versus Marshall Kane, should we just let ’em have it? All right. All right. Give it up For Abbott Elementary. Not bad. And for Marshall Kane. OK. OK. I hear Zak and five other people. All right, cool. <laugh> Right on. All right. We got our, we got our finals,

Bethany Lockhart Johnson (43:45):
We did it. We made it to two. And we know: We left out a lot of people. Right? And honestly, I kind of wish we could poll like everyone. I mean, think you put it on Twitter, right? Like, who would you pick? But I would say we had a pretty solid eight there. I’m excited to see who… Look at the little crown he put, you guys. Come on.

Dan Meyer (44:05):
I worked hard for you. For you. <Laugh> Yeah. I liked that it was a good bunch that had a lot of different kinds of qualities…and lack of qualities in some cases. And it allowed us that—I shouldn’t knock her while she’s down, and she IS down, it’s true. <Laugh> And I appreciate the conversation we’ve had, what they have revealed overall about teaching and what the world wants teaching to be versus what it actually is or actually should be. I appreciate that. So let’s settle this here. Give it up, if you would, for Abbott Elementary. <Audience cheers> And give it up for Tina Fey in Mean Girls. <Audience cheers>

Bethany Lockhart Johnson (44:49):
Wow.

Dan Meyer (44:51):
That was close. I almost give that to Tina Fey.

Audience member (44:55):
Yeah, we do!

Dan Meyer (44:55):
I don’t know. That was a bracket-buster for me right there. Yeah. I lost money in the office pool off that right there. Maybe let’s just find out one more time here. One more time.

Bethany Lockhart Johnson (45:03):
Last time.

Dan Meyer (45:03):
Time to summon up all your conviction on one or the other here. No half-measures right now. All right.

Bethany Lockhart Johnson (45:07):
Emmy Award-winning Quinta Brunson.

Dan Meyer (45:09):
Yeah, you saw Robert Berry on that, right? He was like, “Oh, I got one more card to play. Emmy Award-winning.” That’s admissible. That’s admissible. We’ll take that. All right. So…give it up for Abbott Elementary, one last time. <Audience cheers> OK. All right. All right. And give it up for Tina Fey in Mean Girls. <Audience cheers>

Bethany Lockhart Johnson (45:30):
Drumroll, please!

Chris Nho (45:33):
Best teacher is….

Dan Meyer (45:34):
Tina Fey in Mean Girls! Yeah. Not a bad pick.

Bethany Lockhart Johnson (45:39):
I love it. And I think, too, I think we’re gonna have a little bit of a more reflective lens than we thought we did when we see depictions of teachers in film and television. And, you know, hopefully we’ll see some new tropes come in, right?

Dan Meyer (45:55):
Yep. Yeah. Every dollar we spend on movies with lousy teachers is just encouraging these people to make more lousy teacher movies, you know? Awesome. Thank you for being here for a live taping—

Bethany Lockhart Johnson (46:06):
Thank you for being here.

Dan Meyer (46:06):
—of our podcast, Math Teacher Lounge, in a hot room. Appreciate that. Yeah, it’s been fun for us to have you here. Um, super-important, super-important final remark: Bethany loves Oprah and Oprah occasionally, in the show—

Bethany Lockhart Johnson (46:18):
Is she coming?! Is she here?!

Dan Meyer (46:19):
Not here! Not here! Calm down. Calm down. Um, but we do have in Oprah fashion, not something—

Bethany Lockhart Johnson (46:24):
Oh. Oh, OK. Oh, that’s, that’s OK. Sorry. I got, had really excited for a second. As if the Amplify playing cards, The Amplify t-shirts being chucked at you at high speed—I did try to get a t-shirt cannon, and that was quickly ruled out <laugh>. They didn’t know about my rocket arm, right?

Dan Meyer (46:46):
Yeah, you got a cannon. <Laugh>

Bethany Lockhart Johnson (46:47):
Yeah. Oh, that’s a compliment. Oh, is that a compliment? Thank you, Dan. Thank you. Look under your seat because we have five winners. We wanna thank you for being here in person. We wanna thank the folks who are listening. We wanna thank Amplify. Oh my God. Somebody just pulled off the chair tag. You get to take that chair home with you.

Dan Meyer (47:08):
Does anybody have a prize?

Bethany Lockhart Johnson (47:10):
OK, stand up if you…stand up if you…Yes! Stand up if you have one!

Dan Meyer (47:16):
Free set of classroom dry-erase boards, right here. Congratulations.

Bethany Lockhart Johnson (47:22):
And for you who pulled off the chair tag, I don’t know. We gotta we gotta find something for you.

Dan Meyer (47:27):
Put that in your backpack.

Bethany Lockhart Johnson (47:30):
Thank you again for being here. Thank you. Amplify. Thank you, Desmos. Thank you. Dan Meyer.

Dan Meyer (47:36):
Thank you folks. Chris, thank you buddy.

Bethany Lockhart Johnson (47:38):
Chris! Chris Nho, everybody!

Dan Meyer (47:40):
We will be, we will be at—Bethany and I will be at the booth, if you wanna chit-chat and hang out, sign some stuff. Whatever. You wanna have Bethany sign you, she’ll do that. Um, come on down to the Amplify booth and we’ll—

Bethany Lockhart Johnson (47:50):
We’ll talk to you more about Ms. Frizzle.

Dan Meyer (47:52):
Fun and prizes. I will share with my real thoughts about Ms. Frizzle down there. I’d love to see you. Thanks for being here, folks.

Bethany Lockhart Johnson (47:57):
Thanks for listening. Bye.

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What Dan Meyer says about math teaching

“Teaching, more than other professions, is a generational profession. The kinds of joyful experiences we offer—or don’t offer—now affect the experiences students that haven’t even been born yet will have years later.”

– Dan Meyer

Meet the guests

Dan Meyer

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is currently the Dean of Research at Desmos, where he explores the future of math, technology, and learning. Dan has worked with teachers internationally and in all 50 United States and was named one of Tech & Learning’s 30 Leaders of the Future.

Bethany Lockhart Johnson

Bethany Lockhart Johnson is an elementary school educator and author. Prior to serving as a multiple-subject teacher, she taught theater and dance and now loves incorporating movement and creative play into her classroom. Bethany is committed to helping students find joy in discovering their identities as mathematicians. In addition to her role as a full-time classroom teacher, Bethany is a Student Achievement Partners California Core Advocate and is active in national and local mathematics organizations. Bethany is a member of the Illustrative Mathematics Elementary Curriculum Steering Committee and serves as a consultant, creating materials to support families during distance learning.

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A graphic with the text "Math Teacher Lounge with Bethany Lockhart Johnson and Dan Meyer" on colored overlapping circles.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

S4 – 02. Bethany and Dan share their math biographies

Promotional graphic for "math teacher lounge," season 4 episode 2, featuring photos and names of math teaching guests Bethany Lockhart and Dan Meyer.

In this episode, co-hosts Bethany Lockhart Johnson and Dan Meyer get personal and share their “math bios”—their early experiences with math and how those experiences turned them into the educators they are today.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:00):

We’re recording. What’s up, everybody. This is Dan Meyer with Math Teacher Lounge.

Bethany Lockhart Johnson (00:08):

And I’m Bethany Lockhart Johnson. We are so excited to be back. Season Four, Episode Two. Hi, Dan.

Dan Meyer (00:16):

Hey, Bethany, how are you doing today?

Bethany Lockhart Johnson (00:18):

I’m so excited to be talking with you! You know, as we record this, our reunion at NCTM is getting closer and closer.

Dan Meyer (00:28):

The NCTM live show is gonna be bonkers. I don’t think people are ready for it. You think you know what we’re about on MTL from listening to us, but the live show is gonna be outta control. You cannot imagine how many clowns and elephants Bethany wants to have at the live show. We’re still—we’re trying to talk her down from like three to one, but we’ll see.

Bethany Lockhart Johnson (00:44):

All I want is the t-shirt cannon. Because I used to go to these baseball games and they would have a t-shirt cannon. And I thought, I wanna operate a t-shirt cannon! So like, if I could be standing on stage aiming t-shirts at people who are jumping up and down requesting a t-shirt? I don’t know. Doesn’t that sound fun?

Dan Meyer (01:01):

Sounds awesome. High point of my college education was catching a t-shirt. No, it was—it was a burrito. It was a burrito cannon. But I think it was just a t-shirt cannon, but it was a burrito cannon. And I caught a burrito at a game and it was probably the most memorable moment of all of college education for me.

Bethany Lockhart Johnson (01:16):

Was the burrito still warm?

Dan Meyer (01:18):

Oh yeah. I think it got—like, I think it might’ve been warm at one point and then it got warmed back up through the muzzle velocity of the cannon. So it was a pretty great system they had going on there. <Laugh> Yeah. <Laugh> Anyway, I’m off topic, but, we’re thrilled to—I’m thrilled to chat with you and we’re thrilled to be listened to by you folks out there in MTL land. In the lounge itself. We got a fun show today.

Bethany Lockhart Johnson (01:40):

So if you listen to Episode One—which if you haven’t, hope you go back and listen to it—if you listen to Season Four, Episode One, you’re gonna hear—we asked Huon, KT, who is this delight of a joyful teacher. We asked her to talk to us about what’s her math bio. And we want to ask all of our guests—like, I wanna go back and ask every single guest we’ve ever had to tell us their math bio.

Dan Meyer (02:06):

Yep.

Bethany Lockhart Johnson (02:06):

Because, while seemingly simple in nature, our students enter our math classroom already having had this relationship with math and these notions about their role in math or what they think about math. And it impacts our school year with them if we’re a teacher. And it impacts our relationship with math as we move through our education and beyond. Right? And I I’m so excited about this question, ’cause I think it also ties into this theme for Season Four, which is joyful math, and diving into “When has math felt joyful? When has it not? Does it feel like—how do we think about how our math bio, our relationship with math, has evolved into a joyful or less joyful place?”

Dan Meyer (02:54):

I get it. And what’s really key here, I think, is that teaching more than other professions is a generational profession. You know what I’m saying? Like, no one is like, “Well, you know, I sold insurance to you and now you’re selling insurance to, you know, my grandkids; that’s amazing!” But people are always posting photos when, like, you teach someone who then becomes a teacher later. Teaching is a generational sort of thing. So the kinds of joyful experiences that we offer or don’t offer students now affect the experiences that students who haven’t even been born yet will have, you know, some 20, 30 years later. That, to me, is a trip. And well-worth exploring, you know, how we got here, mathematically speaking.

Bethany Lockhart Johnson (03:39):

I remember a friend had sent me this image of an assignment that her son got that was asking for their Mathography. They wanted to know about their history of mathematics. And this was their first assignment. And this teacher, I would like to imagine, read them all and used it to inform conversations about students’ relationship with math. And, you know, some of the questions they asked were thinking about whether you consider yourself, quote, unquote, “good at math.” Like “what kind of experiences have you had? What do you like or dislike about math? What is, you know—what do you expect to learn in math this year?” Just asking students to actually pause and examine and reflect on their relationship and then also looking forward to, like, what kind of a classroom community do we wanna create? And I loved that assignment. And yeah, so today’s episode Dan, guess what?

Dan Meyer (04:32):

What’s going on? What’s happening?

Bethany Lockhart Johnson (04:33):

I figured we should ask each other about our math bio.

Dan Meyer (04:39):

I think the people out there would love to know this about us. ‘Cause you know, we’re both awesome. But also what’s really cool here is that like, I don’t know this about you. Like not, not a lot. You know, the folks at Amplify, they kind of assembled me and Bethany together in the same way that record labels assembled pop boy bands, girl bands, that kind of thing, back in the day. You know, grabbing some stars from screen or film and just like throwing ’em together and saying, “All right, now you’re here to perform together.” And so it’s just a really good moment for us to, like, settle back and just know who we’ve been working with for the last three seasons and change here. I love it.

Bethany Lockhart Johnson (05:15):

Well, I don’t know. I don’t actually agree with that, Dan. Because don’t you remember? We knew each other beforehand. And while I would like to think of us as…oh, I’ll say One Direction—well, no, One Direction is now defunct. Who’s another band that got formed by one of those shows and is still together and still—

Dan Meyer (05:33):

BTS! K-Pop, you know! Let’s go!

Bethany Lockhart Johnson (05:35):

K-pop. BTS.

Dan Meyer (05:38):

Let’s go, Bethany <laugh>.

Bethany Lockhart Johnson (05:39):

So can we incorporate some K-pop into the NCTM Math Teacher Lounge live episode? Don’t answer now. Don’t answer now. OK. So not only are we gonna share our math bios, but we want to encourage you listeners to share your math bio with somebody in your life. It could be a child in your life, maybe talking to your kiddo about what was it like. What was math like for you? It could be a student that you have. It could be a partner, a friend, a parent. I mean, the sky’s the limit. Share your math bio. And most of all, share with us. We wanna hear about your math bio and you can share it with us at Twitter, at MTLShow, or in our Facebook group, Math Teacher Lounge.

Dan Meyer (06:26):

Stop on by, please. All right. I’m gonna just share like, just a couple of quick, signposts. Not the full bio. Gotta leave them wondering about something here. But here’s a few quick highlights and lowlights of my math bio and how, maybe, it made me the teacher that I was and the educator I am. Is that cool?

Bethany Lockhart Johnson (06:44):

Wait, I didn’t even, I didn’t ask you yet.

Dan Meyer (06:46):

Ask me what?

Bethany Lockhart Johnson (06:47):

Hey, Dan!

Dan Meyer (06:49):

Is there like a magical word? Like, what’s your math bio? <Laugh> Oh, go for it. No, no, that’s right. They won’t know what I’m talking about. Why is he talking about his math bio? Bethany—

Bethany Lockhart Johnson (06:57):

That whole lead-in that we just gave? They might not know.

Dan Meyer (07:00):

Yeah. We just talked about math bios for the last 20 minutes. But yeah, they might not know what we’re—

Bethany Lockhart Johnson (07:04):

<laugh> So Dan, why don’t you go first? ‘Cause I know you were gonna ask me to go first, but why don’t you go first? Dan? What’s your math bio?

Dan Meyer (07:12):

Oh, wow. Well, thank you for the formal invitation to share my math bio, Bethany Lockhart Johnson. So, I’ll just share—I just wanna share a couple items here, not the full history. Gotta leave ’em—leave a little mystery in there, you know what I’m saying? But here’s a few highlights and lowlights, and I think what it means for me as an educator. So, I was homeschooled for eight years. That was big—did a lot of math learning on my own. Couple of lowlights from that, a lot of highlights, in terms of just like being able to, like, learn at my own rate and just jump on ahead and pursue different wacky things. But I tried to switch into public school in fourth grade and I lasted, um, four hours. I didn’t even go to class. I enrolled and then it was like, boom, I was out of there. Because we went to the school; we met the teacher, saw the room, very nice person and place. But I got the homework assignment and the homework assignment was gibberish. I had no idea what to do and such was this feeling of just, like, despair and hopelessness, I was like, I cannot be a part of this. I remember the assignment. It was about identifying scalene, isosceles, and equilateral triangles. I’ll tell you this: I am quite good at that now. But at the time, like, I didn’t know what those words meant. And you know, at that moment we had Encyclopedia Britannica, could not Google this or even Ask Jeeves or AltaVista this so well back then. It just—it was an entry moment of failure and realizing that so much of math is like a, kind of a social kind of construct. And if you’re not part of that social circle, what can you do? So that was a bummer. Another bummer was eighth-grade math, learned it all by way of videotape. You know, put in the tape and watch—not gonna say the person’s name and not this person’s fault—but it was just like watching someone work on a whiteboard. Kind of a precursor to Khan Academy, kind of a drag. Went to high school—

Bethany Lockhart Johnson (09:02):

Wait, wait, wait, wait. We were—I’m not ready to jump to high school. Wait. Can you pause for just a second?

Dan Meyer (09:06):

Yeah. Rock on.

Bethany Lockhart Johnson (09:07):

I just need you to go back to the triangle thing. So in that moment, what did that mean for you that you had had all these experiences with math and then you encounter math in a completely different sphere, a public school, and it did not have a connection or meaning to you because prior to that, it sounds like it was pretty positive. Right? Explore these things you’re curious about; there’s not, like, a level you need to stick with…

Dan Meyer (09:33):

Yep, yep. Yeah. I think that’s right. Maybe it was a little bit of a classic, like, “Oh, I didn’t have a growth mindset; my mindset was like, ‘Oh, I’m good at math because I am, you know, born that way,’” and all of a sudden, that identity was, you know, thrown into question. And, you know, my foundation was all of a sudden quite shaky. And yeah, that’s—you know, I think I taught a lesson recently where I was like, “Hey, this whole thing with a less-than or equal-to sign and a greater-than or equal-to sign, like what those signs are: it’s just, it’s language. And if it’s confusing to you, it’s not because you’re bad at math; it’s ’cause language is oftentimes confusing ’cause people have to agree on it.” So I dunno, that sort of thing is kind of filtered in, filtered back in periodically, some sympathy for like how a lot of math is like just socially agreed upon ways of working with, you know, numbers, shapes, patterns, that kind of thing.

Bethany Lockhart Johnson (10:20):

OK.

Dan Meyer (10:21):

Anyway.

Bethany Lockhart Johnson (10:21):

  1. And in this home school—I have a lot of questions about that, but I’ll stick to one—were you in a community of people that you talked about these math ideas with? Were you homeschooled solo? You have a sibling, so I think you were together, right?

Dan Meyer (10:39):

Yeah. Yeah. I’ve got a twin sister. So we were, you know, like, right on with each other the whole way through there. And yeah, so we had—but it wasn’t, it wasn’t like a—it was a lot of individual work, with my flavor of homeschooling.

Bethany Lockhart Johnson (10:54):

  1. Got it. And the tapes—wait, before you go to high school, the tapes, the VHS tapes, which I’m just loving this image—

Dan Meyer (11:02):

Yeah.

Bethany Lockhart Johnson (11:02):

Was that a positive experience? Was that because that was an area of math that whoever was homeschooling you wasn’t that comfortable with? Why was it that route for the tapes, and what was that? Was that joyful for you?

Dan Meyer (11:15):

Yeah, definitely not joyful. Yeah, it was like, if you had questions, you couldn’t really ask them of the VHS tape. It didn’t work out so well in that way. And it was a lot of operational-type math. It was, you know—there was no give and take; it was all kind of take. From the video teacher. And yeah, I was doing that because my homeschool teacher, my mom, who is very smart in lots of areas, did not have the math knowledge or confidence, especially to help with math at eighth grade. And that was a big reason why, flash-forward to the next year, went to high school.

Bethany Lockhart Johnson (11:48):

Nice segue. OK.

Dan Meyer (11:50):

<laugh> You caught up to high school…I encountered just like four years of just crazy-good, just bonkers-good math teachers who just really changed a lot for me. Especially, Mr. Bishop and Mr. Cavender, very cool folks who did a lot. And especially, I think Mr. Bishop and Cavender both modeled for me what curiosity from a knowledgeable adult looks like. Like someone who, you know, now I can say to myself, “Oh, they were kind of like putting on an act of being very curious about answers they were hearing for the 2000th time from a student,” let’s say, but what a powerful experience that was for me to feel like, “Oh, wow, my thoughts are interesting to someone besides myself.” I got like, maybe it’s two real highlights that I’ll just point to, from my math bio that made me the math teacher and person that I am. Let’s see here. Maybe three, if you you’ll indulge me. One is just like the idea that you could do math wherever you have your brain, a pencil and a paper. And so I remember like in high school, I was in church with my family and kind of a little bit bored of whatever’s going on. And I just had the Bolton and I like drew a pentagon, a regular one, then a hexagon, a regular one, and kept on drawing, like adding sides to the shape. And it was like, it was becoming a circle. And, you know, I was able to take the area of each of those shapes and say, you know, “What happens as you send the number of sides to infinity?” And watch as the formula for area of a circle, Pi R squared, popped out. And it was kind of a literal religious experience, in that moment, just like, “Wow, like my brain’s so cool and math is so cool and paper and pencil’s so cool.” And so there’s that. Just that kind of experience was pretty awesome. And then I would just say like, I’ve had some really fantastic experiences with math in the world itself. Stuff like—let’s see, this is gonna invite more questions from Bethany, probably, maybe I should avoid—I got, I have a Guinness—I have a Guinness world record that’s almost 20 years old. This Guinness world record is—it’s old enough to drive basically at this point. And almost old enough to drink. But like it was—it was a record for chaining the longest paper clip chain together in 24 hours. And the only way I was able to break that record was through mathematics. Where, like, I would be finishing a box of clips. And I would say to my buddy who was there, “I just finished a box of clips.” And that person would type in the number of clips that I had just done. And then a mathematical formula that I had created would tell me how many—how long the chain was at that point. It was being rolled around a spool. And like, it’s just like, wow. So math just made this possible. You know, math revealed that the record I was trying to beat was beatable, because I did the math on it. It was, like, thousands of feet long in 24 hours. And other folks might be like, “Oh, like, that’s that’s huge!” But me, I was like, “All right, let’s divide this out. You know, divide by 24 hours in a day, divide by 60 minutes an hour, 60 seconds in a minute. Oh, that’s like one clip every four seconds. That’s really slow.” You know, think about that <counts aloud>, “Clip, two, three, four. Clip two, three…” It was just slow. So math helped me, you know, wreck that record. Which to my knowledge still still stands. Don’t get any ideas, Math Teacher Lounge Folks! Is this news to you, Bethany? You haven’t blinked in the last, like, five minutes. I’m curious if this is new.

Bethany Lockhart Johnson (15:20):

It is news to me. And I have so many questions. Because OK, if four seconds was slow, so then what was your like—so then I’m assuming a hundred clips per box? Like, what was the rate, you know, per box? How long did it take you to complete a box? What did this friend like? Did this friend stick with you for the whole 24 hours? Did you really do it for 24 hours? Or once you beat the record, did you rest? How did you account for biological function? Like, needs? Like a restroom?

Dan Meyer (15:51):

<Interrupting> Like what?

Bethany Lockhart Johnson (15:51):

Eating.

Dan Meyer (15:51):

Like what, Bethany? OK.

Bethany Lockhart Johnson (15:52):

Um, Sleep.

Dan Meyer (15:55):

So yeah, maybe we dive into some of the specifics in a different time.

Bethany Lockhart Johnson (15:59):

Just tell me one of ’em. Tell me one.

Dan Meyer (15:59):

I’ll just say. So as to discourage other Math Teacher Lounge listeners from taking this on—back off of the record, folks!—this was back in college, so I was a little more limber back then. But I did one—I think it was 1.8 seconds per clip. For an entire 24 hours. Just like, so just like think about it, would you? If you’re gonna step to me on this one, just think about that, OK? And then, and then, you know, make an informed decision.

Bethany Lockhart Johnson (16:28):

Wait. Wait, wait, I just wanna tell you one thing. I’m picturing somebody with a straw, and like, giving you water as you keep clipping. I’m picturing, like, music, I…

Dan Meyer (16:37):

That’s not far. That’s not far. That’s not far from—yeah.

Bethany Lockhart Johnson (16:40):

So many questions! OK. Go on. Sorry, sorry, sorry. Go on. This is your bio.

Dan Meyer (16:44):

We gotta, I gotta wrap this up. I wanna hear your bio. But, like, I would just say like this move to this sense that math is actually a thing that’s useful for more than just a grade; it’s useful for more than just, you know, the societal, you know, adulation that comes from being a math nerd. That kind of thing. And so that, I think that affected a lot of math teaching for me. And, if I gotta, like, summarize math teaching itself in a journey, it went from like, “Hey kids, aren’t I awesome?” to, “Hey kids, isn’t math awesome?” to “Hey kids, aren’t you awesome?” And like that journey was facilitated by lots and lots of people, you know, a lot of personal growth, but at this point, at one point I was like, “Hey, math can help you get records and whatnot. It’s really useful.” And now I’m like, “Wow, your brain’s just doing just really interesting things. I can help you understand how interesting those things are, and maybe make them more interesting, or interesting in a different way, with some help here.” Let’s put a pin in that. That’s the math bio.

Bethany Lockhart Johnson (17:50):

  1. So I have no doubt that if you ask someone in your life, listeners, for their math bio, that you will discover things about them that you never knew. Literally the questions that I have…I have so many question. And Dan is very good at, you know, bringing me back. Bring me back, like, come on, come on. But I just wanna say, overall, your journey seems pretty joyful. It seems pretty joyful. It seems pretty full of confidence. I don’t wanna say “ego” in a negative way, but I wanna say you were buoyed by these experiences that allowed you to feel like math was a place for you to thrive.

Dan Meyer (18:36):

Right.

Bethany Lockhart Johnson (18:36):

Where you could try out things. You could try it out and just, “I could do that!” Right? Like…your relationship just felt very, like…you felt like you had autonomy, agency, perhaps much like you, you operate in this world. Dan, is that, is that right <laugh>?

Dan Meyer (18:54):

Yeah, I think it’s fair to say. And without telling too much of her story, my twin sister with whom I share most things, including genetics, you know—she had a very different experience in math early on. She’s brilliant. She’s a doctor. And not, you know, the book kind of doctor that I am, but like a real, you know, medical doctor. She’s brilliant. But we were—we encountered different messages about who math was made for, early on in, you know, in our entire math learning. And she—we both digested the messages that we were sent, and took, you know, different, different paths because of them, for sure.

Bethany Lockhart Johnson (19:31):

Funny how that works. I thank you, Dan. I do. For in all sincerity, I appreciate you sharing that. And I think that it’s exciting to hear how it influenced your teaching. It feels like you want to cultivate those experiences for your students. And I’ve been in the room when you’ve presented; I was in a room where you taught a class live. It felt like you were making space for the students to have these aha moments. And it feels like in your work at Desmos, and now Amplify, you’re trying to create these products that allow folks to recreate these amazing math moments. Right? And that it’s for everyone and that it’s accessible and it can be very positive. I feel like I have this new perspective on kind of the energy you bring to your teaching. So thank you for sharing that.

Dan Meyer (20:24):

Yeah. Been a pleasure. Thanks for your questions here, Bethany. And it’s been—it’s been fun to reflect on it. And I do—I do feel very lucky in lots of ways. Privileged. Lucky. I know, like—I think the world has been set up for my success in lots of ways, as who I am. But I do just…yeah, I feel—I want more people to experience what it’s like when you walk into a math classroom and it’s like, “Hey, this place is for you. You have interesting thoughts about this. Let’s get ’em out.” So that’s awesome. I would love to hear about you and how you…I mean, we have taught different kinds of kids. You know, I taught kids who I think were somewhat set in, they’re a little bit more solid at secondary in who they are as a math learner. Like “I know who math is and who I am with math.” And I’m really excited to hear what your math bio allowed you to do with students who were perhaps open to the idea that they are very mathematical or at least not yet closed off to those possibilities. So, yeah. What are some of the high, the, you know, the high and low water marks of the making of Bethany Lockhart Johnson, math teacher? <Laugh>

Bethany Lockhart Johnson (21:24):

Thanks for asking, Dan. <Laugh> I’ve shared aspects of my math bio because I think it really informs the way that I talk to people about math and think about math. And I like to share it because I want folks to consider their own journey with math, as we like engage with problem-solving and sense-making and thinking about the students in our classroom. My dad is a math and computer science major. So he had a computer very early on. I wish he had invested in Apple early on when he had like one of the first Apple computers ever. And, sorry, dad, but it’s true. I do wish you had done that.

Dan Meyer (22:10):

I’m sure he does too.

Bethany Lockhart Johnson (22:11):

Oh, he does. So math and computers and conversations about counting, you know, it felt like it was kind of just normal. Like it was around me. And I went to Montessori, which is a private school that—oh, they have some public Montessori—but it’s very self-directed. And so we would have these kind of charts, these goals for the day that you explored. And so we would explore math in very, I don’t know, very organic ways, with these natural materials. And I feel like I excelled at math, but it wasn’t something that I was conscious of. It was just like, “Oh, well, yeah. Math, it’s, you know, something we do.” And then when I went to—when I left Montessori in fourth grade, I remember that year being a lot of like repetition. I was like, well, we did this. We covered this. And except for the mission project that we hadn’t done, that was all new. And that’s it. For another time I’ll share about that. But <laugh> then, they actually, I was moved with a group of students to the fifth grade math class, ’cause we had already done the work that we were doing. And so, it wasn’t that it felt like it came easily, but it did make sense. What we were doing made sense. And then it all kind of changed. There was a lot of change in my family. There was, like, missed school time. And we moved and I went to a new middle school and I was in this environment with students who—it was like an accelerated program. And so I was in this environment with students who were pretty competitive with each other. And I remember going—and I was not from of a competitive environment; like Montessori is not competitive. It’s not about that.

Dan Meyer (24:02):

Right. Right.

Bethany Lockhart Johnson (24:02):

It’s—it was very strange to me that I would be competing against anyone, even competing against myself. And I, you know, knew how to set goals. But it was a different level of energy. And I felt like, because I wasn’t competitive in that nature, I felt like that kind—I felt on the outside of a lot of the energy. Besides the regular, like, middle-school feeling outside of things. And I remember the first friend that I made. Hi, Susan! She had said to me, this was like maybe our second week of school, she’s like, “Oh, at lunchtime, come with me to math club.” And I was like, “OK.” And I remember walking into that room and I had no idea what was going on. And so that was one of the first times where I was just like, “Whoa, I have absolutely no concept of what they’re talking about or what.” These are my peers. I felt very—it was very—it was strange. It was strange. I was like, “This doesn’t feel like a space for me at all.” When I think ordinarily I was kind of excited about the idea of going to math club at lunch, you know? And over middle school, I kind of just got progressively more and more behind. It started with missing some work and then missing more and then checking out. And, you know, the problem was that I really made it about myself. That, like, it wasn’t something that I was then good at or could do. When really it was that well, pre-algebra, I was having a really hard time in like the rest of my life. And so I wasn’t real present in that class. And so when I got to algebra, it didn’t make a whole lot of sense. And then if I missed Monday, Tuesday, and Wednesday, well, Thursday is gonna be hard, you know? And, it just got progressively harder and harder. So I had this great idea that between eighth grade and ninth grade, I was going to take this accelerated geometry class. ‘Cause that was the ninth grade class, it was geometry. And I would take it. It was like geometry in three weeks or something. So then when I entered high school, I would’ve gotten this like jumpstart. But I wish I had said, “Oh, I’ll take this, and then in ninth grade I’ll take geometry.” So like I’ve already kind of gotten a preview of the material. But instead I went to the 10th grade math, which was like intermediate algebra, trigonometry. I had absolutely no clue what was going on. And I had a very, very difficult time and I wasn’t ready for that class. But it was exacerbated by the fact that this teacher felt very free to let the freshmen in that class know that they shouldn’t be in that class. That this class was for 10th graders.

Dan Meyer (26:49):

Oh wow. Oh, wow.

Bethany Lockhart Johnson (26:51):

And we had a rather contentious relationship. And I will never forget that we were in the hallway, and he says to me, “You don’t belong here.” And I’ve talked to—I’ve talked to a girlfriend of mine about her experiences with this teacher and she has the fondest memories.

Dan Meyer (27:13):

Wow.

Bethany Lockhart Johnson (27:14):

She—in fact, almost everyone I’ve spoken with, you know, if we are talking about past teachers or, “Oh, what was that class like?” I mean, they just have these wonderful memories! And for me, my sense of like belonging was already so on a tight rope anyway, that to have this adult, this teacher, tell me, “You do not belong here,” just crushed me. And in hindsight, I think he was saying like, “This class is too hard for you.” I mean, maybe. <Laugh> But all I heard was “You don’t belong here.” And I extrapolated it to connect to math and to anything having to do with math in general. And it just got worse and worse through high school in the world of math. My next math class was even—I had to repeat that class, and still didn’t understand what was going on, and felt more out of place, and, you know, it’s one of those things that I just kind of had started to accept that, I guess, math isn’t for me. I guess I’m just not a math person. Or whatever these stories are that I started to create and build and find evidence for around me that was informing that this wasn’t for me. And I had always done well in school. I was in, you know, accelerated classes. I felt like I was capable of problem solving. And yet in math, I just felt like I had all of this evidence saying that I didn’t belong there. And so when I went to college, I took whatever two math classes were—you know, I was in performing arts and then I did ethnic studies as well. And I remember you had to take two math classes that were GEs. There were these classes that if you don’t wanna deal with math, you go take those classes. And I was like, “Oh yeah, I’ll take that. I’ll take that.” The gulf widened, you know? <Laugh> And I didn’t feel like anxiety when I had to do things like balance my checkbook or navigate math in everyday spaces. It was just, it would never occur to me that I would like seek out opportunities to engage with math or think about it or talk about it.

Dan Meyer (29:35):

That is—yeah, that’s just so wild, how, I don’t know, like it’s often, from the student’s perspective, it is them in a vacuum with math, and the two of them interact and decide if, you know, if they’re right for each other. But from the grown-up perspective, it’s just, you know, it’s a little bit clearer that your story with math was not just you in math, but you with, you know, various external things happening. With family, various teachers playing their different roles—sometimes, you know, really tragic and horrible roles—and then like the compounding mathematical debt that it feels like you were kind of building up, as challenges in one year didn’t get resolved and moved into the next year and so on. And all that makes me wonder—it makes me, like really, really scared, first of all, because I would bet that your teacher might not even remember that moment, that for you is part of just a pivotal moment in your math story, and how many kids have I played—have I been a part of their story in that way and wouldn’t even recall? You know what I’m saying? So that’s a scary part. And then also I’m just wondering, like, how can we, how can we help kids who are in those moments recognize that, “Oh, this kid is like absent a bunch,” and give them more resources to be successful rather than say, “Well, you just gotta try harder now.” Those are things I’m wondering, hearing your story. Thank you for sharing that. I’d love to know more about how you then became a teacher and what all that did for you as you helped students.

Bethany Lockhart Johnson (31:06):

Well, but to answer what you were saying, it wasn’t that I wasn’t—I was always absent physically, but at least like mentally at that point, because it had become so difficult. It didn’t make sense to me. So I was just really checked out in math class, you know? So in hindsight, you know, as a teacher, for sure I can look back, and especially hearing these stories and these experiences my friend had with this teacher and just like chalks up as one of like her most favorite teachers ever! And you know, he clearly did a great job for so many students. But for me, and I think for some people, they would’ve taken those challenges and, you know, it would have fortified them in a different way or something. But for me, I took it upon myself to mean certain things about myself and about my ability and what I was capable of. And so I think, I think in some ways, you know, yeah, it’s all, it’s all interconnected. You know, when your students walk in the door, they’re not this—the things that are impacting them in their life are coming into the room with them. And I don’t think we can take that for granted and think, “Well, if they just focus hard enough…”

Dan Meyer (32:21):

Yeah.

Bethany Lockhart Johnson (32:23):

So let’s go back to my love of Oprah. You know, Oprah talks about living your best life. And something I really appreciate about Oprah is that she encourages you to examine, like, sticking points, right? Like she doesn’t just say, “Well, this…just pretend nothing ever happened, and everything’s fine!” You know, she really talks about making time for reflection. And I kind of got mad that anytime I thought about math, or math schooling came up. Or, you know, whatever, any time that came up that I just felt UGH about it. And I felt like a failure. And I’m like, “You know what, what if I took a math class? And I’m an adult at this point. I’ve graduated. I have—I’ve left college. I have my degrees. But I said, “What if I took a math class?” So I went down to, the city college and I found out that you have to take this exam, like a placement exam. And I went and took the placement exam. And I remember it’s one of the responsive tests where if you get it right, the next question’s a little harder. And so I’m taking it, panicking, because it’s getting more like…I just, you know. And I remember it placed me in like, whatever, Algebra Something, this class that was far more advanced than I thought I should be in. And I was like, there’s been a mistake! You know, and I went to the counselor and said, you know, “I got these results, but I couldn’t answer a lot of the questions on the test.” She’s like, “No, no, no, that’s how it works.” So I go take this class and the class was hard. And I decided that I was just gonna keep showing up. And every day before class, I kid you not, they had a little math…it was like a math center where you could go in and they had a bunch of tables and you’d sit at the table and you could sit and do your work or whatever. If you had a question, you walked up and put your name on a clipboard and then somebody would come and help you. So I did that, every single—like before every single class I would go in. I’d sit there. I’d do the work. I’d go. And I’d get help. Like somebody would walk over and you know, some kid for whom they’re like this…you know, they’re math—it might be you, Dan! It could be you! It could have been you! You know, would walk over and be like—

Dan Meyer (34:38):

Yeah, I was in Help like that. Naw, it’s awesome. Love, love those people. Yeah.

Bethany Lockhart Johnson (34:42):

And you know, I did it. And I did so well in the class. I did exceedingly well in the class. And I said—

Dan Meyer (34:50):

Take that! Take that, everything! Every other math experience!

Bethany Lockhart Johnson (34:53):

I said, what?

Dan Meyer (34:55):

Yeah!

Bethany Lockhart Johnson (34:55):

Wait a second.

Dan Meyer (34:56):

Yeah.

Bethany Lockhart Johnson (34:57):

And it was that I was present. I was not afraid to look at what didn’t make sense. And if something didn’t make sense, it didn’t mean there was something wrong with me. Whaaaaat?

Dan Meyer (35:10):

Yeah. Yeah.

Bethany Lockhart Johnson (35:10):

So I was just in such a different space. And then I took another math class and that class was even harder. And I did the same thing where I went to the little lab and, you know, and it just buoyed me. And it made me realize that, like, this story, that my experience with it was very powerful and that was a real lived experience, but that it didn’t have to define my relationship with math. But then! I decided I wanted to go back to school to become a classroom teacher. And I totally—this was a couple years after that math class experience. So now, you know, I’m healing my relationship with math through basic positive experiences, da, da, da, you know, doing other work. But fast-forward, for a whole number of reasons, decided to become a classroom teacher. And I freaked out. All of my—like, I’m studying for the GRE and the CSET and all the things you have to the hoops you have to jump through to apply to the masters program and the credential program. And I freaked out. I was so close to quitting, Dan. Because I was convinced that the reason I couldn’t be a classroom teacher is because I wasn’t capable in math. Like I was—it was all that resurfaced. And even though I now had evidence to say something different, to the contrary, it was still so visceral. And I was so scared. But I passed that Math CSET.

Dan Meyer (36:47):

Get it.

Bethany Lockhart Johnson (36:47):

I did well enough on the GRE—

Bethany Lockhart Johnson (36:50):

Yes!

Bethany Lockhart Johnson (36:50):

You know, I finished my credential. I worked really, really hard. I had to work so hard in my student placement, when I was student teaching for a fifth-grade class, ’cause I felt like, “Oh my God!” I mean, now I could do the mathematics, but I couldn’t TEACH it to someone, you know? But I had amazing professors at UCI, and my math professors really like just—and my mentor teacher! shout out to Jennifer! shout out to Phil!—these amazing mentor teachers who just loved teaching and who loved—like you said, you have these teachers in your life who you got to see the way that they listened to students. They taught me about that love of listening to students. And then I fell in love with, you know, CGI, cognitively guided instruction, and started learning all about all of these educators who just wanna learn from students’ thinking. And it was just so powerful. And I realize as a kindergarten teacher that I have this really special role in helping to create space for a positive school experience. Like we get to talk about—I talk about my students as mathematicians; they’re writers; they’re thinkers; they’re problem-solvers. And I also want to make space for parents. Some of them, this is their first kid in kindergarten, and they brought all of their experiences, a lot of it negative, that they had had with mathematics. So I felt like it was such an exciting opportunity to help show parents how they could have conversations about math with their students. That also, I hope helped heal their own anxiety with mathematics.

Dan Meyer (38:41):

Right, right.

Bethany Lockhart Johnson (38:42):

Like, I’ve not even scratched the surface of math learning. But I just have such a changed perspective and relationship with math. And I just fell in love with the sense-making. And I fell in love with the journey of it. I still experience math anxiety about a wide variety of things, but I do love it. And I feel like there’s a space for me in relationship with math. And that really excites me.

Dan Meyer (39:09):

Yeah. Wow. Listen to that folks. We, we don’t deserve her! Bethany Lockhart Johnson! She got some math game and could have gone off there and, you know, become an accountant or something. And she chose to hang with kids and their parents. That’s so wild that you’re like rehabbing parents and their self-conception about mathematics at the same time. I think that is so cool.

Bethany Lockhart Johnson (39:32):

Well, thanks Dan Meyer. I gotta tell you, I don’t know when or if I’ve ever shared that much of my math story. So there is a certain amount of vulnerability there. But thanks for listening. And I’m glad that, you know—I think there’s space for us to talk about these things that we care deeply about, but that can be really complicated.

Dan Meyer (39:56):

Yes. Yes. And I love how you you’ve really sharpened the point on what I feel like I know in my brain, but not my body all the time: That individual teachers are huge. Like, individual teachers, and individual moments of teaching, are just not something to play with. You know, like that kid that’s in fifth grade having a tough time, like there could be a month or a day-long period where all of a sudden, like, you’re just like, “Oh yeah, I’m back in the mix; like, me and math are still buddies.” And there’s also like moments that you had, where like one casual word from a teacher can just really put a huge wedge between you and a discipline that needs and wants you and your intellect in it.That’s a really powerful testimonial. Not just for math, but for teaching, your teaching bio.

Bethany Lockhart Johnson (40:43):

I agree with you. And I also, I also…you know, I think we can’t put this—we are human. Teachers are human. And so I’m sure there’s things I’ve said to students. Twenty-second story: a student stapled his finger in my class. <Laugh> And I remember holding his hand and saying, “Why did you do that?” And I wasn’t yelling at him, but it was like, I am sure the panic in my face…like, that’s what he’s gonna remember about kindergarten. Right? <Laugh>.

Dan Meyer (41:19):

Yeah.

Bethany Lockhart Johnson (41:20):

That. He will remember that. He won’t remember the really cool city project we did. He’s gonna remember his teacher holding his hand, in his face: “Why did you do that?”

Dan Meyer (41:30):

Yeah. Yeah.

Bethany Lockhart Johnson (41:30):

You know, so we’re human. And yes, it was awful that that teacher said that to me. There were a thousand other ways that he could have said whatever it was he was thinking. And that did deeply wound me. But despite his influence—because teachers do have a lot of power and I think they need to examine that power, ongoing—it still doesn’t have to define us. So I don’t wanna put this pressure, like—

Bethany Lockhart Johnson (41:55):

Sure.

Bethany Lockhart Johnson (41:56):

“So never ever say anything negative!” You know, we’re human.

Dan Meyer (42:00):

I feel like that kid is currently on some office-supply podcast talking about “your office-supply bio” and saying, “Let me tell you how I first got really freaked out by staples. Here’s the deal: I only use paper clips. And here’s why.”

Bethany Lockhart Johnson (42:15):

“Here’s why.” But then—callback!—he’s going to stumble upon THIS podcast and think, “And because I’m so adept with paper clips, I can beat that record!”

Dan Meyer (42:30):

Though—aaay! whoa! Settle down!

Bethany Lockhart Johnson (42:31):

BOOM.

Dan Meyer (42:31):

Don’t get any ideas, kid. No way. Uh-uh. I don’t like that at all. That’s not what—that’s not what I want to have happen here. No, thank you.

Bethany Lockhart Johnson (42:41):

Well, I’m spent, Dan. I need a nap.

Dan Meyer (42:45):

Yeah. I need a box of Kleenex. I need a nap. I need a—yeah, for sure, a baba. Uh-huh. Definitely. Hey, so look, I’m not expecting you folks out there in the lounge to kind of give us the same depth or breadth. You know, we are here, of course, for your entertainment. Feast on our stories and dramas. But I would love to know at some point, like, what are a few, a few moments that really came to define you mathematically? Came to influence you as a teacher? I think we would do really well for each other to understand that about all of our processes. So yeah, I would just toss in a plug in for Twitter, @MTLShow, or Facebook, Math Teacher Lounge; it would be fantastic to hear from you.

Bethany Lockhart Johnson (43:24):

Thanks so much for listening.

Dan Meyer (43:25):

Thanks, folks. Bye now.

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What Dan Meyer says about math teaching

“Teaching, more than other professions, is a generational profession. The kinds of joyful experiences we offer, or don’t offer, now affect the experiences students that haven’t even been born yet will have years later.”

– Dan Meyer

Meet the guests

Dan Meyer

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is currently the Dean of Research at Desmos, where he explores the future of math, technology, and learning. Dan has worked with teachers internationally and in all 50 United States and was named one of Tech & Learning’s 30 Leaders of the Future.

Bethany Lockhart Johnson

Bethany Lockhart Johnson is an elementary school educator and author. Prior to serving as a multiple-subject teacher, she taught theater and dance and now loves incorporating movement and creative play into her classroom. Bethany is committed to helping students find joy in discovering their identities as mathematicians. In addition to her role as a full-time classroom teacher, Bethany is a Student Achievement Partners California Core Advocate and is active in national and local mathematics organizations. Bethany is a member of the Illustrative Mathematics Elementary Curriculum Steering Committee and serves as a consultant, creating materials to support families during distance learning.

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About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Winter Wrap-Up 03: Ideas to build math fluency

Promotional graphic for "Math Teacher Lounge" episode featuring Valerie Henry, Ed.D., on ideas to build math fluency, with a photo of Valerie Henry in the bottom right corner.

Join us for the third episode in our Winter Wrap-Up! In this episode from season 3 of Math Teacher Lounge: The Podcast, we sit down with Dr. Valerie Henry to talk about math fluency and what that means for students. Listen as we dig into the research, hear Val’s three-part definition of fluency, and explore her five principles for developing it.

Explore more from Math Teacher Lounge by visiting our main page

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Dan Meyer (00:03)

Hey folks. Welcome back. This is Math Teacher Lounge, and I am one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I’m your other host, Bethany Lockhart Johnson. Hi, Dan.

Dan Meyer (00:11):

Hey, great to see you. We have a big one this week to chat about and some fantastic guests. We are chatting about fluency, which is the sort of word and concept that I feel like people have very, very non-neutral associations with it. A lot of them are very negative, for a lot of people.

Bethany Lockhart Johnson (00:26):

I saw you frown a little. What’s up with that, Dan? You kind of, like, shrank.

Dan Meyer (00:30):

I have strong feelings about it. You know, there’s lots of ways that people go about helping people become fluent in mathematics. And a lot of them are harmful for students, and ineffective. And it got me thinking about fluency as it exists outside of the world of mathematics, where we have a lot of very clear images of it. We’re getting fluent in things all the time. Like, as humans. Human development is the story of fluency. And I just was wondering….Bethany, would you describe yourself as fluent at something outside of the world of mathematics? What is that? How’d you get fluent at it? What was the process?

Bethany Lockhart Johnson (01:05):

Hmm, I think I’m a pretty fluent reader. I read all the time. I’m a happier person if I’ve read that day. I once saw this poster in a classroom; it said “10 Ways to Become a Better Reader: Read, Read, Read, Read, Read…you know, 10 times. Get it? Reading? You get better at reading by reading! So I would say reading. And it’s been kind of cool—I have a one-year-old who, it’s been really exciting slash overwhelmingly anxiety-producing to see him get very fluent with walking slash running, ’cause he’s getting faster every day. And it’s kind of fun. When I think of what’s something somebody’s trying to get fluent with…walking! He’s trying to be more fluid. He’s practicing transitions. He doesn’t wanna hold my hand while he traverses rocky terrain. He’s getting better at it. He’s practicing. What about you? What’s something…?

Dan Meyer (02:08):

I think about driving a lot. I’m a very fluent driver and I think a lot about when I was first a driver, you know? And how l have my hands on 10 and 2, vice grip, and do not talk to me; do not ask me anything; don’t ask me my NAME. I need to focus so hard. And then a year later, you know, I’m driving with one hand, smash the turn signal, take a sip off of whatever, change the CD. And then it’s no big deal.

Bethany Lockhart Johnson (02:38):

Wait, did you pass the first time? Your test?

Dan Meyer (02:40):

Yeah, I don’t like to brag about it. <laugh> But I do all the time. <laugh> But I got a hundred on my driving test. I don’t care who knows it. And I hope it’s everybody. But I guess all of this is just to say there are areas of life where fluency feels natural, with the case of walking. There’s areas of life where fluency feels motivating, with like driving—I wanna be able to switch the CD out or whatever. And there’s areas where fluency feels terrifying and hard to come by, like mathematics, sometimes. So we have a set of guests here. Our first guest will help us figure out what do we mean by fluency? And what’s the research say about what fluency is and how students develop it in mathematics? And then our other guests will help us think about what it looks like in practice in the classroom. What are some novel, new ways to work on fluency? So first up we have Val Henry, Dr. Val Henry.

Bethany Lockhart Johnson (03:32):

So we knew we needed help with the fluency definition, because when we think about it, it’s kind of big, right? And we wanted to look at what research about fluency really says. So we called on Valerie Henry. Val is a nationally board-certified teacher, taught middle school for 17 years, and since 2002 has worked with undergraduates graduates, credential candidates as a lecturer at the University of California, Irvine, one of my alma maters. So after doing her dissertation on addition and subtraction fluency in first grade, Val created a project to study ways to build addition and subtraction and multiplication and division fluency while also developing number sense in algebraic thinking. And the pilot grew and grew over the last 18 years into a powerful daily mini-lesson approach to facts fluency called FactsWise. And when we thought of fluency, the first person I thought of was Val. Welcome, Val Henry, to the Lounge! I’m so excited to have you here. Welcome.

Valerie Henry (04:36):

Thanks, Bethany. And thanks to you, Dan. It’s great to be here today.

Dan Meyer (04:41):

Great to have you; help yourself to whatever you find in the fridge. The names that people write down on those things in the bags are just recommendations. It’s potluck-style here. I’m curious, Val, if you’re, like, on an airplane, someone asks you what you do, and you say you study fluency…what is the layperson’s definition of what does it mean to be fluent in mathematics? And if you can give a brief tour through what the research says about what works and what doesn’t that would really help us orient our conversation here.

Valerie Henry (05:12):

The first thing I have to do when I talk to somebody on a plane is define the idea of fluency. And I often use an example of tying your shoelaces. Because that works with first graders as well as adults. This idea that when we first start trying to put our shoes on and get those shoelaces tied, somebody tries to, first of all, just do it for us. But then of course maybe tries to teach us the bunny-ears approach. And we struggle and struggle as little kids and eventually either the bunny-ears approach or something else starts to work for us. But we still have to pay attention to it. We have to think hard and it’s not easy. And then over time we get to the point where we basically don’t even think about it. When I tie my shoes in the morning. I’m not thinking about right-over-left and left-over-right and all of those things. I just do it. And so that’s a good, easy example of becoming fluent with something. I think what we’re talking about today though, is the basics, the adding and subtracting that we hope kids are going to have mastered maybe by second grade, and the multiplication and division facts that we wanna maybe have mastered by third, maybe fourth grade. So now what does that mean to become fluent with those basics? I have a three-part definition that seems to match up really nicely with the common core approach to fluency. Which is, first of all, we want the answers to be correct. And then second, we want the answers to be easy to know. And so what does that mean? Well, to me, it means without needing to count,

Bethany Lockhart Johnson (07:12):

You mean without having to kind of muscle through it? Or say more about you mean.

Valerie Henry (07:16):

Well, I guess what I mean is that when you watch a young child try and solve something even as simple as two plus three, they might put up two fingers and then go 3, 4, 5 with three more fingers winding up on their hand, one or the other of their hands. While they’re doing that, they don’t really have a sense of whether even their answer is right or not, quite often. Especially when you get to the larger adding and subtracting problems, you can see a lot of errors happening as they’re trying to count. And it’s taking up cognitive energy to do that counting process, especially as you get to the larger quantities. So my definition of fluency now is “getting it right without needing to do that hard work like counting.” Now, some people might say, well, we just want them to have ’em memorized. But in my research, I’ve learned that a lot of very fluid adults don’t always have every fact memorized. In fact, if you ask a room full of adults, what’s seven plus nine, you might learn that they can all get it correct quickly, quickly…but they don’t all have it memorized. And so when you ask them, “How did you get that?” Many of them will say, “Well, I just gave one from the 7 to the 9 and I know that 10 plus 6 is 16.”

Bethany Lockhart Johnson (08:53):

That’s such an important distinction. My brain literally just did that actually!

Valerie Henry (08:58):

<laugh> Right? <laugh> But you’re fluid with it, because it doesn’t take you much cognitive energy at all.

Bethany Lockhart Johnson (09:05):

Right.

Valerie Henry (09:07):

So now we have “correct without needing to put that cognitive energy,” which usually means that you’re counting. And then the third thing is “relatively quickly,” so that you’re not spending 15 seconds trying to figure it out. Even that part-whole strategy approach can be done really quickly, almost instantaneously. Or it can take a long time. So if a student can get the answer correct within, you know, three or four seconds— is I’m pretty generous—I figure that they’re pretty darn fluent with that fact. So that’s my three-part definition of these basics, fluency.

Dan Meyer (09:55):

I love the distinction between getting it correct and getting it quick. It’s possible to be quick with wrong answers. It’s possible to be like, “Those are separate components there.” And I echo Bethany’s appreciation for this third option in between knowing it instantaneously through memorization and muscling through it. But there’s like a continuum there of how much energy it took you to come up with it that all feels extremely helpful.

Valerie Henry (10:21):

And you know, one of the things that I’ve noticed is that when kids are pressured to come up with those instantaneous answers, they often default to guessing and get it wrong.

Bethany Lockhart Johnson (10:30):

Mm, yeah.

Valerie Henry (10:30):

So that’s one of the things that I’ve learned is that as we’re trying to help students develop fluency, it’s important to start with building their conceptual understanding of what it means to do, you know, 3 times 9 and what the correct answer is, maybe using manipulatives or representations of some sort. Not skip-counting! I really have found that skip-counting just perpetuates itself in many students’ minds and that they never stop skip-counting, which means they’re putting in not very much mental energy if it’s 2 times 3 but a ton of mental energy if it’s 7 times 8. Because frankly, it’s really hard to skip count by sevens. And by eights.

Bethany Lockhart Johnson (11:18):

I can get to 14 and then I’m like, wait, wait, what was next? Right? No, no, no…21! What do you feel are some misconceptions that maybe teachers, maybe parents have about fluency in math?

Valerie Henry (11:30):

I think maybe one of the first ones is that if students count or skip-count, their answers repetitively over and over and over and over, that they’re bound to memorize them. And the study that I did back in 2004, I actually had a school that had decided that they were going to do time tests with their students every day, all year. And that undoubtedly by the end of the year, those students would be fluent.

Bethany Lockhart Johnson (12:06):

And to clarify by time test, you mean like, sit down, pencil, paper, ready, go, worksheet kind of thing.

Valerie Henry (12:15):

Yes.

Bethany Lockhart Johnson (12:16):

Some of us might remember quite vividly.

Valerie Henry (12:18):

<laugh> Very vividly. And you know, you have to get it done within a certain amount of time. So they made it fun for the students. Apparently the students enjoyed it. I was a little leery about that, but in the end, when I went and checked on the students and I did one-on-one assessments with half of the students in every class that were randomly selected so that I could get a sense of where they were with their fluency—and these were first graders—they basically had nothing memorized. They were simply counting as fast as they possibly could. And, you know, mostly getting the right answers. But they had not memorized. So that’s one of the myths, I think, is that repetitive practice of counting gets you to memorization.

Bethany Lockhart Johnson (13:10):

If I put it in front of you enough times, you’ll become fluent.

Valerie Henry (13:14):

Right, right. Now these students didn’t really get any instruction, any help learning these. They just simply tested over and over and over. So that’s another thing that I think is a misconception. It’s that if we test students, but don’t really teach them fluency, then they’re going to become fluent. If we just test them every Friday or that kind of thing. And that they’ll learn them at home. But really what that means is a few lucky kids who have parents who have the time and the energy and the background to know how to help will take that job on at home. Not that many students are really that fortunate.

Dan Meyer (14:01):

It’s almost like the traditional approach, or the approach you’re describing, confuses process and product. It says, “Well, the product is that eventually fluent students will be able to do something like this, see these problems and answer them, answer them quickly,” and says, “Well, that must be the process then as well; let’s give them that products a whole lot.” But as I hear you describe fluency with bunny ears on shoelaces, there’s these images and approaches and techniques that require a very active teacher presence to support the development of it. That’s just kind of interesting to me.

Valerie Henry (14:35):

My initial project, the pilot project that I tried, was to simply ask teachers to follow five key principles. And the first one was to do something in the classroom every day for—I told them, even if you’ve only got five or 10 minutes, work on fluency for five or 10 minutes a day, and let’s see what happens. So that was one key element was just to teach it and to give students opportunities to get what the research calls for when you’re trying to memorize, which is actually immediate feedback. When I talk about immediate feedback with my student teachers, I say, “I’m talking about within one or two seconds of trying a problem, and then sort of immediately knowing, getting feedback of whether you got the answer right or not so that your brain can kind of gain that confidence. ‘Oh, not only did I come up with an answer, but somebody’s telling me it’s the correct answer.’”

Dan Meyer (15:38):

There’s a lot of apps now in the digital world that offer students questions about arithmetic or other kinds of mathematical concepts and give immediate feedback of a sort: the feedback of “You’re right; you’re wrong” sort. Is that effective fluency development, in your view?

Valerie Henry (15:57):

I haven’t heard and I haven’t seen them being super-effective. The ways I think about this are “Immediate feedback isn’t the only thing we need.” Probably one of the biggest things that we need is for students to develop strategies. And this is one of the other things I’ve learned from international research, from countries that do have students who become very fluent very early, is that they don’t shoot straight for memorization, but they go through this process of taking students from doing some counting and then quickly moving them to trying to use logic. So, “Hey, you really are confident that 2 + 2 is 4; so now let’s use that to think about 2 + 3.” Actually, as an algebra teacher, I would much rather have students that have a combination of memorization and these strategies, than students who’ve only memorized. Isn’t that interesting that my most successful algebra students were good strategy thinkers. Not just good memorizers.

Bethany Lockhart Johnson (17:09):

So you mentioned there were five that kind of helped root this idea in like, “What can teachers do? What is the best thing that teachers can do to support with fact fluency?” So, everyday was key.

Valerie Henry (17:22):

Then the next principle that I really focus on is switching immediately to the connected subtractions so that students—

Bethany Lockhart Johnson (17:33):

Not waiting until you’ve gotten all the way through addition. But making “Ooh!”

Valerie Henry (17:38):

Totally. And I didn’t do that the first year. And when we looked at the results of the assessments at the end of the year, we realized that our students were so much weaker in subtraction than addition. So the following pilot year, we tried this other approach of doing subtraction right after the students had developed some fluency with that small chunk of addition. And we got such better subtraction results.

Bethany Lockhart Johnson (18:11):

What are the other principles?

Valerie Henry (18:13):

The biggest one is to use these strategies. So the strategies makes the third. And then the fourth I would say is to go from concrete to representational to abstract.

Bethany Lockhart Johnson (18:27):

Don’t put away those manipulatives. Don’t put away those tools.

Valerie Henry (18:31):

Oh, so important to come back to them for multiplication and division. And my fifth principle is to wait on assessment. To use it as true assessment, but not race to start testing before students have had a chance to go through this three-phase process. Which is conceptual understanding with manipulatives; building strategies, usually with representations; and then working on building some speed until it’s just that natural fluency.

Bethany Lockhart Johnson (19:07):

I wanna say thank you so much for offering your really learned perspective, because you have not only done the research, but seen it in action and seen how shifting our notions of fluency and what fluency can be and what a powerful foundation it can be for all mathematicians. Really, that shift is so powerful. And I appreciate you sharing it with our listeners and with us. So we’re so excited that we got to talk with you today, Val—

Dan Meyer (19:35):

Thank you, Dr. Henry.

Valerie Henry (19:37):

You’re welcome!

Dan Meyer (19:41):

With us now we have Graham Fletcher and Tracy Zager, a couple of people who understand fluency at a very deep and classroom level. I wanna introduce them and get their perspective on what we’re trying to solve here with fluency. So Graham Fletcher has served in education in a lot of different roles: as a classroom teacher, math coach, math specialist, and he’s continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary math. He’s the author, along with Tracy, of Building Fact Fluency, a fluency kit we’ll talk about, and openly shares so much of his wisdom and resources at gfletchy.com. Tracy Johnson Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of this toolkit, Building Fact Fluency, and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books for teachers at Stenhouse Publishers, including, yours truly. Thank you for all that insight, Tracy, and support on the book.

Bethany Lockhart Johnson (20:49):

Dan and I were talking at the beginning of the episode about things we feel like, “Hey, I’m fluent in that. I’m fluent in that.”

Dan Meyer (20:55):

Just very curious: What’s something you would like to get fluent in outside of the world of mathematics, let’s say?

Tracy Zager (21:00):

I’ll say understanding the teenage brain, as the parent of a 13-year-old and 15-year-old. That’s the main thing I’m working on becoming fluent in!

Bethany Lockhart Johnson (21:10):

Ooh!

Dan Meyer (21:13):

A language fluency, perhaps. All right, Graham. How about you?

Graham Fletcher (21:16):

For me typing, it’s always been an Achilles heel of mine. So voice-to-text has been my friend. But it’s also been my nemesis in much of my texting here and working virtually over the last couple years. So yeah, typing.

Dan Meyer (21:33):

Do you folks have some way of helping us understand the difference in how fluency is handled by instructors and by learners?

Tracy Zager (21:40):

I would say that the lay meaning of fluency is definitely a little different than what we mean in the math education realm. When we’re talking about math fact fluency, which is just one type of fluency. So you gotta think about procedural fluency and computational fluency; there are lots of types of fluency in math. And Graham and I had the luxury of really focusing in specifically on math fact fluency. We’re looking at kind of a subset of the procedural fluency. So the words you hear in all the citations are accurate, efficient, and flexible. There’s this combination of kids get the right answer in a reasonable amount of time and with a reasonable amount of work and they can match their strategy or their approach to the situation. That’s where that flexibility comes in. And there’s like lots more I wanna say about that about sort of…I think one issue that comes up around fluency is that people are in a little bit of a rush. So they tend to think of the fluency as this automaticity or recall of known facts without having to think about it. And that is part of the end goal, but that’s not the journey to fluency. So this is one of the things that Graham and I thought about a lot was the path to fluency. The goal here it’s that student in middle school who’s learning something new doesn’t have to expend any effort to gather that fact. And they might do it because they’ve done it so many different ways that they’ve got it, and now they just know it, or they might be like my friend who’s a mathematician who still, if you say, “Six times 8,” she thinks in her head, “Twelve, 24, 48…” and she does this double-double-double associative property strategy. And it’s so efficient, you would never know. And that’s totally great. That’s fine. That’s not slowing her down. That’s not providing a drag in the middle of a more complex problem or new learning. So we’re really focused on having elementary school students be able to enter the middle and high school standards without having that pull out of the new thinking.

Graham Fletcher (23:53):

And as I think about that, I think about how so many students will memorize their facts, but then they haven’t memorized them with understanding. So that when they move into middle school and they move into high school, it’s almost like new knowledge and new understanding that’s applied from a stand-alone skill.

Bethany Lockhart Johnson (24:10):

So something that felt really unique to me, Graham, as I was diving into the toolkit, is your use of images, Tracy, Graham, is the way that you use images to help students notice and wonder to start making sense of these quantities and the decomposition of numbers using images. Can you talk a little bit about how images played a part in the way that you think about this building a fact fluency?

Graham Fletcher (24:41):

What I realized is so many times when we approach math with just naked numbers with so many of our elementary students, the numbers aren’t visible. The quantities. They can’t see them; they can’t move them. They’re just those squiggly figures that we were talking about earlier on. So how is it that we make the quantities visible, to where students feel as if they can grab an apple and move it around? Because a lot of times we start with the naked numbers and then if kids don’t get the naked numbers, then we kind of backfill it. But what would happen if we start with the images? And then from there, these rich, flourishing mathematical conversations develop from the images. And I think that was the premise and the goal of the toolkit.

Tracy Zager (25:22):

When you look at how fact fluency has traditionally been taught, it’s all naked numbers. And sometimes we wrote ’em sideways. Like, that’s it. That was our variety of task type. Right? Sometimes it’s vertical; sometimes it’s horizontal. And that was it. And I’ve just known way too many kids who couldn’t find a hook to hang their hat on with that. It didn’t connect to anything. And so part of why I knew Graham was the perfect person for this project was his strength in multimedia photography, art, video. And so we started from this idea of contexts that for each lesson string in the toolkit, there’s some kind of context. An everyday object, arranged in some kind of a way that reveals mathematical structure and invites students to notice the properties. So we start with images of everyday objects: tennis balls, paint pots…um, help me out; here are a million of them. Crayons—

Bethany Lockhart Johnson (26:18):

Crayons, markers.

Tracy Zager (26:18):

Shoes, right? Sushi, origami paper, all kinds of things in the different toolkits. So there’s a series of images or a three-act task or both around those everyday objects, and then story problems grounded in that context. And then there are images with mathematical tools that bring out different ideas, but relate in some way to the image talks. And we do all of that before we get to the naked number talk. Which we do, and by the time you get to the number talk, it’s pretty quick, ’cause they’ve been reasoning about cups of lemonade. And now when you give them the actual numerals, they’re all over it.

Bethany Lockhart Johnson (27:03):

I have to say too, as somebody who—particularly in middle school—navigated math anxiety, we recently talked with Allison Hintz and Anthony Smith about their amazing book Mathematizing Children’s Literature.

Tracy Zager (27:14):

Yay!

Bethany Lockhart Johnson (27:14):

And I was explaining, like, if I sat down at the beginning of a math class and my teacher opened a picture book and said, “We’re gonna start here,” I felt my whole body relax. And if we start with this image, if we start with just looking at an image and making sense of an image, I feel like that could be such a powerful touchstone for all the work you do from there.

Tracy Zager (27:41):

That’s core. That’s a core design principle, is that invitational access. There are no barriers to entry. There’s nothing to decode. There’s nothing formal. We’ve been learning from Dan for years about this, right? Of starting with the informal and then eventually layering in the formal. I was in a class in Maine where they were doing an image talk and it’s these boxes of pencils. It’s a stack of boxes of pencils and they’re open and you can see there are 10 pencils in each box. And so there are five boxes of pencils each with 10 pencils in it. And then the next image is 10 boxes of pencils and each box is half full. So now it’s 10 boxes each with five. And the kids are talking and talking and then the third image, I think there are seven boxes each with 10 pencils in it. And she said, “What do you think the next picture’s gonna be?” And this girl said, “You just never know with these people!” <laugh> I dunno!”

Bethany Lockhart Johnson (28:37):

That’s kinda true. Knowing you both, it’s kinda true.

Tracy Zager (28:42):

Like if it’s seven boxes with 10 in it, one kid said, I think it’s gonna be 14 boxes of five. And other kids are like, I think it’s gonna be 10 boxes with seven. And they start talking about which of those there are and the relationships between—

Bethany Lockhart Johnson (28:58):

But they’re making sense of numbers!

Tracy Zager (28:59):

Totally. So all the kids felt invited. They can offer something up. They’re noticing and wondering about that image. They’re talking about it in whatever informal language or home language that they speak. And that was core to us. That was a huge priority, because honestly, one of the motivations to talk about fluency is that it’s always been this gatekeeper. It has served to keep kids out of meaningful math. Particularly kids from marginalized or historically excluded communities. So they’re back at the round table, doing Mad Minutes, while the more advantaged kids are getting to do rich problem solving. And so, we thought, what if we could teach fact fluency through rich problem solving that everybody could access? That was like square one for us.

Bethany Lockhart Johnson (29:45):

That’s huge.

Dan Meyer (29:46):

That’s great to hear. What’s been helpful for me is to understand that students who are automatic, that’s just kind of what’s on the surface of things. And that below that might be some really robust kind of foundation or scaffolding that bleeds to a larger building being built, or it might be just really rickety and not offer a sturdy place to build farther up. It’s been really exciting to hear that. I wonder if you’d comment for a moment about, in the digital age and—I’m at Desmos and our sponsors are Amplify and we all work in the digital world quite a bit. There are a lot of what report to be solutions to the fluency issue, to developing fluency in the digital world. Just lots and lots of them. Some that are quite well used, others that are just like X, Y, or Z app on the market. You can find something. Do you have perspectives on these kinds of digital fluency building apps? Like, what about them works or doesn’t work? Let us know. Graham, how about you? And then Tracy, I’d love to hear your thoughts too.

Graham Fletcher (30:47):

Yeah, I think that’s a great question, ’cause there’s a lot of shiny bells and whistles out there right now that can really excite a lot of teachers. But I always come back to what works for me as a classroom teacher is probably gonna work in a digital world as well. So what are the things that I love and honor most about being in front of students, and how can I capture that in that virtual world? I think one of the things that really helps students make connections is coherence. I think coherence, especially when you leave students for—you don’t get to talk with them after the lesson is done—so I think about how we can purposefully sequence things through a day-to-day basis. I think coherence is something that gets really lost when we talk about fluency, especially with whether it be digital or whether it be print, because what ends up happening is we say, “OK, we have all these strategies we need to teach,” and it becomes a checklist. So how is it that we can just provide students the opportunity to play around in a space, whether it be digital or in person, but in a meaningful way that allows them the time and the space and that area to breathe and think, but be coherent. And connecting those lessons along the way. And I think coherence is one thing that a lot of the times it’s harder to—when we’re in the weeds, it’s so hard and difficult to zoom back out and say, “Do all these lessons connect? How do they intentionally connect? And how do they purposefully connect?” And without coherence, everything’s kind of broken down into that granular level. So when looking at—I think about Desmos and I think about the Toolkit and I think about how Tracy and I talked a lot about, “Well, this, does it connect with the context problem, does it connect with the image talk, or the lessons? Like, how does it all connect and how are we providing students an opportunity to make connections between the day-to-day instruction and lessons that we tackle?”

Tracy Zager (32:44):

I’m reminded of a conversation that Dan, you and I had a long time ago, in Portland, Maine, in a bar. I’ll just be honest. <laugh> And we were talking about how, in the earlier days of Desmos, you were stressed out by what you saw, which was kids one-on-one, on a device, in a silent room. And you were like, no, this is not it. This is not what technology is here to serve. We can do so many things better using technology appropriately, but we can’t lose talk and we can’t lose relationships and we can’t lose formative assessment and teachers listening to kids and kids listening to each other and helping each other understand their thinking. Right? So when I think about the tech that’s out there for fact fluency, most of it is gonna violate all rules I have around time testing. So that a whole bunch of it, I would just toss on that premise. They’re really no different than flashcards. It’s just flashcards set in junkyard heaps. Or, you know, underground caverns. Or with a volcano or whatever. It’s the same thing. There are some lovely visuals—I’m thinking of Berkeley Everett’s Math Flips. Those are really pretty. Mathigon has some really nice stuff that’s digital. And I think that those resources invite you to kind of ponder and notice things and talk about them. All the tools that we design in the toolkit are designed to get people talking to each other, and give teachers opportunities to pull alongside kids and listen in and understand where they are. For example, our games, we didn’t design the games to be played digitally, even though you could, and people did during COVID, because we want kids on the rug, next to each other, on their knees; I’ve seen kids like across tables. I was in a school recently where a kid was like, “I hope you believe in God, ’cause you’re going…!” You know what I mean? <laugh>. Like they’re all pumped up.

Bethany Lockhart Johnson (34:41):

They’re invested!

Tracy Zager (34:45):

They’re psyching each other up and down and they’re interacting and it’s social and the teacher’s walking around and she’s listening to the games. And they don’t actually need any bells and whistles. They need dice and they need counters and they need this game that is actually a game. In all of our conversations, games have to actually be games. Games cannot be “roll and record.” Games have to involve strategy. They have to be fun. So in designing those games, we didn’t feel like it brought any advantage to make that a digital platform. But things that did bring advantages digitally, like the ability to project these beautiful images or to use short video in the classroom, that really was a value-add that enabled us to do something different in math class than we had done before, and to get kids talking in a different way than they ever had before. When I think about fluency, historically, if you say like, “OK, it’s time to practice our math facts,” you hear a lot of groans. And when I see a Building Fact Fluency classroom and I say, “OK, it’s BFF time!” There’s like a “YEAAAAHHH!” You know? And so that’s what we’re after.

Graham Fletcher (35:47):

It’s all about kids, really, for us. And I think at the heart of it, we made all the decisions with teachers and kids at the forefront of it.

Tracy Zager (35:55):

I know of high schoolers who are newcomers, who have experienced very little formal education, and speak in other languages, are using it as high schoolers, because it involves language and math and all the deep work in the properties and it’s accessible, but it’s also not at all condescending or patronizing. Like we designed it to be appropriate for older kids. So that’s just something that I think we’re both really proud of. One thing we thought a lot about, especially in the multiplication-division kit is how a classroom teacher could use it and a coordinating educator in EL, Title, special education, intervention could also use it because there’s so much in it, that students could get to be experts, if they got extra time in it, using something that’s related and would give them additional practice. So they could play a game a little bit earlier than the rest of the classes. And they could come in already knowing about that game, or they could do a related task. We have all these optional tasks that no classroom teacher would ever have time to teach it all. So the special educator could use it and have kids doing a Same and Different or a True/False, or some of the optional games. And then the work in both special education and general education could connect.

Dan Meyer (37:20):

I just wanna say that this is an area that for so many students, as you’ve said, Tracy, it presents a barrier. It’s a very emotionally fraught area of mathematics. And we really appreciate the wisdom you brought here. And just the care you’ve brought to the product itself. Your knowledge of teaching, knowledge of math, and yeah, especially a love for students feels like it’s really infused throughout Building Fact Fluency. If our listeners want to know more outside of this podcast, outside of the product itself, where can they find your words, your voice? Where you folks at these days? Tell ’em, Graham would you?

Graham Fletcher (37:57):

You can find us at Stenhouse, Building Fact Fluency. And then Tracy and I, currently playing around, sharing ideas a lot on Twitter, under the hashtag #BuildingFactFluency. That’s kind of where we can all come together and share ideas. And then also on the Facebook community, where there’s lots of teachers sharing ideas.

Bethany Lockhart Johnson (38:19):

If you were to ask our listeners like, “Hey, if you wanna keep thinking about this, here’s something you could try or here’s something you could go do,” what could be a challenge that we could share that could help us continue this conversation?

Graham Fletcher (38:35):

Online you can actually download a full lesson string. And a lesson string is a series of activities and resources that are purposefully connected. You can pick one or two of those from the Stenhouse web site, Building Fact Fluency. You can try the game. You can try one of those strategy-based games. You can try an image talk and just see how it goes. And just share and reflect back, whether on Twitter or on Facebook. But it’s kind of there, if you wanna give it a whirl. And as Tracy was sharing, even if you’re a middle-school teacher or a high-school teacher, we really tried to think about those middle-school and high-school students keeping it grade level-agnostic. Just so every student has those opportunities for those mathematical conversations. So download a lesson string and give it a whirl, and we’d love to hear how it goes.

Dan Meyer (39:25):

Bethany and I will be working the same challenge with people in our life.

Bethany Lockhart Johnson (39:29):

Yes.

Dan Meyer (39:29):

Enjoying some fact fluency with people in our homes, perhaps. We’ll see. And we’ll be sharing the results in the Math Teacher Lounge Facebook group. Graham and Tracy, thanks so much for being here. It was such a treat to chat with you both.

Bethany Lockhart Johnson (39:42):

I love learning with you and just helping to shift this idea of fluency into something that can be accessible and powerful and positive.

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What Valerie Henry says about math

“A lot of very fluent adults don’t always have every fact memorized. ”

– Val Henry

Meet the guest

Valerie Henry has been a math educator since 1986. She taught middle school math for 17 years and has worked as a lecturer at University of California Irvine since 2002. After doing her 2004 dissertation research on addition/subtraction fluency in first grade, Valerie created FactsWise, a daily mini-lesson approach that simultaneously develops  fluency,  number sense, and algebraic thinking. Additionally, she has provided curriculum and math professional development for K-12 teachers throughout her career, working with individual schools, districts, county offices of education, Illustrative Mathematics, the SBAC Digital Library, and the UCI Math Project.

An older person with short gray hair and glasses, wearing a blue sweater, is outdoors with greenery and a fence in the background.
Podcast cover for "Math Teacher Lounge" with Bethany Lockhart Johnson and Dan Meyer; bold text on orange and teal semicircle background.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Why hands-on learning matters in science

A knowledge board, a child examining a geode, and a hand holding a geode in front of colorful geode art illustrate personalized learning through hands-on science exploration.

Science should be more than just reading about concepts—it should be something students can see, touch, and explore. When students actively engage with science through hands-on activities, technology, and even literature connections, they develop not only essential science skills, but also deeper understanding and lasting curiosity.

Bringing science to life: Hands-on activities

Perhaps the most effective way to engage students in science is to combine a high-quality curriculum with an interactive teaching style to make it experiential. In my classroom, we use the Amplify CKLA Geology unit to dive into earth science concepts. While these strategies can be applied across grade levels and scientific topics, the following is an example from my fourth-grade classroom’s geology lessons:

  • Examining geodes: Students predict what they will find inside before breaking geodes open. Then they analyze the crystal structures, connecting their observations to Amplify CKLA’s science concepts.
  • Writing about Earth’s layers: After learning about the Earth’s structure, students reinforce their understanding by writing creative descriptions or short stories from the perspective of different layers.
  • Diagramming volcanoes and the rock cycle: Drawing detailed diagrams, students visualize how rocks change over time and how volcanic eruptions shape the Earth’s surface.

Connecting literacy skills to science skills

Incorporating literature deepens students’ understanding of science. I use a mix of trade books and digital resources to bring concepts to life through storytelling and informational texts. These books help students connect scientific ideas with real-world applications, fostering both literacy and science skills.

Literacy skills like reading comprehension and critical thinking are key to understanding complex scientific ideas. When students dive into science-related materials, they practice making sense of data, thinking critically about evidence, and building arguments. These practices boost students’ overall literacy, expanding their vocabulary, sparking their curiosity, and developing their media literacy.

Digital resources for students: Exploring science with Google Earth

To further engage students, I integrate Google Earth into our lesson plans. This allows them to explore real-world scientific phenomena—such as geological formations, ecosystems, and weather patterns—making abstract concepts more tangible. Students love zooming in on famous landscapes, discussing how they were formed, and identifying scientific features. This interactive approach using relevant digital tools helps make science feel relevant and exciting.

Final thoughts: The power of engagement in science

By combining hands-on activities, literature, and technology, I’ve helped my students develop a genuine curiosity about science. As the school year progresses, they ask more questions, make deeper connections, and take ownership of their learning.

Engaging students in science doesn’t have to be complicated—it just has to be meaningful. By making learning interactive, Amplify (through Amplify CKLA and Amplify Science) helps students connect with scientific concepts in meaningful ways. I encourage other educators to bring Amplify’s lessons to life with interactive approaches that spark wonder and excitement in young scientists.

Explore more

  • Let’s keep the conversation going! Join the discussion in our Amplify learning communities.
  • Looking for inspiration? Watch Teacher Connections, a video series featuring practical advice and tools straight from fellow educators—our very own Amplify Ambassadors.
  • Dive into our podcast hub to hear from top thought leaders and educators and uncover cross-disciplinary insights to support your instruction.

The Science of Reading and middle school: A perfect match

Perhaps you’re familiar with the Science of Reading—the large (and still-growing) body of research that details how children learn to read and informs instructional best practices to get them there.

And perhaps you also know how important it is to provide kids with evidence-based practices for reading instruction—and how, as the most effective way to make sure that every kid can learn to read, it’s truly crucial in setting all students up for success.

But did you know that the Science of Reading is not just about building foundational skills like phonological and phonemic awareness? It’s not just about how the littlest kids learn to recognize letters and words on a page. The need for research-informed instruction doesn’t go away once kids make the initial shift from not reading to reading. In fact, it’s essential throughout their reading journey—from the earliest years through grade school, and most certainly in the middle school classroom.

Let’s explore why middle schoolers need research-based literacy instruction, and take a look at how teachers can deliver it.

The Science of Reading and middle school literacy

Our brains are wired to learn spoken language, but they are not automatically wired for reading. They don’t just know that certain marks on a page are designed to represent sounds or meanings. That’s why—as the Science of Reading confirms—we have to teach reading explicitly and systematically. Learning to read actually rewires the brain by creating new neural connections and enhancing existing ones.

And when it comes to brain development, middle school is a big moment. The prefrontal cortex, responsible for higher-order thinking and executive function, is still maturing. It’s flexible, adaptable, and perfectly situated to receive the explicit instruction provided by research-based reading instruction.

Students in middle school have typically reached a certain level of automaticity with encoding and decoding. They’ve got the full—and finite—set of phonics skills under their belt, and they’re able to apply them across new and different contexts, even as vocabulary becomes more complex and unfamiliar.

But although this decoding practice remains important, students in middle school are typically able to shift more cognitive energy toward language comprehension.

And we know that background knowledge is crucial for language comprehension—the more prior knowledge you bring to a text, the better you understand it. That’s why middle school presents a major opportunity to deliver strategic and specific instruction in both language comprehension and background knowledge.

Leveraging the power of the Science of Reading

How might you take advantage of this unique developmental moment to accelerate student literacy? Here’s a glimpse at some of the approaches Amplify Chief Academic Officer and Vice President of ELA Deb Sabin explores in this webinar:

  • Choose complex grade-level texts that help build students’ background knowledge and expose them to a variety of structures and genres. Exposure and access to grade-appropriate content is crucial for every student and helps them stay on target towards reading goals.
  • Provide explicit comprehension instruction to help students interpret texts and build mental models for understanding. You might employ graphic organizers or encourage performance for deeper understanding and engagement.
  • Incorporate writing prompts into core instruction. More and more research shows that writing has a strong impact on comprehension, helping students crystallize their understanding while also exposing gaps.
  • Focus on fluency. Research connects oral reading practice to improved comprehension. You might have students practice reading specific passages aloud, encouraging them not only to work on rate and accuracy, but also to reflect on which words they choose to emphasize and why.

That’s just a peek at how you can bring the power of research-based reading instruction to your middle schoolers. To learn more, check out the following resources:

S3-03: Instructional strategies for integrating science and literacy

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We’re continuing our investigations around science and literacy with Doug Fisher, Ph.D., professor and chair of educational leadership at San Diego State University. We talk about the importance of integrating science and literacy, as well as practical guidance for teachers who want to unite the two disciplines in their own classrooms.

Listen as we discuss how science and literacy can be powerful allies and specific strategy areas to focus on when integrating the two disciplines. And don’t forget to grab your Science Connections study guide to track your learning and find additional resources!

We hope you enjoy this episode and explore more from Science Connections by visiting our main page!

DOWNLOAD TRANSCRIPT

Douglas Fisher (00:00):

It’s not that you have to become a reading specialist to integrate literacy into science. It’s how our brains work.

Eric Cross (00:10):

Welcome to Science Connections. I’m your host, Eric Cross. This season, we’re making the case for our favorite underdog, which of course is science. Each episode we’re showing how science can be better utilized in the classroom, and making the case for why it’s so important to do so. In our last episode, we examined the evidence showing that science and English instruction can support each other. And now on this episode, we want to give you some more strategies for really making that a reality in your own home or classroom or community. So to help me, I’m joined on this episode by Dr. Douglas Fisher, Professor and Chair of Educational Leadership at San Diego State University. Dr. Fisher is actually someone who has conducted literacy training at my own school, so I’m excited to be able to share some of his wisdom with all of you. Oh, and just a heads up, Dr. Fisher dropped some gems about the ways teachers can integrate literacy and science in their classrooms. So you may want to have a notepad. Ready. And now here’s my conversation with Dr. Douglas Fisher.

Eric Cross (01:12):

Well, Doug, thank you for your time and for being willing to come and talk about literacy and science. I know you’re busy, all over the place, and so I was super-excited that we were able to lock you in and talk about this. And, on this episode, we’re gonna talk about the ways that science and literacy can support each other. And one of the reasons why I’m really excited for you is because you said some really key things for me as a science teacher, when you talked about literacy and supporting students. That just resonated so deeply in me. And I was like, “I need more Doug!” Because we’re on that same frequency. And I know it’s a subject that you’ve spent a lot of time writing about. So can you tell us a little bit about how this became an area of interest or a passion for you? Just literacy, and all of the work that you’ve put into it?

Douglas Fisher (01:54):

Yeah. So I’ve wanted to be a teacher for a really long time. And I went to San Diego State as an undergraduate, and I was taking English class and we were assigned topics. You know, like, you’ll do an assignment, you’ll write a paper for this English class. And I got the topic “illiteracy,” and I was a freshman at San Diego State reading all of these things about adults who don’t read very well or not at all. And I ended up writing my very first college essay on illiteracy — at the time, you know, called illiteracy, at the time. And so I got super interested in this. And so as I moved through college and into my teaching career, literacy became a really important thing for me to think about, because it’s the gatekeeper. You know, you can be taken advantage of, if you’re not very literate. People can use vocabulary against you, if you’re not very literate. We know that people who have higher levels of literacy have better health outcomes. They have better lifespans, longer lifespans. I mean, there’s just — literacy impacts so much more than “Are you reading your fourth-grade textbook?” It really has lifelong implications.

Eric Cross (03:01):

That part that you said about being taken advantage of … I just got a flyer in the mail yesterday. It was one of these mailers that looked like it was an authentic debt-reduction type of thing, but it was really just like a marketing email. If you read the fine print at the very bottom, it had all of this jargon about “This is a paid, you know, for-profit company.” But when you look at it, it had official stamps all over it. And I could imagine if someone’s receiving that, that probably fools a lot of people. Is that kinda like what you’re talking about, like being taken advantage of?

Douglas Fisher (03:28):

Yes. I had a student turn 18, got a letter from a “credit card company” that was offering her daily compounding interest. And if you don’t know what that means — at 23 percent! — if you dunno what that means, you are gonna be a victim. Literacy really influences a lot of our life. It’s also how our brain works. We have a language-based system in our brain. We read, write, speak, listen, and view. And the things we learn, we learn through speaking, reading, writing, listening, and viewing. From what we know, we are the only species that has an external storage mechanism. Like, we have the ability to store complex information outside of our body, in the form of notes. We can type them. We can write them. And we can then go back and retrieve that information, that complex orthographic information later. And it means the same thing. We can say we have a storage system and we’ve been doing this for a really long time. Way back to, you know, hieroglyphics and messages on cave walls. And throughout the ages of humans learning, how to store information that they can re-access again later. That’s become a super-complicated system. It’s how computers operate. And we send messages to each other and we text each other and we write things down, and we’re really good at putting ideas, information out there. Now, if it’s just speaking and listening, then we can forget it. We can say, “No, you said this,” or “I said that.” But when it’s written, and it’s print literacy, you know, it’s the orthographics there, you can go back to the same message and over and over again. Now, you might change the interpretation of it, but the message is still there.

Eric Cross (05:16):

Right. And that is such a key element, at least of modern education, is this written element of it. It’s what many schools live and die by. They’re quantitatively and qualitatively analyzed by it. It’s public. They can see it. And so there’s this heavy emphasis. And why do you think science and literacy can be powerful allies together?

Douglas Fisher (05:38):

Awesome. Well, it’s hard to learn science if you’re not literate.

Eric Cross (05:42):

This is true.

Douglas Fisher (05:42):

But that’s a one-way direction. And yes, science teachers and scientists do a lot of reading, writing, speaking, and listening and viewing. They use the five literacy processes all the time. When we interview scientists, they spend a lot of their time reading the work of other scientists and writing their findings, writing grant proposals, presenting at conferences, you know. So a huge part of the work of a scientist is not just at a bench conducting experiments. But even if you’re conducting experiments, you’re using your literacy processes to think about what you’re seeing in your experiment. So that’s a one-way direction. And I do think literacy has an influence on science. But since science goes the other way, it influences literacy. As you learn more and you understand more about the world, your background knowledge grows, your vocabulary grows, you become more literate in those different areas. And how you think. So if I’m learning about life science; I’m learning how the world works in a more, biologic physical world. And that knowledge helps me think about when I’m reading a novel, and there’s an appeal to some science knowledge or a concept that gets played with, you know, perhaps time-space continuums … well, if I don’t have the science knowledge of how I think the world works, it’s hard for me to understand what this author is doing. So it does go both ways. They feed each other. And the more literate we become, the more complex science information we can understand. ‘Cause our background knowledge and our vocabulary influence how much we understand about what we read. And as we access more complex science information, it starts to change the way we think about other things in our world.

Eric Cross (07:23):

There was a couple of things that you said in that, but one of the first things that kind of perked my ears is when you said grant proposals. Because I have friends that are scientists — and this is one of the things that when I was in school, they don’t talk about — but how much of their research is reliant upon getting funding —

Douglas Fisher (07:37):

Mm-hmm. <affirmative>,

Eric Cross (07:38):

— which you don’t think about if you’re becoming a chemist or a physicist or a biologist or working in the field, is that that funding, coming from the NSF or anywhere else. And sometimes students ask in class like, “Why am I writing so much? Like, I want to go into science!” Or “I wanna do this!” And this is a real-life example of how the writing could actually apply, in addition to all of the things of collecting data and conclusions and results. But that grant proposal thing just really perked my ears, yeah.

Douglas Fisher (08:01):

And if you can’t write a grant proposal, your ideas and experiments are not gonna get funded. And if you can’t write a strong proposal, that compellingly convinces your readers to fund you, you’re not gonna get funded. But then once you get the grant, you have to write publications. You have to share your work with other people. Make PowerPoint presentations and write journal articles or books or whatever. So it’s a cycle that literacy influences the things we do, including the things we do in science.

Eric Cross (08:31):

Now to get in maybe some data, if you were trying to convince someone that like this happy marriage can exist, what would be like your number one piece of evidence to support this, this back and forth of supporting each other?

Douglas Fisher (08:44):

Awesome. So the quote I’ll often say — and this is from studies from more than two decades ago now — but in general, in high school science, students are introduced to 3000 unfamiliar words, 3000. Each year! Because there are words that are used in a scientific way that are used commonly in other places. And there are discipline-specific words. So 3000 words a year in high school science. The Spanish 1 textbook only has 1500 words in it. So science teachers have double the academic-language vocabulary demand that a typical introductory world-language class has. So just the vocabulary alone should say to us, literacy is gonna be important if you’re gonna learn science. And if you don’t understand these technical words, and you don’t understand the way science uses this particular word in this particular way… . When you say the word “process,” it means something very specific In science. “Division” — cellular division is not the way we think about it in mathematics; there’s a similar concept, but cellular division is different than dividing numbers. And those are words that get used in multiple areas. Then you have all these technical terms that you have to be able to use, to understand the concepts. To share the concepts. To talk to other people. Whether you’re in, you know, fifth grade and talking science, or you’re a university professor, there’s a shared language, appropriate for our grade level, that we have shared meanings of.

Eric Cross (10:22):

And we’re essentially … what I’m hearing you say is … most of the people that are listening to this are science teachers. We’re we’re also language teachers. In a sense.

Douglas Fisher (10:29):

So my frustration is when people say, “Every teacher’s a teacher of reading.” And I don’t like that. I’ve written against that phrase. I don’t think all teachers are teachers of reading, any more than all teachers are teachers of chemistry. Or all teachers are teachers of algebra. But what I will say is the human brain learns through language. And all of us — every teacher that I’ve ever met understands that language is important in my class. If my students don’t have strong listening skills and speaking skills; reading, writing, and viewing skills; I’m gonna have a hard time getting them to learn things. If I can help them grow their speaking, listening, reading, writing, and viewing in my content area, I’m gonna do a service for my learning of my subject and also their more broad literacy development.

Eric Cross (11:16):

  1. So, at a high level, what does it look like to integrate science and literacy? We’ve done education for the last, what, hundred years?

Douglas Fisher (11:24):

Mm-hmm. <affirmative>

Eric Cross (11:25):

—kind of pretty similarly, right? Kind of siloed way. What does this look like at the 30,000-foot level? You’re a professor, department chair. Run schools. Speak everywhere. Like, when you think about this from that high level, what does it look like?

Douglas Fisher (11:39):

A high level? Every time I meet with students in a science class, you know, biology or fifth grade or whatever? They should be reading, they should be writing, they should be speaking and listening. Every class. So what print do you want them to access? And it can be a primary source document, it can be an article, it can be from a textbook. Are they reading something? Are they writing to you? Because writing is thinking. If they are writing, they are thinking. As soon as their brain goes somewhere else, they stop writing. The pen won’t move or the fingers don’t type. And then speaking and listening, of course, is the dynamic of our classes. So every day we should see some amount of reading, writing, speaking, and listening, viewing in our classes. That’s at a high level. There are some generic things that seem to work across the literacy. So, learning how to take notes. Focusing on vocabulary. Using graphic organizers. These are generic things that as educators we can use in our classes. Then there’s more specialized things. So, scientists and science teachers think differently than historians and literary critics and art critics. So scientists, if you look at the disciplinary literacy work, there’s a whole body of research where they interview and study high-end experts in their field: chemistry, physics, biology, et cetera. And there are some characteristics that were more disciplined, specific. Scientists like cause and effect relationships. They look for them when they’re reading. They like sourcing information. “Where this come from?” “What’s the history of this idea?” Scientists have a long view in terms of time. Historians have a shorter view of time. English teachers have even shorter view of time. Scientists tend to think in long periods of time. And so all of that influences how a scientist reads and how we should apprentice young people after they get past the generic “I know how to take notes. I know how to study my vocabulary. I know how to do summary writing for my teacher in my notebooks and things,” there’s some generic tools. Once we get past those, we need to be looking at specifically how do people in science use literacy.

Eric Cross (13:52):

I’ve never had my thought process of reading deconstructed just now, but we just described how scientists read. I was like, “Yeah, that’s pretty much how I read, right there.” I also like how you said how we should apprentice young people. And I feel like you as the literacy guy, you chose that word very specifically, as far as apprenticing young people. That is a view, I think, that’s really important to hold. ‘Cause that’s what we’re doing essentially … is, if we’re doing what we should be doing, we are apprenticing these young people.

Douglas Fisher (14:18):

Yes.

Eric Cross (14:18):

And helping them develop. Now, let’s imagine there’s a listener out there and they’re interested in getting better at integrating science and literacy instruction. They want to start somewhere. Before we dive in, do you have any initial words of encouragement for the person who’s like, “Everything is like a priority right now,” in their classroom or in their world?

Douglas Fisher (14:37):

Yeah. So I’ll talk about elementary for just a moment. When we’re reading informational texts in our literacy block, we should be reading information that is aligned to what kids need to learn in science and history in, in that grade level. Why are we reading things that are gonna be in conflict with what they’re gonna learn in science later that day in fourth grade, for example? So when we look at our standards, our expectations, what is it that third graders need to know in history, science, mathematics, language arts? And when we’re reading text and we’re learning to apply our reading strategies during our literacy block, why aren’t we reading topics that build our background knowledge for our science time? So we’re seeing some synergy there. We should be looking at life cycles in grades that are appropriate for life cycles and knowing there’s more to life cycles than the frog and the plant or the seed. There are all kinds of life cycles. And we call ’em life cycles for a reason. That’s a general concept. Now in science, we’re looking at this particular lifecycle right now. And so that’s a high level. If we could get more connection to the content standards during our literacy blocks, it would be very good. When we talk about the time at which we call “science” in the day, in more of the K–8 continuum, the science needs to include some primary source documents. Some real things that students are reading. Read about a scientist; read about a scientist’s discovery; read about what they discovered. So that we’re building our background knowledge. So when we go to do things, activities, labs, simulations, we have background knowledge and we understand what we’re experiencing. It can’t be like—I watched this awesome lesson on lenses and the teacher had all these different lenses in the room and the students came in and they were brand new. They don’t know anything. They were picking ’em up. They’re exploring them. They’re trying to figure out, and they’re trying to come up with theories about what this is and how it works. And then the teacher gave them a reading, a short reading, on refraction of light. And they read this thing. And the clarity that they had about what these lenses must do, well! All of a sudden they’re putting them up to the lights! They’re asking if they can go get the lights out of the storage unit! ‘Cause there’s — and they’re shining different lights through the lenses to see what happens to the light. Because that little bit of reading turned some focus on for the students. And it allowed them to take what I’m thinking about, what I’m trying to figure out, how this thing works in another direction. That’s the power of using literacy in our classes.

Eric Cross (17:20):

And what I’m hearing essentially is transfer across disciplines, across content areas, ultimately. And in an elementary school classroom, would it be fair to say, probably the teacher has more autonomy to be able to do that, since they’re teaching all the subjects? But secondary, logistically, planning and those types of things … from what you’ve seen, is it fair to say this kind of needs to be like a top-down, full vertical alignment, to teach like this?

Douglas Fisher (17:45):

I think that would be awesome to do that. But if I’m a sixth grade English Language Arts teacher and I’m working with my sixth grade science teacher, the conversation should be, “What units are you teaching?” Because I’m choosing informational text. My job is to teach them how to find central ideas. My job is to teach them how to find the details in the text. My job is to have them make a claim and support that claim with evidence. The stuff I use is generic. Yes, we do read some literature and some narratives, but we also read about 50% of the text in English around informational text. So if I can help you and accomplish my standards as well, fantastic. So let’s have this conversation and say, “Oh, this is what you’re teaching in science in the next three weeks? I’m gonna choose some texts and we’re gonna analyze ’em for central idea. We’re gonna analyze ’em for details. We’re gonna, for mood or tone or whatever that we’re teaching. And by the way, I’m building background knowledge. So when they come to you, they know some stuff about what you’re going to be teaching next.” So I don’t think it’s impossible to say teams of teachers could come together and say, “What do we believe that our students need to know and learn and be able to do? And then how do we choose things that are gonna help them accomplish exactly that?”

Eric Cross (19:01):

And that’s empowering. Because that’s one thing that we can control maybe is this East-West, peer-to-peer, different content areas. A system may not be able to change as quickly, but I can definitely go talk to my English team or math team and check in and kind of see, “Hey, where do we have overlap in that?” And I know the times that I’ve accidentally had overlap with the teams, it’s super-exciting. And the students have been more bought in! Because it’s like, we’ve done something on the human microbiome and we’ve talked about genetics and all these different things, and then when they read The Giver, or they read some book about genetics, they have all this knowledge. And they’re excited. And they talk about colorblindness or they come to my class and they’re like, “Hey, we read about this!” It’s almost like they saw a magic trick, the fact that these things linked up. And the engagement has been so much higher when it’s the same content in different classes, but through different lenses. At least, that’s what I’ve seen in my years of teaching.

Douglas Fisher (19:54):

I saw a lesson on space junk that was so cool. Middle-school students learning space junk. And the history teacher had a part of it, science teacher had a part of it, English Language Arts teacher had a part of it. And these students, I mean, you watch them look up all the time, ’cause there’s space junk up there. Where’d it come from? Why is it there? What are the politics of this? How do we clean it up? I mean, it was just so interesting to watch them when the teachers came together. And the teachers met their standards in this couple-week-long space-junk exploration. Investigation was met. Politics was met. All these different things. Economy. You know, how much does it cost to clean up this problem? So there’s really cool opportunities when teachers come together and realize we can work together and improve the literacy and learning of our students.

Eric Cross (20:50):

Absolutely. So before this recording, we picked your brain a bit. And I know that there were three specific strategy areas that you wanted to touch on. And one of those — which is kind of coming back to the 3000-words language teachers — was vocabulary. So what are the opportunities that you see, as far as the way of educators to approach vocabulary? Because, you know, there’s a lot. We got a lot of it. The 3000 words.

Douglas Fisher (21:14):

Yeah. There’s a lot of it. So the worry is, we make a vocabulary list and have students look up the words in definitional kinds of things. That’s not really gonna help. Students need to be using the words. They need to be using the words in their conversations, in their writing, in how they think about your content in science. So vocabulary is a huge predictor of whether or not you understand things. Vocabulary is also a pretty good predictor if you can read on grade level. So when we think about vocabulary, there’s something called word solving. You show students a piece of text and you’re reading it, you’re sharing your thinking, and you say, “Oh, here’s a context clue!” Or “I know this prefix or suffix or root!” And in science, a lot of the words are prefixed, suffixed, or root words. We tend to add things together with a lot of prefixes and suffixes and have roots and bases in science. So we can help students think about, “Oh, what does geo- mean? We already know what geo- means here. It means the same thing in this word. Let’s apply that knowledge.” So word solving is part of it, showing students how we think about words that we might not know. The second is more direct instruction of vocabulary. As students encounter the words, we work on what it means, how we say it. We practice it a few times. The process is called orthographic mapping. It’s kind of a scientific idea here. But you have the sound and the recognition of by-the-word, by sight, and what it means. And your brain starts to automatically recognize that word in the future. So I don’t have to slow down, disrupt my fluency, and try to figure out what the word is saying. ‘Cause I’ve seen it enough. I’ve heard it pronounced enough, I’ve pronounced it enough, and I know what it means. So teachers should be saying, “What words in sixth grade science, what words in third grade science, do my students really need to know?” And I’m gonna have them encounter those words over and over. I’m gonna have them use the words. I’m gonna have them see the words. I’m gonna have them say the words. I’m gonna say the word and we’re gonna be over and over with these terms, so that students incorporate them into their normal view of, “These are the things I know about the world.” By the way, when they go to read that next thing, and they understand “geology,” you know, for sixth graders, for example, they know how to say it. They don’t stumble on it. And it activates a whole bunch of memories in their brains. “This is what geology is.” There are branches of geology, there’s physical geology, there’s all this thinking that activates as they read.

Eric Cross (23:35):

There was a practice that I participated in and am trying to incorporate — I don’t know what the name of it is. But essentially what happened was we were dissecting a flower. And the instructor had us name parts of the flower. But we got to come up with our own names for it.

Douglas Fisher (23:49):

Ah.

Eric Cross (23:50):

So, for instance, the stamen we call “the fuzzy Cheeto.” And we all used our own words and then everything was legitimized. And so we went through and learned the whole activity using our own vocab words. But then, in the end, after we presented and talked about it, then the words, the actual academic language was attached to our word. And we were able to say, “OK, the fuzzy Cheeto is the stamen,” and this, this, this, and this. But it was such an interesting practice, because it kind of legitimized all of our definitions. But we weren’t stumbling on these long Latin terms and things like that. Is there a name for that? Or. … ?

Douglas Fisher (24:29):

Yes. I don’t know the name for that. I think it’s really smart. So here’s what I would say about that, is: we don’t learn words, we learn concepts. Words are labels for our concepts. So what that teacher did for you was allow you to develop concept, a concept knowledge. “There’s a part of this plant, it goes like this, we’re gonna call it fuzzy Cheeto. Now I have this concept. And look, it occurred in all these plants. And those people called it that and that other group called it that. We called it a fuzzy Cheeto. Here’s the part of it.” And then the concept is in your brains. And the teacher said, “It’s really called stamen.” And it’s an instant transfer, because you already had the concept. What we often see is students are trying to learn a really hard academic word and the concept for the word at the same time. And so it slows down the whole process. And there’s higher levels of forgetting. Because human beings, we don’t learn words; we learn concepts. If you don’t have the concept, if I gave you a word out of the blue that you’ve never seen, never heard, and a week from now I asked you to remember it, you probably would not, because it didn’t register. It wasn’t part of your schema. You didn’t have a way to organize the information. You don’t have a concept. So that teacher? It’s a great idea. Got you to develop concept knowledge. And then said, “Here’s a real label for it: What some other people called it when they had the chance to come up with their own names.”

Eric Cross (25:50):

Shout out to my teacher, who was—

Douglas Fisher (25:51):

Right.

Eric Cross (25:52):

It was learned then. It was a great practice. And the fact that you’re right, like, I just mean from my own personal experience, I agree that learning concepts versus complicated words. And it’s interesting that you said higher levels of forgetfulness, you know. And you often hear that complaint about it: “Students forget! Students forget!” But this complex topic and this complex word that’s new to me, and I have to remember both of those things.

Douglas Fisher (26:12):

That’s right.

Eric Cross (26:13):

And the other neat thing that it did, is it actually honored the background and like the founts of knowledge of all the different groups in the classroom. You just said something about “this group called it this and this group called it this,” and so by letting different groups share all of those names, now we’re starting to build these kind of interesting connections. That’s at least what I remember experiencing. And so this, even this practice of this approach is very layered, beyond just kind of generating new knowledge of things. So I appreciate that aspect of it. Now another area that you mentioned was complex text.

Douglas Fisher (26:41):

Yeah.

Eric Cross (26:42):

And how we can get students into complex text. So what can we do there?

Douglas Fisher (26:46):

I think science is an ideal place to get students reading things that are hard for them. And I do believe that some parts of school should be a struggle. Not all day, every day. But there should be doses of struggle, which are good for our brains. And these complex pieces of texts that don’t give up their meanings easily allow students to go back and reread the text and maybe mark the text and talk to peers about the text and answer questions with their groups. And the whole point of complex text is to say, “We persevere through it. We may not understand it fully on our first read. But we go back and we might underline, we might highlight. We might write some margin notes. Our teacher might say, ‘What did this author mean here?’ And we go back and look at that part and we take it apart. What do we think about that? And we talk to each other. It’s showing that when we read things, we work to understand. We work through our thinking, often in the presence of other people. And our understanding grows as we go into the text over and over and over again.” So I said geology earlier. There’s about a two-page article on “what is geology” that sixth graders often read. And some kids find it super boring. It’s a once-read, “OK, geology, I don’t really understand it. There’s a bunch of words in here that I don’t understand.” But if you go back to it a few times and you start taking apart, “What are the branches of geology? Oh, I’m gonna go reread that.” How are these two branches related to each other?” “What are the subtypes of each branch of geology?” “How do geologists do their work?” You start asking questions where students are going back into the text. You spend a little bit of time. Now, the introduction to geology, the students know so much more. So whatever you do next— video experiments, whatever—they have a frame of reference, because of that deep, complex read. It’s probably better than simply telling them, “Here’s the information.”

Eric Cross (28:45):

Right. And I even feel like as an educator, when I reflect on my own learning in the classroom, and then looking at it through the perspective of an educator <laugh>, you find this difference between how you were taught and then what the data says good teaching is.

Douglas Fisher (28:59):

Mm-hmm. <affirmative> mm-hmm. <affirmative>.

Eric Cross (29:00):

It’s so easy to slide back into how you were taught!

Douglas Fisher (29:02):

Yeah.

Eric Cross (29:02):

Even though, you know, you mentally assent to, “This is the best way. This is the data shows.” And you find yourself kind of sliding back at times.

Douglas Fisher (29:10):

Yep. And there’s good evidence to support what you just said, that most people teach the way they experienced school. And it is very hard to change that. And people have studied this. And it’s very hard to change that. Because it worked for us. And we have an n of 1, and it worked for us. Now, remember, there were a whole bunch of other kids in the class that it may not have worked for. And we chose to be in school the rest of our lives, and some of your peers did not choose to be in school the rest of their lives. In fact, some of them hated school and found no redeeming qualities of their experience. So just because it worked for us in a case of one, n of 1, doesn’t mean it worked for all of the kids, or even the majority of them.

Eric Cross (29:57):

Very well said. It’s that, what is that, the survivor bias? Survivorship bias? Where you were the one that made it. But you don’t think about all the other folks. ‘Cause we’re thinking about ourselves.

Douglas Fisher (30:05):

That’s right.

Eric Cross (30:06):

Great case for empathy too, is thinking about the people left and right. Because my friends are like, “I hated science.” And I say, “Who hurt you? Like, what did they do? It’s so amazing, so much fun!”

Douglas Fisher (30:16):

“What happened to you? Science is the coolest. Right? It’s so amazing!”

Eric Cross (30:21):

But I also had a unique experience in seventh grade with my teacher who did some of these things, and made it accessible for so many of us, in opening opportunities that I wouldn’t have had otherwise. But you’re absolutely right. That was my story. That wasn’t the story of everybody that was around me. And I think that’s really important. Now, I know this is also a big one for you, but I wanna talk about writing. What are the opportunities that you see in terms of writing specifically?

Douglas Fisher (30:51):

So would love it if science teachers had short and longer writing tasks in the science time. Of course, you can integrate some of the science writing, the longer ones, in the English language arts time, especially if you’re the elementary teacher and you can have control of the whole day. But I said this earlier; I’ll say it again. Writing is thinking. While you are writing, there’s nothing else you can do but think about what you are writing. Your brain cannot do something else. So if a science teacher wants to know, do their students really understand the concepts? Have them write. Now some of the shorter ones, I like something called “given word” or “generative sentences”: “I’m gonna give you a word: CELL. C-e-l-l. We’re in science. I want you to write the word ‘cell,’ c-e-l-l, in the third position of a sentence. So it’s gonna go word, word, cell, and then more words.” You could also say, “I want the sentence longer than seven words,” or whatever. But the key is, I’m telling you where I want the word. You will know instantly if your students have a sense of what the word “cell” means in the context of science. If they write “my cell phone,” they don’t get it. If they write about spreadsheet cells or jail cells or whatever, they didn’t get it. But if they talk to you about plant cells and animal cells and the components of those cells, and then once they have that sentence down, you can say to them, “Now write three or four more sentences that connect to that sentence.” It’s super simple. So whatever concepts you’re teaching, put ’em in a specific position. Now you don’t have to only put it in the third position. You can say the first position, the fifth position, the fourth position. But it forces them to think about what they know about the word and then how to construct a sentence for you. That’s a very simple way to get some writing from your students that helps you think about what they understand. Other kinds of writing, you can have quick writes, you can have exit-slip writes. There’s something in the research space called the muddiest part, where halfway through the lesson you have them write so far what has been the least understood or the most confusing part of this lesson. And they do a quick write, right there, at the muddiest part. And as a teacher, you flip through these and you start to say, “Oh, these are the points that are confusing to my students.” So if 80% of them all have the same thing, I gotta reteach that. If these five got, “This is the muddiest part,” If these five thought, “This is the muddiest part,” these seven, “I thought this was the muddiest part,” what do I need to do? Because it’s gonna be hard to move forward if this is their area of confusion. There are also all kinds of writing prompts that have a little bit longer. My favorite one is RAFT. What’s your Role? Who’s your Audience? What’s the Format? And what’s the Topic we’re writing about? Super flexible writing prompt. When you teach something, we don’t want students to only think they write to their teacher. So your role is an atom. You are writing to the other atoms. What do you wanna write about? What’s the topic? What’s the format of it? Is it a love letter? Is it a text message? Is it … so we, we mix it up with students in saying, how do they show some knowledge through a prompt that we give them? And then of course, longer pieces as they get older. More opinion pieces through fifth grade. More claims and arguments starting in sixth grade. So that they’re starting to see, “I have to use the evidence from things I’ve learned, read, listened to, watched, and construct something: an opinion, an argument where I back it up with reasons or evidence.” And those longer pieces, you know, less frequently. The shorter pieces, pretty regularly. So the teacher sees the thinking of the students.

Eric Cross (34:29):

When you were speaking about these really creative writing prompts, there were specific students coming into mind, that were coming into mind … they’re, they’re great science students, but they also have this really strong artsy side drawing, creative writing, and things like that. And when you said something about atoms talking to each other, it elicited, in my brain, certain students that would really love this aspect of creativity in the sciences. And it’s not how we’re typically trained as science teachers, to kind of incorporate this, like you said. A book of props. But I’m imagining, like, as a science teacher, if I took this, this would be a great way to reach more students to be able to show what they know, in a way that might resonate with their own intrinsic “Oh, I get to write creatively!” So I was kind of writing furiously as you were sharing all that information there.

Douglas Fisher (35:12):

So here, I’ll give you another example for elementary people. Again, with RAFT. There’s a book called Water Dance. It’s a pretty popular book for elementary teachers. It’s really about the life cycle of water. For example, you are a single drop of water. You are writing to the land. The format is a letter. And you’re explaining your journey. Now, if they can do this, they’re essentially explaining to you the cycle of water. But you got it in a way that people are now, “Oh, I’m a drop of water. So it’s me. My perspective. Where do I go from? Where do I start?” Because you can start anywhere in the cycle, right? My drop could have started in the clouds. My drop could have started in the ground. My drop could have started in the lake. But it has to show you the journey. So there are many ways of showing you the right answers.

Eric Cross (36:02):

And that’s using the RAFT protocol.

Douglas Fisher (36:04):

That’s RAFT: Role, Audience, Format, Topic. It’s been around 20 or 30 years.

Eric Cross (36:09):

You just gave the name to something a teacher shared in our podcast community, Science Connections: The Community, on Facebook. Teacher shared a Google slide deck and on it were just three slides. And the role that the student had to have is they had to show, then tell, the story of a journey of a piece of salmon being eaten, a piece of starch from pasta being eaten, and then an air molecule in a child’s bedroom. And they had to give the path of travel and the experience from the mouth and then breaking down into protein and all those kinds of things. And this teacher shared it and I wish I knew the teacher’s name because I wanna give ’em credit, but they shared it. And so I used it with my students and then had ’em read aloud their stories and dramatize it. And they were so into it!

Douglas Fisher (36:49):

So cool.

Eric Cross (36:50):

But through it, I was able to see that they understood different parts of the body. They understood cell respiration. The whole thing. And it was fun! To watch them get so into this creative writing. And now I know the name of it. That’s been 30 years they were using RAFT. So you just talked a bit about complex texts and writing. And before we go, I wanted to circle back to something that you said, because I think it’s important, and if you could elaborate on it a little bit, about the value of struggle. Can you talk more about that?

Douglas Fisher (37:21):

Sure. I do believe in a lot of the U.S. we’re in an anti-struggle era of education. And it predates Covid. I think it made it worse during Covid. We front load too much. We pre-teach too much. We reduce struggle. We quote, “over-differentiate” for students. And there’s value in struggle. The phrase, “productive struggle” — if you haven’t heard it, Google productive struggle — it’s an interesting concept, that we actually learn more when we engage in this productive struggle. Now, productive struggle originally came from the math world, and it was this idea that it’s worth struggling through things to learn from it, that you’re likely to get it wrong, and then there was productive success. And there are times when we want students to experience success and we make sure we put things in place for productive success. But there are times where we want them to struggle through a concept. ‘Cause it feels pretty amazing when you get on the other side, when you know you struggled and you get to the other side. If you think about the things, listeners, think about the things in your life where you struggled through it and you are most proud of what you accomplished. I want students to have that. I don’t wanna eliminate scaffolding, eliminate differentiation. But I do want some regular doses of struggle. So if you look at the scaffolding, we have a couple choices. We have front-end scaffolds, distributed scaffolds, and back-end scaffolds. Right now we mostly use front-end scaffolds: We pre-teach, we tell students words in advance, that kind of stuff. But what if we refrained from only using front-end scaffolds, and we use more distributed scaffolds, when they encounter. So there’s a difference between “just in case” and “just in time” support for students. So we tend to plan on the “in advance, here are all the things we’re gonna do to remove the struggle before students encounter the struggle.” What if instead we said, “Let them encounter some struggle. Here’s the supports we’re gonna provide. We’re gonna watch; we’re gonna remove those scaffolds, and allow them to have an experience of success, where they realize, ‘I did it. I got it.’” Every science teacher I’ve ever worked with, when they do an experiment or a lab or simulation, they are looking for productive struggle. They don’t tell the answers in advance. They don’t tell if the answers are right. That’s your data. What does your data tell you? I mean, this is what you do. But then the other part of your day when you move into, like, reading, you don’t do that. You fall into the trap of removing struggle. And so allow them to grapple with ideas. Allow them to wonder what words mean. Allow them to say, “I’m not getting this, teacher! It’s really frustrating!” And you say, “Yeah, this is really hard. This is why we’re doing it at school. ‘Cause it’s really hard. If it was easy, I’d have you do it at home. But we’re doing it here, ’cause it’s really hard and it’s OK not to get it at first.” And create a place where errors are seen as opportunities to learn, and struggling through ideas and clarifying your own thinking and arguing with other people to reach an agreement or reach a place where we agree to disagree is part of the power of learning.

Eric Cross (40:38):

There’s a teacher, who I took this from. My master teacher when I was student teaching. And she said that there’s no such thing as failure in science, just data. And I took that same mantra. And I resonate with what you said about how science teachers, all of us, hold onto that productive struggle, because it’s part of being a scientist. It’s part of the experiments. That genuine “aha” moment. Or it didn’t work out? That’s great! That’s totally fine! Let’s write about it and let’s take photos and let’s publish it and let’s be scientists. That’s totally true. As we wrap up, Dr. Fisher, is there any final message that you have to listeners about bringing science and literacy together? I know you speak everywhere, but for everyone that’s listening, if you can put out your encouragement or message or suggestion … you’ve given so many great tips and practical applications. But, any final thoughts on the subject?

Douglas Fisher (41:32):

I think many science teachers are intimidated because they think they have to be reading teachers. And there’s a knowledge base to reading. And some teachers are reading teachers and science teachers, and I don’t wanna dismiss that. But it’s not that you have to become a reading specialist to integrate literacy into science. It’s how our brains work. And so as you think about the way in which you are learning and the ways in which you want your students to learn, what role does language play? What role does speaking, listening, reading, writing, viewing, play in your class? And then provide opportunities for students to do those five things each time you meet with them.

Eric Cross (42:12):

Dr. Fisher, thank you so much for being here and for your encouragement, and sharing your wisdom and experience. And then personally serving my city, here in San Diego, and my students, when they make it to your high school and ultimately the alma mater of San Diego State University.

Douglas Fisher (42:30):

That’s right.

Eric Cross (42:31):

Yeah. We really, really appreciate you in serving all kids and lifting the bar and making things more equitable for all students. And encouraging teachers. So thank you.

Douglas Fisher (42:39):

Thank you very much.

Eric Cross (42:42):

Thanks so much for listening to my conversation with Dr. Douglas Fisher, Professor and Chair of Educational Leadership at San Diego State University. Check out the show notes for links to some of Doug’s work, including the book he co-authored titled Reading and Writing in Science: Tools to Develop Disciplinary Literacy. Please remember to subscribe to Science Connections so that you can catch every episode in this exciting third season. And while you’re there, we’d really appreciate it if you can leave us a review. It’ll help more listeners to find the show. Also, if you haven’t already, please be sure to join our Facebook group, Science Connections: The Community. Next time on the show, we’re going to continue exploring the happy marriage between science and literacy instruction.

Speaker  (43:26):

I had this moment of realization I felt a few months ago: I’m like, if I don’t teach them how to use the AI as a tool, as a collaborator, then they’re gonna graduate into a world where they lose out to people who do know how to do that.

Eric Cross (43:39):

That’s next time on Science Connections. Thanks so much for listening.

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What Dr. Douglas Fisher says about science

“There are really cool opportunities when teachers come together and realize we can work together to improve the literacy and learning of all our students.”

– Dr. Doug Fisher

Professor and Chair of Educational Leadership, San Diego State University

Meet the guest

Douglas Fisher, Ph.D., is professor and chair of Educational Leadership at San Diego State University and a leader at Health Sciences High & Middle College having been an early intervention teacher and elementary school educator. He is the recipient of an International Reading Association William S. Grey citation of merit, an Exemplary Leader award from the Conference on English Leadership of NCTE, as well as a Christa McAuliffe award for excellence in teacher education. He has published numerous articles on reading and literacy, differentiated instruction, and curriculum design as well as books, such as The Restorative Practices PlaybookPLC+: Better Decisions and Greater Impact by DesignBuilding Equity, and Better Learning Through Structured Teaching.

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About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. 

S3 – 03. Math professional learning experiences with Elham Kazemi

Podcast episode poster for "Math Teacher Lounge" featuring Elham Kazemi, a Mathematics Education Professor at the University of Washington.

How do we continue to grow and be more reflective about our own teaching? In this episode, Bethany Lockhart Johnson and Dan Meyer chat with Elham Kazemi to explore how to look at teaching as a collaborative experiment. Moving more toward analyzing student thinking and how that contributes to teaching itself, leaves more space for one’s own understanding of math to grow throughout your career. When one revises their teaching based on the data we’re collecting from students and peers, this allows us to be both teachers and learners forever.

Explore more from Math Teacher Lounge by visiting our main page.

Download Transcript

Dan Meyer (00:04):
Hey folks, welcome to math teacher lounge. My name is Dan Meyer

Bethany Lockhart Johnson (00:07):
And I’m Bethany, Lockhart Johnson.

Dan Meyer (00:09):
And this is the teacher learning week. We’re thinking this week about how we grow as teachers. And to start with, I just wanted to ask Bethany, uh, first Bethany, how are you doing? And second <laugh>. Um, what is, what, what has been your like most favorite and least favorite, most effective least effective professional learning experience when you were a classroom teacher?

Bethany Lockhart Johnson (00:30):
I think for me, most effective was definitely when I could use it right away. Right. Whatever we were talking about, whatever we were learning, like I got to go put it into practice. Sure. Uh, I, I remember we did something where we designed a lesson and then we went and taught it like one person taught it and the rest of the people watched. And then we kind of like got to workshop it, which that was like a one off the fact that we got to go out of our classroom and go observe somebody teaching. It was gold. It was gold. Um, so that was probably the most effective, because there was so much opportunity for reflection and least effective was something that felt like just completely unconnected to, you know, kind of either so theoretical that it wasn’t like touching on what we were navigating right there in the classroom. I don’t know. What about you? What can you think of times that, are you gonna say times you led a PD? Those were the most effective?

Dan Meyer (01:26):
Yeah. My favorite ones are my sessions, of course. But if I had to throw those out for a second, um, yeah, I, I like, I want, I want both, I want it all. I want the, um, the big ideas that take a long time to settle in that also have like small bits that can carve off and use relatively quickly to test my understanding of the ID is, yeah. I’ve had some, some PD where I’m like, this is very relevant to tomorrow. And I also don’t care. Like for instance, like how to use the CD, the, the, like the, the software, you know, on the, on my curriculum, for instance, it’s like, okay, yeah, this is just a little, little too practical. You know what I’m saying? I want some bigger ideas to chew on. Um, I would also say like, I love my favorite PD by a long was writing up thoughts about how the day went and putting that on the internet in a public place that we used to call a blog and where people would come along, cuz there was like 10 blogs and like, tell me like that’s no good.

Dan Meyer (02:16):
Like the thing that you like is not a thing you should like, here’s the thing you should like instead, or try instead, or just this weird community that sprung up, you know, when I was, uh, starting to teach relatively new teacher and uh, I feel like I grew a lot

Bethany Lockhart Johnson (02:28):
Go back to this idea blog. If people would call you, they’d call you on the phone. What, what

Dan Meyer (02:32):
Was they would fax me? They, it would be a fact. So

Bethany Lockhart Johnson (02:35):
Fax,

Dan Meyer (02:36):
I got it. Fax a comment. Yeah. Got it. So, uh, that’s, that’s Bethany and I, and we’re super excited to have people who have a bit broader of a perspective, a bit more of the land than what, what the two of us, um, think about with our own professional learning experiences.

Dan Meyer (02:52):
We’ve invited on an expert. We hope will help us understand alternate ways to do professional learning as teachers to grow as teachers besides, you know, all of us getting into the same room once every, every, uh, few months together, Elm Cosmi is a professor of mathematics education at the university of Washington, Elm studies, how strong professional communities develop in schools and how schools can be organized. So teachers learn from and what their students, this work is informed by equity oriented research on thinking, uh, on children’s mathematical thinking and classroom practice. She is co-author with Allison hints of intentional talk, which focuses on leading productive discussions in mathematics. And she edited coral counting and counting collections with Megan Frankie and Angela tau, which focuses on the importance of counting from preschool to fifth grade. Looking forward to a great chat with Elham, welcome Elham to the show.

Elham Kazemi (03:43):
Thanks for having me, my favorite topic ever to talk with you both about,

Bethany Lockhart Johnson (03:47):
I think something that I just deeply, deeply respected admire is that I feel like you are constantly sharing about how you are learning. You’re continue to learn, continue to, to try out new ideas and you do a very good job of like highlighting things that you’ve learned, whether that’s sharing it through a tweet or sharing it amongst colleagues or peers. And I, I just really appreciate that because I feel like being in the mathematics community with you, I feel like I grow by, I just like paying attention to like, Hey, she’s a learner, she’s done all these amazing things and thinks in these amazing ways and has shifted my thinking in such amazing ways. But she’s saying, Hey, I I’m still learning. So yeah. Hi, thank you. Thank you for your, I don’t know. We’re just glad to have you here.

Elham Kazemi (04:41):
Thanks. I do feel like the perpetual student, like I’ve never left school and I wonder like one day maybe I will, when I grow older, when I grow up, will I ever leave school? Maybe not.

Bethany Lockhart Johnson (04:52):
<laugh>

Dan Meyer (04:53):
Great. Let’s dig in. Yeah. So please tell us you partnered with a school for some professional learning that wasn’t the sort where you would go in and offer brilliant ideas and then leave. But rather it, it seemed like it was more of a job embedded sort, the sort of thing that might have a life of its own after, you know, after the, the grant ends or the program ends. Can you describe what it was you did and what the effect was?

Elham Kazemi (05:15):
I think I wanna first say that everything that I have done and experimented with as really the result of working with fabulous people, teachers, coaches, principals, other, um, colleagues and peers in the field who are constantly trying to work on what good teaching looks like and how you learn to do it. And mostly because we care about kids and we care about what students experience in the classroom. And we want kids to love school, to have school, be a place where they’re known, they’re loved, um, that they look forward to being in every day. And I think there’s that, um, the why that, that, um, per that makes you want to learn is really about the students and being, doing things in service of them. Because when, uh, as one of my colleagues said, when children thrive, teachers thrive. So what does it mean for us to thrive?

Elham Kazemi (06:06):
If we are focused on our kids’ experiences in schools, what we did at this, this particular school and a group of schools is kind of tap into a, all that curiosity and drive that teachers have to do a good job and to use their imaginations well, and to engage the actual ideas that children have in their classroom together, not separately, not like get a great idea and be inspired by it and then go figure it out by yourself, but be inspired by ideas and then try to figure them out together. Because, um, as you both know, very talented teachers, uh, who also have been inspired to change your classroom teaching. Once you figure something out or as you’re figuring it out, there’s all kinds of intricacies. Like I remember when I first learned about three act tasks, I thought what a brilliant idea, but it’s not so simple to try to enact the brilliance of it because you can simplify it too much or you can get stuck and not really know how do you move from one act to the next, or what’s the point of the third act?

Elham Kazemi (07:12):
Do you just like reveal the answer and that’s it. And then you move on. Um, how do you even do design the tasks to begin with all of those things, raise questions and working on them together, uh, and carving up that space and time to work on them together is sorely missing in schools. And so that’s what we were able to do with the schools that I parted and it is find the time and then design the structures so that teachers could, um, <affirmative> think about their teaching together and then also be in the classroom together with kids. So the kids see that we are also learning to be responsive to them. That’s the point. So we have to work stuff out when kids are present, which is the part that usually trips a lot of people up.

Bethany Lockhart Johnson (07:55):
Well, that to me is I think the part that shifted my teaching and continues to is this, it is a culture shift to tell your students, to invite your students into your learning, to tell them I’m, I’m learning too. It was an invitation to, to be vulnerable in a way that I think sometimes teachers are very afraid to be vulnerable. Uh, if they don’t know what the student response is gonna be, or they don’t know, they don’t wanna seem like they don’t know the answers or they don’t know how to figure out a problem. I think that’s a real shift in the, in the culture for, for compared to maybe what we, we experienced growing up.

Dan Meyer (08:33):
I hated not knowing the answer to a math problem. I admitting I, I was uncertain with the mathematics, but to admit that I am like a, a work in aggress as a teacher, feels like an extra admission, an extra layer of humility, which is, I don’t know, it’s a really special thing that you were up to with that school. I’d love to hear like about specific structures that you worked with to help make that transition feel, you know, more natural, more welcoming, more productive.

Elham Kazemi (08:58):
So, I mean, you probably have experienced common planning time, right? This is a thing that often happens for us teachers. I think that common planning time looks a lot sometimes like, uh, what are we gonna do on Monday, Tuesday, Wednesday? Okay. What do we need? What are the materials we need? Who is gonna do that? Will you write this? And that’s what kind of common planning time, and then it’s over. And then you might see each other at lunch and say, well, how did that go? And you’ll talk a little bit about it, but common planning time and learning labs, which is sort of what the, what we call the, the PD that we designed means. Okay. So let’s take three act task. We, we write a little bit about it. We’ve seen a couple, but okay. What would it really mean to plan this particular one?

Elham Kazemi (09:42):
So common planning time is thinking like, how are we gonna launch that first act? What are we actually gonna say? What do we think the kids are gonna say? Why would we say it that way? What if they say something else? Um, and then, okay, so what does it actually sounds like to transition from act one, to act two? What might we say, what would happen with this particular task and actually getting into the details of how you imagine, like, what, what you would do when you were actually planning the specifics of a particular lesson, but leaving it loose enough that you’re not trying to make it perfect. And I think that’s the trick. So, so that you are not so invested, that goes in that particular way or that you fail. If it doesn’t go that way. Um, but that you have something you wanna learn together and trying out this three act task with a particular group of kids so that when you go into the classroom, first of all, you’ve all thought through the full R of the lesson.

Elham Kazemi (10:40):
And you’re curious enough about what’s gonna happen at particular points that you’ve left room for uncertainty and the taking of some risks. So then when you go together into a classroom and kids start to say things that you didn’t anticipate you or, or they start to do something that you’re so jazzed about, that you didn’t anticipate that you’re like, this is the thing we should pursue more. You give each other permission to do that. You’re like, whoa, wait, did you hear what so? And so said, I think we should follow that road and see where it takes us, or, huh. Okay, hold on. And that’s what we call teacher timeouts, where you actually confer briefly and you tell the kids, this is a super special day. We’ve tried to design something. We’re very curious how you are gonna react to it. So we’re gonna try it out. And along the way, we might pause to get your ideas or for us to make some decisions and steer the ship in a, in a new directions and see what happens. So we’re gonna be sitting closely to you among you. Um, and you get to be our teachers today while we teach. That’s how it’s framed.

Bethany Lockhart Johnson (11:46):
Like, what were you seeing in professional development or in that wasn’t happening amongst teachers? Like where, where are the gaps? Because it feels like so much of your work. You’ve just looked in such nuanced ways at how teachers can continue to grow and be more reflective of their own teaching. And I’m just kind of curious where that came from or where you’re seeing the landscape.

Elham Kazemi (12:10):
Yeah, that’s a good question. Well, I, oh, everything I know about, children’s thinking to Megan Frankie and the beautiful body of work called CGI, but, um, one of the things that we noticed, there’s so many great CGI workshops, and even like all the seminars and conference presentations and amazing things that you can design to have engaging work time for teach in, in professional development, outside of their classroom, people get super jazzed, you know, they get, um, uh, they have meaningful experiences, but to contextualize that back into their classrooms with their own students is like where, where often I would see like, wait, the same group of teachers I just saw in my classroom or in either in math methods or in this PD seminar, or even myself, like noticing, like I have seen and thought about stuff a lot. But when I went to go do it with a particular group of kids, holy moly was that so hard. And I saw all kinds of new complexities that I didn’t anticipate. And if I were just left to my own devices, I might very easily say, whew, this seems a little too hard.

Bethany Lockhart Johnson (13:21):
Right,

Elham Kazemi (13:22):
Right. And that’s the thing that I always hated. I was like, oh, if only we had, or you, or if you watched somebody do a demo lesson and you saw something that was like, kind of cool that you wish you had done afterwards. I often this happened in reflections. I wish we had, because we weren’t allowed to interrupt each other during teaching. Cuz somehow that would be rude or that would undermine the teacher’s authority. But that’s only the way we frame it. If we say actually we’re all capable people. So a question we ask ourselves during instruction doesn’t mean you don’t know what you’re doing. It means actually we’re thinking together then the interruptions aren’t about undermining authority. They’re about thinking together.

Dan Meyer (14:04):
There’s a performative aspect to a lot of teaching. Like the like teaching feels like a performance and you don’t, the movie’s playing or there’s a play that’s going on. It feels like inappropriate to interrupt that in any way. Cause the performance is going and I, I love what this that’s. I love what this idea does to kind of, to redefine teaching is not a performance, but this, this co-constructed thing. Or if it’s a performance, it’s a performance, the stars, all of us, like we’re all a part of the cast and always a it’s always the dress rehearsal.

Elham Kazemi (14:30):
<laugh> it is like the dress rehearsal. Although some of my brilliant colleagues with backgrounds in drama and theater, Sarah Kavanaugh and Holly GU and Elizabeth dure, they actually were at a meeting together. And they talked about how this like breaks the fourth wall, you know, mm-hmm, <affirmative> like, which is out of theater, um, where the performer speaks to the audience, you know, I know you’re there and I have something to say to you. Yep. And I was like, well, we should, why can’t we do that in teaching? So we actually wrote a little paper, um, that’s called breaking the fourth wall as a way. That’s so cool as a metaphor for understanding and reframing what these interruptions could meet. Cuz we often get people when we about this for academic audience who say like, aren’t you using the children and what are the children gonna do while you just pause? Are they supposed to freeze? And uh, you know, while you talk about them, but it’s not really that it’s like, Hey students, we’re here because of you. So shouldn’t, we try to involve you and are decision making. To some extent, it’s not like we don’t know what we’re doing, but we’re doing things because we wanna advance your learning.

Bethany Lockhart Johnson (15:40):
I mean, I still remember the first time I did a teacher time out and it, it was, I, it was breaking the four, it was this like, okay, you’re gonna see what happens, kids like, look at my, my tap dances stopped. And you’re you mean like, you know, whoa, wait a second. And I think it is about how you frame it. Right? It’s a celebration of their thinking and you, you use the term ambitious teaching and it, to me that is such a joyful way to think about it.

Elham Kazemi (16:06):
It is risky. And you would never say anything to shame any student, no. Or to shame your colleagues. Clearly it’s not a about that kind of discussion. Right. And they’re so brief. They’re like, it, it seconds. It’s not like you’re wasting time. You’re actually trying to understand what’s happening here. And I’ve just had so many instances where something goes on. Um, like we were doing a growing patterns task in a classroom and the student built the fourth term and they built stuff that did not follow the pattern. And I was so confused. I, I just didn’t understand like what was going on. And one of the kids said, well, if you, if you did follow the pattern, that’s not her words. But you know, she’s like, well, if we built it this way, that would be too obvious. Because if you just, if you saw that and you’re like, oh, that lesson failed.

Elham Kazemi (16:59):
Now we, our kids don’t understand what patterns are. We did it. Like, we gotta pause here and we gotta say, and we’re like, well, what do you mean? Can you say more about that? And basically what they said is that, um, well, first of all, they’re, they’re right. A pattern could change at any time, but it’s like, it would be more interesting if they, they knew how many cubes it would take for the fourth term that it would be nine, but they’re like, Hey, let’s rearrange that nine in some cool new ways. <laugh> cause that’s more interesting. It was like more interesting to them if, if they didn’t keep the pattern. So like, you kind of had to wrestle with that in the moment <affirmative> with them. And that’s how they can actually be partners with you in the teacher, timeout.

Bethany Lockhart Johnson (17:40):
Right. That’s making it about them and their learning. It’s not about that. It’s not about your performance and like looking all shiny and, and I’ve got it all together and I know exactly how this lesson’s gonna go. It that’s so interesting.

Elham Kazemi (17:53):
And sometimes you pause and like some cuz somebody else who’s watching is noticing something about what the kids are doing. And while you’re, if you’re happen to be the person who’s upfront at the time leading, you’ve got so many things going on in your head that some times the person who’s just been sitting on the rug with the kids mm-hmm <affirmative> has noticed something. And they’re like, can I ask something right now? And that’s a great teacher timeout too. Mm. Because they’re interrupting you cuz they’re like, I think I, I wanna see what kids will say. If we ask this question next and those moments have been like amazing because someone has noticed something that another person hasn’t in the room and it’s been very helpful to illuminate how kids are processing something or what two ideas they could connect. That would be really powerful based on what we were hoping to learn that day or do with the kids that day.

Dan Meyer (18:47):
It’s like you have a bonus brain attached to you there in the room. Sounds really powerful. I wonder a couple about the student experience of this. I’m imagine if I was a student in the room and I heard the two teachers like kind of pause, take this time out and like talk about how interesting my thinking was like behind my back a little bit, like trying to strategize about something interesting. I had said, I just imagine I would, I would feel very good about like, that would be a very positive experience for me. Um, but I’m just curious, can you speak to how students reacted when they’re,

Bethany Lockhart Johnson (19:16):
You mean, if you had been a student in the class and you saw two teachers conferring about your work?

Dan Meyer (19:21):
Yeah. Yeah. Like I, my classmates had of thing that was like, it, it kind of like was so novel that it stymied the teachers and then they like had to pause and like talk about what are we doing? Oh, I don’t know. I can imagine that’d be like know a fun feeling. Maybe I just tell more about me than about the kids, but

Elham Kazemi (19:35):
<laugh> it points to like, how would you go about starting to do this work? Right. Because one is you do, you do have to tell kids, Hey, I’m here with so and so and so, and so, and so, and so it might be just two of you. It might be five of you. It might be more and you know how we’ve been working on X thing in class? Well, today we wanted to try this new thing and, but we’re not sure how it’s gonna go and we need, we need your feedback. Right. So here’s something that might happen. We might pause you, you, I mean, you really do directly tell the kids to do that. And then we’re gonna ask you how it felt and we’re gonna share those feelings with one another. So you do that, you do a little exit card or you,

Bethany Lockhart Johnson (20:19):
How, what felt the pause or how,

Elham Kazemi (20:22):
How, yeah. How did it feel that, how did this lesson go or how did a lesson, how did it feel when you heard, you know, ALM and Dan talk to each other, doing this lesson and they might say, Hey, it’s cool. It’s fun. Kids have definitely chimed in, in like, if we ask a question like, should we do this next or this, somebody will pipe in and say, do that, you know, do this thing. Instead. If, if you kind of pipe in to say, can I ask a question? They just turn to you and look at you and answer your question. Right. So, and we always thank them and we just like pump it up. Right? Like this is so cool because this is all about you. And usually when you say today, you’re gonna be our teachers, especially the little kids. They like get all giggly. Totally.

Bethany Lockhart Johnson (21:02):
Right.

Elham Kazemi (21:04):
Love it.

Bethany Lockhart Johnson (21:05):
You know, you, you were sharing about this really unique situation, which I wish it wasn’t as unique where you had the whole school involved, but how did that happen? And what if you don’t have the whole school involved? What if it’s just me in my grade level, who’s like, I kind of wanna try this, but what

Elham Kazemi (21:22):
<laugh>, I think you could start with your, a peer in your school or a colleague in your school. Yeah. I mean, it’s a little seed, right. And it’s a little seed and then you could make it grow. I also believe in starting small and growing, cuz you do have to invite people into a different way of thinking about what it means to learn together. So you need to experience it, um, in order to believe it.

Dan Meyer (21:49):
Yeah. It feels like we would not want to write off any student as like, oh, they just don’t wanna learn. I think a lot of, a lot of us just like don’t buy that, that there’s other reasons why people need that. A teacher shouldn’t like shouldn’t, that’s not true of students that they have been told they can’t learn or there’s various circumstances the same. I, I suppose the same as like should be true is true of teachers. Like no teacher doesn’t want to learn more about teaching is at least a helpful Axiom to use, to approach the work of teacher growth. And so maybe they, yeah, maybe I feel like I’m the only person in my school who wants to do this, but perhaps that’s not actually true. Perhaps it’s just a matter of creating an imagination or the right kind of enticement or I don’t know what, um, but to start small and grow from there makes a lot of sense.

Elham Kazemi (22:32):
I feel now, like it would be weird and a lot harder for me to invite someone to just come in and watch me teach and sit quietly in the back when I don’t know anything about what they’re thinking and wait until afterwards to get their opinion.

Bethany Lockhart Johnson (22:46):
Oh yes.

Elham Kazemi (22:47):
I would be much more willing to co-plan with someone so that we were both on the same page about what we were trying to do and then when you’re in the classroom with me. So that’s the other thing that’s important cuz I don’t think you can just be in the classroom together and I, you know, interrupt each other’s teachers, if you haven’t planned together, cuz you do have to have some common understanding of what are we trying to do here? Oh the

Dan Meyer (23:10):
Intent here.

Elham Kazemi (23:11):
Yeah. So I would definitely say don’t just show up in each other’s classroom and start interrupting each other. <laugh> if you don’t know what the heck is going on. Yeah.

Dan Meyer (23:21):
Yeah. I, I know that’s directed at one person on this call in particular. I hear that.

Elham Kazemi (23:25):
I know who we’re talking about, but you know, I would be way more intimidating for me if I was trying to do a three act task and Dan just came to watch me do it <laugh> and he hadn’t planned with me. He didn’t know why I selected that task. I had no opportunity to talk to him. Then it would be, Hey Dan, would you just like do this with me? Let’s think through this. Why would you do this then? What, what have you normally done? Oh, okay. Why have you done that? Right. And then to like, okay, let’s try it together. Um, and then, and then along the way, if I have questions, you’re there with me. So sometimes there is someone more experience like if right. And sometimes you’re both just like, I just don’t have that much experience with this. I’m learning this for the first time.

Elham Kazemi (24:04):
Right. And the beauty of the math ed community, whether it’s on Twitter or is that we’re kind of pretty accessible to each other. Right. So if I read something and I have a question about it, you bet I’m gonna reach out to the author <laugh> and say, I’ve been thinking about your work and this is what’s been coming up for us. Can you? So like, it definitely happened with hands down conversations. We tried it in the learning lab and we just couldn’t figure out like that. How do you intercede, like into the hands down conversation cuz the kids are supposed to have a conversation. So we had to like give Kaia and her co-author a few specific examples so they could help our thinking so that we could try it again. Right. And make it better. And I think that is, is what it means to be learning in community is that you use the resources more broadly.

Bethany Lockhart Johnson (24:52):
That’s a beautiful reminder too. And it also helps me feel a little better about all the messages I’ve sent you. Like what does this mean? Can you help me with this?

Elham Kazemi (24:59):
<laugh> I mean, that just makes you feel alive. <laugh> I think

Bethany Lockhart Johnson (25:06):
So. I think P part of the beauty of you talking about starting small is that it does give those of us who maybe aren’t seeing that those opportunities for collaboration reflected in our school culture, it gives us kind of some hope for like, wait, don’t just like, think you can’t start. I, how do you, how do you see, how do you see it growing? Or, or do you think like if you could magically <laugh> like wave your wand and, and create some shifts around, around, uh, the culture where folks are feeling isolated or maybe don’t feel like they have the needs to do this work. What could that look like?

Elham Kazemi (25:51):
Yeah. What could that look like? So time, like we need some imagination around the use of time in schools and I have seen some really amazing opportunities where teachers get to co-teach, which means that they really have to co-plan when, um, there’s a break in a regular school session and there’s like an intercession or like a, like an elective that, um, that doesn’t, I haven’t seen it happen a lot in public schools, but I have seen it happen a lot in independent schools where they’ll have like, stop, stop the presses. It’s like a drop everything and read, but it’s like a drop everything and do an R arts week. And then all the kids in the school get shuffled. So they into multiage groupings and the teachers get to plan something special for like the week. But you could start with like a day, which would at least get you to plan something together and try to teach together and be just in each other’s spaces. And I think that might be kind of an interesting way to start where you have to like mess with the schedule somehow. Cuz the schedule is the beast in schools

Bethany Lockhart Johnson (26:59):
Is kind of the first step. Like we are going to create a shared activity, a shared instructional goal, a shared like where do I start?

Elham Kazemi (27:09):
What, where do you start? I mean, there’s so many good books. We all read, start with something that grabs your imagination. That you’re like, if I got to do this in my class, I’d be so jazzed. And I think my kids would love it. Why would they love it? You know, whatever it is. There’s so many good ideas that people are instantly blogging about publishing, um, slow reveal graphs. I love those two. I have like all these things. I was like, I would love to try these out, but I, I gotta do them with somebody cuz I need a sounding board about like how, what does it mean to do it well? And what does it mean to just do it at the surface level and do it a, you know, in a kind of a crappy way. And we don’t wanna do a crappy job. We wanna do a good job, but you have to start, you have to start sometimes in an awkward, crappy way. Like, you know, and get past that stage. Cause often we try a bunch of stuff, eh, and then we drop it. But like you gotta work on it to make it really

Bethany Lockhart Johnson (27:58):
Good. And if you’ve already tried it and it didn’t go so well it’s, this could be an invitation, like, you know, it doesn’t mean give up on the idea. It means like, Hey let, let’s let’s collaborate. Let’s you know, come into my class. Let’s co plan this.

Elham Kazemi (28:10):
So I would challenge people to think about the schedule. <laugh> try to do something just a little bit different. You know, like when we do learning labs, people are like, well, how do you do that? And there’s no money for it. Actually. We just use our money in a slightly different way to make or that everybody four people get a sub, which I know right now, sub shortages is crazy, crazy, but then combine your classes or do something different. Yeah. You know, um, involve people differently somehow in your, in your school environment to get that time,

Bethany Lockhart Johnson (28:43):
Really see this as a priority. This is a, this is there’s is intense value in this time to collaborate. Yeah.

Elham Kazemi (28:51):
Yeah. There’s so many side benefits for, I think for kids and teachers when you’re able to do this.

Dan Meyer (28:58):
Yeah. You’ve heard of folks. Uh, usually our, our math teacher challenge, our lounge challenge has been, uh, pedagogical in nature or a new CU. And uh, this is a different kind of one. This is, uh, go, go be a Rabel Razr go Rouse rabble at your, uh, front office and figure out the right way to get some funding or some time or shuffle a master schedule in such a way that you have collaboration, time to plan to co-teach to interrupt one another and uh, let us know how it goes. We are super excited and super interested in all of that. Thank you, uh, Elham for being with us here today and sharing all of your wisdom about how teachers grow.

Elham Kazemi (29:36):
Thanks for reminding me. You too loved

Bethany Lockhart Johnson (29:38):
It. We’re never done learning. We’re never done learning. Nope.

Bethany Lockhart Johnson (29:44):
Aha. Thank you so much for joining us in the lounge. I think all of us have sat through effective and ineffective professional learning sessions and just helping us to envision of how this can truly help PD can truly transform our classrooms. It is it’s exciting. It’s exciting. And I think we’ve all learned a lot from our conversation. So thank you. Thank you. Thank you. And don’t forget, you can connect with us in the lounge on Facebook at math teacher lounge or on Twitter at MTL show. Let’s keep this conversation going. Keep it going. Thanks so much for joining us. Thanks

Speaker 4 (30:20):
Everybody. <silence>.

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What Elham Kazemi says about math

“ When children thrive, teachers thrive. So what does it mean for us to thrive if we are focused on our kids’ experiences at school?”

– Elham Kazemi

Professor of Mathematics Education, University of Washington

Meet the guest

Elham Kazemi is a professor of mathematics education at the University of Washington. She studies how strong professional communities develop in schools and how schools can be organized so teachers learn from and with their students. This work is informed by equity-oriented research on organizational learning, children’s mathematical thinking, and classroom practice.  She is co-author with Allison Hintz of Intentional Talk, which focuses on leading productive discussions in mathematics. She also edited Choral Counting and Counting Collections with Megan Franke and Angela Turrou, which focuses on the importance of counting from preschool to 5th grade.

Follow Elham on Twitter

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About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

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S3 – 04. Ideas to build math fluency with Valerie Henry, Graham Fletcher, and Tracy Zager

Promotional image for "Math Teacher Lounge" Season 3, Episode 4 titled "Ideas to Build Math Fluency," featuring Valerie Henry, Tracy J. Zager, and Graham Fletcher.

Fluency in math can oftentimes be associated with negative experiences with its development— timed worksheets, for example. Bethany and Dan are joined by three guests to better understand fluency and how to make its approach fun. Dr. Val Henry shares her three-part definition of fluency and her five principles for developing it. Additionally, Tracy Zager and Graham Fletcher join Bethany and Dan to better understand fluency through a lens of equity and using multimedia as a tool.

Explore more from Math Teacher Lounge by visiting our main page

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Dan Meyer (00:03)

Hey folks. Welcome back. This is Math Teacher Lounge, and I am one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I’m your other host, Bethany Lockhart Johnson. Hi, Dan.

Dan Meyer (00:11):

Hey, great to see you. We have a big one this week to chat about and some fantastic guests. We are chatting about fluency, which is the sort of word and concept that I feel like people have very, very non-neutral associations with it. A lot of them are very negative, for a lot of people.

Bethany Lockhart Johnson (00:26):

I saw you frown a little. What’s up with that, Dan? You kind of, like, shrank.

Dan Meyer (00:30):

I have strong feelings about it. You know, there’s lots of ways that people go about helping people become fluent in mathematics. And a lot of them are harmful for students, and ineffective. And it got me thinking about fluency as it exists outside of the world of mathematics, where we have a lot of very clear images of it. We’re getting fluent in things all the time. Like, as humans. Human development is the story of fluency. And I just was wondering….Bethany, would you describe yourself as fluent at something outside of the world of mathematics? What is that? How’d you get fluent at it? What was the process?

Bethany Lockhart Johnson (01:05):

Hmm, I think I’m a pretty fluent reader. I read all the time. I’m a happier person if I’ve read that day. I once saw this poster in a classroom; it said “10 Ways to Become a Better Reader: Read, Read, Read, Read, Read…you know, 10 times. Get it? Reading? You get better at reading by reading! So I would say reading. And it’s been kind of cool—I have a one-year-old who, it’s been really exciting slash overwhelmingly anxiety-producing to see him get very fluent with walking slash running, ’cause he’s getting faster every day. And it’s kind of fun. When I think of what’s something somebody’s trying to get fluent with…walking! He’s trying to be more fluid. He’s practicing transitions. He doesn’t wanna hold my hand while he traverses rocky terrain. He’s getting better at it. He’s practicing. What about you? What’s something…?

Dan Meyer (02:08):

I think about driving a lot. I’m a very fluent driver and I think a lot about when I was first a driver, you know? And how l have my hands on 10 and 2, vice grip, and do not talk to me; do not ask me anything; don’t ask me my NAME. I need to focus so hard. And then a year later, you know, I’m driving with one hand, smash the turn signal, take a sip off of whatever, change the CD. And then it’s no big deal.

Bethany Lockhart Johnson (02:38):

Wait, did you pass the first time? Your test?

Dan Meyer (02:40):

Yeah, I don’t like to brag about it. <laugh> But I do all the time. <laugh> But I got a hundred on my driving test. I don’t care who knows it. And I hope it’s everybody. But I guess all of this is just to say there are areas of life where fluency feels natural, with the case of walking. There’s areas of life where fluency feels motivating, with like driving—I wanna be able to switch the CD out or whatever. And there’s areas where fluency feels terrifying and hard to come by, like mathematics, sometimes. So we have a set of guests here. Our first guest will help us figure out what do we mean by fluency? And what’s the research say about what fluency is and how students develop it in mathematics? And then our other guests will help us think about what it looks like in practice in the classroom. What are some novel, new ways to work on fluency? So first up we have Val Henry, Dr. Val Henry.

Bethany Lockhart Johnson (03:32):

So we knew we needed help with the fluency definition, because when we think about it, it’s kind of big, right? And we wanted to look at what research about fluency really says. So we called on Valerie Henry. Val is a nationally board-certified teacher, taught middle school for 17 years, and since 2002 has worked with undergraduates graduates, credential candidates as a lecturer at the University of California, Irvine, one of my alma maters. So after doing her dissertation on addition and subtraction fluency in first grade, Val created a project to study ways to build addition and subtraction and multiplication and division fluency while also developing number sense in algebraic thinking. And the pilot grew and grew over the last 18 years into a powerful daily mini-lesson approach to facts fluency called FactsWise. And when we thought of fluency, the first person I thought of was Val. Welcome, Val Henry, to the Lounge! I’m so excited to have you here. Welcome.

Valerie Henry (04:36):

Thanks, Bethany. And thanks to you, Dan. It’s great to be here today.

Dan Meyer (04:41):

Great to have you; help yourself to whatever you find in the fridge. The names that people write down on those things in the bags are just recommendations. It’s potluck-style here. I’m curious, Val, if you’re, like, on an airplane, someone asks you what you do, and you say you study fluency…what is the layperson’s definition of what does it mean to be fluent in mathematics? And if you can give a brief tour through what the research says about what works and what doesn’t that would really help us orient our conversation here.

Valerie Henry (05:12):

The first thing I have to do when I talk to somebody on a plane is define the idea of fluency. And I often use an example of tying your shoelaces. Because that works with first graders as well as adults. This idea that when we first start trying to put our shoes on and get those shoelaces tied, somebody tries to, first of all, just do it for us. But then of course maybe tries to teach us the bunny-ears approach. And we struggle and struggle as little kids and eventually either the bunny-ears approach or something else starts to work for us. But we still have to pay attention to it. We have to think hard and it’s not easy. And then over time we get to the point where we basically don’t even think about it. When I tie my shoes in the morning. I’m not thinking about right-over-left and left-over-right and all of those things. I just do it. And so that’s a good, easy example of becoming fluent with something. I think what we’re talking about today though, is the basics, the adding and subtracting that we hope kids are going to have mastered maybe by second grade, and the multiplication and division facts that we wanna maybe have mastered by third, maybe fourth grade. So now what does that mean to become fluent with those basics? I have a three-part definition that seems to match up really nicely with the common core approach to fluency. Which is, first of all, we want the answers to be correct. And then second, we want the answers to be easy to know. And so what does that mean? Well, to me, it means without needing to count,

Bethany Lockhart Johnson (07:12):

You mean without having to kind of muscle through it? Or say more about you mean.

Valerie Henry (07:16):

Well, I guess what I mean is that when you watch a young child try and solve something even as simple as two plus three, they might put up two fingers and then go 3, 4, 5 with three more fingers winding up on their hand, one or the other of their hands. While they’re doing that, they don’t really have a sense of whether even their answer is right or not, quite often. Especially when you get to the larger adding and subtracting problems, you can see a lot of errors happening as they’re trying to count. And it’s taking up cognitive energy to do that counting process, especially as you get to the larger quantities. So my definition of fluency now is “getting it right without needing to do that hard work like counting.” Now, some people might say, well, we just want them to have ’em memorized. But in my research, I’ve learned that a lot of very fluid adults don’t always have every fact memorized. In fact, if you ask a room full of adults, what’s seven plus nine, you might learn that they can all get it correct quickly, quickly…but they don’t all have it memorized. And so when you ask them, “How did you get that?” Many of them will say, “Well, I just gave one from the 7 to the 9 and I know that 10 plus 6 is 16.”

Bethany Lockhart Johnson (08:53):

That’s such an important distinction. My brain literally just did that actually!

Valerie Henry (08:58):

<laugh> Right? <laugh> But you’re fluid with it, because it doesn’t take you much cognitive energy at all.

Bethany Lockhart Johnson (09:05):

Right.

Valerie Henry (09:07):

So now we have “correct without needing to put that cognitive energy,” which usually means that you’re counting. And then the third thing is “relatively quickly,” so that you’re not spending 15 seconds trying to figure it out. Even that part-whole strategy approach can be done really quickly, almost instantaneously. Or it can take a long time. So if a student can get the answer correct within, you know, three or four seconds— is I’m pretty generous—I figure that they’re pretty darn fluent with that fact. So that’s my three-part definition of these basics, fluency.

Dan Meyer (09:55):

I love the distinction between getting it correct and getting it quick. It’s possible to be quick with wrong answers. It’s possible to be like, “Those are separate components there.” And I echo Bethany’s appreciation for this third option in between knowing it instantaneously through memorization and muscling through it. But there’s like a continuum there of how much energy it took you to come up with it that all feels extremely helpful.

Valerie Henry (10:21):

And you know, one of the things that I’ve noticed is that when kids are pressured to come up with those instantaneous answers, they often default to guessing and get it wrong.

Bethany Lockhart Johnson (10:30):

Mm, yeah.

Valerie Henry (10:30):

So that’s one of the things that I’ve learned is that as we’re trying to help students develop fluency, it’s important to start with building their conceptual understanding of what it means to do, you know, 3 times 9 and what the correct answer is, maybe using manipulatives or representations of some sort. Not skip-counting! I really have found that skip-counting just perpetuates itself in many students’ minds and that they never stop skip-counting, which means they’re putting in not very much mental energy if it’s 2 times 3 but a ton of mental energy if it’s 7 times 8. Because frankly, it’s really hard to skip count by sevens. And by eights.

Bethany Lockhart Johnson (11:18):

I can get to 14 and then I’m like, wait, wait, what was next? Right? No, no, no…21! What do you feel are some misconceptions that maybe teachers, maybe parents have about fluency in math?

Valerie Henry (11:30):

I think maybe one of the first ones is that if students count or skip-count, their answers repetitively over and over and over and over, that they’re bound to memorize them. And the study that I did back in 2004, I actually had a school that had decided that they were going to do time tests with their students every day, all year. And that undoubtedly by the end of the year, those students would be fluent.

Bethany Lockhart Johnson (12:06):

And to clarify by time test, you mean like, sit down, pencil, paper, ready, go, worksheet kind of thing.

Valerie Henry (12:15):

Yes.

Bethany Lockhart Johnson (12:16):

Some of us might remember quite vividly.

Valerie Henry (12:18):

<laugh> Very vividly. And you know, you have to get it done within a certain amount of time. So they made it fun for the students. Apparently the students enjoyed it. I was a little leery about that, but in the end, when I went and checked on the students and I did one-on-one assessments with half of the students in every class that were randomly selected so that I could get a sense of where they were with their fluency—and these were first graders—they basically had nothing memorized. They were simply counting as fast as they possibly could. And, you know, mostly getting the right answers. But they had not memorized. So that’s one of the myths, I think, is that repetitive practice of counting gets you to memorization.

Bethany Lockhart Johnson (13:10):

If I put it in front of you enough times, you’ll become fluent.

Valerie Henry (13:14):

Right, right. Now these students didn’t really get any instruction, any help learning these. They just simply tested over and over and over. So that’s another thing that I think is a misconception. It’s that if we test students, but don’t really teach them fluency, then they’re going to become fluent. If we just test them every Friday or that kind of thing. And that they’ll learn them at home. But really what that means is a few lucky kids who have parents who have the time and the energy and the background to know how to help will take that job on at home. Not that many students are really that fortunate.

Dan Meyer (14:01):

It’s almost like the traditional approach, or the approach you’re describing, confuses process and product. It says, “Well, the product is that eventually fluent students will be able to do something like this, see these problems and answer them, answer them quickly,” and says, “Well, that must be the process then as well; let’s give them that products a whole lot.” But as I hear you describe fluency with bunny ears on shoelaces, there’s these images and approaches and techniques that require a very active teacher presence to support the development of it. That’s just kind of interesting to me.

Valerie Henry (14:35):

My initial project, the pilot project that I tried, was to simply ask teachers to follow five key principles. And the first one was to do something in the classroom every day for—I told them, even if you’ve only got five or 10 minutes, work on fluency for five or 10 minutes a day, and let’s see what happens. So that was one key element was just to teach it and to give students opportunities to get what the research calls for when you’re trying to memorize, which is actually immediate feedback. When I talk about immediate feedback with my student teachers, I say, “I’m talking about within one or two seconds of trying a problem, and then sort of immediately knowing, getting feedback of whether you got the answer right or not so that your brain can kind of gain that confidence. ‘Oh, not only did I come up with an answer, but somebody’s telling me it’s the correct answer.’”

Dan Meyer (15:38):

There’s a lot of apps now in the digital world that offer students questions about arithmetic or other kinds of mathematical concepts and give immediate feedback of a sort: the feedback of “You’re right; you’re wrong” sort. Is that effective fluency development, in your view?

Valerie Henry (15:57):

I haven’t heard and I haven’t seen them being super-effective. The ways I think about this are “Immediate feedback isn’t the only thing we need.” Probably one of the biggest things that we need is for students to develop strategies. And this is one of the other things I’ve learned from international research, from countries that do have students who become very fluent very early, is that they don’t shoot straight for memorization, but they go through this process of taking students from doing some counting and then quickly moving them to trying to use logic. So, “Hey, you really are confident that 2 + 2 is 4; so now let’s use that to think about 2 + 3.” Actually, as an algebra teacher, I would much rather have students that have a combination of memorization and these strategies, than students who’ve only memorized. Isn’t that interesting that my most successful algebra students were good strategy thinkers. Not just good memorizers.

Bethany Lockhart Johnson (17:09):

So you mentioned there were five that kind of helped root this idea in like, “What can teachers do? What is the best thing that teachers can do to support with fact fluency?” So, everyday was key.

Valerie Henry (17:22):

Then the next principle that I really focus on is switching immediately to the connected subtractions so that students—

Bethany Lockhart Johnson (17:33):

Not waiting until you’ve gotten all the way through addition. But making “Ooh!”

Valerie Henry (17:38):

Totally. And I didn’t do that the first year. And when we looked at the results of the assessments at the end of the year, we realized that our students were so much weaker in subtraction than addition. So the following pilot year, we tried this other approach of doing subtraction right after the students had developed some fluency with that small chunk of addition. And we got such better subtraction results.

Bethany Lockhart Johnson (18:11):

What are the other principles?

Valerie Henry (18:13):

The biggest one is to use these strategies. So the strategies makes the third. And then the fourth I would say is to go from concrete to representational to abstract.

Bethany Lockhart Johnson (18:27):

Don’t put away those manipulatives. Don’t put away those tools.

Valerie Henry (18:31):

Oh, so important to come back to them for multiplication and division. And my fifth principle is to wait on assessment. To use it as true assessment, but not race to start testing before students have had a chance to go through this three-phase process. Which is conceptual understanding with manipulatives; building strategies, usually with representations; and then working on building some speed until it’s just that natural fluency.

Bethany Lockhart Johnson (19:07):

I wanna say thank you so much for offering your really learned perspective, because you have not only done the research, but seen it in action and seen how shifting our notions of fluency and what fluency can be and what a powerful foundation it can be for all mathematicians. Really, that shift is so powerful. And I appreciate you sharing it with our listeners and with us. So we’re so excited that we got to talk with you today, Val—

Dan Meyer (19:35):

Thank you, Dr. Henry.

Valerie Henry (19:37):

You’re welcome!

Dan Meyer (19:41):

With us now we have Graham Fletcher and Tracy Zager, a couple of people who understand fluency at a very deep and classroom level. I wanna introduce them and get their perspective on what we’re trying to solve here with fluency. So Graham Fletcher has served in education in a lot of different roles: as a classroom teacher, math coach, math specialist, and he’s continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary math. He’s the author, along with Tracy, of Building Fact Fluency, a fluency kit we’ll talk about, and openly shares so much of his wisdom and resources at gfletchy.com. Tracy Johnson Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of this toolkit, Building Fact Fluency, and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books for teachers at Stenhouse Publishers, including, yours truly. Thank you for all that insight, Tracy, and support on the book.

Bethany Lockhart Johnson (20:49):

Dan and I were talking at the beginning of the episode about things we feel like, “Hey, I’m fluent in that. I’m fluent in that.”

Dan Meyer (20:55):

Just very curious: What’s something you would like to get fluent in outside of the world of mathematics, let’s say?

Tracy Zager (21:00):

I’ll say understanding the teenage brain, as the parent of a 13-year-old and 15-year-old. That’s the main thing I’m working on becoming fluent in!

Bethany Lockhart Johnson (21:10):

Ooh!

Dan Meyer (21:13):

A language fluency, perhaps. All right, Graham. How about you?

Graham Fletcher (21:16):

For me typing, it’s always been an Achilles heel of mine. So voice-to-text has been my friend. But it’s also been my nemesis in much of my texting here and working virtually over the last couple years. So yeah, typing.

Dan Meyer (21:33):

Do you folks have some way of helping us understand the difference in how fluency is handled by instructors and by learners?

Tracy Zager (21:40):

I would say that the lay meaning of fluency is definitely a little different than what we mean in the math education realm. When we’re talking about math fact fluency, which is just one type of fluency. So you gotta think about procedural fluency and computational fluency; there are lots of types of fluency in math. And Graham and I had the luxury of really focusing in specifically on math fact fluency. We’re looking at kind of a subset of the procedural fluency. So the words you hear in all the citations are accurate, efficient, and flexible. There’s this combination of kids get the right answer in a reasonable amount of time and with a reasonable amount of work and they can match their strategy or their approach to the situation. That’s where that flexibility comes in. And there’s like lots more I wanna say about that about sort of…I think one issue that comes up around fluency is that people are in a little bit of a rush. So they tend to think of the fluency as this automaticity or recall of known facts without having to think about it. And that is part of the end goal, but that’s not the journey to fluency. So this is one of the things that Graham and I thought about a lot was the path to fluency. The goal here it’s that student in middle school who’s learning something new doesn’t have to expend any effort to gather that fact. And they might do it because they’ve done it so many different ways that they’ve got it, and now they just know it, or they might be like my friend who’s a mathematician who still, if you say, “Six times 8,” she thinks in her head, “Twelve, 24, 48…” and she does this double-double-double associative property strategy. And it’s so efficient, you would never know. And that’s totally great. That’s fine. That’s not slowing her down. That’s not providing a drag in the middle of a more complex problem or new learning. So we’re really focused on having elementary school students be able to enter the middle and high school standards without having that pull out of the new thinking.

Graham Fletcher (23:53):

And as I think about that, I think about how so many students will memorize their facts, but then they haven’t memorized them with understanding. So that when they move into middle school and they move into high school, it’s almost like new knowledge and new understanding that’s applied from a stand-alone skill.

Bethany Lockhart Johnson (24:10):

So something that felt really unique to me, Graham, as I was diving into the toolkit, is your use of images, Tracy, Graham, is the way that you use images to help students notice and wonder to start making sense of these quantities and the decomposition of numbers using images. Can you talk a little bit about how images played a part in the way that you think about this building a fact fluency?

Graham Fletcher (24:41):

What I realized is so many times when we approach math with just naked numbers with so many of our elementary students, the numbers aren’t visible. The quantities. They can’t see them; they can’t move them. They’re just those squiggly figures that we were talking about earlier on. So how is it that we make the quantities visible, to where students feel as if they can grab an apple and move it around? Because a lot of times we start with the naked numbers and then if kids don’t get the naked numbers, then we kind of backfill it. But what would happen if we start with the images? And then from there, these rich, flourishing mathematical conversations develop from the images. And I think that was the premise and the goal of the toolkit.

Tracy Zager (25:22):

When you look at how fact fluency has traditionally been taught, it’s all naked numbers. And sometimes we wrote ’em sideways. Like, that’s it. That was our variety of task type. Right? Sometimes it’s vertical; sometimes it’s horizontal. And that was it. And I’ve just known way too many kids who couldn’t find a hook to hang their hat on with that. It didn’t connect to anything. And so part of why I knew Graham was the perfect person for this project was his strength in multimedia photography, art, video. And so we started from this idea of contexts that for each lesson string in the toolkit, there’s some kind of context. An everyday object, arranged in some kind of a way that reveals mathematical structure and invites students to notice the properties. So we start with images of everyday objects: tennis balls, paint pots…um, help me out; here are a million of them. Crayons—

Bethany Lockhart Johnson (26:18):

Crayons, markers.

Tracy Zager (26:18):

Shoes, right? Sushi, origami paper, all kinds of things in the different toolkits. So there’s a series of images or a three-act task or both around those everyday objects, and then story problems grounded in that context. And then there are images with mathematical tools that bring out different ideas, but relate in some way to the image talks. And we do all of that before we get to the naked number talk. Which we do, and by the time you get to the number talk, it’s pretty quick, ’cause they’ve been reasoning about cups of lemonade. And now when you give them the actual numerals, they’re all over it.

Bethany Lockhart Johnson (27:03):

I have to say too, as somebody who—particularly in middle school—navigated math anxiety, we recently talked with Allison Hintz and Anthony Smith about their amazing book Mathematizing Children’s Literature.

Tracy Zager (27:14):

Yay!

Bethany Lockhart Johnson (27:14):

And I was explaining, like, if I sat down at the beginning of a math class and my teacher opened a picture book and said, “We’re gonna start here,” I felt my whole body relax. And if we start with this image, if we start with just looking at an image and making sense of an image, I feel like that could be such a powerful touchstone for all the work you do from there.

Tracy Zager (27:41):

That’s core. That’s a core design principle, is that invitational access. There are no barriers to entry. There’s nothing to decode. There’s nothing formal. We’ve been learning from Dan for years about this, right? Of starting with the informal and then eventually layering in the formal. I was in a class in Maine where they were doing an image talk and it’s these boxes of pencils. It’s a stack of boxes of pencils and they’re open and you can see there are 10 pencils in each box. And so there are five boxes of pencils each with 10 pencils in it. And then the next image is 10 boxes of pencils and each box is half full. So now it’s 10 boxes each with five. And the kids are talking and talking and then the third image, I think there are seven boxes each with 10 pencils in it. And she said, “What do you think the next picture’s gonna be?” And this girl said, “You just never know with these people!” <laugh> I dunno!”

Bethany Lockhart Johnson (28:37):

That’s kinda true. Knowing you both, it’s kinda true.

Tracy Zager (28:42):

Like if it’s seven boxes with 10 in it, one kid said, I think it’s gonna be 14 boxes of five. And other kids are like, I think it’s gonna be 10 boxes with seven. And they start talking about which of those there are and the relationships between—

Bethany Lockhart Johnson (28:58):

But they’re making sense of numbers!

Tracy Zager (28:59):

Totally. So all the kids felt invited. They can offer something up. They’re noticing and wondering about that image. They’re talking about it in whatever informal language or home language that they speak. And that was core to us. That was a huge priority, because honestly, one of the motivations to talk about fluency is that it’s always been this gatekeeper. It has served to keep kids out of meaningful math. Particularly kids from marginalized or historically excluded communities. So they’re back at the round table, doing Mad Minutes, while the more advantaged kids are getting to do rich problem solving. And so, we thought, what if we could teach fact fluency through rich problem solving that everybody could access? That was like square one for us.

Bethany Lockhart Johnson (29:45):

That’s huge.

Dan Meyer (29:46):

That’s great to hear. What’s been helpful for me is to understand that students who are automatic, that’s just kind of what’s on the surface of things. And that below that might be some really robust kind of foundation or scaffolding that bleeds to a larger building being built, or it might be just really rickety and not offer a sturdy place to build farther up. It’s been really exciting to hear that. I wonder if you’d comment for a moment about, in the digital age and—I’m at Desmos and our sponsors are Amplify and we all work in the digital world quite a bit. There are a lot of what report to be solutions to the fluency issue, to developing fluency in the digital world. Just lots and lots of them. Some that are quite well used, others that are just like X, Y, or Z app on the market. You can find something. Do you have perspectives on these kinds of digital fluency building apps? Like, what about them works or doesn’t work? Let us know. Graham, how about you? And then Tracy, I’d love to hear your thoughts too.

Graham Fletcher (30:47):

Yeah, I think that’s a great question, ’cause there’s a lot of shiny bells and whistles out there right now that can really excite a lot of teachers. But I always come back to what works for me as a classroom teacher is probably gonna work in a digital world as well. So what are the things that I love and honor most about being in front of students, and how can I capture that in that virtual world? I think one of the things that really helps students make connections is coherence. I think coherence, especially when you leave students for—you don’t get to talk with them after the lesson is done—so I think about how we can purposefully sequence things through a day-to-day basis. I think coherence is something that gets really lost when we talk about fluency, especially with whether it be digital or whether it be print, because what ends up happening is we say, “OK, we have all these strategies we need to teach,” and it becomes a checklist. So how is it that we can just provide students the opportunity to play around in a space, whether it be digital or in person, but in a meaningful way that allows them the time and the space and that area to breathe and think, but be coherent. And connecting those lessons along the way. And I think coherence is one thing that a lot of the times it’s harder to—when we’re in the weeds, it’s so hard and difficult to zoom back out and say, “Do all these lessons connect? How do they intentionally connect? And how do they purposefully connect?” And without coherence, everything’s kind of broken down into that granular level. So when looking at—I think about Desmos and I think about the Toolkit and I think about how Tracy and I talked a lot about, “Well, this, does it connect with the context problem, does it connect with the image talk, or the lessons? Like, how does it all connect and how are we providing students an opportunity to make connections between the day-to-day instruction and lessons that we tackle?”

Tracy Zager (32:44):

I’m reminded of a conversation that Dan, you and I had a long time ago, in Portland, Maine, in a bar. I’ll just be honest. <laugh> And we were talking about how, in the earlier days of Desmos, you were stressed out by what you saw, which was kids one-on-one, on a device, in a silent room. And you were like, no, this is not it. This is not what technology is here to serve. We can do so many things better using technology appropriately, but we can’t lose talk and we can’t lose relationships and we can’t lose formative assessment and teachers listening to kids and kids listening to each other and helping each other understand their thinking. Right? So when I think about the tech that’s out there for fact fluency, most of it is gonna violate all rules I have around time testing. So that a whole bunch of it, I would just toss on that premise. They’re really no different than flashcards. It’s just flashcards set in junkyard heaps. Or, you know, underground caverns. Or with a volcano or whatever. It’s the same thing. There are some lovely visuals—I’m thinking of Berkeley Everett’s Math Flips. Those are really pretty. Mathigon has some really nice stuff that’s digital. And I think that those resources invite you to kind of ponder and notice things and talk about them. All the tools that we design in the toolkit are designed to get people talking to each other, and give teachers opportunities to pull alongside kids and listen in and understand where they are. For example, our games, we didn’t design the games to be played digitally, even though you could, and people did during COVID, because we want kids on the rug, next to each other, on their knees; I’ve seen kids like across tables. I was in a school recently where a kid was like, “I hope you believe in God, ’cause you’re going…!” You know what I mean? <laugh>. Like they’re all pumped up.

Bethany Lockhart Johnson (34:41):

They’re invested!

Tracy Zager (34:45):

They’re psyching each other up and down and they’re interacting and it’s social and the teacher’s walking around and she’s listening to the games. And they don’t actually need any bells and whistles. They need dice and they need counters and they need this game that is actually a game. In all of our conversations, games have to actually be games. Games cannot be “roll and record.” Games have to involve strategy. They have to be fun. So in designing those games, we didn’t feel like it brought any advantage to make that a digital platform. But things that did bring advantages digitally, like the ability to project these beautiful images or to use short video in the classroom, that really was a value-add that enabled us to do something different in math class than we had done before, and to get kids talking in a different way than they ever had before. When I think about fluency, historically, if you say like, “OK, it’s time to practice our math facts,” you hear a lot of groans. And when I see a Building Fact Fluency classroom and I say, “OK, it’s BFF time!” There’s like a “YEAAAAHHH!” You know? And so that’s what we’re after.

Graham Fletcher (35:47):

It’s all about kids, really, for us. And I think at the heart of it, we made all the decisions with teachers and kids at the forefront of it.

Tracy Zager (35:55):

I know of high schoolers who are newcomers, who have experienced very little formal education, and speak in other languages, are using it as high schoolers, because it involves language and math and all the deep work in the properties and it’s accessible, but it’s also not at all condescending or patronizing. Like we designed it to be appropriate for older kids. So that’s just something that I think we’re both really proud of. One thing we thought a lot about, especially in the multiplication-division kit is how a classroom teacher could use it and a coordinating educator in EL, Title, special education, intervention could also use it because there’s so much in it, that students could get to be experts, if they got extra time in it, using something that’s related and would give them additional practice. So they could play a game a little bit earlier than the rest of the classes. And they could come in already knowing about that game, or they could do a related task. We have all these optional tasks that no classroom teacher would ever have time to teach it all. So the special educator could use it and have kids doing a Same and Different or a True/False, or some of the optional games. And then the work in both special education and general education could connect.

Dan Meyer (37:20):

I just wanna say that this is an area that for so many students, as you’ve said, Tracy, it presents a barrier for their inclusion in mathematics. It’s a very emotionally fraught area of mathematics. And we really appreciate the wisdom you brought here. And just the care you’ve brought to the product itself. Your knowledge of teaching, knowledge of math, and yeah, especially a love for students feels like it’s really infused throughout Building Fact Fluency. If our listeners want to know more outside of this podcast, outside of the product itself, where can they find your words, your voice? Where you folks at these days? Tell ’em, Graham would you?

Graham Fletcher (37:57):

You can find us at Stenhouse, Building Fact Fluency. And then Tracy and I, currently playing around, sharing ideas a lot on Twitter, under the hashtag #BuildingFactFluency. That’s kind of where we can all come together and share ideas. And then also on the Facebook community, where there’s lots of teachers sharing ideas.

Bethany Lockhart Johnson (38:19):

If you were to ask our listeners like, “Hey, if you wanna keep thinking about this, here’s something you could try or here’s something you could go do,” what could be a challenge that we could share that could help us continue this conversation?

Graham Fletcher (38:35):

Online you can actually download a full lesson string. And a lesson string is a series of activities and resources that are purposefully connected. You can pick one or two of those from the Stenhouse web site, Building Fact Fluency. You can try the game. You can try one of those strategy-based games. You can try an image talk and just see how it goes. And just share and reflect back, whether on Twitter or on Facebook. But it’s kind of there, if you wanna give it a whirl. And as Tracy was sharing, even if you’re a middle-school teacher or a high-school teacher, we really tried to think about those middle-school and high-school students keeping it grade level-agnostic. Just so every student has those opportunities for those mathematical conversations. So download a lesson string and give it a whirl, and we’d love to hear how it goes.

Dan Meyer (39:25):

Bethany and I will be working the same challenge with people in our life.

Bethany Lockhart Johnson (39:29):

Yes.

Dan Meyer (39:29):

Enjoying some fact fluency with people in our homes, perhaps. We’ll see. And we’ll be sharing the results in the Math Teacher Lounge Facebook group. Graham and Tracy, thanks so much for being here. It was such a treat to chat with you both.

Bethany Lockhart Johnson (39:42):

I love learning with you and just helping to shift this idea of fluency into something that can be accessible and powerful and positive.

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What Valerie Henry says about math

“A lot of very fluent adults don’t always have every fact memorized. ”

– Val Henry

Meet the guests

Valerie Henry has been a math educator since 1986. She taught middle school math for 17 years and has worked as a lecturer at University of California Irvine since 2002. After doing her 2004 dissertation research on addition/subtraction fluency in first grade, Valerie created FactsWise, a daily mini-lesson approach that simultaneously develops  fluency,  number sense, and algebraic thinking. Additionally, she has provided curriculum and math professional development for K-12 teachers throughout her career, working with individual schools, districts, county offices of education, Illustrative Mathematics, the SBAC Digital Library, and the UCI Math Project.

Graham Fletcher has served in education as a classroom teacher, a math coach, and currently as a math specialist. He is continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary mathematics. He is the author of Building Fact Fluency and openly shares many of his resources at gfletchy.com. Follow him on Twitter.

Tracy Johnston Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of the Building Fact Fluency toolkits and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books by teachers, for teachers at Stenhouse Publishers. Follow her on Facebook.

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About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

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The power of high-quality math assessments

Two women sit at a table looking at an open book together; one woman points at the page as they both smile, engaging in innovative teaching practices for effective literacy instruction.

When students learn math, it’s crucial for them to understand not only right and wrong, but why and how. The same is true of math assessments.

High-quality, asset-based math assessments can show you how each student thinks, where their strengths lie, and what their next learning step should be.

And we need them now more than ever. Math scores have hit their lowest point since 2005, with nearly half of high school seniors scoring below “basic” achievement in 2024. This moment presents our biggest opportunity yet to transform K–12 math assessments.

Keep reading to explore how asset-based assessments help all students succeed—by starting with their strengths.

K–12 math assessments: True or false

Let’s establish some facts about math assessment first:

True or false: Math assessments can tell you only “right” or “wrong.”

False. Asset-based assessments go way beyond simple correct/incorrect scoring, showing you how students work through problems to give you insight into their thinking and what they already know. This provides a much clearer path for next steps.

True or false: Understanding student thinking is the key to improved student performance.

True. The path to math proficiency requires more than just benchmark scores. The better you understand how your students think, the better you can support their growth. When assessments recognize students’ individual strengths and strategies, the data becomes more helpful and complete.

The good news? We don’t have to throw out everything we’re doing, but we do need to enhance it. The current achievement trends aren’t telling us to stop what we’re doing. They’re telling us to do even better.

What high-quality math assessments actually look like

So what makes a math assessment truly powerful? Here are the key ingredients:

They show student thinking. Great assessments don’t just capture right and wrong answers—they reveal the “why” behind student responses. You get to see the logic, the creativity, and the problem-solving strategies each student brings to math. This visibility helps you understand not just what students know, but how they know it.

They welcome different approaches. There’s rarely just one way to solve a math problem. Quality assessments celebrate multiple solution paths and help you understand how each student’s mind works. This flexibility creates more opportunities for students to demonstrate their mathematical understanding.

They work for all learners. Research shows that 3–7% of students experience dyscalculia, meaning that they process numbers differently. The best assessments are designed so every student can show what they really know about math concepts, regardless of how their brain processes numerical information.

They connect to real life. When math problems relate to students’ actual experiences, engagement soars and understanding deepens. Students see math as relevant and useful, not just something they have to endure.

They guide your next teaching move. Instead of functioning like traditional summative assessments that just give you a grade, high-quality assessments tell you exactly what to teach next. They transform assessment from a final judgment into a roadmap for growth.

How asset-based assessment approaches change the game

Here’s where things get really exciting. What if your assessments started by looking for what students can do, instead of what they can’t?

That’s asset-based assessment. And it can change everything.

This approach recognizes that every student walks into your classroom with mathematical knowledge. Even the student who “hates math” or “isn’t good with numbers” has mathematical thinking waiting to be discovered and built upon.

Asset-based assessment strategies help you spot the sophisticated reasoning your students already have, even when they don’t use formal math language yet. Instead of starting with gaps, you start with strengths; instead of deficit thinking, you build from abundance.

When you weave asset-based approaches into your assessment practice through formative assessment lessons, magic happens. Students feel more confident. Their mathematical identities grow stronger. And you get clearer insights into how to help each learner thrive. Perhaps most importantly, these approaches help close achievement gaps by ensuring every student’s mathematical contributions are valued and developed.

The data tells a clear story: Our students need assessment approaches that match not just their current performance, but their true potential.

More to explore

Ready to unlock the full potential of your math assessments? We’ve put together everything you need in our Math Assessment Power Pack, featuring practical tools, proven strategies, and ready-to-use resources that’ll make it simple and easy to enhance your assessments.

S5-01. Investigating math anxiety in the classroom

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Season 5 is here! This season, we’ll be talking all about math anxiety: what it is, what causes it, and what we can do to prevent or ease this anxiety in the math classroom. To launch this very important theme, we sat down with Dr. Gerardo Ramirez, associate professor of educational psychology at Ball State University.
 
As someone who’s been studying math anxiety for more than a decade, he had some interesting research and advice to share on why math anxiety affects so many students (and adults), and tips for how to start reducing it.
 
Listen now and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!
 
Enjoy this episode and explore more from Math Teacher Lounge by visiting our main page.

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Dan Meyer (00:01):
Hey, folks. Welcome back to Math Teacher Lounge. I’m one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:05):
And I am your other host. I’m Bethany Lockhart Johnson. Season five! Hello!

Dan Meyer (00:11):
Bethany, how are you doing? How have you been spending the long break between our recording sessions?

Bethany Lockhart Johnson (00:16):
As much as I loved sharing content from previous seasons, I am so thrilled that we’re back for season five. I have been, you know, chasing a toddler. I think he’s already tired of me saying, “Ooh, can we count that?” He’s like [sighs] “One two, one two.” Like, he’s done already.

Dan Meyer (00:36):
Too much counting. Yeah, I worry about that so much, that my love of mathematics might be perceived by my kids as smothering. Yeah, I worry about the same. We shared with you folks some bangers of reruns, in my humble opinion. Some great guests. But, we’ve been excited—me and Bethany—to hop back on the mics, on the ones and twos, and explore some new ideas together.

Bethany Lockhart Johnson (01:01):
Well, I loved our season talking about joy in mathematics. And personally I could…like, we could turn this whole podcast into joy in mathematics. However, we’re kind of going a different route. Because if you ask folks why they don’t feel joy in mathematics, a lot of times at the root of that is some really intense math anxiety. So this whole season, we’re going to be delving into math anxiety. Exploring what it is, who has it, why do we think it happens, what do we think we can do about it, and how can we navigate through it, so that we can experience that joy in math? These are questions that we’re gonna explore over the course of the season. Dan Meyer, how do you feel about that?

Dan Meyer (01:49):
It feels big and it feels personal. I mean, as we shared in our math stories back from season…whatever it was, math anxiety was a huge part.

Bethany Lockhart Johnson (01:59):
It was last season, Dan.

Dan Meyer (02:00):
Last…? I mean, who can remember? Big part of your journey. I’ve had some very punctuated but intense moments of anxiety in math class. And socially, we have built math up to be this incredibly powerful thing. You know, restricting movement on economic ladders, preventing people from getting into careers they want. Whether or not they have much to do with math class, math anxiety is a really large part of educational but also social life. And yeah, I’m really excited to explore it with you. We’re bringing on some really excellent guests. Some researchers, yes. But not just researchers! Also people who practice in the field and know firsthand what it looks like to resolve issues of anxiety with students.

Bethany Lockhart Johnson (02:45):
Yeah, you’re right, Dan. My math story contained quite a bit of math anxiety, so I am particularly invested in this season. I mean, I still navigate math anxiety. And, you know, many of us do, and let’s talk about it. And let’s—I love that you reminded me. We’re gonna have a lot of great researchers all throughout the season, and a lot of times folks feel like the research happening, there’s sometimes a gap between researchers and what’s actually happening in the classroom. Not in all cases, but a lot of times. Right? And I remember a lot of conversation about the latest research when I was in grad school, but unless you’re actively studying something, sometimes we don’t know what’s happening. Right? We’re really focused on what’s happening right in front of us in our classroom. So let’s take some of that research; let’s break it down; let’s talk to some of the folks who are thinking about this for the bulk of their day, right?

Dan Meyer (03:41):
Yep. So we got our first guest coming up in a moment here.

Bethany Lockhart Johnson (03:45):
So to kick off this season, we’re starting episode one by talking to Dr. Gerardo Ramirez, Associate Professor of Educational Psychology at Ball State University. And he’s been researching math anxiety for more than a decade. He’s worked with so many amazing folks in the field. He’s worked with students, he’s worked with teachers, with educators…I’m just so excited to talk to him. If you look up math anxiety, you see his name as one of the folks who is really thinking about this at so many different angles, and we get to talk to him. So enjoy our conversation with Dr. Gerardo Ramirez.

Dan Meyer (04:29):
We are so excited to have Dr. Gerardo Ramirez on the show with us. Dr. Ramirez is an Associate Professor of Educational Psychology at Ball State University. Thanks so much for joining us.

Dr. Gerardo Ramirez (04:40):
Yeah, thank you for inviting me to talk about math anxiety.

Bethany Lockhart Johnson (04:43):
So with your interview, Dr. Ramirez, we are actually launching the season. We’re gonna be talking about all different aspects of math anxiety, and it feels pretty perfect that you are first guest of the season, because of the sheer breadth of research and conversations you’ve had about math anxiety. Could you start us off kind of telling us a story of how did you get interested in studying math anxiety? Or why, you know, why did you dive into this topic that, you know, I think a lot of folks might…like, if you’re on a plane, and you say, “Oh, I study math anxiety,” what kind of reaction are you gonna get?

Dr. Gerardo Ramirez (05:24):
Oh, sure. Yeah. I think most people are actually very interested because they all have their own story about feeling anxious about math, or just being anxious about evaluation situations that involve math. And, yeah, they wanna share those stories. People feel quite comfortable talking about their anxiety about math, for some reason. But for me, I started off, when I was in undergrad, I was studying to take the GRE quiz. I was hoping to go into a psych program. But I wasn’t exactly sure what direction yet. As I took some of the practice tests, there’s some situations in which I was very nervous about taking the practice test. And I just noticed that I did really poorly on some of these exams. And so I became very interested in issues like choking under pressure, which means when you underperform relative to what you expected to perform. And so, as I was researching these issues, I started to come across this whole field of math anxiety. And I saw that while there are some people who choke under pressure during tests, there are other people who just have a strong general fear of mathematics.

Dan Meyer (06:29):
That’s really helpful. I can imagine you’re doing a lot of free psychology sessions, free therapy for people on airplanes when they bring to you their own stories of math. So let’s thank you for your service in that sense. I’m super-curious. So Bethany and I have both taught math. We both have seen firsthand what it looks like when a student is anxious in math class, though maybe we don’t have kind of the clinical language to describe it. And I’m curious, from a clinical sense, how do we define math anxiety?

Dr. Gerardo Ramirez (06:57):
Sure. So first off, math anxiety is not something that you would find in the DSM, for instance. But we generally define that as a fear or apprehension to situations that involve math. So it doesn’t have to necessarily be educational situations. It could be someone asks you a math-related question during a party, or you have to calculate the tip at a restaurant, for instance. It doesn’t have to be about schooling situations, although that’s obviously where it seems to matter a lot for many people. So it is basically a fear or apprehension to situations that involve math. And I think distinguishing the term “fear” from “anxiety” is really important here. A lot of times people use those terms interchangeably, and the term “fear” is obviously within our definition of math anxiety. But oftentimes what differentiates anxiety from fear is that, anxiety is—think of it like a recipe. Anxiety is fear plus a little bit of unknown. OK? So if, for instance, if you hated snakes, and they threw a snake at you, you’d be in intense fear. Whereas if you hated snakes and they said, “There is a snake in the room, but I’m not gonna tell you where,” that’s gonna cause anxiety. And so the reason why we call it math anxiety is because a lot of times people experience this fear for a possible unknown future that involves math or possible unknown evaluations that people might have about your competence, because of math. And so for a lot of kids, they feel anxious about how they’re gonna do on a test or whether they’re gonna be able to pass a class or whether they’ll be able to understand what you’re saying in your lessons, for instance. And so the anxiety component really gets at fear of something that’s unknown, but related to mathematics situations.

Dan Meyer (08:47):
Math is somewhere in the ceiling right now. Perhaps I might be surprised with a math situation!

Dr. Gerardo Ramirez (08:52):
Yeah. yep.

Dan Meyer (08:52):
So I have this tendency to assume that every other subject that we teach has it better and easier than math does. It’s not true. I know this is not true. But I’m kind of curious here. Is math anxiety, like, part of a general just set of anxiety around schooling itself? Like, is there a reading anxiety, a writing anxiety, and does that all just flow from the same kind of fount of anxiety around schooling or situations about learning? And what makes math special in this regard? If it is its own special anxiety, for instance?

Dr. Gerardo Ramirez (09:27):
There are different…so some people obviously suffer from generalized anxiety. Right? And so they would, you know, feel anxious both for evaluative and non-evaluative situations. But in the research that we’ve done and that other people have done, there are differences between things like reading anxiety, math anxiety; I’ve also studied spatial and creativity anxiety. A lot of times what we’re trying to do in these studies is we measure all of the above, and we try to show that, look, math anxiety predicts math situations above and beyond these other things. So yeah, we definitely distinguish those things. And so what’s special about math is that, well, I think the symbolic nature is a big part of it. The abstract symbolic nature is just not as tangible to students. They can’t touch it. And so it doesn’t allow ’em to use their full cognitive faculties to play with it, as you might see, for instance, in science. Or it doesn’t allow people to relate math to their own interests the way you might see, for instance, in English. So maybe I hate reading novels, but I’m interested in zombies and you give me a book on zombies, well, ok, great, you’ve connected my personal assets to the topic. Whereas with math, either that’s harder to do or instructors don’t do such a good job of setting that connection up.

Bethany Lockhart Johnson (10:46):
Also, I think, you know, I’ve heard of students being really anxious, let’s say, during a reading session, when teachers used to do—hopefully they’re still not doing it—the popcorn reading, where you just randomly call on a student to read out a sentence. Right? But you don’t really hear students or adults talking about, “Oh, no, no, no, I don’t read; I don’t mess with reading.” You know? Whereas with math, you do hear, “Oh, I’m not a math person. Oh no, no, no, don’t ask me any math questions.” And that is such a distinction.

Dr. Gerardo Ramirez (11:18):
Yeah. And I think a lot of that’s because it’s just so common. As an adult, to be nervous about reading is kind of an uncommon thing. So people feel a stigma around admitting that. But math is something that everyone feels like they’re inadequate in. And so there’s a lot of comfort in telling you how they’re just one of the many people who don’t like math. And that, you know, can have a lot of different consequences and outcomes. I think on the one hand, I think for a lot of kids it becomes a normalized message that if you fear math, that’s OK, join the club. Right? But we have to be careful about that, ’cause a lot of math anxiety researchers will oftentimes say, part of what leads to math anxiety is adults normalizing that it’s OK to be scared of math. So I think a lot of times adults, teachers, for instance, math teachers, they’ll tell kids, “You know, if you’re scared, that’s OK.” And so a lot of the math anxiety community says, “No, no, no, you’re not supposed to do that.” But my recent view is different. I view that as a form of validation. Because math is hard. And so telling kids, “Hey, look, it’s actually easy if you just try,” I don’t think that’s true. It’s actually just hard. And I think even if it was easy, to the kid, it feels hard! And I think something that’s not really well-studied right now in our field is the value of validating people’s math negative math experiences. We don’t want to validate that, ’cause we think that we’re gonna reinforce that. But actually, I think the opposite. I think when you validate people’s negative math experiences, it helps ’em to feel that they can handle it. They can start to take control over their own emotions.

Bethany Lockhart Johnson (12:52):
I love that. And I, I actually, I think that’s so powerful, what you’re talking about, that validation. I taught kindergarten, and I vividly remember being in a parent-teacher conference and that parent saying, “Oh, I wasn’t a math person either,” right? Or, you know, their language and their experience with their own math schooling, their anxiety about math was actually impacting their students’ experience of math. Or the conversation that, when I would go to talk about a math assessment, let’s say, you could see the parent actually tensing up. And there was this moment of validation, that I felt like we needed to make space for that in the conversation with the parents, right?

Dr. Gerardo Ramirez (13:38):
Yeah.

Bethany Lockhart Johnson (13:38):
Like, this is a real thing. And we are working on teaching students that math is something that gets to—your experience with math gets to look all sorts of different ways. And it’s OK if we, you know, make a mistake, or if we kind of only get this part, but we’ve really got that part. Or let’s talk about it; let’s write about it. So I really feel like that that validation is something that’s so missing. And instead of the validation, like you said, you see folks being like, “Oh yeah, me neither. I’m not a math person either.” Right?

Dr. Gerardo Ramirez (14:10):
Yeah. I think…part of the reason why people are comfortable sharing this because they’re looking for validation also. When they say, “Oh, I’m not a math person,” you know, I think they’re hoping that, you’ll say like, “Yeah, me neither,” or “Of course not, ’cause math is terrible.” Right? They’re looking for validation, not to reinforce their perspective, but to feel that it’s OK not to be a math person. And I think that’s one of the techniques that I’m trying to work on in my research right now, is to provide evidence that actually people will work harder when you validate their math experience. You don’t have to tell them a positive story per se. If your current story is “Math is hard and I’m very, very anxious; I’m scared,” then we can just validate that and help you work through that. And it actually will strengthen our relationships. Because if you’re a student and you’re struggling with math and I tell you, “Yeah, it’s hard; it’s OK to struggle with math,” that makes you feel seen. And that’s gonna lead you to want to ask me more for help, because I’m someone who understands you. And that’s a great, you know, remediation opportunity.

Dan Meyer (15:14):
A common thread that I think I’m seeing here in several answers is that math sometimes asks students to disassociate part of themselves. Where success in math oftentimes means working from an a level of abstraction with symbols, like you said, that can feel alien. Like, who am I here? And in the same way, I love that you’re proposing we validate and reassociate people with a very deeply felt part of themselves that is anxious about mathematics.

Dr. Gerardo Ramirez (15:44):
Yeah. I mean, I think that’s what validation’s supposed to do, right? So a lot of us, when we feel these strong emotions, we wonder, “Is this even a real thing? Are other people feeling this? Is there something wrong with me?” So we feel the emotions, but we can’t actually deal with them, because we wonder if they’re legitimate. And so when someone says, like, “Yeah, this is hard,” it crystallizes that emotion. And once something is made real, you can actually choose how you want to deal with it. Some kids are gonna deal with it by staying anxious. But some people are gonna choose to deal with it by saying, “Well, there’s nothing I can do about it now; I have to take this math test, so I’m just gonna think positive.” And that’s great. If the kid can end up saying that to themselves, that’s much more effective than me telling the kid, “Hey, you just gotta think positive. You’re gonna start the test anyway.” And so we want the kid to make meaning of their experience, and the way we do that is by crystallizing their emotions through validation.

Dan Meyer (16:36):
Yeah. I love that. And so what you’re proposing there, I think, sounds like, a solution, like a post-talk solution after students are feeling anxiety.

Dr. Gerardo Ramirez (16:43):
Yes.

Dan Meyer (16:43):
To validate and empathize.

Dr. Gerardo Ramirez (16:45):
Yes.

Dan Meyer (16:45):
And over the course of our season, we hope to explore a lot about solutions to math anxiety that are preventative, that reduce the odds of anxiety arising, through instruction and curriculum, before it arises. And I’m just wondering if you’ve seen anything that would hint at either specific or general words of wisdom you wanna share with the educators, about not just addressing it after the fact, but preventing math anxiety before it arises?

Dr. Gerardo Ramirez (17:14):
To be honest, at this point, I haven’t seen enough evidence for me to recommend anything concretely as an intervention for math anxiety, or an intervention to prevent its development. All I can really do here is rely a lot on the more broad cognitive-behavioral research on anxiety, which says that one of the ways we prevent people from developing anxiety is by helping them to make more positive appraisals of challenge situations. So a lot of times, when kids are challenged, they don’t know how to interpret that. “What does it mean that I’m struggling with this thing?” And so that’s where I think a lot of teachers can help students’ interpretations of that. ‘Cause if you leave kids to their own devices, they’re gonna think, “I’m struggling because I’m stupid. I’m struggling because I’m not good enough. I’m struggling because my dad is right; I’m gonna be a failure.” You know? They’re going to impose an interpretation to a challenge situation regardless. And so, as teachers, one thing we can do is we can help shape that interpretation and say, “What does it mean to struggle with math? People will say it means you’re stupid. That’s one interpretation. What’s another one? It means that your brain is working really hard to think through something. That’s another interpretation. What’s better? What do you think is more helpful?” And then, helping students to see how interpretations matter to how you ultimately feel about something. And that’s a very metacognitive way of thinking about things. So yeah, I would say that one way to prevent it is to help students to take more positive interpretations of their experience. But another way, and I think a more successful way, I think, is to give students early experiences where they feel efficacious dealing with math. One of the ways you do that, for instance, is by obviously making sure that the students understand the material—but that’s obvious; people are trying to do that. One of my favorite recommendations is to keep reassigning assignments, the same exact assignment, for, say, three weeks, back-to-back. So if in week one you do the homework assignment, you do OK, you don’t do so great, when week two you do it, you give the exact same assignment, and now the student can see like, “Wow, OK, this was much easier.” And then, week three, you give the exact same assignment; now the kid’s feeling really confident. And the reason why that’s great is because it helps kids to see that they’re growing in confidence. A lot of times kids don’t get to see that because we’re constantly throwing new assessments at them. And so they’re never seeing that growth. All they’re seeing is a new challenge, a new challenge, a new challenge. So I think we need to set up situations where they can feel that they’re growing, when we keep the assessment static. That can be a formative assessment, for instance—doesn’t have to be a summative assessment.

Bethany Lockhart Johnson (19:55):
That feels so powerful and it feels like it really connects to that validation piece, right? We are actually helping to create a culture in our math classroom where we might struggle with something, but we keep revisiting it. And it’s not so much to reach mastery, but as Dr. Megan Franke — we talked to her about this partial understanding and about pulling on those threads of things that you do understand, so that you can build your confidence…build, not just confidence, but build your…I guess, kind of get your footing, right? You’re saying, “Well, I do understand this. I see how this works.” And if I’m revisiting an assignment, I feel like that would give me permission to like, “Hey, I don’t have to have this figured out on the first pass. You know?

Dr. Gerardo Ramirez (20:44):
Yes, yes. Yeah. I mean, I’m gonna give you a silly analogy, but I think it works. You know, a lot of times people will have nightmares, right? And they’ll keep having the same nightmare over and over again, right? And so one reason that we suspect this happens is because they haven’t worked through whatever that nightmare’s supposed to be about. So if, say, I’m scared of driving, I may be having the same dream about driving and crashing over and over. And we keep having these nightmares. And I think math anxiety is kind of like a waking nightmare, where you keep rehashing something because you haven’t had the chance to finally address that dragon. You know? And so if someone was having a lot of fear over driving, then one behavioral approach would be, you know, to work with a therapist to actually get behind the wheel and maybe drive around the same track over and over until you feel comfortable at that, and then the nightmares stop. Well, the same thing is true, I think, about math, math and math anxiety, is that you wanna give people these opportunities to feel confident by going back to that original experience that caused them to feel anxious, and saying, “This one assignment that we did in week three that really freaked you out, let’s try it again now in week five. How was that?” “Yeah, it wasn’t so bad. It was still kind of annoying.” “OK, we’ll we’ll come back to it.” “Now it’s week seven. Now let’s go back to that assignment. How is it now?” “That’s actually…it wasn’t that terrible.” And that gives people the opportunity to reflect on how they’ve grown past that nightmare.

Bethany Lockhart Johnson (22:05):
I have to say, Dan talked about you being like a therapist. I’m like, wait, “How did you know, Dr. Ramirez? I did have this recurring dream! I did! And I had to face it. No, but I had such intense math anxiety in high school and it was debilitating. And the biggest thing for me, I thought I was the only one. I thought there was something wrong with me. I thought, “Why can’t I figure this out?” There wasn’t a conversation about “Here are some tools,” or “Here are some, some, some…”. Like, “This is OK, for you to feel scared about this or overwhelmed!”

Dr. Gerardo Ramirez (22:41):
Mm-hmm. Mm-hmm.

Bethany Lockhart Johnson (22:42):
You know, I think often when we talk about how widespread math anxiety is, I think a lot of folks automatically jump to high schoolers or college students avoiding math courses. But we see this in really young kids.

Dr. Gerardo Ramirez (22:56):
Yeah. So people are…people are just constantly making meaning of themselves, regardless of the age range. And that’s true even with young kids; they are trying to figure out who they are. Right? And so one of the things you see oftentimes with young kids is you ask ’em, “What are you good at?” And they say, “Everything!” And that’s their attempt to, you know, make meaning of themselves. But sometimes they’re not good at everything. Sometimes they actually struggle in math. And I think even early on, they have to make meaning of that. They say, “Well, I’m good at everything except math.” And how do you make sense of that? Well, why not math? “Oh, because math is terrible. It’s not for everybody. You know, it’s not something that I like.” And so, yeah, in a lot of the studies that we did early on, we basically went into these first-grade classrooms with the purpose of trying to assess whether we can actually show variability in kids’ math anxiety, even early on. In other other words, do kids even report feeling anxious about math situations? Or do they tell us that they’re great at everything? And what we found was that in fact, a good chunk of kids are, again, perfectly willing to tell you that “No, certain situations involving math make me very anxious.” Counting or addition, or doing a problem on the board. And the way we do that is by—I think there are probably more sophisticated ways that can be done, but this is the best we have at this point—is we go in there and we ask them, we show them a bunch of smiley faces and anxious faces. And we say, “I want you to tell me how you feel about these different situations that involve math.” And so we say, “If you feel kind of nervous, I want you to point to this face. If you feel very nervous, point to this face.” And we basically will read to them situations. We’ll say, “How would you feel if your teacher asked you to open up your new math textbook and you saw all the numbers inside of it?” And they’ll point to the really nervous face. So right now, those are some of the more reliable assessments for math anxiety among young kids. And that work showed us that even young kids are self-reporting math anxiety.

Dan Meyer (24:51):

Obviously this is worth our study, because we would hope people would not feel anxious in general, and especially if we have a mandated…kids are mandated to be in math classes for their entire childhood. So I see the need for this study, these studies. I’m curious: What are the consequences, though? Like what, what correlates with math anxiety? What are other reasons why we should care about math anxiety and work to remediate it?

Dr. Gerardo Ramirez (25:16):
Oh, sure. So it correlates with their actual math performance. It can correlate when they choose to do homework. Right? So a lot of times, the parents report having to fight with their kids over math homework a lot. And you also oftentimes see a lot of frustration over mathematics specifically. And so it can, you know, not only affect their academic ongoing outcomes, like math tests and math assignments, but it can also affect their relationship with their parents. So if every time you come home, your dad’s screaming at you because you haven’t done your math homework, and when he asks you to solve the problem in front of them, you don’t remember, ’cause you were checked out, ’cause you’re so stressed out, that’s gonna cause a really negative experience. You know, a lot of times people grow up and they still remember their dad screaming at them over the math homework. You know, it’ll affect your relationship with your teacher. So if you’re making me feel incompetent, if you’re stressing me out, you’re not the kind of person I wanna come to for help. So it can predict relational outcomes as well as academic outcomes. And down the line, of course, when it affects students’ opportunities to get into things like AP classes, it affects students standardized test performance and their choice of colleges, as well as scholarship opportunities.

Dan Meyer (26:29):
Once you show that it correlates to performance, then that opens up a whole range of other correlations that are pretty important, it sounds like. Whether that’s career options or, you know, post-secondary education and the like.

Dr. Gerardo Ramirez (26:40):
Yeah. And a lot of times, when people are choosing a career at college, a lot of times students will make a decision specifically based on what career has less math requirements or less math courses. So I think this finding needs to be verified further. But, there’s some studies showing that, for instance, elementary ed teachers, one factor that feeds into the decision to go into elementary ed is the math requirements are very low in elementary ed. So that can…obviously it’s not what we wanna hear, because these are our first formal math teachers, right? For our kids.

Bethany Lockhart Johnson (27:16):
It feels so powerful, the impact that math anxiety can have, not only while you’re in, let’s say, elementary school, high middle school, high school, but then the impacts beyond that in terms of your career. And I shared this last season, when we talked about our personal math story, but I know when I was navigating the deepest part of my math anxiety, I really felt like, maybe this is a reason I can’t be an elementary school teacher. Because I was so worried that I wouldn’t be able…not that I wouldn’t understand the math for fourth grade, fifth grade, but that there was something about my ability to teach it or understand it or develop a love and passion for it that I wouldn’t be able to do. And I really had to reclaim it in my own way. But, you know, something that I think is so powerful about your research is just the applicability — not only to the field of mathematics, but folks’ everyday lives. And the way that you have talked in the past about math being a gatekeeper…I have a family member who, brilliant American Sign Language interpreter. I mean, amazing. Like a dance with her fingers. I could just watch it all day. And she actually didn’t complete the program because she couldn’t complete the math requirements. And I remember talking to her about like, “Well, have you gone to the free tutoring? Have you gone to, you know, this or that?” But it was a paralyzing fear, you know? So Dr. Ramirez, what do you wish educators understood about math anxiety? Or the research about math anxiety? Or maybe even the general public at large, what do you wish folks understood about math anxiety?

Dr. Gerardo Ramirez (28:58):
Oh, I think that a lot of students, they struggle with math. And I think we wanna normalize that struggle as much as possible. We want to create a culture where it’s OK to do math slow; it’s ok to take your time. And I know that’s not possible with a lot of these requirements that a lot of math teachers have to do. But I think if we want to prevent math anxiety, we have to create opportunities to tell better stories. So that’s ultimately what I tell people is, why do people develop math anxiety? Because they had experiences that challenged their competency and they told a negative story. And so making space to reflect in math classrooms about what does it mean to go slow in math, or what does it mean to make mistakes, and then helping kids to tell better stories, I think it’s really the best thing we can do as math educators. ‘Cause you know, your job is not to be a therapist ultimately. You know, there’s only so much math teachers can do. But I think one of the most powerful things we can create is setting up students’ experiences where they feel confident, and they can tell better stories, so they can have better dreams about math.

Dan Meyer (30:06):
Really appreciate this introduction to math anxiety. It’s been a fantastic kickoff to our season. Dr. Ramirez, thank you so much for joining us.

Dr. Gerardo Ramirez (30:14):
Sure. Thank you.

Dan Meyer (30:16):
Thank you folks so much for listening to that conversation with Dr. Gerardo Ramirez, Associate Professor of Educational Psychology at Ball State University.

Bethany Lockhart Johnson (30:25):
Dan, OK, if not for your frantic signaling, I would’ve probably asked another 20 questions. I need to know what you thought .

Dan Meyer (30:34):
I found it interesting at all points. And especially I think I started to understand a little bit better where the anxiety comes from for some students. I got a little bit here, which is that I think math, more than other disciplines, involves alienation. Check that word. You like that? Alienation? I’m into it. I’m feeling it. It’s like…to get good at math, to be successful in math, you gotta, as a kid, lose your attachment to the world you understand. And I mean, “got to” as in like, “you are asked to” — many times, unfortunately, by curriculum and instruction. Which is to say, you’re turning things you can hold onto into numerals. Right? You’re turning the world and its patterns that you can see and touch into Xs and Ys. And I just don’t know that other disciplines deal with that as much. Maybe I’m wrong and just guilty of, you know, “grass is always greener” syndrome here. But I think that’s an experience that kids have in math. And I thought that Dr. Ramirez got at that when he’s talking about the need to validate a student’s experience of anxiety. Like, in treating anxiety, sometimes we alienate people further by just like saying, “Oh, no, no, no, it’s just like, you need to, you know, drill yourself more, practice more,” and kind of invalidate that. So this feeling of alienation, I think permeates a lot of math instruction. I’m looking forward to learning more about that with our future episodes

Bethany Lockhart Johnson (32:00):
Alienation. That’s interesting. I definitely felt, I definitely felt isolated and alone many times in my math journey, when I was having my…you know, in high school, when I was feeling like, “Clearly everyone can look at tan, sign, cosign, and that means something to them.” Right? I think it’s really interesting, because I’m thinking about the other disciplines; I’m running through them, and I’m like, even in science, which can seem abstract, so oftentimes there’s these experiments that accompany these concepts, where you’re like, “Look at this concept made real in front of you.” Right? . And so yeah, that’s really interesting.

Dan Meyer (32:39):
You’re always one step away from blowing something up! Or, you know, dissecting something that’s tangible to you.

Bethany Lockhart Johnson (32:46):
Yeah. That’s really interesting. I did really love how he brought up the abstract. And how, I think, even validating it…he talked so much about validation. Which to me was like, YES. If somebody just said, “Hey, it’s not only possible to have math anxiety, but it also doesn’t mean that you don’t belong here.” If somebody had said that, it would’ve literally changed the trajectory, you know? And I wonder what those conversations could look like in our classrooms, where teachers celebrate that. Like, WHOA, this is a new way to think of this. This is a new way. Asking how many, or what do you notice for this image, through a mathematical lens, or looking…we talked to Alison Hintz and Antony Smith, like mathematizing books, like looking through these lenses — it’s an invitation to step into this other world, right? But there’s not only one way to do it. And I think oftentimes it’s like that anxiety of “Am I gonna say the right thing?” or “Am I gonna notice the right thing?” Right? How do we create that space more, where there’s so many possibilities and we want kiddos to notice what they notice, right?

Dan Meyer (33:54):
You gotta become a certain kind of person to be successful in math class. I feel like is part of the implied deal. Where you’ve gotta—like how you said—say a certain thing or think about a certain thing a certain kind of way. You’re trying to become someone who is not necessarily you. Which I think is fundamentally an experience of alienation, separating you from important parts of yourself.

Bethany Lockhart Johnson (34:19):
I will never, ever dive into mathematics on the scale and level that you have with your PhD. You understand math in a way that my brain just…I won’t get there, right? And yet I’m allowed to call myself a mathematician, with all of my deep dives in elementary math and my love of early numeracy and thinking about how we start thinking about counting and numbers. Right? It’s like, if we make more space for what mathematicians can look like, and what is your personal relationship with math…I mean, that to me feels really exciting. ‘Cause I think we both have something to offer each other.

Dan Meyer (35:03):
I think I have never found early math more interesting than when I talk to early math educators. And learn just like all the different ways that students come to understand a concept that I had thought was simple. Like addition of whole numbers. Whoa! There’s a lot of ways kids do that work, and their brains think those thoughts. And, yeah. That’s a good word there you’re offering us and our listeners.

Bethany Lockhart Johnson (35:27):
Yeah. Yeah. I’m really excited about this season. I think there’s — again, there’s no way we’re gonna cover all facets of math anxiety. But I think having the chance to explore it over the course of a season is going to be really fascinating. And really, I hope, destigmatize it and open up the conversation for our listeners. And, you know, if you listeners…we wanna know what you thought of this episode. Do you have any particular questions? Do you have questions related to math anxiety? Questions related to this episode? We are in development for this season, so we’re gonna do our best to get those questions answered. You can keep in touch with us in our Facebook discussion group, Math Teacher Lounge Community, and on Twitter at MTLshow.

Dan Meyer (36:14):
Next time, we’re gonna go deeper into the causes and consequences of math anxiety.

Dr. Erin Maloney (36:20):
It’s not just the case that people who are bad at math are anxious about it. It’s actually that the anxiety itself can cause you to do worse in math. And that for me is really exciting, ’cause it means that if we can change your mindset, then we can really set you on a path with several more options available to you.

Dan Meyer (36:41):
Til next time folks,

Bethany Lockhart Johnson (36:41):
Bye.

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What Dr. Gerardo Ramirez says about math

“A lot of students struggle with math, and we want to normalize that struggle as much as possible. We have to find opportunities to tell better stories and reflect on our experiences.”

– Dr. Gerardo Ramirez

Associate Professor of Educational Psychology, Ball State University

Meet the guest

Dr. Gerardo Ramirez obtained his Ph.D. from the University of Chicago, where he studied the  role of teachers and parents in shaping the math attitudes of their students, as well as reappraisal techniques to help students cope with anxiety during testing situations.

Dr. Ramirez is currently an associate professor at Ball State, where he examines the role of frustration, empathy, and cultural capital in shaping students’ success and persistence.

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About Math Teacher Lounge

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

S5-04. Coaching tips for managing math anxiety in teachers

A blue graphic with text reading "Math Teacher Lounge" in multicolored letters and "Amplify." at the bottom, with abstract geometric shapes and lines as decoration.

So far this season, we’ve investigated math anxiety in students and its causes with passionate researchers and curriculum experts, including one from Sesame Workshop! Now we hear from Dr. Heidi Sabnani, consultant, coach, and co-host of Math 4 All, as she gives us research-based tips for teachers who are facing math anxiety themselves! Listen as we discuss Heidi’s own math anxiety and journey through math, the effects teacher math anxiety can have on instruction, and practices educators can implement right away for overcoming math anxiety.

Listen today and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!

Download Transcript

Dr. Heidi Sabnani (00:00):

Coaching is the opportunity to provide that just-in-time kind of professional development for teachers, if we go at it in a slightly different way.

Dan Meyer (00:10):

Hey folks, welcome back to Math Teacher Lounge. I’m your host, Dan Meyer.

Bethany Lockhart Johnson (00:14):

And I’m Bethany Lockhart Johnson.

Dan Meyer (00:16):

Bethany, how are you doing, and how are you feeling about our current trajectory through this exploration of math anxiety?

Bethany Lockhart Johnson (00:24):

Dan, I gotta tell you — let me make it about me for a second. <laugh>.

Dan Meyer (00:29):

Go. Do it.

Bethany Lockhart Johnson (00:30):

If only I had known that so many other people experienced math anxiety, and I wasn’t the only one. I mean, I’ve said it before, but you know, I hope that this series so far is helping to reframe math anxiety for folks who maybe have a narrow definition of it … and I guess expand, reframe. And also, for those folks who are working with students who have math anxiety, or who they themselves have experienced math anxiety, I hope they’ve found some tools, some resources. Right? Like, “Yes!”

Dan Meyer (01:04):

Yes! Same.

New Speaker (01:06):

And what about you? How are you feeling?

Dan Meyer (01:08):

Yeah, I hope this has been cathartic for all of our listeners who have experienced math anxiety, and not re-traumatizing, that there are lots of people who feel this way about math in particular. And that it’s so well-experienced, so broadly experienced, that people have decided to study it a whole bunch. Which is great. And now we’re moving into our kind of solutioning. You know, in my relationships, I’m sometimes told that I rush too quickly to solutions before trying to understand what’s going on. So I’ve loved our episodes that have been about what is going on. And now, with Dr. Truglio last episode and our guest today, we’re moving more into some solutions, which I’m excited about.

Bethany Lockhart Johnson (01:49):

I don’t know, Dan, I think next time I see you I’m gonna bring a list of some concerns or worries I have, and I would love if you just get right to the solution. I’m actually OK with that.

Dan Meyer (02:01):

All right. Good to know. Good to know. I’ll say I am coming off of a day where I was feeling some teacher anxiety today, because I taught really real students. So just to let you know where I’m coming from here. I taught some seventh grade students at Montera Middle, here in Oakland Unified School District. Taught ’em a lesson outta the Desmos curriculum. And it was one of those lessons where some thorny stuff comes up. I’m talking students who are wrong for smart reasons, who are right for the wrong reasons, and their minds are working so hard trying to figure out inequalities. And I’m like trying to just step into that process as an educator with some curriculum and help shape those ideas. But it’s just … I don’t know, you want it to be as easy as like, “let me just show you how it’s done a few times, and now you got it.” But whew, some of these ideas, they take a long time to form up and they’re really easily reshaped by lots of stuff going on. So that’s where I’m at, anxiety-wise, right now. The teacher anxiety stuff.

Bethany Lockhart Johnson (03:04):

I think there’s probably plenty of teachers who do kind of just say, this is how you do it. And so, from what I have seen of your teaching and what I know of the Desmos curriculum, it is such an opportunity to think hard about the things that we are assuming about our students, assuming about what we know about the math itself. And yeah, that requires some thought.

Dan Meyer (03:30):

Yeah, for sure. I came in ready, like, “When you multiply both sides of an inequality by a negative, this sign flips around.” And I could just say that to kids and say, “Hey, remember that! Write that down!” And a lot of them would do it really well, you know, provided the assessment problems looked like ones we’ve gone over in class. And they’re also learning — in addition to that math, they’re learning that math is a giant sack of tricks they gotta memorize, right? So there’s just these pros and cons. And at the end of the one period I’m gonna teach this week, I was like, “Well, your teacher’s gonna go over that tomorrow, when they’re with you instead of me.” So it felt a bit like I copped out on that one. And I’m just in in my feelings about that right now. And I’m gonna try to come on down here and be present in the math-anxiety world.

Bethany Lockhart Johnson (04:25):

I appreciate you sharing that, Dan. And I think … I have a feeling that you could write a pretty catchy rhyme to allow the students to flip and <starting to rap> “multiply by negative. and dit-dit-dit-dit.” Can you feel it? You picking up that beat?

Dan Meyer (04:40):

Ooh, yeah. A nice little beat. Uh-huh. Yup.

Bethany Lockhart Johnson (04:41):

Yeah. You know, you could come up with something pretty clever, and yet you did not lean on your wordsmithing skills. You said, “No, let us dive in.” So what are you gonna do with this lesson, by the way? What happens now? You popped in for one period, and then what happens?

Dan Meyer (05:03):

Yeah. So this is gonna be a blast. I hope you folks tune in. We’re gonna actually release the footage of me teaching this lesson live. You know, it’ll be replayed live. And on top of that, a couple of my favorite teacher coaches and just smart people about teaching are going to be giving commentary. They are gonna be giving the director’s commentary, the sports announcers’ commentary on what they’re seeing. I beg for their generosity in their commentary. But I think it’ll be a lot of fun. I’ve never seen anything like this before, a commentary track on top of a teaching lesson, in this way. So I’m just gonna gonna be excited to see what they noticed that I didn’t, what they might have done, the thoughts they might have. Maybe I’ll do a post-game interview, you know.

Bethany Lockhart Johnson (05:50):

Ooh, yes!

Dan Meyer (05:50):

With my towel around my neck, <laugh> looking all sweaty.

Bethany Lockhart Johnson (05:54):

Ready, set, grow!

Dan Meyer (05:55):

Like, “Yup, we gave it all out there, you know, just a real team effort.” You know, that kind of thing. We’ll see how that goes.

Bethany Lockhart Johnson (06:02):

I actually love that idea. I love that it’s not just this one random lesson that just kind of floats out there, and it’s about, you walk away with whatever feelings you have, and the students obviously walk away, but that this is gonna help other educators.

Dan Meyer (06:17):

Yeah. Yeah. We’ll multiply my anxiety and make it more people’s anxiety. We’ll see how that goes. So stay tuned on the Math Teacher Lounge feed for that. All right?

Bethany Lockhart Johnson (06:25):

All right! And speaking of anxiety, Dan Meyer, we gotta get to today’s show. You know, last time we had some amazing strategies for helping students from Dr. Truglio from Sesame Workshop. I gotta tell you, I sent that episode to so many of my friends, like, “Listen to these ideas!” and have had some interesting follow-up conversations. And we would love to hear what you think about this season so far, at MTLShow on Twitter or in our Facebook group, Math Teacher Lounge. So today, we’re gonna focus on strategies for supporting teachers.

Dan Meyer (07:00):

Yes. Which is why we’re so excited to bring to you folks Heidi Sabnani, who — we’ve had researchers. We’ve had Sesame Workshoppers. And Heidi Sabnani has been a classroom teacher; she’s teacher-consultant; newly minted doctoral degree holder. We’re so pumped to bring to you folks: Heidi Sabnani.

Bethany Lockhart Johnson (07:25):

Dr. Sabnani, thank you for being here. Can we call you Dr. Heidi? What would you. …

Dr. Heidi Sabnani (07:31):

You can just call me Heidi. Yeah. Heidi is good.

Dan Meyer (07:36):

Right on.

Bethany Lockhart Johnson (07:36):

  1. Heidi, thank you for joining us in the Lounge. We’re so excited to talk with you.

Dr. Heidi Sabnani (07:41):

I am super-honored to be here. It’s really exciting and I just really appreciate the opportunity.

Bethany Lockhart Johnson (07:47):

I will say I don’t have a PhD, although the two people I’m talking with right now, both do, and you’re both like holding up your degrees as we speak and saying, “Wah-wah.” But I imagine that if I did, I’d wanna throw that doctor in more frequently, so.

Dr. Heidi Sabnani (08:02):

Well—

Bethany Lockhart Johnson (08:03):

If I sneak in a “Doctor,” Heidi, it’s only out of respect.

Dr. Heidi Sabnani (08:05):

  1. I appreciate it.

Bethany Lockhart Johnson (08:07):

Dan makes me call him Dr. Meyer all the time.

Dan Meyer (08:10):

You don’t call me Dr. Dan or Dr. Meyer, ever. So—

Bethany Lockhart Johnson (08:13):

I will now!

Dan Meyer (08:14):

—this respect only goes towards Dr. Heidi, it seems. But yeah, we’ll take that off the air.

Bethany Lockhart Johnson (08:19):

Well, we are going to delve into your research on math anxiety soon, because I actually — speaking of becoming a doctor, a new doctor, I have some questions. We have questions about your research, but on a personal level, I really appreciated the way that you share that you yourself experienced math anxiety as a student. So I’m wondering if you could tell us a bit about your own math anxiety, your <laugh> journey through math.

Dr. Heidi Sabnani (08:50):

Yeah, so much like the people in the research that I did, and with the research that I read by others, many of us can tie the beginnings — or like the evil villain origin story of math anxiety — to a particular event, or series of events. And my series of events started, the big blow-up, I guess, in fourth grade. And I had had some struggles in school — I have mild dyslexia and dyscalculia. And so I had always been in the special group of kids who got some extra attention <laugh> from the teacher, or from an aide, or whoever happened to be in the room. But in fourth grade — at that time, they taught multiplication and division facts in fourth grade. Many, many moons ago. And I struggled greatly with just understanding what was happening and why we were moving so quickly. And, my teacher was probably not the best person to be entrusted with my learning at the time. Like, her style may have been OK for others, but it was obvious that she felt like kind of wasting her time with some people in the classroom. And I happened to be one of those people.

Bethany Lockhart Johnson (10:26):

Mmm. You said that really diplomatically, though. <Laugh>

Dr. Heidi Sabnani (10:30):

Well, you know, you look back at things from the perspective of many years. And having made lots of mistakes myself in the classroom as a teacher, I try to give some grace to things that happened, and how you remember them. Yeah, that’s my story, but maybe she had a different one, right?

Bethany Lockhart Johnson (10:55):

Yeah. But fourth grade Heidi was still, you know, still experiencing that. Yeah.

Dr. Heidi Sabnani (11:01):

Yeah. Fourth-grade Heidi didn’t like being in the “dumb group” and didn’t like being told that she would probably not graduate from high school. So that was kind of the general environment. And I got further and further behind in math. The dyslexia was less and less of an issue the older I got, because I had great comprehension. And so I could figure out the fluency thing just by the pattern of language, because mine is mild in comparison to so many who struggle with that. But math was not working in that same way. And I got more and more behind and to the point where I was having to stay in every day at recess. And I had had it after like a month. Like, I’m not staying in at recess anymore to do this math that I don’t understand, by myself. Like, not doing it. So I—

Bethany Lockhart Johnson (11:53):

Which, by the way, if there’s one way to make you hate it, <laugh> like, to engender, to endear you to a subject, could it be, “Let’s have you stay in at recess”?

Dr. Heidi Sabnani (12:07):

Right. And so one day I just stormed out of the classroom, I was like, “I’m not coming. I’m not staying, I’m not doing this anymore. I’m done.” And I can remember her standing up at the top of the hill screaming at me to come back, and I was like, “No way. Not doing it. Done with this.” I went to a parochial school, though, and my dad is a pastor. So that whole little incident blew up in the greater community in a way that I didn’t really anticipate as a fourth grader. And my parents had no idea that this was going on. And so they were shocked and dismayed that their — up until that point — oldest child, rule-follower, had done this. But then even more upset when they found out what was happening with my math understanding, or lack thereof. And they did what they knew best at the time. So my mom was a great memorizer. She has a brain like an elephant. And my dad grew up in the British system in India and Singapore, and it was at that time very much based on memorization. And so they were like, “We are gonna just work really hard. We’re gonna buckle down and do this thing <laugh>.” And so that’s what we did, and that’s where all of it began. It was not — it was just about “We’re gonna learn the facts. We’re not gonna ask questions; we’re not gonna think about it, because it’s just the rules. And if you can figure out the rules or the system or what the teacher wants, and mimic what the teacher is doing, then you’ll be successful.” And it was really successful for me, once I figured that out all the way through. My whole goal in high school when I took high school math was to take enough math courses with a high-enough GPA that when I got my BA in college, that I would never have to take math again. And I succeeded in that and got an English degree and a Master’s in world lit. And I was in no way doing math ever again.

Bethany Lockhart Johnson (14:31):

But little did you know that Future You was going to be researching math anxiety. How did you wind up researching it then? How did you wind up researching math anxiety?

Dr. Heidi Sabnani (14:43):

So I took a job in school improvement when I was working in Ohio, after a number of years teaching high school English in Southern California and Guatemala and Michigan, all over the place. And I took a job in school improvement with a co-consultant who was gonna be doing the math end, and I was gonna be doing the literacy end, and we were just gonna go in, and I was gonna make kids love reading, and she was gonna make kids love math, and it was gonna be so fun. And then she decided she didn’t like working with adults and they couldn’t find anyone else. And my boss said, “So you’re just gonna do both for the rest of the year.” After that year, I got requested to go back and, and do this again. I said, “Well, if I’m gonna do this, I’m going to go back and reteach myself the math in ways that I wish that fourth-grade Heidi had learned it, and fourth-grade-and-up Heidi had learned it.” And so that was like the, the beginning of the switch. And so now equal amounts of time in my career have been spent in both. But when I started, when I continued working, when I left the classroom to continue working with teachers, and when I transitioned more into an elementary setting, I began to notice the same behaviors that I had in high school of avoiding math, and avoiding teaching math, were happening in the classrooms that I was supporting. And so I would have teachers come and say, “Oh, can we talk about this literacy thing?” And even if it was like a math meeting, or we were supposed to split the time evenly, and ohhh, for some reason the literacy time talk would just like move over <laugh>. And then there was no time to talk about math at the end. And “Oh, that’s just too bad.” Like, we’re just gonna move on to this next thing. Funny how that happens, right?

Bethany Lockhart Johnson (16:32):

Yeah. <laugh>.

Dr. Heidi Sabnani (16:34):

And noticing teachers’ behaviors around going to and or avoiding math professional development that I was giving. Or getting sick. Or like having to leave the room for a long period of time. And so I began to notice these behaviors. And initially I thought I wanted to look at math anxiety in children, which is one branch of the research that I started with. But as I got into things more, the people that I have the most influence in are adults right now.

Dan Meyer (17:09):

Right.

Dr. Heidi Sabnani (17:09):

And so as I started looking at the research that had already been done, I feel like we do a really nice job of admiring the problem of math anxiety, and we do less in the “what to do about” phase. And so I was like, “Well, if I’m going to continue to be in this career and in this profession, then I need to be doing something in the space of ‘what are we gonna do about it?’” And so that’s how I switched to looking at “what do we do to help teachers?” Particularly elementary school teachers, because that’s the area of greatest need, based on previous research that we could at least do something to help.

Dan Meyer (17:51):

Yeah. A previous guest mentioned that a lot of research is better understood as me-search, especially in this kind of arena, where we’re going back in to try to understand what it was that happened for us and how to prevent it for future generations. And I have nothing but respect for that motivation right there. And your point is well-put, that it is very possible to spend a ton of time examining math anxiety from every angle, every facet, you know, put it up there on a mounted board and admire it … and there’s a lot of value there, but I appreciate that you’re moving into, “So, now what?”

Dr. Heidi Sabnani (18:27):

Yep.

Dan Meyer (18:28):

And so I’d love if you’d share with us and our listeners the broad details of your study, and what you ultimately found. Like, if there are any large takeaways here, what were they?

Dr. Heidi Sabnani (18:40):

Yeah. So a couple of things to kind of just lay a little bit of the groundwork. One out of four teachers say that they have math anxiety. Those numbers increase rapidly, the younger of the grades that the teachers teach. So if we think about preK to two, it’s about 88%, based on other people’s research. So I was like, “Well that’s a lot of people <laugh>!” And so, that’s the scope of the problem. And so I was thinking, “OK, what do we do in these moments?” Because other researchers had said they’re spending — when they don’t like it, they’re spending less time teaching math and avoiding it, or relying on methods that were done to us. Just out of fear of trying something different, at many times. And so one thing that has become more prominent in math education since I transitioned 16 years ago into this has been the role of coaches in school systems. And so one of the questions I wanted to think about was, “What can coaches or math specialists who work with adults as well do to help the teachers that they work with?” So that was kind of the lens that I was looking at. Like, let’s think about the systems that we currently have in place. Is there something that we could be doing that would help teachers, that wouldn’t be so huge or so monumental that with little shifts in our own behavior as coaches or professional development providers that we could make that would make a difference? So that being said, this was a qualitative study, so a small group of people in very intense settings. So I kind of always wanna preface that, because in academic world, you know, there’s <laugh> all sorts of thoughts about that. So I had asked teachers from districts that I work with who self-identified as having math anxiety if they would be interested in the study. So, this is what we’re thinking of, this is what it would look like, and the scope of the support they would have.

Bethany Lockhart Johnson (20:50):

So basically you’re tracking these four teachers who self-identified as math anxious. And were you serving as their coach and kind of seeing what was working?

Dr. Heidi Sabnani (21:00):

I was serving as their coach. Yeah. I was serving as their coach during that time period. And some fairly recent research that had been done was in the idea of “Can we do some reflective conversations or reflective writing around where your math anxiety started, and how that makes you feel both as a teacher of mathematics now, because you are teaching math, and how that affects your identity as a mathematician?” And so that was the first starting point. And that was a really critical moment that I’m glad that I had stumbled across the research on, because it turned out that having someone hear and acknowledge that what happened to them was both wrong and inappropriate, in many cases, and in a couple instances, was traumatic and also abusive — that that mattered. That it was OK to feel anger and hurt and frustration based on what happened to you in the past. And then have that moment to reflect on, “OK, so what do you want the classroom environment that you’re building as a teacher to feel like for your students?” So it was turning that moment of how they felt to thinking about, then, what kind of environment do we wanna make within the math classroom? And what steps can we take to ensure that happens? So that was like, Step One is just thinking about what that looks like. What kind of math identities then do you want to create for your students? Because all of the teachers were very concerned with not continuing the cyclical nature that often happens with math anxiety, from teacher to student and back again.

Bethany Lockhart Johnson (22:54):

Well, and even that validation, right? Like, how many of them hadn’t even had, like you said, had that? We had another, when in our first episode, Dr. Gerardo Ramirez talked about that validation and how key.

Dr. Heidi Sabnani (23:09):

Yeah. That was the first thing. The next step of it, which very different from what I often do — I don’t generally go in and model for teachers — just me, taking over your classroom. I really like to co-plan with teachers and co-teach with teachers and have it not feel like they’re losing control over what’s happening in that moment. And that’s generally the way that I go in when I’m doing professional development in a classroom, right? Like, I’m working with the teacher and we’re a team; we’re doing this together. But in these four cases, these teachers were very, very resistant <laughs> to co-teaching. And so I said, “OK, well, let’s throw everything out. Let’s try whatever it happens to be.” So the modeling aspect turned out to be really important, in part when three out of the four cases, because they were like, “Oh, I can do that.” <laugh> like, Well, yeah, I know you can! Like, it was that having a moment to sit back and see someone else doing it — which is harder to do when you’re co-teaching, right? It’s harder to be reflective in the moment when you’re still thinking about the teaching choices you’re making, because you’re both co-teaching.

Bethany Lockhart Johnson (24:24):

Right. Or sometimes you see, like in co-teaching, it falls into “one teach, one manage,” you know, or something like that.

Dr. Heidi Sabnani (24:31):

Yes.

Bethany Lockhart Johnson (24:31):

I have definitely fallen into that. But you, by modeling … it was almost, I don’t know, it feels like you’re kind of holding their hand. Like, “I’ll show you!” And not that it has to exactly look like that, right? But you found if a coach is coming in and the teacher gets to sit back and basically watch their students learn, they’re probably gettinga ton of information about their students, and they’re really learning some teaching strategies for mathematics that they can then like dip their toe in. I think? <Laugh> Am I kind of thinking of this? I’m trying to picture this and it feels rich and rife with possibilities <laugh>.

Dr. Heidi Sabnani (25:16):

Well, and it, it turned it from … I think sometimes, when I go into a classroom, I learn so much from watching teachers and being able to sit and listen to students, that you don’t always have the luxury of when you’re the teacher. <Laugh> Right? It’s so much harder to be like, “OK, I’m gonna be watching what a kid does, because I’m hoping someone uses this strategy, so I can connect it to this other person’s strategy, so that we can take that apart and look at it and really have immediate discussion around it.” Those are all so many things that are happening in the moment as a teacher. You don’t get to sit back and look at it from a researcher kind of lens. Or look, you know, from the up-above lens. And when I had these conversations with teachers, I was like, “That’s what I want you to do. I want you to be able to sit back and look at all the things that are happening.” Because then you begin to notice not only the moves that the teacher — in this case, me — who was modeling for them was doing, but also the student conversations. And it was almost like having a case study within that moment, where they got to sit back and just experience, versus thinking about all the decisions that they would make at the moment. So that was something that was really surprising to me.

Dan Meyer (26:33):

Yeah. And I love the idea that they’re seeing the pedagogical moves, but they’re also experiencing perhaps a sense of math that’s de-stressed. You know, they are allowing themselves to sit next to students and feel as though they are a student, in ways that if you’re co-teaching, you are still like enmeshed in the gears of the whole lesson. I wonder if that’s a part of this too. So I’m hearing from you that we’re taking these teachers who have all admitted to some math anxiety, and that one of the interventions, or one of the findings, was that modeling worked really well for, again, this set of teachers. But you modeling lessons that highlighted mathematics, that was less anxious, that helped the teachers see that students were engaging in really productive un-anxious ways, brave ways. Were there other kinds of takeaways that you experienced there?

Dr. Heidi Sabnani (27:24):

Yeah. So in addition to that, we had to think about and start at Step One. One of the teachers that I worked with had done her student teaching with a teacher who had math anxiety, and who never taught math. And so she entered her teaching career, never having taught math before or seen it taught. And so in her situation, she had had one course in her teacher preparation program, that was on fractions.

Bethany Lockhart Johnson (27:54):

That’s often the case, right? One math methods course! Help, we have to get it all in in this semester! <Laugh>

Dr. Heidi Sabnani (28:01):

<Laugh> Yes. And so she came in and said, “I feel like I have to start at the beginning.” And so there was no question that was inappropriate, or that we weren’t going to explore or think about. And so that was, I think, the starting place with that particular teacher. And then one other, who was kind of in her same age range, where we had to start thinking about, “OK, how did you learn as a learner? What ways are you seeing your students learn as learners? And then let’s focus on those first as the areas that you wanna explore in your teaching.” And so a lot of that ended up being much more visual and hands-on ways of exploring. And so those were some of the changes in, I think, pedagogy that were the most significant. In a couple of cases, these are early elementary teachers who had had one experience with manipulatives in their whole teaching career up until that point. And so one teacher brought me a bucket of Cuisenaire rods and said, “These are in my room. I don’t know what they are. <Laugh> Are we building things with them? Are they blocks that are just small? <Laugh> Like what are they for?”

Bethany Lockhart Johnson (29:20):

Yes!

Dr. Heidi Sabnani (29:21):

And so, <laugh> it was that idea of, “OK, let’s, let’s explore all the different ways that we can use these, and that we can think about how your students might learn best with this particular tool that you have in your room.”

Bethany Lockhart Johnson (29:34):

So hearing you talk about this research — which by the way, I know, you’re like, for our listeners, it’s all, “Quick, boil down your years and hours of research and synthesize it for us.”

Dan Meyer (29:50):

Your life’s work.

Bethany Lockhart Johnson (29:50):

In a little tiny neat package. But really though, even though I know there’s so many layers to your research, and your work with these teachers, I wanna flag for our listeners that even the things that you’ve identified for us, you were giving teachers space — as coach, giving teachers space, and validating their experience as a mathematician, as you know, as a young student, right? Making space for that experience and validating “Yeah, that was really lousy and your math anxiety is real.” Like, Step One is already powerful. And then you’re creating space where they get to be in their classroom as a learner, right? And have a lesson modeled. And then you’re creating more <laugh> space for them to learn and ask questions. And I have absolutely seen teachers like, “I don’t know what to do with these,” and kind of shove aside the district-provided tools or the curriculum-provided tools. And so even those things, Heidi — Dr. Heidi <laugh> — you know, even if … I don’t know, for me, I am listening to you and just holding those points in mind and feeling like that, alone, if a coach did even just that … I know there’s so much more to it, but what a powerful opportunity for reclaiming math as an educator, right? That’s what I’m feeling.

Dr. Heidi Sabnani (31:25):

Well, and I was hoping that there wouldn’t be … I mean, OK, it’s a double-sided hope. If there was something like so novel and so fantastic that was so different from the things that we have already at our disposal, that would’ve made a much better book or dissertation. <Laugh> But the reality is, there are things that we already know work. And we don’t often take the time or, or are given the time to be able to explore those things. Right? So even as coaches, you have district initiatives or things like, “this is what we’re working on this year,” and that’s fantastic, right? We keep those things moving forward. But if we’re thinking about coaching teachers with math anxiety, no teacher with math anxiety is going to be coming to NCTM.

Dan Meyer (32:16):

Right. Right. Or the training.

Dr. Heidi Sabnani (32:19):

Or the training. They’re like, “Oh, PD day? Literacy! Yes, please! Bye!” You know, it’s that piece of it. So when we have these moments, the coaching is the opportunity to provide that just-in-time kind of professional development for teachers, if we go at it in a slightly different way. It does not have to be huge. It can be things like, they feel that they’re stronger in literacy. Well, then, let’s explore some of the ideas around math, anxiety and math identity and examples of people who’ve overcome either those things or other barriers in their life. And how can those things help form not only your students’ math identity, but your math identity. And it gives entry points in ways that you have access to if you’re a person’s coach.

Dan Meyer (33:18):

So in that sense, I’d love to know from you, if someone came to you at a coach’s meeting at NCSM and asked you, “What is something I can do right now to support the teachers at my site and my district, who are commonly experiencing math anxiety?” What is something that you would offer them in that brief moment you had with that coach?

Dr. Heidi Sabnani (33:40):

So it is hearing their story first. That’s the big one. And then, can you, in your coaching, provide opportunities to slow down? We all have these pacing guides in some form or another, that drive the things that are coming. Is there a way that you can set up meetings a month or more in advance of the content that those teachers are going to teach? Can we explore a month in advance, that content? And ways to teach it and understand it? There’s the ways to teach it, but there’s also like, “What is this math and how do kids experience this math?” What kind of experiences do we want to have ourselves as learners and then have as kids? If we can create cycles like that, that then don’t feel so rushed. It’s so hard when we’re like, “Oh, we have a planning meeting and we’re meeting with our coach!” And you’re teaching this lesson tomorrow. “Learn all this stuff about adding and subtracting on a number line. Go!” It’s so fast. And so if we had those opportunities to build in cycles, where we could slow down that process, it would make a huge difference in the lives of so many teachers. And it’s finding that time and the willingness. If you listen to teachers, they will work with you. If you validate what happens to them, and acknowledge that sometimes that still happens to us. I mean, I still have experiences like that. Sometimes I’ll walk into a classroom and I’m like, “Oh, I forgot how to do that!” You know, like, “I’ve not reached that far in my remaking of my own education!”

Bethany Lockhart Johnson (35:24):

Yehhhh, heh heh heh.

Dr. Heidi Sabnani (35:25):

<laugh>. And you think, “I don’t wanna look like an idiot. I’m the math consultant who’s here to duh duh duh.” All of those things still come up. Yeah. And stopping and saying like, “OK, everybody, this is what’s happening to me right now.” <laugh> The vulnerability you have, you have to think about that. Even if you don’t have experiences of math anxiety in your own life. Let’s say you always rocked out in math, and you’re now a math specialist and you love it. You think it’s the most spectacular thing. There’s some other element in your life where you face some anxiety. All of us do. So it’s about thinking about, “OK, this is where I experience anxiety. Can I find that in the teachers that I work with? And then, can my teachers find that in the students they work with?” You know, the teachers, as they begin to reflect on their own experiences, began noticing which students always went to the nurse during math time, always asked to go to the bathroom during math time, always couldn’t find a pencil, or whatever it happened to be. And they began to be more aware of their students’ behaviors as well, and could then say, “Hey, let’s sit and talk about how you feel in math class. Like, I’ve been noticing that when it’s time for math, like your stomach hurts. Can we talk about like why that might be?” Because those teachers with math are more attuned, often, to those students. And so it just … the time factor, I guess is, is the bottom line.

Bethany Lockhart Johnson (36:59):

I just wanna say, it’s so great to have you in the Lounge. Because I think you’re really bringing this perspective that we haven’t talked about, which … we are not expecting coaches to walk in and know it all. That’s actually the exact opposite. You are allowed to be vulnerable. We are not saying, “Come,” quote-unquote, “Fix this.” It’s like, “Hey, how can you facilitate and make space?” And I feel like you have given us just a taste of like how that might be possible. And you know, I think even if it’s just a chance for teachers to reflect on their own experience in math, even that would probably be kind of revolutionary for — and I don’t say that word lightly — for some PD spaces, especially if they have another peer in their team that is like quote-unquote, “a whiz,” or like, “Oh, I don’t feel like I can be vulnerable in my math anxiety because this teacher seems to know it all.” But you’re creating space where it’s like, “Hey, we all have strengths. We all have areas where we could support each other.” And I love that invitation for coaches. I love that invitation for teachers. And … yeah. I’m just, I’m so glad we get a snapshot of your research. Again, I know, I respect that this is not the whole thing!

Dan Meyer (38:22):

Can we find … is there a link to your dissertation in the show notes, for those of us who peruse dissertations? Can we add something here? Think about —

Dr. Heidi Sabnani (38:29):

Oh, I have no idea!

Dan Meyer (38:30):

Just think about it. Just think about it. But —

Dr. Heidi Sabnani (38:34):

It’s somewhere on ProQuest. It did get some. …

Dan Meyer (38:36):

Right on.

Bethany Lockhart Johnson (38:36):

Is that a thing, Dan? Could I go, like, Google your dissertation?

Dan Meyer (38:39):

You definitely could. Yeah, for sure. It’s around. Yeah, same way. Well, that’s awesome. And I think it’s so helpful for those who write those enormous unwieldy essays to, you know, distill it in different ways. I hope it’s been … we’ve enjoyed so much, hearing you carve up a huge project into pieces that were really helpful for us to think about here in the Lounge. Thank you so much for coming on and hanging out with us. Dr. Sabnani, it’s been a pleasure.

Dr. Heidi Sabnani (39:06):

Hey, I’m happy to do it any time. Always the biggest joy in the work that I do is little changes in a positive direction.

Dan Meyer (39:18):

Right on.

Dr. Heidi Sabnani (39:19):

That’s all that this is about. Right? Whether it’s kids, whether it’s teachers, whether it’s administration. The work that we all do is so valuable, and it is more and more difficult over time. And just giving ourselves a little bit of space to think about and acknowledge that, I think, is really important. So I appreciate you all making space as well. And thinking about this idea. Because <laugh> we’re math people! And we don’t have math anxiety! Right?

Bethany Lockhart Johnson (39:51):

<laugh>

Dan Meyer (39:51):

So people would assume

Dr. Heidi Sabnani (39:54):

<laugh>. Yeah.

Bethany Lockhart Johnson (39:54):

Thank you so much. You’re welcome back in the Lounge anytime. <laugh> Thanks so much for listening to our conversation with Dr. Heidi Sabnani, consultant and co-host of the show “Math for All.” I can’t get enough about talking about math anxiety!

Dan Meyer (40:13):

Especially from people who are working with teachers so closely.

Bethany Lockhart Johnson (40:18):

Yes, totally. I loved that lens of, “Hey, look at what happens if we actually focus on the teacher’s experience and help them kind of reclaim this comfort, this sense of identity, relationship with math that’s positive. How does that impact their teaching?” I loved talking about it, and I’m really interested in how that work continues to evolve. So thank you so much Dr. Sabnani, for your time. And you know, listeners, please keep in touch with us on our Facebook, in our discussion group, Math Teacher Lounge Community, or you can find us on Twitter at MTL show.

Dan Meyer (40:58):

If you haven’t already, please subscribe to Math Teacher Lounge, wherever you get podcasts. Also, if you like what you’re hearing, please rate us and leave us a review. It will help more listeners find the show. And it just makes me and Bethany feel good about ourselves, too. You can find more information on all of Amplify’s shows at our new podcast hub. Go to Amplify.com/hub.

Bethany Lockhart Johnson (41:20):

You know, Dan, I also always like to say, I find most of my podcasts through recommendations from other listeners, friends, folks. So if you like what you’re hearing, share it in your teacher lounge. Just, like, on break, turn it up and start vibing and having the conversation right there.

Dan Meyer (41:40):

Yep. Yep. I got a better idea. Take the link to this podcast and then copy it and find the longest — the thread in your inbox with the most people on it. One of those ones that’s like, someone accidentally cc’d like 500 people, everyone at your school. Press “reply.” This is crucial. Not “reply,” but “reply all.” Paste that link in. Press “send.” Watch what happens.

Bethany Lockhart Johnson (42:04):

Nothing but good —

Dan Meyer (42:04):

Good fortune will be yours.

Bethany Lockhart Johnson (42:06):

Nothing but good things can happen when you send this to 500 people in the next 10 minutes. Next time on Math Teacher Lounge, we’re gonna be joined by Dr. Marjorie Schaeffer of St. Mary’s College for a conversation about math anxiety, and specifically Dan, how parents and caregivers, how their disposition influences the way their kiddos feel about math.

Dr. Marjorie Schaeffer (42:29):

I think the most important thing we know from literature right now is that high-math-anxious parents, when they interact with their children, their children learn less math over the course of the school year.

Bethany Lockhart Johnson (42:40):

And get this, she’s gonna talk to us about an app that just might be something worth, you know, heading over to the app store for.

Dan Meyer (42:49):

I’ve used some apps, I have opinions, and I can’t wait. We just share recommendations on apps with Dr. Schaeffer.

Bethany Lockhart Johnson (42:56):

That’s next time on Math Teacher Lounge. Thanks so much for listening.

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What Dr. Heidi Sabnani says about math

“Much like the people in my research, many of us can tie the beginnings or the ‘evil villain origin story’ of our own math anxiety to an event or series of events.”

– Dr. Heidi Sabnani

Consultant and Co-host of Math 4 All

Meet the guest

Heidi Sabnani is always surprised that she works in math education. She developed math anxiety as a young student and spent much of her school life and early career avoiding math. After teaching English in the United States and Guatemala, and earning her MA in World Literature, she found herself in the uncomfortable position of working in math classrooms as a school improvement consultant. Once she realized that her life was going to involve math, Heidi decided to relearn math in the ways she wished she had learned the first time around. 18 years later she is still learning with and from the students and teachers she has the privilege to serve.

Heidi’s doctoral research at Northeastern University focused on interventions for math anxiety in elementary teachers. She currently works as a consultant, speaker, and author.

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About Math Teacher Lounge

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Math Teacher Lounge

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode, co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with expert guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

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Current episode

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S5-05. Math technology & hacks for math anxiety: research-based tips for caregivers

We’ve been very lucky to have so many prolific and brilliant researchers on this season of Math Teacher Lounge, and our next guest is no exception.

Listen as we sit down with Dr. Marjorie Schaeffer to discuss what causes math anxiety, math hacks, and how the right math technology can make an incredible impact in children and caregivers coping with math anxiety.

Listen today and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!

Enjoy this episode >

Available episodes

Listen to our available episodes below!

Season 5

Listen to Season 5!

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Season 5, Episode 04.

Coaching tips for managing math anxiety in teachers

So far this season, we’ve investigated math anxiety in students and its causes with passionate researchers and curriculum experts, including one from Sesame Workshop! In this episode, we hear from Dr. Heidi Sabnani, consultant, coach, and co-host of Math 4 All, as she gives us research-based tips for teachers who are facing math anxiety themselves! Listen as we discuss Heidi’s own math anxiety and journey through math, the effects teacher math anxiety can have on instruction, and practices educators can implement right away for overcoming math anxiety.

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Season 5, Episode 03.

Cultivating a joy of learning with Sesame Workshop

In this episode, listen as we chat with Dr. Rosemarie Truglio, senior vice president of curriculum and content for Sesame Workshop! Continuing our theme of math anxiety this season, we sat down with Dr. Truglio to chat about Sesame Street and her thoughts on how to spread a growth mindset to young children and put them on course to academic achievement and long-term success.

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Season 5, Episode 02.

Uncovering the causes of math anxiety

We’re continuing our season theme of math anxiety, going beyond the basics, diving deeper into what causes it, and how we can help students move forward. In this episode, we talk to Dr. Erin Maloney from the University of Ottawa to better understand what’s actually happening in the brain when a person experiences math anxiety, and how we can take steps to shift student mindsets in a positive direction.

Investigating math anxiety in the classroom

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Season 5, Episode 01.

Investigating math anxiety in the classroom

This season, we’ll be talking all about math anxiety: what it is, what causes it, and what we can do to prevent or ease this anxiety in the math classroom. To launch this very important theme, in this episode, we sit down with Dr. Gerardo Ramirez, associate professor of educational psychology at Ball State University.
As someone who’s been studying math anxiety for more than a decade, he had some interesting research and advice to share on why math anxiety affects so many students (and adults), and tips for how to start reducing it.

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Winter Wrap-Up episodes

Listen to the Winter Wrap-Up!

Ideas to build math fluency

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Winter Wrap-Up, Episode 03.

Ideas to build math fluency

In this episode, we sit down with Dr. Valerie Henry to talk about math fluency and what that means for students. Listen as we dig into the research, hear Val’s three-part definition of fluency, and explore her five principles for developing it.

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Mathematizing Children’s Literature

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Winter Wrap-Up, Episode 02.

Mathematizing Children’s Literature

While we’re hard at work producing the exciting fifth season of Math Teacher Lounge: The Podcast, we’re continuing to share some of our favorite conversations from our first four seasons. This time around, we’re revisiting our popular episode that connected literacy and math!
In this episode, we sit down with Allison Hintz and Antony Smith, authors of Mathematizing Children’s Literature, to talk about what would happen if we were to approach children’s literature, and life, through a math lens–and how we can apply those same techniques to classroom teaching!

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Problem solving and facilitating classroom discussions

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Winter Wrap-Up, Episode 01.

Problem solving and facilitating classroom discussions

In this episode, In this episode, hosts Bethany Lockhart Johnson and Dan Meyer are looking back at the amazing speakers and conversations from past episodes and sharing some of their favorites!
First up: A season 2 double feature of The Power of Problem-Solving with Fawn Nguyen and Facilitating Classroom Discussions with authors Christy Hermann Thompson and Kassia Omohundro Wedekind.
Fawn is a specialist on Amplify’s advanced math team, and is a former math teacher and math coach—so she knows her stuff! You’ll hear about her five criteria for good problem-solving problems, and the power and importance of exposing all students to problem solving.
Then, we’ll move into Bethany and Dan’s conversation with Christy and Kassia to learn how hands-down conversations allow students to become better listeners and the steps you can take to implement hands-down conversations in your classroom.

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Season 4

Listen to Season 4!

Cultivating mathematical joy

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Season 4, Episode 05.

Cultivating mathematical joy

In this episode, Bethany and Dan explore mathematical joy while visiting a math teacher conference in Southern California. During this program, Dan describes his attempts to cultivate mathematical joy in his own school-aged kids.

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Dear Math

Season 4, Episode 04.

Dear Math

In this episode, Bethany and Dan chat with Sarah Strong and Gigi Butterfield, authors of Dear Math: Why Kids Hate Math and What Teachers Can Do About It. Listen in as they chat about their experiences with finding joy in math, and how their passion helped them tell the stories of other students’ journeys to find (or not find!) joy in math.

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LIVE from NCTM with Bethany and Dan

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Season 4, Episode 03.

LIVE from NCTM with Bethany and Dan

In this episode, co-hosts Bethany Lockhart Johnson and Dan Meyer are LIVE with more than one hundred Math Teacher Lounge listeners at the recent National Council of Teachers of Mathematics conference. Listen in as they answer the pressing question: Who is the best teacher in film or television?

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Bethany and Dan share their math biographies

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Season 4, Episode 02.

Bethany and Dan share their math biographies

In this episode, co-hosts Bethany Lockhart Johnson and Dan Meyer get personal and share their “math bios”—their early experiences with math and how those experiences turned them into the educators they are today.

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Joyful math teaching with Kanchan Kant

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Season 4, Episode 01.

Joyful math teaching with Kanchan Kant

In this episode, Kanchan Kant joins Bethany Lockhart Johnson and Dan Meyer to discuss the key, early investment she makes at the start of the school year to ensure her math teaching will be joyful for herself and for her students for the rest of the year.

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Season 3

Listen to Season 3!

Dan and Bethany Take on Twitter!

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Season 6, Episode 06.

Dan and Bethany Take on Twitter!

In this episode, Bethany and Dan take a look at several tweets that caught the most fire on Twitter during the 2021-2022 school year. The pair answer questions about viral teaching methods, the best teaching advice you can give in three words, and if students should use pencils or pens in class. Join them as they take on those questions and several others in a fast-paced episode.

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Developing an asset orientation with Lani Horn

Season 3, Episode 05.

Developing an asset orientation with Lani Horn

In this episode, math education professor Lani Horn shares with us what it means to have an asset orientation towards students, contrasting it with a deficit orientation, and helping Bethany and Dan understand the many ways students experience one or the other. Their conversation hit both high notes and low notes and included a challenge that Bethany and Dan both found extremely valuable for helping a teacher develop an asset orientation towards their students.

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Ideas to build math fluency with Valerie Henry, Graham Fletcher, and Tracy Zager

Season 3, Episode 04.

Ideas to build math fluency with Valerie Henry, Graham Fletcher, and Tracy Zager

In this episode, Bethany and Dan are joined by three guests to better understand fluency and how to make its approach fun. Dr. Val Henry shares her three-part definition of fluency and her five principles for developing it. Additionally, Tracy Zager and Graham Fletcher join Bethany and Dan to better understand fluency through a lens of equity and using multimedia as a tool.

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Math professional learning experiences with Elham Kazemi

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Season 4, Episode 03.

Math professional learning experiences with Elham Kazemi

In this episode, Bethany Lockhart Johnson and Dan Meyer chat with Elham Kazemi to explore how to look at teaching as a collaborative experiment. Moving more toward analyzing student thinking and how that contributes to teaching itself, leaves more space for one’s own understanding of math to grow throughout your career. When one revises their teaching based on the data we’re collecting from students and peers, this allows us to be both teachers and learners forever.

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Mathematizing Children’s Literature with Allison Hintz and Antony Smith

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Season 3, Episode 02.

Mathematizing Children’s Literature with Allison Hintz and Antony Smith

In this episodeMathematizing Children’s Literature authors Allison Hintz and Antony Smith join Bethany Lockhart Johnson and Dan Meyer to discuss what would happen if we were to approach children’s literature, and life, through a math lens – and how we can apply those techniques to classroom teaching.

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Making math viral with Howie Hua

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Season 4, Episode 01.

Making math viral with Howie Hua

In this episode, Howie Hua (you may know him from his viral TikTok videos) joins Bethany Lockhart Johnson and Dan Meyer to discuss making math accessible for students through multiple social media platforms, creating an engaging space for students to share their ideas.

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Season 2

Watch Season 2!

Math potluck favorites

Bethany Lockhart Johnson and Dan Meyer are hosting a Math Teacher Lounge potluck. Instead of bringing a casserole (or a store-bought item passed off as homemade), Bethany and Dan are bringing you a cornucopia of math topics. Be sure to join our Facebook group (facebook.com/groups/mathteacherlounge) as we will be announcing some exciting changes in the new year!

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The power of problem solving with Fawn Nguyen

Rio School District Teacher on Special Assignment and Amplify Math advisor Fawn Nguyen joins Bethany and Dan to discuss the power of problem solving. Hear from Fawn about:

  • Her five criteria for good problem solving problems.
  • How problem solving should involve all students.
  • The power of exposing all students to problem solving.
  • And much more!

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Hands Down, Speak Out | Facilitating classroom discussions

Authors Christy Hermann Thompson and Kassia Omohundro Wedekind chat with Bethany and Dan about facilitating student conversations in the math and literacy classrooms. Watch the video to learn how hands down conversations allow students to become better listeners and learn about steps you can take to implement hands down conversations in your classroom.

Be sure to head over to our Facebook group to participate in our book club study with Christy and Kassia.

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An asset-based return to school | Math teaching ideas

A lot of great learning occurred over the last school year. Watch Bethany and Dan’s conversation with math educators (Zak Champagne, Natali I. Gaxiola, Howie Hua, Janaki Nagarajan, Brian Shay, and Dolores Torres) to hear what learning, practices, and ideas they want to bring with them to the 2021-2022 school year.

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Season 1

Watch Season 1!

Episode 6, Segment 1: Math in public with Molly Daley and Chris Nho

Where is the most unusual place you have seen math in the last year? In this segment of Math Teacher Lounge, Public Math’s Molly Daley (@mdaley15) and Chris Nho (@nhoskee) join Bethany Lockhart and Dan Meyer to discuss all the unique places one can find math, including a laundromat, to elicit and invite math conversations.

Learn more about Public Math by visiting public-math.org.

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Episode 6, Segment 2: Math in public with Molly Daley and Chris Nho

Molly Daley and Chris Nho are back in the lounge to answer this question. In this segment they join Bethany and Dan for a mathematizing public places game. Watch the video to join in the game and see how you can spot and make sense of math in public spaces.

Learn more about Public Math by visiting public-math.org.

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Episode 6, Segment 3: Math in public with Omo Moses

MathTalk’s CEO Omo Moses enters the Math Teacher Lounge to chat with Bethany Lockhart Johnson and Dan Meyer. Watch their conversation to learn about how communities can create positive math experiences for all.

Episode 5: Slow reveal in an 8th grade classroom

In the latest segment of the Math Teacher Lounge series, Dan Meyer (@ddmeyer) substitute teaches an 8th grade class. Students interact with a few activities authored by Dan using the slow reveal described first in the Power of Data Science segment.

Curious how Dan found his way to this class? Our Math Teacher Lounge Facebook group made it happen! Join the group today and catch up on previous segments and stay in-the-know with all things MTL.

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Episode 4, Segment 1: Wrong and brilliant

Is there a different and better way to teach rightness and wrongness in math class? In this segment, Bethany and Dan use a Desmos activity to discuss how wrong and brilliant answers can reveal student understanding and inform your instruction.

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Episode 4, Segment 2: Wrong and brilliant with Mandy Jansen

University of Delaware professor and author Mandy Jansen (@mandymathed) joins Bethany Lockhart Johnson and Dan Meyer to continue the discussion around wrong and brilliant and the idea of rough draft math.

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Episode 4, Segment 3: Wrong and brilliant with Megan Franke

The conversation around wrong and brilliant in the classroom concludes with UCLA Professor Megan Franke (@meganlfranke). Professor Franke discusses with Bethany (@lockhartedu) and Dan (@ddmeyer) the amazing things students are doing in math (in a pandemic!) and more.

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Episode 3: The power of data science with Jenna Laib

Curious how data science can reveal profound noticings in your math class? Special guest Jenna Laib joins Bethany Lockhart Johnson and Dan Meyer to discuss this and the power of data science in the classroom.

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Episode 2: Effective and ineffective technology in the math classroom

Bethany Lockhart Johnson and Dan Meyer discuss technology in the math classroom with the following special guests: Idil Abdulkadir, Robert Berry, Lauren Carr, Steve Leinwand, Francis Su, and Theresa Wills.

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Episode 1: Welcome to MTL, let’s talk distance learning!

In this episode, Bethany and Dan talk distance learning. You’ll learn a little about what’s in store for series subscribers, listen to your hosts figure out the topic du jour by playing a game, and hear from Idil Abdulkadir as the group discusses real vs. fake Zoom norms.

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About your hosts

Learn more about your hosts!

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Bethany Lockhart Johnson

Bethany Lockhart Johnson is an elementary school educator and author. Prior to serving as a multiple-subject teacher, she taught theater and dance, and now loves incorporating movement and creative play into her classroom. Bethany is committed to helping students find joy in discovering their identities as mathematicians. In addition to her role as a full-time classroom teacher, Bethany is a Student Achievement Partners California Core Advocate and is active in national and local mathematics organizations. Bethany is a member of the Illustrative Mathematics Elementary Curriculum Steering Committee and serves as a consultant, creating materials to support families during distance learning.

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Dan Meyer

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is currently the Dean of Research at Desmos, where he explores the future of math, technology, and learning. Dan has worked with teachers internationally and in all 50 United States and was named one of Tech & Learning’s 30 Leaders of the Future.

Follow us on social media!

Check out our social media!

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Facebook groups

Join in the Math Teacher Lounge conversation by joining our Facebook group or by checking out our Facebook community group!

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Instagram

Join in the Math Teacher Lounge conversation by following us on Instagram @Amplify.education.

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Twitter

Join in the Math Teacher Lounge conversation by following us @MTLShow.

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Desmos Classroom

Desmos Classroom is a teaching and learning platform offering a collection of free digital lessons and lesson building tools. Learn more about Desmos Classroom on Twitter and on Facebook.

Winter Wrap-Up 01: Problem-solving and facilitating classroom discussions

Promotional graphic for Math Teacher Lounge podcast, episode 1, featuring Fawn Nguyen, Christy Thompson, and Kassia Omohundro Wedekind discussing classroom problem-solving and discussions.

As we prep for an exciting new season of Math Teacher Lounge: The Podcast, hosts Bethany Lockhart Johnson and Dan Meyer are looking back at the amazing speakers and conversations from past episodes and sharing some of their favorites!

First up: A season 2 double feature of the power of problem-solving with Fawn Nguyen and Facilitating Classroom Discussions with authors Christy Hermann Thompson and Kassia Omohundro Wedekind.

Fawn is a specialist on Amplify’s advanced math team and a former math teacher and math coach—so she knows her stuff! You’ll hear about her five criteria for good problem-solving problems, and the power and importance of exposing all students to problem-solving.

Then, we’ll move into Bethany and Dan’s conversation with Christy and Kassia to learn how hands-down conversations allow students to become better listeners and the steps you can take to implement hands-down conversations in your classroom.

Explore more from Math Teacher Lounge by visiting our main page.

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Dan Meyer: (00:01)

Hey folks. Welcome back to Math Teacher Lounge. My name is Dan Meyer.

Bethany Lockhart Johnson: (00:03)

And I’m Bethany Lockhart Johnson. Hello! Happy New Year! Hello, Dan Meyer.

Dan Meyer: (00:09)

HNY, Bethany. HNY to you and to all of the listeners out there in Math Teacher Lounge. HNY is the abbreviation that I use sometimes.

Bethany Lockhart Johnson: (00:18)

Oh, is that what that is? Is that—I wasn’t sure what that was. If on my birthday you send me HBD…no.

Dan Meyer: (00:25)

Yeah.

Bethany Lockhart Johnson: (00:25)

No. Unacceptable.

Dan Meyer: (00:27)

I will. No, you want the full thing. To demonstrate my care for your birthday, I gotta spell the whole thing out. I’m just trying to stay relevant. You know, I’m just trying to stay relevant and youthful. So I’m using The Abreevs.

Bethany Lockhart Johnson: (00:38)

The Brevvies.

Dan Meyer: (00:40)

To the extent of even abbreviating the word “abbreviation.” . So, any New Year’s resolutions you wanna share with the listeners, Bethany? While you think, I’ll just share mine real quick here. This is the year of the perfect Wordle streak for yours truly, Dan Meyer. I’m going the full 365. Watch. Watch me do it, folks. I’m naming it here. Live on air. recorded on air. Perfect Wordle year. What you got for the listeners, Bethany?

Bethany Lockhart Johnson: (01:10)

Let’s see. It’s raining very hard here in Southern California, and my newest resolution is to embrace nature. My child wants nothing more than to go and splash in all the puddles.

Dan Meyer: (01:22)

Nice.

Bethany Lockhart Johnson: (01:23)

And be amongst the mud. And what I’m gonna keep telling myself—and so far, so far, I’ve been doing pretty good with this—thrive, child. Splash. Squish. We can dry you off. You will not melt. So I want to keep finding opportunities. Like, for instance, my response is, “It’s pouring rain. Let’s stay under covers and let’s read this book together!” And his response is like, banging on the windows, like, “Please let me go outside.” So I myself have some rain boots. I’m going to go forth and splash with my child. So hopefully you’ll see me doing that a bit more.

Dan Meyer: (02:08)

Love that.

Bethany Lockhart Johnson: (02:09)

Ask me what I’m doing. I’m outside, splashing in nature.

Dan Meyer: (02:12)

I don’t wanna put words in your mouth, but I have felt a bit like parenting is a means for rounding out aspects of my own personality that I have felt are—or habits or hobbies that are lacking. Like, I’ve never been real outdoorsy or into camping, but I don’t want that to limit my own kids’ aspirations or interests. So let’s do the thing that’s not super natural for me, for their own sake. Which is kind of what I’m hearing a little bit from you, which—that sounds exciting.

Bethany Lockhart Johnson: (02:35)

Do you wanna go camping together? Like, our families?

Dan Meyer: (02:38)

Uhhh. Let’s take this one off the air. I also love something that’s more relevant to a teachers audience that you said, that I think is super interesting, is how there’s ways that we can make the jobs harder for ourselves, that are optional. And what I hear from you is like, “I’m just not gonna freak out. We’re getting wet. We’re getting soggy. And I’m just not gonna freak out.” And I just think that that’s interesting to think about, the things that we take on, you know, that’s optional. Freaking out is optional, sometimes. And there’s other areas, I think, for parenting or for teaching, where it’s like, “Oh, do I really need to choose this particular battle?” And to reconsider that.

Bethany Lockhart Johnson: (03:19)

And in that spirit, our whole Wordle episode that we talked about? Do you remember you talked about how beautiful Wordle mistakes are, and how you keep learning from mistakes? I mean, you obviously want the final correct answer, but just, you know, when you get on a losing streak, Dan, I hope you’ll continue to pat yourself on the back.

Dan Meyer: (03:38)

Well, I will not be taking on a losing streak, or even lose one day. This is what’s gonna happen here. I’m just speaking that and putting it out in the universe.

Bethany Lockhart Johnson: (03:49)

Speak it!

Dan Meyer: (03:50)

But if it happens, I will be taking a long break from all human interaction. And lamenting, as I do.

Bethany Lockhart Johnson: (03:59)

Camping. Dan’s off in the woods, weeping.

Dan Meyer: (04:01)

That’s right. That’s right. Yeah. Well, we wanna share with you folks—an exciting programming note is that we are currently working very hard on producing a special fifth season of this podcast. You thought the other seasons were special? Let me tell you, this fifth season gives new meaning to the word “special.” And we can’t wait to tell you more about that. But in the meantime, Bethany, you wanna tell ’em what we’re up to in the meantime?

Bethany Lockhart Johnson: (04:26)

Well, Dan and I went back and we were having a conversation about some of our most favorite conversations, or the conversations that people bring up to us. Like, when we were at the CMC conference, or NCTM, folks, when we talk about the podcast, they’re like, “Oh, I loved this one.” “Oh, I love this one.” And that, to me, I don’t know, that is exciting. And so, while we’re putting together this new season over these next few weeks, we’re gonna feature a few of our favorite conversations from our first four seasons. Dan, four seasons!

Dan Meyer: (04:59)

We’ve been at this for four seasons! And I do want to just emphasize something you said, Bethany: that all of our conversations are our favorite conversations. They’re all our special children. What we just felt like you, the listeners, did not quite learn enough from some of these, and so we really needed you to hear them again to make sure you got everything that you should get out of them. So, let’s tell ’em who’s up first. And who’s up first is a conversation we had about problem-solving with Fawn Nguyen, who’s an advanced math team specialist here at Amplify. Been a former math coach, math teacher. Just really done the work, is what I’d say about Fawn.

Bethany Lockhart Johnson: (05:38)

If you have been listening to this podcast, you’re like, “Whoa, whoa. Wait, I have not missed an episode. I didn’t hear Fawn’s interview.” That is because we used to be video only, not podcasts. So this conversation with Fawn was from, what, our second season?

Dan Meyer: (05:55)

Yeah.

Bethany Lockhart Johnson: (05:56)

And we were on video. And another thing about it is it was, this is a conversation that, when folks talk about problem-solving, a lot of the responses we’ve gotten are like, “Wait, I’ve never thought of problem-solving this way.” In fact, you’ll hear us say that exact thing . So we really appreciated the time with Fawn. And yeah.

Dan Meyer: (06:17)

Enjoy it, folks. Especially enjoy Fawn’s—I think a four-part?—definition of problem-solving, a word that’s often kind of mushily defined. And Fawn really goes into, I think, precision and depth on it. So hope you folks enjoy it.

Dan Meyer: (06:35)

Give a wave, Fawn, to the camera. Would you? Cool. Fawn has been a teacher for a very long time. She is someone who could have left the classroom at any point and taken any number of jobs in the math-teaching universe. But I’ve always admired that Fawn has taught kids for a very long time, and that has given her, in my view, just a lot of clarity on what is important to her about students. I’ve seen her not get upset or obsessed with certain kinds of small niche issues that a lot of us, like, they get a lot of us down in the classroom, sometimes. And she’s maintained a laser focus on among many other things, problem-solving as a virtue in mathematics classrooms. So, please welcome Fawn to our show. Fawn, thanks so much for being here.

Fawn Nguyen: (07:18)

Hey, thank you so much. Thank you. I am so excited and honored that you guys invited me for this, Bethany and Dan.

Bethany Lockhart Johnson: (07:24)

Thank you for being here.

Fawn Nguyen: (07:26)

I love you, Bethany. Dan, I can tolerate, but I love you.

Dan Meyer: (07:30)

I really worked myself up there on that complimentary opening for you, and that’s how you get me back, here? OK. Problem-solving is fully on the consciousness of math teachers. Every math teacher knows that they need to say, like, “Yeah, oh, problem-solving. Yes. Love it. Do it. I dig it.” But even so, I feel like it’s become kind of a buzzword. Like, it’s not always obvious what that means…or am I doing problem-solving, really? So we’re curious: As someone who is a problem-solving expert, who is asked all over the world to talk about problem-solving: How do I know if I’m doing problem-solving in my classroom?

Fawn Nguyen: (08:12)

This is not my definition of it, but—nor am I an expert, by the way, Dan, thank you! but I try really, really hard and work on it!—my definition—or it’s not my definition, but I like it because it’s short and honest—is “problem-solving is what we do when we don’t know what to do.” And so—

Bethany Lockhart Johnson: (08:32)

Ooh!

Fawn Nguyen: (08:32)

—with that mind-frame, I’m hoping teachers think more about what they task. Because I think it gets mislabeled a lot, as to what is problem-solving. If the kids already know what to do, there’s a solution path. Then it’s not problem-solving.

Dan Meyer: (08:48)

Yeah. So what are examples then? An example of, like, I might call something problem-solving, but it it fails that particular definition that you just proposed there. Very short, very honest definition.

Fawn Nguyen: (08:59)

Just, it needs to have constraint and contradiction to what the kids think naturally. It should come as a surprise. There’s an element of surprise in it. There’s tension.

Dan Meyer: (09:11)

Maybe if there’s harder numbers or, you know, decimals or fractions in the same kind of procedure…I can feel myself thinking, “Yeah, this is hard. This is problem-solving. Problem-solving equals hard. But we already know what to do.”

Fawn Nguyen: (09:27)

Or just word problems. That’s the most common thing. As soon as it just has words attached to the math, it becomes problem-solving. But that’s just coding it to me. That’s just coding it with words, wrapping it around. It doesn’t mean anything until we read through and see if there’s true problem-solving in it.

Bethany Lockhart Johnson: (09:45)

Like, what’s the moment that it becomes problem-solving? In the way that you envision it?

Fawn Nguyen: (09:53)

Well, I think there’s the bigger problem-solving of really bringing a task…I wanna call it left field. It just—we rarely ever, if ever, see it in the regular coursework, but it can also be problem-solving if we just take what we expect the children to do at the end of the unit, how about we front-load that? To me, that’s also problem-solving. And I’m trying to encourage teachers to do that last problem first. The task writers put more thought—not that they don’t do the rest of it!—but you know, this is a special one, because they label it “challenge,” or “enrichment,” or “are you ready for more?” I’ve seen those. And so it is this really special problem. And I would love for us to think about “do that first.” Because my biggest fear is that because it comes at the end, that not all the children are involved. And so that to me is the saddest part. Because we might not get to it, right? In mathematics, we always think, “OK, well, let’s do these problems and then we don’t have time for the rest.” But I think that’s your richest task right there, is at the very end. So why don’t we front-load it, start it, and it’s OK—of course it’s OK!—that we don’t all get it. But the exposure to all students is so important. Talk about, you know, equity. Talk about that, everybody gets the same thing. If everyone dug into that first one with everybody’s collaboration, and we get to share that, and then we leave it, because “Yeah, OK, now we learn more of the other stuff, right? That hopefully support. And then we can go back. And now everybody had a chance to go get into it, and then we can come back to it as, as many problems, we need to go back to it.”

Bethany Lockhart Johnson: (11:37)

And that feels so powerful. Because it feels like—as a teacher, I’m thinking it would also inform my work, how I approach the unit, and how I approach the next steps. Right? Like, what kind of work would we be doing if I let it, if I allow it, to change the way that I approach the unit.

Dan Meyer: (11:58)

Yeah. What you’re describing is so powerful, and really asks a lot of the task designers as well, I think. There are problem-solving tasks that really require, like, abstract knowledge of the way formulas and variables fit together. And what I love about what Amplify is doing with their problem-solving, what you’re helping them do, is that they start with a true low floor that can draw in every student. And they might get stuck at different places; that’s fine. But everyone has a way in. That’s exciting.

Fawn Nguyen: (12:24)

It’s a big deal for me to have this opportunity and this trust, to integrate problem-solving into the curriculum, make it intentional. It’s difficult to implement. It is, to be honest. Because for me, what is a good task? This makes one of my four criteria: One is, it is non-routine. It is simply stated. Simply stated—that’s like your low floor. And then has multiple solutions. And the fourth: This makes it. Because that the teacher enjoys solving it. And so you have to enjoy solving it to bring it. Because so that way I can say to my kids, “This is my gift.” It really is, Because, you know, it has so much fun and joy. And I appreciate the struggle. And I wanna illustrate an example. For example, let’s say Dan and I are classmates. And I know that Dan gets A’s on his tests and the lowest score he ever got was an 89%. I, on the other hand, just sitting right next to him, I average D. I have a D average on everything. While Bethany, our amazing and wonderful teacher, brings in a problem. And when she brings it in, she says, “I worked on this problem. I found this problem; I worked on it; and I struggled with it. And it was amazing. I enjoyed it so much, I’m sharing it with you.” And all of a sudden it’s like, “OK!” And I”m sitting there, right? My teacher loves this problem so much; she’s bringing it in to share with us. And now, all of a sudden, it’s not, you know…and I know she only gives us non-routine. When she talks about problem-solving, it’s non-routine. So it’s not directly tied to the textbook that I’ve been struggling with. So it gives me a chance, it gives me a chance to contribute. To think differently. And now, suddenly I look forward to working with Dan, because in this space, in this problem-solving space, Dan is no longer Mr. Know-It-All. And so that’s what I mean by—I am saying this a hundred times, and I will not stop saying it—problem-solving levels the playing field. Our world is filled with unsolved problems. Are you kidding me? Right? We look around us, we have so many things that are not solvable, or people are working on it, and yet in mathematics, what happens? The bell rings; we start; and we solve everything during that time, and we leave. And that’s…yeah. No! No! We need to wrestle with problems.

Dan Meyer: (15:04)

And that was our conversation with Fawn Nguyen, which we first released way back in November, 2021. You folks can follow Fawn on Twitter at Fawn P Nguyen. Um, that’s @ F A W N P N G U Y E N.

Bethany Lockhart Johnson: (15:18)

So our episode today is a double feature. We are featuring another conversation that we loved from Season Two. This is a conversation with Christy Hermann Thompson and Kassia Omohundro Wedekind. They’re authors of the book, “Hands Down, Speak Out: Listening and Talking Across Literacy and Math.” And I don’t know if you remember, but not only did we have a conversation with them, but we did a whole book study on Facebook, a Facebook Live book study, over the course of several months. And it was one of my most favorite things. And then they did a webinar at the end. So our conversation with them on the podcast for me felt like such a beautiful dive into their book. And you know, I’ve said it before, you think you have something down in the classroom, you’re like, “Oh, hand-raising, I’ve got that down.” You think you have it down, but then somebody says, “OK, but have you ever considered thiiiis?” You know, and it just—

Dan Meyer: (16:17)

NOT that??

Bethany Lockhart Johnson: (16:18)

, Not that? Something totally different? And I loved talking with them. They’re a lot of fun. And I loved the book.

Dan Meyer: (16:23)

Wonderful conversation, great book. Very provocative ideas. Yeah. As someone who’s like, “OK, classroom management, I gotta get the hand-raising going…”. In the classroom before we talked, they offered a really potent challenge to some really standard classroom management ideas. Yeah. Loved it.

Bethany Lockhart Johnson: (16:40)

And this conversation also offers some really practical tips for facilitating student conversations. So we think you’ll enjoy it. Here’s our conversation with Christy and Kassia.

Bethany Lockhart Johnson: (16:53)

So today we are talking about “Hands Down, Speak Out: Listening and Talking Across Literacy and Math, K—5.” And we have the authors here, Kassia Omohundro Wedekind and Christy Hermann Thompson. Before we begin, let’s define what a hands-down conversation is. A hands-down conversation is just another way to structure discourse in your classroom. So in a typical classroom, you might see students raising their hand and waiting on a teacher to call on them before they share their ideas or engage in discussion. But in a hands-down conversation, it’s students’ ideas and voices that are taking the lead, and teachers are stepping back and focusing on listening and facilitating. Hello! Welcome to the Lounge.

Kassia Omohundro Wedekind: (17:44)

Thank you. We’re excited to be here. We’re fans of Season One. So we’re ready to go.

Dan Meyer: (17:50)

I was a secondary teacher but I still found so much to love about the book. I think facilitating conversations is just generally challenging, and perhaps even more so in math, where answers feel so tightly dialed-in, in lots of ways. But I loved it. I would love for you to just explain to our audience, what is a hands-down conversation and how does that contrast with what might be standard practice for some people? For some classes?

Christy Hermann Thompson: (18:13)

We just started using the term hands-down conversation because we wanted to differentiate the fact that there are different times to have different types of dialogue in the math classroom, in the literacy classroom. And we use this as one of our tools. Right? It’s not that every day, all day long, we’re very against hand-raising and should never see that again. We find that having this as one of our tools will be where we make really clear to the students that this is a moment where we’re turning it over to you to negotiate the space and make the decisions about when your voice comes in and who speaks next. You know, carry on kind of like that dinner table or that playground or, you know, whatever is your natural habitat for talk. And bringing that into the classroom and then hoping that it also someday transfers back out of the classroom back into the real world.

Bethany Lockhart Johnson: (19:09)

For the teachers who feel like that’s terrifying to have students just start speaking, and speaking without any sort of control or my little equity sticks, my little popsicle sticks, or my popcorn, or whatever other thing they’re using, what would you say is the first step?

Christy Hermann Thompson: (19:25)

So I think recognizing and naming that fear is part of it. And then saying to yourself, “What’s the worst that could happen here?” You know, I think the worst that could happen is that nobody talks and it’s totally silent. Or on the other hand, everybody talks at the same time. And both of those things will happen! And so what? It’s gonna be messy. And if you just acknowledge that it’s gonna look messy, and that’s part of growing; that every child as they learn—and every adult—is messy as they grow.

Kassia Omohundro Wedekind: (19:59)

And we have to see what kinds of things will happen in a hands-down conversation. Like there’s no prerequisite. You just start and then you see what happens. And those are the signs that tell you, “What can help this community grow as talkers and listeners? If everyone’s talking at the same time, and they’re kind of pushing each other over with their words by saying, “I have something to add!” “I have something to add!” or something like that, that’s a common thing that sometimes happens at the beginning. Then you know that the next step is to do some work about how to hold your thoughts back, how to add, wait for a space in the conversation to talk. And those are all things we need people to know out in the world.

Bethany Lockhart Johnson: (20:41)

So can you give an example of a micro-lesson that…well, first, what do you define as a micro-lesson? And then, what’s an example of one that maybe somebody who wants to dip their toe into the world of hands-down conversations that they could try?

Christy Hermann Thompson: (20:56)

The reason we call them micro-lessons is because we wanted to differentiate from the term mini lesson, which is out there and tends to describe about 10 or 15 minutes that might take place at the beginning of a work period of time. And this is much smaller than that. We usually follow a pretty predictable structure of naming. Here’s this thing that’s so helpful when we’re having conversations, and we love to especially be able to name something that a student had done: “Kaylee did this yesterday and it really helped us.” So what we might call that is, “And then here’s how Kaylee and other people might do that. They might do something like this.” And, you know, having a little anchor chart, so there’s a visual reminder of that skill. “So when we’re having a conversation today, you could try…”. And that’s basically a micro-lesson, just in a nutshell.

Kassia Omohundro Wedekind: (21:51)

When I was doing these hands-down conversations and I had more space for myself to listen as a teacher, I’m like, “Well, look at those kids, like, slumped onto the ground, like, pulling the carpet apart, but they’re having this amazing conversation!” And so I learned that listening is a lot broader. So in this lesson that I’m thinking about, we just talk with kids about what are lots of different ways that listening can look like. Sometimes with younger kids, I’ll take pictures of them listening in different ways and we’ll notice things about them together. And then we invite them to talk with their Turn and Talk partner about like, “How do you like to be listened to?” Or “Tell me about how you listen.” And just kind of broaden that. And really, I like to think that like the micro-lessons are for the kids, but also I’m saying those things to say them for myself. Like, “Remember, you don’t have to insist that kids are staring each other down in the eyes all the time. Like, “It’s OK when they’re doing other things. There’s other ways of listening.” So I think I’ve learned as much from the micro-lessons each time I do them as the kids that I’m trying to help grow as listeners and talkers, as well.

Dan Meyer: (23:00)

You folks have a lot of really eloquent ideals you express, around democratic classrooms and engagement. But you also have just some very tangible, practical…even down to, like, how a teacher positions their body in space and the way they use their eyes to connect. I think it would be really helpful for teachers to hear that it’s not just they’re signing on to a manifesto of sorts, but there’s ways they can act their way into the beliefs that you both expressed here.

Christy Hermann Thompson: (23:26)

When I’m starting hands-down conversation work, if I put myself a little bit outside of the circle and look down, and give myself a clipboard, it, it helps me bite my tongue and it helps me give better wait time and see what the kids are doing before I have that tendency to jump in and teach and do lots of teacher-y things.

Bethany Lockhart Johnson: (23:48)

Kassia and Christy, thank you so much for joining us. We are so excited to have this conversation and to share your work. This is exciting. And I feel like this conversation is just the beginning of a deeper dive into this book.

Kassia Omohundro Wedekind: (24:01)

Thanks for having us.

Christy Hermann Thompson: (24:02)

Thank you.

Dan Meyer: (24:03)

Thank you both.

Bethany Lockhart Johnson: (24:06)

Thanks so much for listening to our conversations with Fawn Nguyen and Christy Hermann Thompson and Kassia Omohundro Wedekind, both of which were released in 2021, part of our second season. And, you know, we hoped you enjoyed listening to it for a first, second, maybe third, fourth time.

Dan Meyer: (24:24)

Let’s be real. There’s some real fans out there.

Bethany Lockhart Johnson: (24:26)

We loved it then. We love it now!

Dan Meyer: (24:28)

Yep, yep, yep. Please keep in touch with the show by following us on Twitter at MTL Show, and join our Facebook group, the Math Teacher Lounge community. We’d love to hear from you there. And please stay tuned for more info on what we’re cooking up here in the Math Teacher Lounge. Thank you folks for listening. Take care, Bethany.

Bethany Lockhart Johnson: (24:47)

Bye now.

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What Fawn Nguyen says about math teaching

“It’s a big deal for me to have the opportunity and this trust to integrate problem-solving into the curriculum.”

– Fawn Nguyen

Specialist, Math Advance Team, Amplify Desmos Math

Meet the guests

Fawn Nguyen

Fawn began her work with Amplify in 2022 as a Math Advance Team Specialist. She was a math coach for a K-8 school district for three years, and a middle school teacher for 30 years before that. Fawn has also received a number of accolades as an educator.

Christy Thompson

Christy Thompson is a Literacy Coach in Fairfax County Public Schools in Virginia. She has spent her teaching and coaching career particularly focused on listening to and learning from the talk of our youngest students.

Kassia Omohundro Wedekind

Kassia Omohundro Wedekind spent many wonderful years as a classroom teacher and math coach in Fairfax County Public Schools in Virginia and now splits her time between being an independent math coach and an editor at Stenhouse Publishers. Her favorite days are spent in classrooms learning from the many ways children talk, listen and negotiate meaning together.

Three women are pictured separately in circular frames, each smiling and facing the camera, against a white background with overlapping pastel shapes—perfect for highlighting math teacher lounge discussions or sharing essential math teacher resources.
A graphic with the text "Math Teacher Lounge with Bethany Lockhart Johnson and Dan Meyer" on colored overlapping circles.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Four steps administrators can take to shift to the Science of Reading

Four steps administrators can take to shift to the Science of Reading

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Winter Wrap-Up 02: Mathematizing Children’s Literature

Promotional graphic for Math Teacher Lounge podcast, episode 2, featuring Allison Hintz and Antony Smith, discussing how mathematizing children's literature can build math fluency.

While we’re hard at work producing the exciting fifth season of Math Teacher Lounge: The Podcast, we’re continuing to share some of our favorite conversations from our first four seasons. This time around, we’re revisiting our popular episode that connected literacy and math!

In this episode, we sit down with Allison Hintz and Antony Smith, authors of Mathematizing Children’s Literature, to talk about what would happen if we were to approach children’s literature, and life, through a math lens–and how we can apply those same techniques to classroom teaching!

Explore more from Math Teacher Lounge by visiting our main page

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Bethany Lockhart Johnson (00:02):

Hi, I’m Bethany Lockhart Johnson.

Dan Meyer (00:04):

Hi, I’m Dan Meyer.

Bethany Lockhart Johnson (00:05):

And we are so excited for another episode of Math Teacher Lounge. And as you know, podcast format; you’re listening now. I think one beautiful thing about the podcast format is that it gives us a little bit more time to have these rich conversations. And I promise I won’t do it, but I could talk to our guests for hours, hours! Authors Allison Hintz and Tony Smith have just released Mathematizing Children’s Literature: Sparking Connections, Joy, and Wonder Through Read-Alouds and Discussion. And today we get to talk to the authors. Allison, Tony, welcome. Welcome to the lounge.

Allison Hintz (00:53):

Thank you. We’re so grateful to be here.

Bethany Lockhart Johnson (00:55):

We’re so excited to have you here. And I wanna say that my very first—was it my first math conference? Maybe it was my first math conference—up in Seattle, the CGI conference, and I’m all like, you know, wide-eyed and just like, “Can this be a place for me, this math community?” Re-envisioning my relationship with math and thinking about myself as a math teacher, what? And I went to your session on mathematizing children’s literature, and I was just so fired up. I was so wowed by your ideas, your energy, and your passion for students’ thinking. And I feel like as I read this book, I felt like I was hanging out with you. Like you were just so encouraging all the way through. Of educators, of other folks working with young people, and really guiding us how to listen with joy and with an open curious mind.

Dan Meyer (02:03):

Yeah. I would love to hear a bit about the genesis of this book for you folks. Like, I’m coming at this from a secondary educator lens. I’ve got small kids, so that’s also part of my interest here. But I love any book, any idea that seeks to merge what seems like two disparate worlds. Like it’s often the case that we feel like, well, there’s approaches for ELA and approaches for math, and they’re kind of separate disciplines. And these poor elementary teachers have to learn all of them and be experts at all of them. And here you both come along and say, “Hey, what if they are the same kind of technique?” Can you just speak to how this came about?

Allison Hintz (02:38):

Definitely. Tony, do you wanna take a try? Do you want me to start us off?

Antony Smith (02:42):

I can start. We oftentimes present and talk together and so we kinda switch back and forth. So that’s just how we are. So probably about eight or nine years ago, Allison and I, our offices were next to each other on our small campus. We’re both professors and we just happened to have a few children’s books that we looked at together and we were just thumbing through the pages. We really liked children’s literature. And we noticed that I would stop at certain points wondering about character motive or plot or sequence of events or language use. And Allison would stop at very different points in the book and notice number and concepts or something about mathematics. And that’s when we started to wonder, what would it be like if we were sharing a children’s book with a group of children and we put our ideas together? Where would we stop? What would we talk about? What would we ask children about in terms of their thinking and what they notice?

Allison Hintz (03:42):

And so we started playing with these questions that we had and started approaching stories with multiple lenses to see what kinds of things would children notice and what kinds of things might they say. And we were also on our own journey in trying to understand how to plan for and facilitate lively discussions and classrooms that surface really complex mathematics. And it felt like stories were a place where that might be a fruitful context for hearing children’s thinking. We’ve worked with a lot of teachers and students in our region. We live in the Seattle area and we’ve applied for some funding over time that’s really helped us be in a lot of community-based organizations and educational contexts and libraries and pediatricians’ offices and classrooms, various classrooms, and see what’s interesting about this and what might teachers and children do with stories that would surface complex mathematics to think about together.

Antony Smith (04:41):

Over time, we came to the realization that if we wanted to hear children’s ideas, we had to stop bombarding them with questions. <laugh> Yeah. And at first it made it worse that we were asking them math and literacy questions at the same time. And so we realized that what we needed to do was to back off and to ask children what they noticed and wondered.

Bethany Lockhart Johnson (05:01):

Can you say more about that and how that kind of evolved into mathematizing children’s literature?

Antony Smith (05:07):

We did work with a number of very thoughtful, talented classroom teachers and children’s librarians in public library systems who were just so masterful at asking open-ended prompts and questions, rather than kind of like the de facto reading quiz, that a read-aloud can become, which I’ve always disliked as a literacy educator. And we realized in our observing these read-alouds or interactive read-alouds or shared reading experiences that given the opportunity in the space and an adult who was actually listening, that children came up with all of the ideas we would have asked them about and more. So we didn’t have to be bombarding them with questions. They were already much more thoughtful than what would’ve been sufficient to answer our questions.

Allison Hintz (05:58):

And much like mathematics, it was really an iterative process. You know, we had some clunky read-aloud discussions where we were trying to accomplish so much and toggling multiple chart papers and different colored pens and all sorts of “how do we capture these ideas” and “do we separate ’em? do we keep ’em together?” And so it’s really been over time that with partners, we’ve learned these ways of having multiple reads of the same story that allow us to hear what children notice and wonder, and then to delve more deeply into their questions and their ideas through multiple reads where we might spotlight literary ideas that they notice; we might spotlight mathematical ideas that they notice. We might make purposeful integrations between those. But we found it to be most productive—and Kristin Gray really help us think about this—to have an open Notice and Wonder, get everything out much like an open-strategy share. We welcome here, record all the ideas, and it goes all over everywhere. You know, it can be a really not math-y noticing! And those are amazing! So there’s a lot of, um, yes, there is a ladybug on this page! The grandma is wearing green triangle earrings! Oh, your grandma wears green earrings! I mean, it all comes out.

Bethany Lockhart Johnson (07:27):

Wait, have you been in my classroom? ‘Cause that’s exactly— <laugh>

Allison Hintz (07:29):

<laugh> And then, you know, we think of it a lot like if math teachers might use the 5 Practices for selecting and sequencing, or if you might move from an open-strategy share to a targeted share, how can we get out all the questions that children are asking and then step back from them, take some time to really think about what they’re telling us they’re curious about, and plan some purposeful, intentional subsequent discussions that can delve more deeply into their ideas.

Dan Meyer (08:02):

I’d love to go into that a little bit more if that’s all right. Um, I’m gonna speak from someone who doesn’t have an elementary background and I’m gonna voice some worries that I had, some anxiety. One anxiety I have like in a classroom or a curriculum is when there’s no room for student ideas. Right? When it’s like, oh, there’s just room for the curriculum author or the teacher here. That is a sadness. But I when I see an instructional environment like you’re describing here, where there is openness to all kinds of different student ideas, of different levels of formality, from different kinds of cultural fonts of knowledge or wherever, I also get a little bit nervous because that, like, increases the risk that a student might come to understand that “my ideas are not good enough,” whereas in the class with no room for their ideas from their home or their language or their hobbies, like, they’re not gonna internalize the message that, “that wasn’t good enough.” And so I’m really curious as you move from the open Notice and Wonder where kids share all of themselves with you, and then you move to a targeted focus on some sort of disciplinary objective, how do you navigate that tension and help students feel like their contributions are valuable, even though we aren’t taking them up per se?

Allison Hintz (09:18):

That’s such an important question. I mean, I think we’ve grappled with this broadly in math education. I think any time we’re thinking about which ideas we choose to take up to pursue to consider, we have a responsibility to think carefully about whose ideas are being taken up and heard and considered. And so one of the tensions I hear you naming, I think, Dan, is when we engage in lively discussion where children’s thinking’s at the center, how do we make sure to upend and interrupt kinda status norms that run the risk of being deepened? Um, and I think by paying attention to whose ideas are taken up as much as which ideas are taken up, and what’s the mathematics we wanna explore is one tension. Um, another tension I might hear you naming is, you know, the complications that teachers face with time and pressure and coverage, and which mathematics ends up getting worked on. And, um, you know, it’s something we’ve really had to struggle with in mathematics education, where we move to more discussion-oriented classrooms that are really centered in sense-making to know that it takes a lot of time to do this thoughtful, thoughtful work. Um, does that begin to get at some of the tensions you’re raising? Is there, is there more you’re thinking about?

Dan Meyer (10:53):

I think it’s really helpful that you kind of broadened the scope of the question beyond your book to “this is an issue that we are, you know, really challenged by and focused on broadly in math education.” And, um, I appreciate you bringing the element in of whose idea—not just which idea is taken up, but whose idea is taken up—is an opportunity where, let’s say, multiple people raise an idea that is towards an objective the teacher has, they have the opportunity to disrupt certain kinds of status, like ideas about status, in that moment. From your perspective, like, are there techniques to say, I don’t know, parking-lot certain kinds of questions and say like, “Hey, like these are awesome”? I don’t know. I just know that I see kids at like ninth grade. They are very reticent, often. They’ve internalized totally this sense of like, “I’m not gonna just, like, share about the pants the grandma’s wearing, you know; that will not be received well.” And so I’m just kinda wondering how that happens and like, what are the ways we can disrupt that? That process?

Antony Smith (11:54):

So thinking about that, Dan, from the teacher’s perspective, in those kinds of scenarios where you wanna honor each child’s contribution, a couple of things that come to mind: One is that by, you know, initially by modeling what I as a teacher, something that I notice or wonder about, helps kind of set the expectation for what kind of response would be encouraged. And it’s broad, but it gives an example. And then also we really try to record or to chart all of the ideas that are shared so that we can revisit and honor those together. And then either later or on another day, if we choose one or two of those to explore in some way within a more focused read, then another thing that we do is have the idea investigation afterward that continues that thought, but goes back to being as open-ended as possible, so that those students or children who maybe didn’t have their idea as the one that was focused on by the group could go back to that or explore some other idea of their own, so that the idea investigation isn’t a lockstep extension activity, which is why we don’t call it that. So they could again bring in their own perspective. But I have to say from the teacher’s point of view, there is that moment of potential panic <laugh> because there is that power transfer when you’re asking children to help steer where this is going. And if you really mean it, you have to let them steer a little bit. And that can be terrifying. And, um, I always think of one teacher, Ashley, we worked with who read an adorable book, Stack the Cats, by Susie Ghahremani. And in that book, there’s a point where there are eight cats and they’re kind of trying to be a tower of cats and they fall and they’re sort of in the air on that page. And she asked her first graders—she stopped, and she asked, “How, do you think, how will the cats land?” And for about a minute and a half, the entire <laugh> class, was silent. They had their little papers; they had chart paper; they had clipboards; they had everything they needed. But that unusual phenomenon of a group of six- and seven-year-olds actually just sitting and thinking and not being peppered with activities was really stressful, but amazing. And then, after about the 90 seconds, they started out into their exploration of how the eight cats might land. They just needed a minute to think. And it’s so rare that we’re able to let children have that.

Allison Hintz (14:40):

In that same moment, Ashley, who’s a learning partner to us, she turned to us kind of quietly, like, “Should I pose a different question?” And <laugh>, we’re like, “No, let’s stick with it. Let’s see what happens.” So I think it creates this space too, this thinking culture, right? And this culture of “what does that mean to really pose a rich task?That’s open-ended, where there’s multiple access points?” Those eight cats could land in so many different ways. And there was broad access, there was a wide range of all the cats landing, and one’s on their feet, ’cause cats always land on their feet <laugh>, and there was every combination. And so, um, I think what’s really interesting—and to me, this brings back to your wonder, Dan—is, you know, “What’s the risk in openness?” And there’s always risk in openness. Um, it’s scary as a teacher, right? If I’m not the authority of knowledge and I don’t have control over where we’re gonna go, it might get into places that I didn’t anticipate. Or I don’t really feel as solid in the math as I want to. Or I don’t know what it sounds like to stick with silence and wait time, to know if my students are really in productive struggle or if that question was a flop. And so, um, I think this is some practice space for young mathematicians and teachers of mathematics, and just teachers, to explore with that openness and kind of the risk of the openness required for complex thinking to emerge.

Bethany Lockhart Johnson (16:12):

You know, it feels like the way you’re both describing this, it really is a culture shift, right? I kept feeling like I was given permission to be a beginner as I read this book. Like I was really…I loved how you said, I believe it was you, Allison, when you were in the class, you had a couple index card that you kept on your clipboard and that as you walked around, you were like, “Hey, if I don’t know what to ask, I ask one of these questions.” You know? And just this idea that, that, like Dan was saying, there is that loss of control, but that’s also a way to create this culture where students ideas are valued and we are allowing students to really generate the questions, which I thought was such an important idea to explore.

Allison Hintz (17:00):

We started this work long ago, super-excited about math-y books. And we saw a lot of potential in them and we still do. But the limitation we saw is that math-y books, they, they put forth a certain mathematics to be curious about. In some ways they tell you what mathematics to think about. So we started asking ourselves what would happen if we considered any story a chance to engage as mathematical sense-makers. And we started playing with non-math-y books and we got to a place where we could consider every story an opportunity to engage in mathematical thinking. And so we started noticing things over times, oh, these books tend to be really math-y. We call those text-dependent. We’d have to pay attention to the mathematics to understand the story. Whereas this pile of stories, these, they’re not overtly math-y. You could really enjoy the story and not pay attention to mathematics and have an amazing conversation. But what would happen if we thought of about this story as mathematical sense-makers and how might it deepen our understanding of the story? And then this other teetering pile of books, these are books where, you know, children didn’t tend to engage as overtly as mathematicians in it, but there’s opportunities in this story to go back to something—to a moment, to an illustration, to a comment—and think as mathematicians. And those were more about illustration exploring. And so, as we notice these different kinds of books, we really broaden what we thought about. And I think one of the things we really wanna think about in community through this book is what happens if we approach any story, every story, as mathematical sense-makers, because stories are alive in children’s lives, in homes and communities and in schools. And it’s a broad opportunity that we wanna take up. I was thinking, as I stay in this strait for just a moment about book selection, before we move into that process, um, Bethany in a previous MTL, you talked about representation.

Bethany Lockhart Johnson (19:12):

Mm, yeah.

Allison Hintz (19:14):

And do you remember when you shared the image of hair braiding?

Bethany Lockhart Johnson (19:19):

Yes. Vividly, yes. <laugh>.

Allison Hintz (19:22):

Yeah. And can you say just what that meant to you? What that….

Bethany Lockhart Johnson (19:27):

Yeah. Well, it was from a conference; Sunil Singh had used it and was talking about the artistry in mathematics and beauty in hair braiding. And, um, particularly, he was showing this particular image of this Black woman with her hair braided in profile and looking at the angles and the symmetry. And I shared that, you know, I spent so many hours in the beauty shop with my aunties and my mom and my grandma and continue to, to this day, that it just, it struck me immediately as familiar. And it struck me immediately as seeing an image that was reflective of my lived reality, projected as valuable and worthwhile for consideration in the world of mathematics. Which is not what I felt as a student of mathematics as a young adult or child. So it was this beautiful moment of, for me, the power of when we see images and we allow opportunities for re-envisioning what may be a common practice for that student, or may be something that they see every day.

Allison Hintz (20:44):

And in that same way, that image that was put up, we wanna think really carefully about representation in the stories that we select. And when we think of stories as mirrors or windows, we really wanna be mindful in story selection of whose stories are told and whose stories are heard. And when you said that you would sit down to listen to a story and you felt at ease or that you saw an image and you saw yourself that can be and should be something we really think carefully about when we select the stories that we select.

Dan Meyer (21:21):

It’s a wider path for representation of different kinds of people in literature, because people’s stories seem so much more present and towards the surface of their lives, versus, say, the abstractions and numbers and shapes in mathematics. It feels like more of a struggle to find ways to show people, hey, like you’re here, this, this place belongs to you. So in all these reasons, I think it’s really great you folks are using literature, which has this history of humanities, literally humanities, as a vehicle for mathematics. That seems pretty special here.

Antony Smith (21:56):

We both go to libraries and bookstores and look through books as often as we can, but also our partner, a children’s librarian, Mie-Mie Wu, helped us go through—when we would meet, she would bring three or four hundred books at a time.

Bethany Lockhart Johnson (22:13):

When you described her wheeling in the cart, oh, I wish I been in that room! <Laugh>

Antony Smith (22:18):

And the cart was, you know, probably three or four times bigger than she was sometimes. And we would go through hundreds of books and look at them and listen to her thoughts as a skilled librarian sharing with families, diverse families, and what catches the attention of a three-year-old sitting with her grandfather. And that was really a valuable, helpful experience. And it’s a partnership that continues. So in Last Stop on Market Street—and this is in the book; we talk about this, this children’s book quite a bit—in this story, CJ with his Nana, his grandmother, are riding the bus to the last stop on Market Street in San Francisco, to go, as we will find out, to help serve in a soup kitchen to help the community. And the teacher, Susan Hadreas, had the children record their ideas. She charted them in an open Notice and Wonder read. And one of the ideas that a young boy noticed was that CJ on the bus…a man with a guitar starts playing the guitar on the bus and CJ closes his eyes and it says CJ’s chest grew full. And he was lost in the sound and the sound gave him the feeling of magic. So this boy said, “I wonder, what does that feel like if you’re feeling the magic? What’s that?” And that was one of many ideas in the open Notice and Wonder, and Allison will talk about the math lens read, but first Susan went back and read with them. She had that idea, she circled it on the chart paper, and another day that week, she said, let’s go back and visit this story we really liked. And remember, we wondered what feeling the magic was like. Let’s go back through and let’s keep track of all the feelings and emotions that CJ had across the journey to the soup kitchen in this book. And so they did another read of the story; they were very familiar with it, of course, but they noticed new things and they also, every few pages, stopped and she helped chart all of the emotions that CJ experienced from envy to excitement to sadness. There’s a huge range in this book. And it was fascinating.

Allison Hintz (24:36):

I think one of the things that the children noticed was that CJ’s feelings were shaped by community. And that he shaped and shaped…he was shaped by and helped shape his community. And so the ways that he felt across the story were impacted by the other characters that he comes across. The guitar man on the bus. The bus driver who can pull a coin out from behind someone’s ear. The lady with the butterflies in the jar. Nana helping him to see the rainbow. And the students started, you know, being curious about that. How do we shape and how are we shaped by community? What communities are we a part of? This class is one community. I’m in many communities across my life. And they started to quantify the number of people in the story. So Mrs. Hedreas went back for a math lens read, and she said, let’s just keep track of and pay attention to how many people are in CJ’s life in this day. Because I can hear you starting to think about quantity. This class at the same time in other areas of the day had been working on counting collections, how to keep track, so they got out their tools. Some people pulled out ten frames, some people pulled out clipboards. They had a wide range of things they could use to help them keep track. They developed their own strategy, keep track however you want. She did a quicker read through it, flipping the pages, and then they get into these debates: <laugh> “We already counted that person!” “But they took their hat off and put it down to collect money!

Antony Smith (26:10):

“What about the dog?”

Allison Hintz (26:11):

“That’s the same person!” “Yeah, there’s a dog pound in his community!” <laugh> “Do animals count in our community?”

Bethany Lockhart Johnson (26:17):

I love it!

Allison Hintz (26:17):

“Yes, they count!” Uh, and so we went through and quantified and there was really this understanding as you saw these people throughout the story that communities can be of different sizes, but community has impact. And you have responsibility in your community to show up and to lean in and to know that bringing your full, authentic, vulnerable self, you shape people and they shape you. And what communities are people a part of. And it turned into this really interesting discussion about quantity and helped us think more about quantity and community. I think a really important moment for us and for that class was the transition from being people who almost did mathematics to a story, like counted things on a page, um, count acorns on a page in an autumn book, to being mathematicians who thought within the story.

Antony Smith (27:17):

And then two idea investigations that came from that —not at the same time, of course, but with the same group of children—one was they identified an emotion of their own and wrote and drew about that. And also, who helped them address or get out of or acknowledge that emotion. And then the other idea investigation was that all of the children drew or kind of mapped out a community that they were part of. Whether it was their neighborhood or their classroom or their soccer team or whatever it was. And so then those investigations strengthened the connections of those concepts to the lives of those children.

Bethany Lockhart Johnson (28:05):

Well, I, actually wanted to ask you about idea investigations. Because I feel like that was such an important invitation in your book. And the way I understood the idea investigation is you’re really paying attention to what’s coming up in your other reads. Right? And then these are opportunities to extend the thinking, or like you said, to extend a particular aspect: What’s your community? Can we map your community? Or what’s a particular emotion? And it was in such contrast to what I think I have probably done in my classroom more than once, which was like, “Oh, we read this story about seals. So now my story problem is gonna be about seals, right? <laugh> Like in the story, you know, Jojo, the seal had five balls. <laugh> So if Jojo still had five balls and two of them bounced away…” You know, or whatever. Right? But that’s not what an idea investigation is. Right?

Allison Hintz (29:03):

Yeah. I think this is where we also had some stumbles and can totally relate to what you’re saying as previous classroom teachers as well. We have come to a place where we are pretty in favor of a super open-ended idea investigation that takes up the things that have surfaced in the multiple reads and making sure it’s a rich task with many, many ways children can engage with that. There’s many, many, many right answers or ways to engage. Less is more there. So we moved way away from, like, even a worksheet that might have an idea from it to blank paper and math tools and places to get into some productive struggle around some of the complex things that were raised.

Antony Smith (29:59):

A challenge with worksheets is that they put a frame around children’s ideas. So either there are only three lines to write on, or there’s only a small box to draw in. Whereas a blank page really opens up the possibility. Um, and so—is it Ann Jonas who wrote Splash!? sorry, I don’t have it in front of me—the book Splash!, about animals that end up in and out of the pond, including a cat that is not happy about ending up in the pond, an idea investigation after that for very young children was, with the list of the different creatures displayed at the front of the room: On blank paper, hey, draw your own pond and decide how many of which and each type of animal you want in your pond and then write about it. Just on blank paper. And so that allowed some children to draw, like, three giant goldfish. But other children drew 17 frogs and three cats. And, and just, it lets children follow—

Bethany Lockhart Johnson (31:02):

It was theirs, right? It was theirs.

Antony Smith (31:04):

Their idea. <laugh> And that comes partly from, I think, as Allison mentioned, we both were classroom teachers before moving into academia. And I remember giving children worksheets, particularly math worksheets, where they weren’t necessarily bad, but right at the bottom, it says like, explain your strategy. And it gives two lines.

Bethany Lockhart Johnson (31:23):

Right! <laugh>

Antony Smith (31:25):

The only thing a seven-year-old can write there is “I thought.” Or “I solved it.” <laugh> And that’s not where we need to go.

Dan Meyer (31:34):

Yeah. If I could just ask the indulgence of the primary crowd here, like, I’m trying to make sense of all this. And I just wanna like, offer my perspective. My summary statement of what’s going on here. I’m trying to—I love how you both came here—

Bethany Lockhart Johnson (31:45):

<laughs> How ya doin’, Dan? How ya doin’?

Dan Meyer (31:47):

<laughs> I’m, ah, A, I’m loving this a lot. Um, B, I came in here loving how you folks are broadening the work of primary education to kind of find commonalities between these sometimes seemingly disparate kinds of teaching in ELA and math. Love that, I wanna say. But I think you folks are describing, with all these teachers you observed and your own work, is the work of attaching meaning to what students might not realize yet has meaning. Or they might think it only has one kind of meaning. But you, the teacher, with their knowledge, realizes that there are many more dimensions of meaning that can be attached to those thoughts. And I’m hearing that from you folks, when you describe A, what math is and the power of a teacher to name a thing as mathematical. Like, “Oh, you didn’t think math was that, but math is noticing; math is wondering; math is asking questions,” for one. But also this work you’re describing of how, like, first the task has to invite lots of student thoughts and then to say like, “Oh, I see that there’s a similarity to these two.” And to raise those up for a conversation or to ask a question like to extend one person’s, one student’s question a little bit more. But it’s always…I’m just hearing you folks attaching more meaning than the student might have originally thought. I appreciate the conversation. That’s really interesting.

Bethany Lockhart Johnson (33:03):

Well, and now that the book is out, I think it’s gonna keep evolving, right? Now that it’s gonna be in the hands of teachers and librarians and educators and caregivers, it’s exciting to see kind of where it goes next. Which actually brings us to our MTL challenge. Dan Meyer, do you wanna share?

Dan Meyer (33:22):

Math Teacher Lounge, we have a challenge for the folks who listen and we’d love for them to hop into the Facebook group Math Teacher Lounge, or hit us up on Twitter at @MTLShow and just, like, kind of exercise beyond listening, exercise the ideas you folks are talking about, some kind of a challenge that can help us dive deeper into your ideas. So what would you folks suggest for our crowd, for our listeners?

Allison Hintz (33:42):

I would love to invite people to playfully experiment with a favorite story, with a story that’s new to you. I would love to invite listeners to sit with a story maybe on your own, and just ask yourself as a mathematician: What do you notice and wonder in this story? Don’t feel any pressure. Maybe sit with a child or some children and listen to what they notice and wonder. Like, really listen! Don’t ask questions! But hear their questions and place children at the center and consider multiple reads. Consider continuing to pursue their questions. And we have a planning template that might support people in kind of sketching out some ideas if you’re open to playing with that too.

Bethany Lockhart Johnson (34:34):

And we will post—

Dan Meyer (34:36):

That’s awesome.

Bethany Lockhart Johnson (34:36):

—a link for that planning template in our Facebook group and on Twitter as well. So thank you so much for that resource, because I think it’ll definitely help. It could help you, like you said, it could help you kind of organize your thoughts or help you think about this work in a new way. So thank you for that resource and thank you for the amazing resource that is Mathematizing Children’s Literature. I am so excited to continue to engage with you both and with listeners as they dive into this book. If folks want to engage with you more, where can they find you? How can they reach you?

Allison Hintz (35:12):

Well, we’re on Twitter.

Bethany Lockhart Johnson (35:14):

Great.

Dan Meyer (35:15):

What’s your home address? <laugh>

Bethany Lockhart Johnson (35:24):

Wait, let me try that again. <laugh> ‘Cause it does sound like I’m like, <fake ominous voice> “Where can they find you?”

Allison Hintz (35:29):

4-2-5…. <laughs>

Antony Smith (35:32):

At the bookstore!

Bethany Lockhart Johnson (35:34):

Y’all, if folks want to continue this conversation or share these ideas or the math challenge, how can they tag you? How can they, they reach you on the World Wide Web, besides the Math Teacher Lounge Facebook group?

Antony Smith (35:50):

Yeah. Well, we are both on Twitter, and we’ve been trying to promote the hashtag #MathematizingChildrensLiterature. It’s very long, but once you type it once, your phone or computer…

Bethany Lockhart Johnson (36:01):

Easy. Yeah, those click, right? Is that what it is now?

Antony Smith (36:03):

<laugh> The other is that we do for our project, we have an Instagram account that is @MathematizeChildren’sLiterature.

Allison Hintz (36:11):

We care really deeply about hearing from people. You know, we think our ideas are constantly evolving and that there’s such exciting room to grow. And we just felt compelled to share what we were learning now so that together we could learn and build vibrant experiences for young children and teachers and families through stories. So we want to hear from people! We wanna learn about stories that are important in your lives and what children say, and grow these ideas together.

Bethany Lockhart Johnson (36:42):

And credit to Dan, you told me you went and ordered a bunch of the books they have on the suggested read list.

Dan Meyer (36:48):

Oh my gosh.

Bethany Lockhart Johnson (36:49):

You read ’em to your son.

Dan Meyer (36:50):

I got such a side-eye from my significant others around here for what I dropped on Amazon in one night! <laugh> Uh, all these books I didn’t have. Some of them I did. We are not fully illiterate around here! We do love the written word at the Meyer household! But there were a bunch that that I grabbed. I’m morseling them out day by day.

Bethany Lockhart Johnson (37:09):

Wait, at bedtime I read my one-year-old One Is a Snail, Ten Is a Crab. <laugh> And let me tell you, he had vigorous pointing and “Da? Da da da da?”

Allison Hintz (37:22):

<laugh> Aww, da da!

Bethany Lockhart Johnson (37:22):

So hey, we’re on the road. <laugh> <music> Deeply grateful, not only for your work and your beautiful book and your work, but also for the invitation to dive into the world of children’s literature in a way that many of us have not before. And it’s fun! Thank you, Tony. And thank you, Allison. And thanks for hanging out in the lounge.

Allison Hintz (37:48):

Thanks for having the lounge!

Antony Smith (37:49):

It’s been fun!

Allison Hintz (37:52):

Thank you both.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Allison Hintz says about math

“We started asking ourselves, “what would happen if we considered any story a chance to engage as mathematical sensemakers”.”

– Allison Hintz

Author and Associate Professor, University of Washington Bothell

Meet the guest

Allison B. Hintz: Dr. Hintz’s research and teaching are in the area of mathematics education. Her focus on mathematics came about during her years as a fifth grade teacher – it was alongside her students that she developed her own positive identity as a mathematician! Today she studies teaching and learning, specifically facilitating engaging discussion. Her research and teaching happen in partnership with educators and children in formal and informal settings and focuses on beliefs and practices that support all children in lively mathematics learning. She is a co-author, with Elham Kazemi, of Intentional Talk: How to Structure and Lead Productive Mathematical Discussions.

Twitter: @allisonhintz124

Antony T. Smith: Antony T. Smith is an associate professor of literacy education at the University of Washington, Bothell. He works alongside teachers to create engaging literacy-mathematics learning experiences through exploring and discussing children’s literature. He is committed to the concepts of motivation, engagement, challenge, and creativity in literacy teaching and learning.

 Twitter: @smithant  Instagram: mathematizechildrensliterature

Two people appear in separate circular frames; the woman is smiling and wearing headphones, while the man stands in front of bookshelves, perhaps discussing Mathematizing Children’s Literature.
Podcast cover for "Math Teacher Lounge" with Bethany Lockhart Johnson and Dan Meyer; bold text on orange and teal semicircle background.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Supporting multilingual learners—by supporting their families

Woman smiling in front of a brick wall, surrounded by colorful illustrations of a turtle, toucan, book, and nature, with the word "¡Hola!" at the top left—celebrating technology in the math classroom and boosting the performance of students.

Teachers know that multilingual/English learners (ML/ELs) are an important and fast-growing population in today’s classrooms. In 2021, more than 10% of students enrolled in public schools across the U.S. were identified as English language learners, with some projections suggesting this number could reach 40% by 2030.

But when it comes to partnering with the families of ML/ELs for student success, we’re just beginning to tap into what’s possible.

I’m an ML/EL teacher and former homeroom teacher at a school serving many ML/ELs.

Here’s what I’ve learned about best practices for bridging the school-to-home communication gap and partnering with families (all families!) to ensure their child’s success.

Recognizing the communication gap: Common challenges with multilingual families

In my experience, three common barriers can stand in the way of strong family engagement and student success:

  • Cultural expectations around parent-teacher communication: In many cultures, school is considered the teacher’s domain. Reaching out may be seen as crossing a line—or simply not expected at all.
  • Logistical challenges: Unpredictable schedules may lead to missed messages, delayed responses, or inconsistent availability.
  • Language barriers: If a message isn’t in a language a caregiver understands, it’s unlikely they’ll respond—not because they don’t care, but because they can’t fully engage.

Supporting multilingual learners starts with recognizing these barriers not as signs of disconnection, but as invitations to shift our approach. There are best practices we can adopt to help bridge the gap—and build the trust and relationships our students need to thrive.

Tools and strategies for better parent-teacher communication

If you want to communicate with families who speak a variety of different languages, the first step is finding the method of contact that works best for each of them. My school uses an auto-translating app called ParentSquare for home communications—but not all families I’ve worked with respond to ParentSquare messages. So if a family isn’t responsive to one mode of communication, try another!

It’s a good idea to ask families on Back-to-School Night—or whenever your students first arrive—if they have a preferred mode of communication. I’ve found I get the best response rate by creating a Google Voice number and communicating via text, first translating through an app if needed.

Keep a log of this information so you have it on hand when you need it. In the long run, this will be easier for both you and your students’ caregivers than you chasing them down to get them to download, log into, or check a specific app.

The important thing is to consider making contact essential, and to keep trying until you find the mode that works for both you and the parents of your ML/EL students.

Setting the tone for strong family engagement

If you want to forge a strong family-school partnership (and you should!), you also need to set the tone. When families have a different cultural understanding of school engagement than what you’re used to, I’ve found that it helps to explicitly solicit parent input, explaining how a partnership between caregiver and teacher will help support their child’s success.

Let them know how and why they should get in touch with you, and make it easy by reaching out proactively with brief, positive updates.

What multilingual families really want to know

Perhaps most importantly, ask families what they want to know! I’ve attended many parent-teacher conferences—both for my own students and as an interpreter—and I’m frequently struck by how many multilingual families respond when I ask what questions they have. Many families who haven’t previously reached out are suddenly overflowing with questions.

The most common one I get is how they can support their child’s academic journey at home. Parents also frequently request updates about behavior. Understand that just because a family isn’t asking these questions proactively doesn’t mean they don’t care. When I explicitly ask parents what they need, their responses make it abundantly clear that they are deeply invested in their child’s schooling and success.

I’ve also learned that many families—especially those who speak a language other than English at home—may not know that there are many ways to support their child’s growth, even if classroom instruction is not in their home language.

Think about what tips and resources you can most easily provide: Do your students’ parents know that reading or reciting poems, songs, or chants in their home language helps literacy growth? Could you send home simple board games from the classroom to reinforce key skills? Would signing up for a library card give them access to resources they didn’t know were available? Many caregivers of ML/EL students have told me they lack the tools to get involved—but are eager to engage once given tangible strategies.

How teachers can go the extra mile

In order to give our students and their families the support they need, it’s critical that we challenge our internal biases and assumptions. If we assume parents are uninterested or uninvolved, we avoid an opportunity to think creatively about how to bridge communication gaps and facilitate family involvement. We also cut off a world of possibility for our students and limit their access to the academic success that comes from parent involvement.

Working with the families of ML/ELs may bring added responsibilities—but it’s also a unique privilege, full of new opportunities. In teaching ML/ELs, I’ve found that I get to be a cultural bridge—one of the people providing warmth, stability, and welcome to families navigating a new culture. School can be overwhelming in a new country or different language—but a teacher who goes the extra mile can ensure success for both students and families.

Additional resources

Families & Caregivers — Welcome to Amplify Desmos Math New York for grades K–5!

This is the initial version of the Caregiver Hub for Amplify Desmos Math New York. Para la versión en español, haga clic aquí.

Welcome to the Amplify Desmos Math New York K–5 Caregiver Hub for grades K–5. We’re so excited your student’s school has chosen our program! We designed this space to help you support your student in their math journey this year. Your hard work plays an essential role in your student’s math experience.

We hope your student enjoys using technology to explore math, working with friends to solve problems, and learning all sorts of new and interesting concepts. And we hope you love experiencing it with them!

Excited to learn together,
—The Amplify Desmos Math team

A math activity interface instructs to determine platform heights using a tube length. A student workbook titled "Amplify Desmos Math, New York, Volume 1" featuring children playing is also visible.

Introducing Amplify Desmos Math

Amplify Desmos Math is a core math curriculum built for kindergarten through grade 5. We developed the program around the idea that a structured approach to problem-based learning builds on students’ curiosity to develop lasting grade-level understandings for all students. Each lesson offers opportunities to develop students’ understanding; connect their ideas; grow their skill fluency; and empower them to ask questions, explore, and make discoveries.

Amplify Desmos Math uses a student-centered approach to instruction, which has been proven to significantly increase math learning. Our mission is for your students to learn math—and to love learning math!

In every lesson, the Amplify Desmos Math curriculum poses engaging and relevant problems to solve, giving students daily opportunities to think critically, work collaboratively, and actively participate in their own learning.

Screenshot of the Amplify Desmos Math New York, K-5 section on the Desmos Classroom website displaying a list of ADM lessons for different grade levels.

About student-centered math instruction

Student-centered instruction may look different from the way students have learned math in the past, and perhaps from the way you learned math. Instead of memorizing formulas and tricks, student-centered learning focuses on giving students opportunities to figure out how math works. Research shows that students and teachers alike prefer this method, and teachers report that student-centered instruction has helped their students learn more math.

A diverse group of students, one wearing a unicorn headband, looks at a teacher pointing to an amplify math bar graph on a board.

This way of learning helps students:

  • Understand how math concepts work.
  • Remember what they learn in class and apply their knowledge to new situations.
  • Perform better on standardized tests and have more growth in their grades than their peers who learn through other methods.
  • Learn to communicate in writing and verbally, understand and challenge the opinions of others, and build confidence in solving new problems.
  • Develop key skills for success in college and the workplace, like using technology, completing projects independently and with others, and persevering through difficult problems.

What materials do students use?

Amplify Desmos Math supports blended learning with supportive print materials and a unique digital experience. All Amplify Desmos Math K–5 lessons are available in a write-in Student Edition book. Many of the lessons are designed to include hands-on activities with manipulatives. An age-appropriate number of lessons are designed for students to use digital devices like laptops or tablets. These include enhanced digital experiences that teachers can assign to students.

Three animated women of diverse ethnicities smiling and discussing a math curriculum around a laptop at a table, with colorful abstract shapes in the background.

Here’s what you can expect for your students from Amplify Desmos Math:

  • Lessons that drive classroom discussions so students can work toward a shared understanding and sense of community.
  • Responsive feedback that interprets student responses in context and encourages perseverance and revision.
  • Easy-to-follow lesson plans tested in classrooms across the country, with clear teaching suggestions, strategies, and Math Language Routines.
  • Practice problems to support fluency and help students review previous topics.
  • Recommended differentiation suggestions for teachers so that they can meet the needs of diverse learners.
  • Formative assessments that provide information on student understanding so that they can adjust their instruction to meet the needs of all students in their class.
  • Summative assessments that help teachers understand what students know about the math content they have been learning.
  • Daily lesson-level assessments so that teachers can frequently check for understanding.
  • A caregiver resource for each unit that includes explanations of key math concepts and problems to try with your student.

When students use devices, teachers can monitor students’ work in real time, making sure they get the exact support that they need at every part of the lesson, in and outside of class. Here is a sample of what a teacher sees on their dashboard to help them monitor thinking and support student learning.

Screenshot of a digital class attendance and activity tracker with student names and checkboxes indicating their participation in various New York math tasks.

Students are also able to access their digital work at home. Here’s an article on how to navigate the student home page.

What does a lesson look like?

Students in an Amplify Desmos Math classroom can be seen (and heard!)—asking questions, debating answers, justifying their thinking, grappling with problems, and working together and independently.

Two students, one male and one female, are sitting at a desk with a laptop, discussing a project under a "math club" sign, with speech bubble icons above them.

Here’s what a typical Amplify Desmos Math lesson includes:

  • Warm-up: A short, attention-getting problem to get students interested in the lesson.
  • Activities: 1-2 mini-activities that challenge students’ problem-solving skills.
  • Synthesis: Discussion to review and bring together the important concepts from the lesson.
  • Show What You Know and Reflection: Questions for students to show what they know from the lesson. (Note: The “Show What You Know” lesson assessment is optional for the teacher to assign in kindergarten and grade 1)
  • Centers: Student-led activity stations that reinforce the math learned during lesson activities through interactive and often game-like formats. In kindergarten and grade 1, time for Centers is built into the last 15 minutes of every lesson.

Here’s what is available after the lesson to support, strengthen, and stretch students’ learning:

  • Differentiation: Mini-lessons, Centers, extensions, personalized learning, and fluency practice.
  • Practice: Additional problems your student’s teacher may assign for classwork or homework.

How can caregivers support math learning at home?

Use our Unit Support for Caregivers

We’ve created a Caregiver Resource for every unit of the program that provides a summary of key concepts, plus a problem from the lesson practice set you can work through with your student. Within each of the grade-level links below, you’ll find a Caregiver Resource document for each unit, in both English and Spanish.

Grade 1
Unit 1: Adding, Subtracting, and Working With Data
English
Spanish

Grade 3
Unit 1: Introducing Multiplication
English
Spanish

Grade 5
Unit 1: Volume
English
Spanish

Review practice problems together

Your student’s teacher may assign practice problems at the end of each lesson for classwork or homework. If your student has already completed the practice problems for the lesson, ask your student to walk you through how they solved each problem, or talk about any parts that were challenging for them. Ask your students follow-up questions to encourage the use of math language as they explain their thinking, such as: “How do you know?,” “How can you show your thinking?,” or “How would you describe that?” If students are stuck, ask support questions such as, “What information do you know here?” or “How could you represent this problem?”

Getting stuck is okay!

Emphasize that getting stuck is part of the process and a necessary part of learning. Many students (and adults!) fear making mistakes. However, research shows that making mistakes helps your brain grow more. When your student gets stuck on a problem, encourage them to try different strategies, even if they are not sure if they are right.

Find the math in everyday life.

Relate math to daily activities at home, whether grocery shopping, preparing a meal, or planning for a trip to the store. Your student can help you figure out how many more apples there are than oranges in the grocery cart, show how to split a sandwich into fourths, or figure out how much change you’ll receive in exchange for a ten dollar bill. Encourage your student to point out ways that you use math in daily tasks.

Read the Unit Story with your student.

Each unit in Amplify Desmos Math K–5 begins with a read-aloud story to engage students and provide context for the math of the unit. Elements and characters from the Unit Story then appear in lessons throughout the rest of the unit.

Access our Featured Collection of free K–5 Lessons and Activities.

Explore our latest free K–5 content in our Desmos Classroom Featured Collection. With our free collection, you can access:

  • Digital Lessons: Engaging interactive lessons
  • Mini-Lessons: A mix of print and digital activities designed for small-group instruction
  • Math Routines: Short digital activities to kick-start instruction and encourage math discussions
  • Bite-Sized Math Moments: Digital practice activities that use Polypad virtual manipulatives, designed to be used flexibly

Click here to access the collection and sign up for a free account.

How do caregivers access the program at home?

Your student will have access to all learning, practice, and assessment materials through the Amplify platform. Students can access the digital curriculum in school and at home by following these simple instructions.

  • Click the orange Login to Amplify Desmos Math button below.
  • Select Log in with Amplify.
  • Enter your student’s username and password provided by your student’s teacher.
  • Select your student’s grade level.

The 5 patterns we found in schools with improved reading

After a decade of tracking students’ pathways in early reading, we’ve been able to identify the schools getting outsized results—so we called them to ask what they’re doing! And so far, we’ve identified five consistent patterns.

1. Start early.

Schools that deliver the strongest results work hard to get kids on track — and often ahead — in kindergarten. Why? Those who get through the decoding stage by age eight begin building vocabulary and background knowledge through reading itself. These schools reason that it’s easier to get students ahead from the start than to try to catch them up later.

2. Surround kids with books.

Reading at the right level improves decoding, vocabulary, knowledge, and stamina. In a recent study, 11 students who read an extra seven minutes per day in class had substantially higher reading rates than other students. Those minutes add up to 160,020 additional words read each school year, and reading volume is important in building knowledge—even more so than cognitive ability.

3. Measure.

All schools collect data; the best ones think of it as measurement. For instance, they measure whether an intervention is having the expected impact. If not, they introduce new, temporary measures for attendance, perhaps, or fidelity of implementation. They are constantly tinkering and learning. They describe themselves as never satisfied.

4. Create a support team.

One of the most effective practices we found is ensuring that students get extra support when they need it. Classroom teachers can have a hard time reaching everyone, even with the best intentions. A cross-classroom team can base its decisions on careful data analysis and do whatever it takes to ensure extra resources are found and allocated where they’re needed most.

5. Beat summer.

Summer is brutal. Students often lose as much as half of their hard-won gains from the school year over the summer weeks, and the loss is especially steep for students from lower-income households. But even a few minutes a week of reminder exercises can reverse these losses, just as using a muscle prevents atrophy.

Reading at a college-entry level is a virtuoso performance. Even reading on level by third grade requires a constellation of successes — from mastering the sound-spelling patterns of English, to the painstaking accumulation of vocabulary and knowledge necessary to make sense of sentences. The simple verb to read hardly feels adequate to describe what students are doing when they make sense of the text. Ensuring the effortless enjoyment of reading for all is one of the great social undertakings of our time. We’re so happy to be working toward this noble goal with you.

Amplifying Your District Award winner

This Amplifying Your District Award honored two district leaders who are driving change using the Science of Reading in 2021. Motivated by low literacy rates in her school district, Alli Rice dug into the research behind the Science of Reading because she was determined to increase equity. Through various events and Knowledge Builders for the teachers in her care, she then effectively led the shift to a research-based curriculum in her district. Read on for our conversation with Alli about her work with the Science of Reading!

What does the Science of Reading mean to you?

For me, it’s really about equity. Thousands of kids are already a step behind because of their skin color, their neighborhood, or their zip code,  all of these things that really shouldn’t define their academic ability or their opportunity in life. I’ve looked at statistics around prison populations and illiteracy rates. Some, so many adults are functionally illiterate and they can’t fully understand. They can’t even read their prescriptions.

I also work for a district where most of our kids are on the lower end for socioeconomic status. We have a very high ELL population and 63 home languages spoken in my district. And we are the urban center of our area. Historically, we have been a balanced literacy district, but we have watched our test scores decline.

Since discovering the Science of Reading and this completely different approach to teaching literacy, I feel like I have unlocked Pandora’s box of potential. By addressing our core and aligning our teaching practices, our students can feel success and our teachers will, too. My teachers here have the biggest hearts of any educators I have ever worked with, and they work tirelessly day in and day out to support our students. We try to provide as many enrichment opportunities to all of our kids and to expose them to the greatest and the best. The ability to read, to me, is the greatest civil right. If we’re not providing them that, I can’t sleep at night.

What news, materials, or information do you consume to help you teach?

We use Amplify CKLA and Amplify Reading and those programs are just wonderful. I am also an avid listener of Science of Reading: The Podcast. We arranged for Natalie Wexler and Susan Lambert to do a live professional development session in our district, which was so fantastic, especially for our most reluctant coaches and administrators. Our district-wide LETRS training has also been life-changing. We currently have 800 people who are completing the training, which has helped to align the district and put us all on this path to success.

One particularly impactful thing, and that I rely heavily on for support, is my teacher cadre. Each cadre is about 14 teachers in the district and they represent all of our clusters. We’ve partnered up with our Diversity, Equity, and Inclusion department to do text bias reviews on materials, which has been important for our adaptations for cultural responsiveness. Our selection cadre came from that as well, when we landed on Amplify CKLA for K–3. The teacher input and camaraderie I get from my cadre is so instrumental and I am so grateful for them.

What advice do you have for teachers starting out with the Science of Reading?

Find your people, find your community. I remember Margaret Goldberg’s presentation during last spring’s Science of Reading symposium, and how she said you need to find your dots,  you need to seek out like-minded people and go where they are. Find those people who are ready to make the change like you are, or perhaps have already done it, and can be that positive support system you need to make a difference. Don’t be afraid to message people on Twitter or Facebook or LinkedIn, ask about their experiences, and build that community around you. Find the ones who are going to partner with you, who will lead you the right way, who will take your calls. And read all the books!

Watch the Science of Reading awards show!

Bringing joy to learning in the science classroom

As we prepare for an exciting new season of Science Connections: The Podcast, we’re looking back at past seasons and sharing some of the amazing conversations we’ve had so far.

We’re so grateful to our 15 guests whose insight, expertise, and generosity have made our podcast (if we may!) one of the best science podcasts out there.

If you’re new here, welcome! In Amplify’s Science Connections: The Podcast, host Eric Cross talks to educators, scientists, and subject matter experts about ways to best support and inspire the next generation of 21st-century scientists.

Get ready for season 3, with all-new topics and speakers, premiering in March!

Our first featured throwback episode, Bringing community and joy to the learning process in K–8 science instruction, features physicist Dr. Desiré Whitmore!

First, meet Dr. Whitmore

Dr. Whitmore has nicknamed herself “Laserchick.” It’s a reference to the focus of her postdoc work at UC Berkeley, where she designed and built attosecond lasers. (These laser pulses, which emit x-ray light, are the fastest ever measured).

She later became a professor of laser and photonics technology at Irvine Valley College, as well as a science curriculum specialist for Amplify. She’s now senior physics educator in the Teacher Institute at the ExplOratorium in San Francisco.

There, she works to support middle and high school science teachers in teaching through inquiry. On a given day, she says, her role may include “making fudge or blowing darts with marshmallows across the room.”

But it all began with bubbles—the ones she’d blow as a child with her beloved great-grandmother. She was also the kind of kid who would do experiments in the microwave or take apart the vacuum cleaner. “I was always asking questions,” she says.

“Everything we do is science”—and more.

Here are some key takeaways from Dr. Whitmore’s conversation with Eric Cross.

  • Let students do their thing. Whitmore and Cross talked about students who didn’t hew to the letter of the assignment—and actually went beyond. That’s more than okay.

I think it’s amazing when we can realize as teachers that no, our job is not to just enforce rules on our students. Our job is to help students achieve more learning.

—Dr. Desiré Whitmore
  • Representation truly matters. Dr. Whitmore, who is Black, recalls a chemistry teacher she had in high school who was also Black. “He looked like me and spoke the way I spoke,” she says. He also recognized that she knew a lot about chemistry, and half-jokingly encouraged her to teach the class sometimes. In Whitmore’s experience, representation like that can supersede content knowledge.
  • Science is everything and everywhere. “Science is something that everyone in the world should and does do,” says Whitmore. She sees part of her job as “helping people understand that everything we do is science.”
  • Show scientists as real people. Whitmore recalls a time when an eighth-grader she’d known growing up was thrilled to recognize her in an Amplify Science video. The student knew her as a “regular human” who likes “Star Trek” and “Star Wars,” but now also sees her as a scientist. “That really brought home for me the importance of my work,” she says.
  • Put teachers in students’ shoes. As part of professional development, Cross and Whitmore agree that it’s important for teachers to remember how it feels to have a question—to not know. “That helps me be in the position of my students emotionally,” says Cross.

Perhaps that’s the most powerful way for teachers to connect with their future scientists: “To experience science as a learner,” says Whitmore.

Additional resources

Inquiry-based learning: 3 tips for science teachers
New professional development series for science educators
Celebrate student scientists with classroom posters, activities, and a special giveaway!

The power of technology in the math classroom

You might say math and tech go hand in hand. And these days, of course, kids and tech go literally hand in hand. So it makes sense that using digital tools in the math classroom can help teachers reach students, and teach the math content they need to learn. But truly integrating technology into math instruction is not just a matter of adding random gadgets and gizmos. We need to do more—especially if we want to leverage the power of math technology to engage all students.

Why integrate technology into the math classroom

Integrating technology into instruction delivers numerous benefits in the classroom–perhaps especially in the math classroom.

Numerous studies suggest that technology can support student learning in the math classroom. This tech might take the form of graphic calculators, digital manipulatives, or learning software. In general, such tools have been shown to help students improve both their understanding of math concepts and their performance on tests.

Thoughtful tech has these effects in part because it can make math more engaging. Students are generally more excited to dive into a visually appealing and interactive program than a black-and-white math textbook.

Integrating technology into a math classroom also means:

  • Personalized learning: Students can work at their own pace and get tailored guidance and feedback.
  • Collaboration: Students can work together regardless of their physical location.
  • Real-world applications: Technology can simulate real-world scenarios that require mathematical reasoning and critical thinking skills.
  • Saving teachers time: Technology helps teachers assess learning more effectively, providing real-time feedback and helping them identify where students need support.
  • Preparing students for the future: After all, most jobs require the use of technology!

How to integrate technology into the math classroom

The most effective technology approaches in the math classroom are active, not passive. They also invite deep thinking and productive struggle rather than speed and rote memorization.

The National Council of Teachers of Mathematics (NCTM) includes this guidance in its Principles to Action:

“An excellent mathematics program integrates the use of mathematical tools and technology as essential resources to help students learn and make sense of mathematical ideas, reason mathematically, and communicate their mathematical thinking.”

The NCTM recommends that teachers: “incorporate mathematical tools and technology as an everyday part of the mathematics classroom, recognizing that students should experience ‘mathematical action technologies’ and physical or virtual manipulatives to explore important mathematics.”

Here are just a few approaches that enhance engagement:

  1. Use interactive whiteboards or projectors: You can display math problems and solutions, diagrams, graphs, and simulations, allowing students to interact with and manipulate visual representations of math concepts.
  2. Use graphing calculators and virtual manipulatives: They can help students visualize and solve complex math problems, and prepare them for more advanced mathematical concepts.
  3. Use gamification techniques: Can make math more engaging and fun for students.
  4. Use online collaboration tools: These tools can help students work together on math problems and projects, even when they are not in the same physical location.
  5. Use select social media and other online platforms: To create math communities where students can collaborate, share resources, and ask questions.
  6. Use math software and apps: These programs can help students practice math, solve problems, and visualize math concepts in 3D or interactive models.

How Desmos Math 6–A1 delivers

Desmos Math 6–A1 is just that kind of program. It provides dynamic and interactive digital math learning experiences, alongside flexible and creative print activities. Its teacher dashboard is designed to encourage classroom discussion and collaboration. It invites students to explore a variety of approaches—and invites teachers to celebrate and develop interesting thinking in their classrooms.

The dashboard also shows teachers actionable formative assessment data for each student and the entire class, and allows them to leave written feedback for students in their lessons.

And we know it works. Teachers and students in our pilot program said that students learned more with Desmos Math 6–A1 than with their prior program. (See case studies in a large midwestern school district and in Naugatuck Public Schools.)

What’s more, Desmos Math 6–8 has earned perfect scores and an all-green rating from EdReports. This is a powerful affirmation not only of our program, but also of high-quality instructional materials, student-centered instruction, and thoughtful technology in the math classroom.

Learn more

Start your 30-day free trial of Desmos Math 6–A1.

Beyond prompts: How to teach writing for middle school student success

Writing is hard. Natalie Wexler, who co-wrote The Writing Revolution: A Guide to Advancing Thinking Through Writing in All Subjects and Grades, has described it as “the hardest thing we ask students to do.”

And writing is also hard to teach—perhaps especially to middle schoolers.

Writing education experts such as Steve Graham, Ph.D., say that, as important as writing is, it often gets less attention due to competing educational demands, like the need to teach subjects connected to high-stakes testing, the pressure to teach to a given test, and the siloing of writing as an independent skill untethered to content.

But writing is essential—not just as a means of expressing knowledge, but also as a means of building it. That’s why, when it comes to middle-school writing instruction, we need to go beyond just writing prompts. So how can teachers provide the strongest possible writing instruction for middle-school students? Keep reading.

Student writing: Why it matters

Learning to write makes you a better writer, but it also makes you a better reader—and a better learner.

In a meta-analysis of more than 100 studies, Steve Graham and Michael Hebert, Ph.D., found that writing about text improves comprehension and learning even more than reading alone, reading and rereading, or reading and discussing.

“Combining reading and writing is part of the Science of Reading,” writes literacy educator Tim Shanahan, Ph.D. “If you want better reading scores, the Science of Reading says do not neglect writing, nor dispatch it to someplace else in the curriculum. When you feel especially pressured to improve reading achievement, that is the time to embrace more tightly the combination of reading and writing.”

Shanahan also notes that readers who write and writers who read are best equipped to observe what authors do to convey meaning and what readers need in order to understand writing.

Current ELA standards recognize the interplay between reading and writing by articulating these goals: using writing to improve learning from text and using the reading of multiple texts to improve the writing of syntheses or reports.

Writing activities for middle school

Even with challenges and constraints, educators can find ways to engage students and transform their writing. When planning writing activities with your middle-school students, it’s important to keep them captivated, incorporate writing instruction throughout your lessons, and differentiate to meet the needs of all of your students. Here are some principles that will help:

  • Detach writing from getting it “right.” Seymour Papert theorized that students become better thinkers when they’re not attached to one outcome—not afraid to be “wrong.” Of course, sometimes there is a correct answer, but it’s the process of seeking it that counts. Offer writing assignments that encourage—and reward—risk-taking and creativity.
  • Integrate writing everywhere. Help students build both knowledge and writing skills by including writing exercises across subjects, including science.
  • Scaffold with sentence frames and modified prompts. Middle-school students often know what they want to say, but not how to say it, especially if they are multilingual learners. Sentence frames and modified prompts—such as “Tom convinces his friends to whitewash the fence by saying…”—can help with that. They reduce linguistic barriers, enabling students to produce writing and speech more complex than what they could have done on their own—and giving you a sense of their level of understanding.

Writing can be a powerful tool to help students deepen their comprehension of written text, expand their knowledge, and develop as communicators. Learn more about the best strategies and activities to use in your classroom. These will put you on the best path for helping your students thrive as writers, readers, communicators, and lifelong learners.

More to explore

Nurturing young children’s curiosity and wonder in the math classroom

Based on my experience in math education, I find that many pedagogical structures or moves sound great in theory, but are often easier said than done. Because of the complexity, asking students to construct mathematical arguments has been one of those things for me. Fortunately, over the years, I have had the joy and privilege to work with Jody and Chepina, whose thinking around math argumentation is grounded in theory and paired with practical and actionable advice and structures. I am so excited for others to share in their deep thinking and look forward to seeing the impact their work will have in classrooms.

—Kristin Gray, Executive Director, Math suite, Amplify

Mathematical argumentation as an opportunity for curiosity

Students bring curiosity and wonder to the classroom every day. When we’re attending to their ideas, we can find more opportunities for mathematical argumentation in our math lessons. Let’s look at how these opportunities arise in a first-grade classroom.

The lesson and card sort activity

The purpose of the lesson was for students to identify equivalent addition expressions by sorting cards, each with a different expression. Students quickly noticed that there is more than one way to get the same value. They could even begin to see the commutative property in action when shown cards with addends in opposite order: 4 + 3 = 3 + 4.

While sorting addition expressions, rather than organizing the cards in piles by their value, one student named Jenna organized the cards in columns. This student-led creative modification to the card sort structure allowed for different noticings and wonderings to emerge. She started by creating a row across the top with cards showing one addend of 0. At first, she wasn’t consistent with the top card being 0 + x or x + 0, but over time changed them so that they were all 0 + x. Then she filled in the last column with expressions equal to 10. As she added cards, she started to change the order so that the first addend on the cards increased going down the column and the second addend decreased.

Math lesson and card sort activity.

As Jenna added each card to her organizational structure, the teacher asked where that card would go and how she knew. When asked about the 2 + 6 card, for example, Jenna said, “Because this is counting to 8, and this”—she pointed to a gap—“has to be 7, because [the 6 is] 2 less than 8. It fits here because these are all twos” (in the row). Jenna was coordinating several characteristics of rows and columns within the structure of the chart.

As Jenna continued to fill in the chart, she noticed yet another pattern. Pointing to the step pattern, Jenna noticed that, “There is a stair step. The pattern keeps going. There’s one more way to make the total as it gets bigger.”

Rows of flashcards with math lessons.

We could state this conjecture more precisely as: “For any whole number n, there are n + 1 ways to add two whole numbers to get a sum of n.” Jenna was making sense of big math ideas and noticing structure embedded in arithmetic.

Reflecting on the experience

As we step back and reflect on what we experienced with Jenna, we wonder what could happen next. How might Jenna justify her thinking? She noticed the stair-step pattern and multiple ways to arrive at the total. What might she say if we asked her, “Why is that happening?” Or if we gave her a tool such as linking cubes and asked if she could use the cubes to show why that works? Are there other questions that could have nudged her to extend her thinking, such as, “Will that always work?” or “What numbers does it work for?” Is there a tool or representation that would help her continue her reasoning?

We can also think about what might happen if we shared Jenna’s idea with the other students. How might they respond to Jenna’s noticing? Would her ideas lead others to see and use structure in similar ways? How would they make sense of her ideas? Perhaps this is an opportunity to engage students in each other’s ideas.

Opportunities for curiosity

The opportunity for Jenna and her classmates to make sense and explore their natural curiosity emerges from a classroom environment that’s playful and filled with wonder—where children are given time to explore and interact with materials and each other. We noticed that as Jenna progressed through the cards, she refined and added on to her thinking. This is evident in the first row of cards. She grouped cards with 0 as an addend, then began to sequence them, and later considered the positioning of the addends to 0 + x. As we might infer from the interaction of the teacher, there isn’t one right way to think about the task, nor one way for the teacher to encourage students to think about it. We hear the teacher ask Jenna to share her reasoning: It’s not a question posed to evaluate Jenna’s thinking, but rather to gain insight into her thinking—something the teacher is genuinely curious about.

In addition to the classroom environment, the card sort also presented an open-ended opportunity. Students made sense of the sort in many different ways, some finding related pairs and starting to identify (not yet naming) the commutative property, others grouping problems with a common addend in piles. All students had access to the task and time to make sense of it.

We share the story of Jenna as one of many instances where young children have shared their brilliance with us. Their wonder and curiosity inspired us to explore their ideas along with K–2 teachers. We saw students notice, wonder, conjecture, justify, and extend ideas that led to a deep understanding of key mathematical concepts while integrating mathematical argumentation.

We share ideas like the brilliance from Jenna in our new book, Nurturing Math Curiosity with Learners in Grades K–2, where we also make connections among instructional routines, center, and card sorts. Our book also discusses supporting students in curious exploration, building on what they already bring to the classroom as a way to bring opportunities for mathematical argumentation into our lessons.

Rumsey, C., & Guarino, J. (2024). Nurturing Math Curiosity with Learners in Grades K–2. Solution Tree. Bloomington, IN. ISBN: 9781960574367

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5 ways to boost biliteracy with the Science of Reading

Research shows that bilingual instruction (including dual language instruction and dual language immersion) supports the long-term success of dual language learners—in both languages, and beyond.

How do we best support those students?

More precisely, how are we serving our emergent bilingual students so that they can develop their biliteracy? This is a question posed by biliteracy expert and Amplify product specialist Alestra Flores Menéndez. And in our recent webinar Leveraging the Science of Reading to Boost Biliteracy, she and other experts attempt to answer it.

The power of biliteracy

Knowing more than one language is a powerful tool for opening up new worlds, meeting different people—or even just asking directions in an unfamiliar place.

But that’s not all. Bilingualism itself is a cognitive strength. Research conducted in 2015 by Claude Goldenberg and Kirstin Wagner links bilingualism to increased control over attention, improved working memory, greater awareness of the structure and form of language, and better abstract and symbolic representation skills.

“Our multilingual learners really are using their brains differently,” says Flores Menéndez.

And as with all students, we need to start early to make sure they’ve got their best shot at literacy.

The number of emerging bilingual students in our classrooms is growing, with 15.5% of them in grades K–3. That group includes the key developmental year—third grade.

Third grade is seen as the last year students learn to read before they start reading to learn. Without proficiency by fourth grade, they’re at risk of struggle across subjects.

And for many students, literacy is biliteracy. So how to make sure they get there?

Helping all multilingual learners succeed

“Bilingual instruction has been proven to be the most effective,” says Amplify biliteracy specialist Ana Torres, M.Ed., citing research by Virginia Thomas and Wayne Collier.

Other models (English immersion, transitional bilingual) are a fit for students with certain language profiles. As Torres notes, “We have to be intentional and purposeful to make sure there are positive outcomes for all students.”

But the proven impact of the bilingual model shows this: Knowledge of, and in, a second language builds from the first.

Foundational skills, vocabulary, and knowledge are essential, and all transfer to the second language—through explicit, research-based instruction.

Key elements of that instruction:

  1. Assessing literacy in both languages. “Assessing what [students] know in their native language is crucial to their success in acquiring that second language,” says Torres. A 2019 study at the University of Oregon looked at phonological awareness among Spanish-speaking pre-K students. (Phonological awareness represents the understanding that words are made up of a series of discrete sounds.) When assessed in English, 63% of students needed Tier 2 or 3 intervention. But when assessed in Spanish, only 21% did. “We need to look at the overall picture of students’ literacy,” Torres says. “Otherwise they’re going to get the wrong instruction.”
  2. Deliberately bridging from the native language to the new one. Spanish and English share many elements, among them letter sounds. If students know the sounds of the letter m in Spanish, they’ll be able to map that sound onto the same letter in English.
  3. Grounding in the Science of Reading. The Simple View of Reading has been validated in more than 150 studies across multiple languages. Foundational skills, vocabulary, and knowledge can all transfer through explicit instruction.
  4. Honoring students’ home languages, cultures, and community experiences. “It’s well documented that when children feel a sense of belonging, they’re more motivated to learn and experience more success in school,” says Menéndez. “Students should see themselves reflected positively in any curricular material.”
  5. Emphasizing knowledge. Perhaps you’re familiar with the iconic baseball study. Students with prior knowledge of baseball greatly outperformed their peers on reading comprehension—even those peers who were stronger readers. “Building knowledge is absolutely essential for literacy development,” says Menéndez.

Learn more

Explore Amplify Caminos.

Watch the full webinar: Leveraging the Science of Reading to Boost Biliteracy.

Biliteracy and Science of Reading principles in English and Spanish.

Read about The Importance of Dual Language Assessment in Early Literacy.

Binge our biliteracy podcast playlist.

Dyscalculia: What educators should know

Two children seated at a table engage with colorful number cubes and a pencil beside a worksheet—a delightful way to explore math. This playful setup subtly acts as an informal dyscalculia screener, helping spot characteristics of dyscalculia in young learners.

Some kids love math. Some kids like math. Some kids struggle with math, or struggle with math anxiety. And some kids have dyscalculia, a specific learning disorder that affects one’s ability to understand numbers and learn math facts.

As awareness has continued to grow, educators today are curious to know: What are the characteristics of dyscalculia? How can I help a child with dyscalculia? What should I know about dyscalculia screeners? We’re here to provide some answers.

Dyscalculia: What it is and is not

According to the Child Mind Institute, dyscalculia (sometimes called “developmental dyscalculia”) is a term used to describe specific learning disabilities that affect a child’s ability to understand, learn, and perform math and number-based operations.

Honora Wall, Ed.D., founder of the Dyscalculia Training and Research Institute, calls it “a type of neurodivergence: A difference in brain development or function.”

That’s an important distinction: Dyscalculia is a neurological condition that affects numerical cognition and processing. It has nothing to do with being “bad at math” or not “trying hard enough.”
Between 5 and 7% of elementary school-aged children may have dyscalculia, which is believed to affect girls and boys equally.

It is important to note that not all difficulties in math are caused by dyscalculia. Dyslexia, ADHD, and other conditions can also pose challenges for math students.

Nor is dyscalculia simply “math dyslexia.” Dyscalculia and dyslexia are entirely separate learning disorders that affect different areas of cognition and involve distinct difficulties.

How dyscalculia might present itself

Dyscalculia manifests in various ways in the math classroom. Here are some examples of how it can appear:

  • When engaging in activities like games involving dice, students may need to count the individual dots to recognize a number rolled, rather than intuitively recognizing it.
  • Students might have difficulty connecting the numerical symbol “5” (for example) to the word “five.” Making this connection is essential for associating numbers with their meanings.
  • Students may be delayed in learning to count, or lose track or rely on visual aids (like their fingers) when they count.

Such students may also have a hard time:

  • Solving math problems.
  • Recognizing or creating patterns.
  • Learning basic math functions.
  • Estimating how long a task will take.
  • Processing visual-spatial ideas such as charts and graphs, or even telling left from right.
  • Remembering phone numbers or zip codes.
  • Playing games that involve counting or keeping score.
  • Telling time.

The connection between mathematics anxiety and dyscalculia

Math anxiety is an emotional response to math that presents as apprehension or fear. Some call it mathematics phobia. It may include physical symptoms such as sweating, rapid heartbeat, shortness of breath, and other physical symptoms of anxiety. It’s similar to other types of anxiety, but it’s exclusive to math.

But, most important in this context, it’s not itself a neurological or cognitive condition.

So dyscalculia and math anxiety are not the same, but they may go hand in hand—perhaps with one exacerbating the other. Students with dyscalculia might develop math anxiety due to repeated challenges and frustrations in learning math.

Understanding this connection—and working to alleviate math anxiety—is crucial for educators aiming to create a supportive learning environment.

Tips for assisting students with dyscalculia

Here are some practical strategies educators can use to support students with dyscalculia:

  • Teach positive self-talk and persistence: Encourage students to develop a “growth mindset,” reinforcing that effort and persistence (as well as making mistakes) are essential to overcoming challenges.
  • Provide organizational aids: Use graph paper to help students line up numbers correctly, which aids in precision during calculations.
  • Use manipulatives: Tools like counters and blocks can make math feel more tangible, helping students grasp abstract concepts.
  • Focus on singular tasks: Present one math problem at a time to prevent students from feeling overwhelmed and allow for focused attention.
  • Allow more time: Give students the opportunity to work at their own pace, acknowledging that they may need more time to process numerical information.
  • Grant calculator access: Allowing calculators can reduce stress and help students solve problems more efficiently.
  • Make math fun and engaging: Incorporate interactive platforms such as Desmos Classroom to create an enjoyable and interactive learning experience.

More to explore

S3 – 06. Bethany and Dan take on Twitter!

Promotional graphic for Math Teacher Lounge Season 3, Episode 6, featuring Bethany Lockhart Johnson, Educator, and Dan Meyer, Director of Research at Desmos.

In this episode, Bethany and Dan take a look at several tweets that caught the most fire on Twitter during the 2021-2022 school year. The pair answer questions about viral teaching methods, the best teaching advice you can give in three words, and if students should use pencils or pens in class. Join them as they take on those questions and several others in a fast-paced episode.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:02):

Hey folks. Welcome back to the Math Teacher Lounge. I’m your co-host, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I am Bethany Lockhart Johnson. And I’m your co-host, Dan! Hi!

Dan Meyer (00:12):

We’re co-hosts! Hey! Great to see you.

Bethany Lockhart Johnson (00:13):

Dan, this is the last episode of Season 3. Three seasons!

Dan Meyer (00:19):

It’s gotta have a cliffhanger. What will the cliffhanger be? You know?

Bethany Lockhart Johnson (00:22):

The cliffhanger is that we love having guests! It’s one of our most favorite things, because selfishly, we love to talk to all of these amazing folks who are doing this interesting research and thinking about amazing things. But for this last episode, it’s just you and I, Dan. Cliffhanger!

Dan Meyer (00:40):

Yeah. I like this. I like this. So the cliffhanger was last episode, and people are all like, “So who’s the last guest gonna be of the season before we roll out into summer?” And yes, as Bethany said, we love all the fascinating guests we’ve had on throughout these last few seasons. And we realized…who is more fascinating to each other than both of us? You know, let’s talk to each other about things, right? <Laughs> You get that! You get that! Or am I alone here in this? We had this idea about what we should talk about here, and that’s this: I am on Twitter a lot. I’m @DDMeyer on Twitter; throw me a follow; might follow back; who knows? I don’t tweet much. Bethany, what’s your handle on Twitter? Let ’em know.

Bethany Lockhart Johnson (01:22):

I’m @LockhartEdu, and I was much more active pre-mamahood. But I’m still up in there. Go ahead.

Dan Meyer (01:30):

Yep. In there. Yeah, great. So I’ve been keeping track of the hottest conversations in math education Twitter, the conversations that the most people who kind of describe themselves as math teachers in their bios and whatnot have been replying to. We’ve got some little things working in the background, keeping track of this sort of thing. And so we are gonna bring you folks some of those extremely hot conversations, and even better than the questions—which we hope you’ll reply to and tag us in your replies—even more than those questions, we’ll bring you our answers—our answers!—to those questions. Can you believe that? We’ll fully settle these questions! Won’t we, Bethany? My gosh, won’t we?

Bethany Lockhart Johnson (02:15):

Jeez Louise! No! Dan Meyer, the point is not our final word on it! The point is this episode, we’re furthering the conversation. We wanna hear from listeners about what do you think?

Dan Meyer (02:25):

Right. You’re right. You all need someone in your life like Bethany who will help you become the best version of yourself. So here’s the deal. We have several questions in a few different categories. We’re gonna bust through some quick ones, pretty quick. And, uh, there’s some meaty ones as well. Let’s get into it! The first questions come to you all, and us, courtesy of MTL guest Howie Hua, who has a renowned knack for just creating math memes, but also conversation starters that really capture the curiosity and answers of of a grateful nation. So Howie’s first question, which I’ll pose to Bethany, is, “What’s your favorite number?” Bethany? And why is it your favorite number?

Bethany Lockhart Johnson (03:14):

Oh, I love it. OK. Well, the first thing that came to my mind is 12. ‘Cause It’s a highly divisible number. I mean, 2, 6, 3, 4—I love it. And it coincides with the day and month of my birth. Which, like, the double-digit…come on, 12, 12, 12, 12. I dunno, am I giving away, like, my bank security code <laugh> or anything by saying that?

Dan Meyer (03:41):

Yeah. What’s your favorite PIN?

Bethany Lockhart Johnson (03:43):

Let me change my PIN. Yeah, it’s just such a happy, happy number. Well, 12 is, you know, 10 and 2. Two more. Anyway. Love it. What about you, Dan? What’s your favorite number and why?

Dan Meyer (03:55):

I’m into it. I’m into it. I think I would choose 16. Because it’s the first number for me when it was like, “Oh, you can keep on making numbers forever!” Where I’m like, OK, 2times 2 is 4. Great. That’s kind of an elemental expression in mathematics. Four times 2 is 8. OK. But then, 8 times 2 is 16, and it’s like, “Oh, you can just keep doubling that thing over and over and over again!” And I can recall feeling pretty excited that numbers are just like, out there for the finding. For the taking. Cool stuff.

Bethany Lockhart Johnson (04:33):

I’m sorry. Wait, I have to interrupt. You went 2 times 4 is 8 and you didn’t go 4 times 4 is 16? You went 8 times 2 is 16? You wanted to keep the 2 the same?

Dan Meyer (04:49):

Yup. Yup. You can keep on doubling. You can keep on doubling numbers and it just keeps on going.

Bethany Lockhart Johnson (04:53):

More evidence that our brain works very differently.

Dan Meyer (04:56):

We learn more about each other…let me keep this rolling with Howie questions. OK? Howie says, “If you could co-teach with one teacher from Twitter, who would you choose?”

Bethany Lockhart Johnson (05:06):

Oh, oh, it has to be a teacher?

Dan Meyer (05:11):

Or anybody, I guess. I mean, like, I know you love Oprah.

Bethany Lockhart Johnson (05:15):

Can I co-teach with Oprah?

Dan Meyer (05:16):

Yup, yeah, so there we are. <Laugh> Yup. OK. Fair enough. We have to work Oprah into every single episode.

Bethany Lockhart Johnson (05:23):

I’d just love to sit and like, we’d read together, we’d read to the students, and then we’d talk…I mean, obviously it’d be Oprah. But if we’re thinking more of like MTBoS, like math Twitter blogosphere-land, I suppose the person I would wanna co-teach with honestly would probably be Allison Hintz. One of our former guests as well. Her book, Mathematizing Children’s Literature, with Antony Smith, that book—I just love the idea of sitting and doing a read-aloud and then diving into some juicy math that’s inspired by what comes out of that read-aloud. So yes, that’s who I pick. Allison! Let’s co-teach!

Dan Meyer (06:00):

<Laugh> Shout-out to Allison.

Bethany Lockhart Johnson (06:01):

What about you?

Dan Meyer (06:03):

I would choose MTL guest Idil Abdulkadir—because, and this relates to Allison and also Elham Kazemi—they talked about, in our episode about teacher time-outs. And I’m choosing someone who I think is—like I’ve never seen Idil teach, but I work with Idil at Desmos and think she’s fantastic. But what I really want in a co-teacher is someone that I can say, “Whoa, time out, do you see what’s going on here? This is really interesting. What should we do next about this?” And have a little strategy sesh in front of the kids and no one gets freaked out by that. And I think that that’d be a pile of fun. Idil seems like she’d be receptive to that kind of interaction, teacher to teacher. So that’s my vote right there.

Bethany Lockhart Johnson (06:48):

Opportunity for you to grow your own practice, Dan.

Dan Meyer (06:52):

Yeah, yeah, exactly. 100%.

Bethany Lockhart Johnson (06:56):

So Dan, I actually have a question for you from Howie. If we’re on the Howie tweet train, I have one from Howie too.

Dan Meyer (07:04):

Howie had some fire tweets, some fire tweets this current year. Yep.

Bethany Lockhart Johnson (07:08):

Dan, I wanna know: Do you prefer doing math in pen or pencil?

Dan Meyer (07:16):

Ooh, yeah. Oh, I see that Howie says, “I don’t mean to start any drama, BUT,” and then asks the question–

Bethany Lockhart Johnson (07:23):

But!

Dan Meyer (07:24):

I think that Howie lives for drama. I think he knows he’s messy. He lives for drama. He knows what he’s doing this with this question here. He knows.

Bethany Lockhart Johnson (07:32):

DRAAAAMAAAA!

Dan Meyer (07:32):

He knows what he’s doing. Yup. So I would just say it depends. Is that cheating? Like if I’m doing math to learn, or if we are learning in that process, then I want to use pen, actually. I wanna see the tracks of the thinking. And if we’re doing it for presentation, like if I’m presenting something, I wanna…I guess that’s an area where I’d be fine to not erase things. I don’t wanna prep it so it’s, you know…I guess you could use pen for presentation also. Just pen. Period. But I wanna see the tracks of the thinking if we’re doing some learning versus presentation. What about you?

Bethany Lockhart Johnson (08:09):

Well, I heard the voice in my head telling one of my kindergartners, “No, you cannot do that in sparkly pen. You need to do it in pencil.” And I was like, “Wait, whose voice is that?” It was one of my math teachers telling me I couldn’t do it in pen! Why couldn’t this kid do it in pen? Sure! Do it in a sparkly pen! So I wanna say do it in pen. And since usually pen is what I have around…I mean, I do crosswords in pen, Dan.

Dan Meyer (08:36):

Wow, wow. With a piece of paper and math, you have lots of room to re-revise and cross off…but those little, little boxes on the crossword, that says a lot about your commitment to pen.

Bethany Lockhart Johnson (08:46):

I got really good at making an A into an H or a P or whatever we need. So I would say, “Hey, if you’re in the room with your kiddos and you’re doing math, if somebody wants to do pen, let them do pen.” But I do know that I’ve seen teachers say you need to do pen so that I can see all of your thinking. So I think I hear what you’re saying. But do you think it should be like a classroom rule or something?

Dan Meyer (09:13):

Oh, no, no, no. I mean, I’m gonna ask you like, “How’d you get to this destination?” And I wanna know process somehow, and I think you’ll get tired of having to explain it verbally rather than just, like, showing. Just don’t erase stuff. Don’t scratch stuff off. Let’s let’s see how you’re getting there. That is what I’m into.

Bethany Lockhart Johnson (09:30):

Thanks, Howie, for that trio of thought-provoking tweets, because I genuinely wanted to know what Dan thought and what our listeners think. I mean, Dan, I gotta say: Howie, you say you don’t wanna cause drama, but I gotta say I’m with Dan on that—

Dan Meyer (09:50):

Got the gift. Got the gift for drama. We’re still friends though. So I’m happy about that. Our next section, I got a few more questions queued up here and these ones relate to advice for educators, advice for yourself. Good advice, bad advice, that kind of thing. So let’s jump in. I would love to know—this one’s from Pernille Ripp—I’m very curious, Bethany, what is the worst teaching advice you have gotten in your life, ever?

Bethany Lockhart Johnson (10:19):

<Laugh> Ooh. OK. Um, worst teaching advice was: “That’s OK, just move on anyway.” And that was in terms of pacing. It was like, students needed to do a deeper dive and the teacher who I was chatting with said, “No, no, it’s fine; it’s fine; just move on. Just move on to the next chapter.” That was probably the worst advice, because no, I don’t think that’s what I should have done at all! <Laugh>

Dan Meyer (10:48):

Right.

Bethany Lockhart Johnson (10:48):

But I was a first-year teacher and I was trying to figure it out. And I learned that that was not good advice. And I understand the pressure of pacing. But it was totally antithetical to the type of listening to my students that I want to do in my craft. And this teacher meant well, but that was not good advice, teacher! <Laugh> What about you, Dan? What is the worst teaching advice?

Dan Meyer (11:13):

I dig that. That feels similar to one of the replies to Pernille here. Frances Klein says, “Never let them know you’ve made a mistake” being particularly bad advice. You know, just this like idea of like moving along, covering your tracks, not backtracking or admitting mistakes, those all feel kind of a piece. The worst advice I think I’ve ever received, and I wasn’t given this often, but it’s echoed by a lot of the commenters here on this tweet, which is “Don’t smile until X, Y, or Z,” where X, Y, and Z are like Christmas, October, December, January. Just the idea that you’ve gotta develop—

Bethany Lockhart Johnson (11:54):

Wait, what?

Dan Meyer (11:55):

<Laugh> Did you never hear this from anybody? Don’t smile until Christmas? Perhaps this is more—

Bethany Lockhart Johnson (11:59):

I’m a kindergarten teacher! Can you imagine? If I don’t smile the second they walk in? The tears?! The parents’ tears?! The kids’ tears?! If I’m just like, stoic?

Dan Meyer (12:07):

Yeah. Well.

Bethany Lockhart Johnson (12:08):

So explain it to me.

Dan Meyer (12:10):

Well, the idea is, is that, you know, for older kids, they’re scoping you, they’re clocking you for weakness, they’re looking at you, they’re looking to take advantage. And so “don’t smile until Christmas” is like, hey, you can always relax. You can always relax your discipline, but you can’t UN-relax it if you start out, you know, Mr. Happy Pants Meyer. Which—

Bethany Lockhart Johnson (12:33):

Smile perceived as weakness.

Dan Meyer (12:36):

Yeah. Very obviously poor advice. Eventually you come to realize that like having a rapport and a relationship that is trusting and warm and demanding, that has high expectations, that’s the best kind of classroom management. Not some kind of persona built around intimidation or stoicism, that kinda thing. So, terrible, terrible advice!

Bethany Lockhart Johnson (13:01):

I feel like I did have a few of those math classes. Yeah.

Dan Meyer (13:04):

Yeah, exactly. <Laugh> You loved them, right? They were like your favorite math classes. It was a blast, right?

Bethany Lockhart Johnson (13:11):

<Laugh> So we have to ask the opposite. Thank you, Daniel Willingham, who said, “What’s the best advice you got?” But hold on, Dan, he didn’t just want the best advice. He wanted the best advice in three words.

Dan Meyer (13:26):

Oh yeah. He doesn’t, he doesn’t want a book or dissertation or even a blog post or even a tweet. He wants just three words.

Bethany Lockhart Johnson (13:32):

I think maybe that might have been to me. <Laugh>

Dan Meyer (13:34):

This is someone who’s doesn’t have much time for this advice, wants it distilled down. I’m just obviously stalling here as I try to think about this. I don’t know, there’s just like so much nuance lost here. I would say, listen to students, listen to students. I can’t say more that, I guess. I guess I’m done. I can’t say more than that there. But you’re in a bad place if you’re not listening carefully to students. How about you?

Bethany Lockhart Johnson (14:04):

  1. Mine is “Ask…lots…questions.”

Dan Meyer (14:11):

Nice. ‘Cause I filled in the word! I filled in the word! I was able to kinda infer that. I did that. I got that.

Bethany Lockhart Johnson (14:17):

Wait, wait, wait, wait! I could have said many! Wait, I could have said “Ask many questions.”

Dan Meyer (14:22):

Strong, strong.

Bethany Lockhart Johnson (14:25):

So yeah. You know, no isolation, like don’t put yourself in a bubble. Ask, not just, not just your students, but the teachers! Ask a lot of questions. You don’t have to have it all figured out.

Dan Meyer (14:34):

Into it. Very much into it.

Bethany Lockhart Johnson (14:37):

Thanks. Daniel. Thanks, Pernille.

Dan Meyer (14:40):

Yeah. Daniel and Pernille, Both great questions there about advice, best and worst. Another fire tweet popped up earlier this year from Dr. Khristopher Childs, which was “Name one thing every educator should stop doing.”

Bethany Lockhart Johnson (14:57):

Oh, I don’t know. This kind of ties into my best advice about asking questions.

Dan Meyer (15:03):

Stop not asking questions?

Bethany Lockhart Johnson (15:06):

<Laugh> Avoid the isolation. I really love this idea of when we can, popping into each others’ classrooms, co-teaching, building this collaborative nature. Elham Kazemi, in our interview, talked about this idea of, like you said, the teacher time-outs, learning from each other. So I feel like if we could stop isolating ourself…and I don’t mean at lunch—sometimes you need to not be in the teacher lounge at lunch. Like if you need a minute, take the minute! But in general, as a practice, how can we not be isolated and instead be learning with, and from, each other? How can we stop the isolation? That’s what I would hope every educator would stop doing. What about you, Dan?

Dan Meyer (15:54):

I think that educators should…this is gonna require a little bit of elaboration. I think educators should stop taking responsibility for things that are not in their zone of influence. I think that as a society we are asking teachers to do more and more, to become more and more of a central fixture holding together with chewing gum and twine all the various parts of a student’s life. From their health, their fitness, emotional health, that we feed students at school. It becomes very tempting, I think, there’s a lot of pressures to blame outcomes, disparate and unjust outcomes later on in life, on teachers. And teachers should just flatly refuse. And to yeah, understand what the job has been set up to do. What it’s good for. And do that with excellence and intent and a lot of effort. And then not take responsibility for the rest of it.

Bethany Lockhart Johnson (16:53):

If I asked five different people about the definition of what a teacher should be doing, I would get five different answers. So I think it’s really interesting that you say that because yeah, many, many hats, which I think, yes, can lead to burnout. Can lead to all sorts of things. We’re asking schools to be all things to all, all people. Interesting. I’m gonna think about that more. I need to hear folks’ response on that, Dan.

Dan Meyer (17:18):

Mm-Hmm. I’m curious too. I mean, yeah, there are definitely things that are in teachers’ responsibility and some that are not. That’s a tough one.

Bethany Lockhart Johnson (17:26):

OK, for help, name an example of each. And what’s something that you think every teacher should not and should be doing. ‘Cause I feel like my brain goes to some things like, you know, I had teachers who were saying, “Well, I don’t wanna have my kids have to have breakfast in my classroom in the morning. That shouldn’t be my responsibility to serve breakfast in the morning.” But I’m like, “But then your kids are eating and they’re gonna be able to learn and be more focused.” Should that be the teacher’s responsibility? I’m not saying it necessarily should, but I’m saying…I don’t know. It gets murky for me.

Dan Meyer (18:06):

Yeah, for sure. I mean, I think that we should, as a country, have a really generous social welfare net so that everyone has food at home. Where a school is not the place where some students have to go to in order to receive nutrition and nourishment. That seems sad to me. And uncommon in developed nations. I think that teachers should watch out for, should be responsible for, the mathematical development of the students they teach, up to a point, they should be responsible for learning math and creating relationships in their classes. I don’t think that teachers should accept responsibility for larger kinds of outcomes, like the health of a democracy or international competition, who goes to the moon first. That kind of thing has historically been placed at the feet of teachers. And it’s tempting when you’re a teacher, I think, to take on that responsibility because it kind of develops your social importance. And I just say, we should say no to that. And get compensation, not in terms of social importance, but rather like in spendable dollars and monies.

Bethany Lockhart Johnson (19:10):

I’m learning more about you, Dan. And you know, this is what I’ve gotten from that answer: If you’re gonna dream, dream big. Right?

Dan Meyer (19:17):

Is that what you got from that? I don’t know. I think I’m trying to dream realistically.

Bethany Lockhart Johnson (19:23):

No, like if we’re gonna say, “Maybe teachers shouldn’t be responsible for serving breakfast in the morning,” well, because we want every child to have access to nutritious and filling food at home and time to eat it in the morning, right? It’s bigger than just, “I don’t want the teacher to have to do this.” So we’re dreaming big. We’re saying this should be the LEAST that students have access to, right?

Dan Meyer (19:53):

Yeah. Yeah. I’m here now. I’m with you. I like that dream. Where we take care of folks in their lives outside of schools. So schools don’t have to be the one linchpin for every kind of social outcome. Like currently a lot of them run through a school ’cause we don’t do a good job of setting up other ways to meet those needs. And we should.

Bethany Lockhart Johnson (20:16):

And we’re also recording this in, what, two weeks, a week, after a tragedy where students and teachers were killed in the classroom. And I think both of us are taking some deep breaths and recognizing that there’s a lot of debate that is happening about what teacher’s role should be in preventing this in the future. And I don’t know if you’ve done drills in your classroom that are supposed to help mitigate disaster, but you know—collective deep breaths— <laugh> is where we’re at right now.

Dan Meyer (20:52):

Yep. The idea of “we should arm teachers” is another example of no, we should not do that. We should solve the tendency towards violence outside of the classroom so that teachers and students can teach and learn. That sounds awesome to me.

Bethany Lockhart Johnson (21:06):

Collective deep breath. Whew. OK. So what else you got for me, Dan?

Bethany Lockhart Johnson (21:33):

Ooh. So I feel like I’ve heard that in many teaching PDs. “I Do, you do, we do.” Actually I feel like I’ve seen like more “I do, we do, you do.” Like graduated release. I do it, then we’ll do it a little bit together, and then now you have permission to do it. And I feel like in directed draw, that’s a hundred percent true. Like I’m gonna show you this and then you draw it. And then you cut here and then you do it. If we’re trying to create this, like I’m teaching this new art technique. But in mathematics, I feel like that’s really not what I want my classroom to look like. I want to support my students and set them up for sense-making, and then I want them to try it out and I don’t want them to solve it the way it first comes to mind for me. I wanna see how they make sense of it and how they solve it. And then I want us to share it with each other so we can grow together. So I think time and place for “I do, you do, we do,” or “I do, we do, you do.” Or shoo-be-doo-be-doo-be. Yeah. You?

Dan Meyer (22:44):

I’ve got nothing. I have nothing to add. I thought that was just an excellent summary of a classroom I would love to be a part in, love to teach. I think it’s a certain tool in the toolbox that I think is overused. But it’s also a tool that can be useful in the case of certain kinds of operations. There are some operations that do benefit from “let me just show you how, like one way you might do this.” I don’t know. I’m like helping my kid whack a nail into a board and there’s a moment where it’s like, “Hey, actually, lemme just show you one way you can do this,” and do it, and then that’s helpful in some moments. But for so much of math, a lot of math does not relate to the operational kinds of fluency. And in those instances, it’s a little bit…it’s not a useful tool, I don’t think, for those kinds of skills and ideas.

Bethany Lockhart Johnson (23:34):

I’m thinking of tool talks in my classroom. So in kindergarten, many of the tools that we use in math and just in class in general, are new to the students. And if I tell them, this is exactly how you should use this tool, then I feel like I’m taking a lot of the sense-making away from them. But if I introduce the tool, show them how to use the tool safely, show them this is not a safe way to use the tool, chewing on this is not safe. That’s not how we use this tool. This is how we take care of it, et cetera. But then support different modes of using the tool that are gonna help them use it to solve problems and make sense, I think…but I guess—Dan, have you heard “I do, you do, we do,” or is it “I do, we do, you do”?

Dan Meyer (24:22):

I’m with you. And I think that it got clarified post-tweet. But yeah, it typically is “I do, we do, you do,” the gradual release of responsibility it’s often called. And I, I have heard people do what you described, which is…what is it? It’s “You do, we do, I do”? Like an inversion of that? Like have people do a thing that I can do that’s not too, too abstract for them, and then like “We all do something together, and then I’ll offer a summary of what we learned,” is one way that goes. I like that tool as well.

Bethany Lockhart Johnson (24:53):

I think particularly, at least I’ve seen in elementary classrooms, there’s sometimes this fear of letting students just try it out before I’ve really showed them, “but this is how it has to be.” And what I am most excited about is supporting students and creating a classroom environment where students don’t need my permission or need my direct “this is the only way to do it.” Instead, it’s like, yes, there’s lots of things we model. But there’s also like, “Hey, what do you think? How do you think this should be used?” And the joy of that exploration.

Dan Meyer (25:30):

Yeah. There’s a feeling of efficiency that comes from “I do, we do, you do,” for some kinds of math, but it’s undercut in my experience by what it cultivates in the students, which is “I’ve gotta wait until the teacher does before I can do anything.” So it pays off real diminishing returns over time. And it’s, just for me, an exhausting way to teach. Always being the bottleneck for new learning is a total drag.

Bethany Lockhart Johnson (25:55):

Ooh, what a great way to describe it. You do not wanna be the bottleneck. You want to be…what’s the other thing? The facilitator? What’s the opposite of a bottleneck? The flowing river? The…The…Help me!

Dan Meyer (26:10):

Hit us up in the replies. I dunno. The opposite of a bottleneck. That’s what you wanna…you wanna not be the opposite? No, you want, yeah. We got this here. We’ll figure it out. We’ll get back to you. <Laugh> OK. Well, folks, those were a few of this year’s fire tweets. It’s been fantastic chatting with you—

Bethany Lockhart Johnson (26:29):

Dan.

Dan Meyer (26:29):

—Bethany, About all those—

Bethany Lockhart Johnson (26:32):

Dan. You know, my favorite thing to do is interrupting you, Dan. I have to interrupt you because we can’t end fire tweets, Dan, without including a tweet from you.

Dan Meyer (26:43):

Oh, that’s true. I do have my moments. Yeah, we should. We really should. <Laugh> Do you have one in mind?

Bethany Lockhart Johnson (26:50):

No. Dan. Yes. I loved…you tweeted recently, “How many years have you been teaching?” Which, OK. “What Has been like the most influential? Like, what, OK, blah, blah, blah.” <blathering noises> You tweeted, “How many years have you been teaching? And at this point, what has most influenced how you teach?” And you gave some ideas: A methods course, PD sessions, curriculum, TV and movies, et cetera, et cetera. And I love that you put that out there because this episode is coming out as we’re wrapping up another school year. And it also got me thinking about summer and what teachers sometimes do during the summer, but what we might need to do this summer for self-care. But I’m really curious. I love that tweet. And I’m curious, Dan, what did folks say was the thing that had most influenced their teaching and what’s most influenced your teaching?

Dan Meyer (27:49):

Ooh, yeah. People’s responses to this one were really fantastic. I came into this, I was flying to the Association of Mathematics Teacher Educators conference. And I just found myself wondering, so, the pre-service year, the one year of, like, you’re learning how to teach, is how we did it in California. Like how much of that has still infused my practice? And in what ways? I don’t think I think about that stuff consciously, but I think that did like set me up with a lot of images that I would be unpacking for going on two decades now working in education. I think conversations with people, I think observing classes, I don’t think that like the one-day PDs, the one-day development days throughout the year, four times per year, I don’t think those stuck to me much. I think that this summer, I have learned so much, just an embarrassment of riches, from non-educational sources. From other disciplines. From storytelling, for instance. From how people have constructed movies I like. I am proud of the way…one of the aspects of my character that I’m proud of—it takes a lot to admit this, as I’m sure you understand, Bethany—but to integrate lots of wacky stuff and pick from it and use that to affect my practice and teaching has been really positive. So for this summer, I hope that people read a good beach book and just kinda let your teaching mind rest a little bit. And in doing so, create some openings for new ideas about education from other parts of the world. Kids! Having kids has been helpful. I don’t know! Just everything! It’s such a big job, education. Everything has so helpful. What about you? What’s an influence on your practice that might surprise me or other folks out there in MTL land?

Bethany Lockhart Johnson (29:52):

Well, I don’t know about surprise. I mean, I definitely feel similarly, like methods courses absolutely impacted my teaching. But I feel like opportunities where I was able to observe other teachers and where I was able to have conversations with folks about their practice, that has deeply impacted me. And books I’ve read. I mean, honestly, I’ve learned so much from sharing with other teachers. Like, for example, maybe I’ll bring student work and we’ll talk about it. And we kind of create this conversation together about how we wanna come back to the students based on the work we see. Those type of moments where we’re collaborating and we’re bringing multiple perspectives to the table, that I think, has really often shifted me out of my first initial reaction or what I thought I was going to do in the classroom the next day. So that continues to surprise and delight me. And thinking about this summer, I think there’s a lot of creativity and joy that can come out of the marination process, when you’re just kind of sitting back and healing yourself, whether through sleep or sunshine or time with friends and family or whatever that looks like for you. I think there’s a lot of creativity that can come from that place of fertile, you know, wellness. I never think of that as wasted time. I think of that as getting the soil ready for all that’s gonna come in the fall. And that being said, I also think it could be a fun time to dip your toes into something that you are excited to read, that you might not have a chance to read during the school year that could be teaching-related. So it’s like very low pressure, like, “Oh, I’ve really wanted to read more by this author. I’ve wanted to read this article. I’ve wanted to dip into this topic.” And not with a pressure, but just with a curiosity. And, yeah, I think so often we as teachers love learning, and to give yourself space to learn in whatever that looks like can be a real gift.

Dan Meyer (32:09):

Yes. And if you need book recommendations, hit the MTL back catalog of episodes. Loads of folks that we interviewed have real good books out.

Bethany Lockhart Johnson (32:16):

Yes!

Dan Meyer (32:16):

Think about it. Think about it.

Bethany Lockhart Johnson (32:22):

One quick recommendation: Again, gotta plug Antony Smith and Allison Hintz’s book. I read Mathematizing Children’s Literature before we did the interview, but this summer I wanna read all the children’s books that they mention. I just wanna go to the library and read all those children’s books. I wanna read them to my son. I wanna read ’em to myself. So, you know, diving into some good YA, children’s books, just, like, TLC. Dan, thank you for such a rich season and a chance to have so many interesting conversations. It is genuinely a joy to learn with and from you.

Dan Meyer (33:00):

Likewise. And always hope to see you folks on Twitter now and then. Let us know what you’re up to this summer at MTLShow on Twitter or in our Facebook group, Math Teacher Lounge. We’ll be there tuning in now and then. It’s been a treat interacting with you folks over this last season. Take care and until the new season, so long.

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What Bethany Lockhart Johnson says about math

“I’ve learned so much from sharing with other teachers… Those type of moments where we’re collaborating and bringing multiple perspectives to the table, I think, has really often shifted me out of my first initial reaction or what I thought I was going to do in the classroom the next day.”

– Bethany Lockhart Johnson

Meet the guests

Dan Meyer

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is currently the Dean of Research at Desmos, where he explores the future of math, technology, and learning. Dan has worked with teachers internationally and in all 50 United States and was named one of Tech & Learning’s 30 Leaders of the Future.

Bethany Lockhart Johnson

Bethany Lockhart Johnson is an elementary school educator and author. Prior to serving as a multiple-subject teacher, she taught theater and dance and now loves incorporating movement and creative play into her classroom. Bethany is committed to helping students find joy in discovering their identities as mathematicians. In addition to her role as a full-time classroom teacher, Bethany is a Student Achievement Partners California Core Advocate and is active in national and local mathematics organizations. Bethany is a member of the Illustrative Mathematics Elementary Curriculum Steering Committee and serves as a consultant, creating materials to support families during distance learning.

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About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Creating lasting change in K–5 math and literacy instruction

Two women seated at a table engage in a lively conversation. One is using a laptop, likely discussing innovative teaching practices. Bookshelves filled with resources for empowering students are visible in the background, perhaps hinting at their dedication to star awards in education.

Transforming math and literacy education takes more than just tips and tricks—it requires vision, commitment, and the right support. Whether you’re rethinking early literacy skills instruction, refining math core curriculum, or fostering a culture of collaboration, you need strong leadership and proven strategies for real change to occur.

“Sustained, meaningful change doesn’t happen overnight,” said Kymyona Burk, Ed.D., a senior policy fellow at ExcelinEd and the keynote speaker at our recent Leading With Vision symposium. “It requires commitment, collaboration, and a clear vision for supporting both educators and students.”

At the symposium—which included keynotes, panels, and math and literacy tracks—education experts from across the country shared experiences navigating instructional shifts, leading curriculum implementation, and setting schools up for success. From building buy-in to making data-driven decisions, their actionable insights can empower you with the knowledge and tools to create lasting change in your district.

Read on for a recap of the core presentations. You can also watch or listen along—and, for extra credit, download the workbook to deepen your learning.

Opening keynote: Key Factors for Successful Transformation in Literacy and Math

Kymyona Burk, Ed.D.
Senior Policy Fellow, ExcelinEd

In her session, Kymona Burk made the case that real student learning progress in literacy and math doesn’t come from policy alone—it requires systemic, research-based change in classrooms. Too often, schools focus on interventions for struggling students instead of strengthening core instruction to prevent gaps in the first place. She pointed to Mississippi’s success in narrowing achievement gaps as proof that evidence-based teaching, teacher support, and family engagement drive meaningful, lasting improvement.

A key factor in that success, she argued, was a firm commitment to the Science of Reading. “We have decades of research on how children learn to read, and we can’t afford to ignore it,” she said.

Burk also stressed math’s similarities to literacy when it comes to effective teaching methods. Just as students need structured, research-backed reading instruction, they also need math teaching and instructional materials that build deep understanding rather than rely on rote memorization. Achieving this, she said, requires strong materials, better teacher training, and a commitment to using data to refine strategies. The path to better outcomes isn’t a mystery—what’s needed is leadership and persistence.

Key takeaways:

  • Tier 1 instruction is the foundation. Schools must prioritize high-quality core instruction to prevent learning gaps.
  • Literacy and math both need urgent attention. Math reform has lagged behind literacy efforts, but both require evidence-based teaching and structured support.
  • Teachers need more than just training. Professional development must be paired with coaching, collaboration, and access to the right materials.
  • Sustained effort leads to results. Mississippi’s success proves that achievement gaps can be closed with consistent investment in people, resources, and accountability.

Leadership Lessons Learned in Baltimore City Schools That Impact Change Everywhere

Janise Lane
VP of Customer Transformation, Amplify; former Executive Director of Teaching and Learning, Baltimore City Schools

Janise Lane’s talk centered on Baltimore City Schools’ multi-year effort to implement a more effective literacy curriculum, highlighting the importance of managing both the logistical and emotional aspects of change. While the district had strong, committed educators, student performance remained stagnant, prompting a curriculum audit and a shift toward evidence-based instruction.

Lane described how to build buy-in and sustainability by ensuring that change is not dictated solely by district leadership. “We had to shift from a system where decisions were made at the top, to one where teachers, families, and community members were true decision-makers,” Lane said.

She also emphasized the need to recognize and address resistance. “Everybody approaches change differently, and it’s our job as leaders to attend to all of those emotions,” Lane said. The key to success, she noted, is creating structured pathways for implementation while remaining adaptable and open to feedback and real classroom experiences.

Key takeaways:

  • Balance structure with flexibility. A clear plan is necessary, but it must adapt based on feedback, data, and the realities of implementation.
  • Small wins build momentum. Celebrating early progress helps shift mindsets from skepticism to belief in the change.
  • Trust and transparency matter. Educators need to see that leadership is engaged, responsive, and committed to making change work for everyone.

Making Math People: Key Shifts in How We Think of Math Assessment

Patrick Callahan, Ph.D.
Educator; Founder, Math ANEX

During his talk, Patrick Callahan emphasized the ways that asset-based assessments measure not just what students don’t know, but the depths of their mathematical thinking. Instead of relying on traditional multiple-choice tests, his approach encourages open-ended responses, allowing teachers to analyze how students arrive at their answers.

Callahan noted that by looking beyond correctness to understand reasoning, teachers can better target instruction. “If all I see is that 37% of my students got an area problem right, I might think I need to reteach area,” Callahan explained. “But if I analyze responses, I see that some kids are correctly multiplying but misunderstanding overlapping rectangles, while others are actually calculating perimeter instead. That tells me exactly where to focus my instruction.”

His research also shows a correlation between students who demonstrated conceptual understanding (such as interpreting remainders in division problems) and higher performance on standardized tests—evidence that fostering deep thinking supports both engagement and achievement.

Key takeaways:

  • Assessments should focus on thinking, not just accuracy. Open-ended questions provide deeper learning opportunities.
  • Targeted teaching saves time. Knowing why students struggle prevents unnecessary reteaching.
  • Classroom discussions boost comprehension. Encouraging students to explain their thinking deepens understanding.

Creating a Supportive Environment for Educators During Times of Instructional Change

Ricky Robertson
Educator; author; consultant

“The number one influence on team effectiveness is psychological safety,” Ricky Robertson said during his symposium session. “Not how talented the individuals are, but how they interact with one another.” His talk focused on how the knowledge that one can speak up without fear of punishment or humiliation affects school culture, educator well-being, and student success, citing research such as Google’s Project Aristotle that demonstrates how high-performing teams thrive not on individual expertise but the quality of interactions among team members.

He also noted that toxic workplace dynamics—such as fear-based leadership, cliques, and bullying—contribute to burnout, disengagement, and resistance to change. Stressing that “strategies don’t transform schools, systems do,” he shared case studies of schools that changed their culture by fostering open communication, restructuring leadership teams, and implementing clear decision-making processes. Creating a safe environment isn’t just about being nice, Robertson said. Robertson noted that creating a safe environment isn’t just about being nice, but about building systems that allow educators to collaborate, support one another, and better serve their students.

Key takeaways:

  • Psychological safety boosts performance. Schools that report a high sense of psychological safety see increased collaboration, innovation, and teacher retention.
  • Structured collaboration matters. Schools with clear communication protocols and leadership structures create more productive teams.
  • Change starts with educators. Supporting teachers’ well-being and professional growth is the foundation for student success.

More to explore

What my wedding taught me about choosing curriculum

The right curriculum choice isn’t only about the product—it’s about who’s by your side from start to finish. Here’s how one district found that with Amplify CKLA.

By Kelly Pruitt, Instructional Facilitator, Peninsula School District | May 28, 2026

A teacher leans over a group of elementary students who are working together at a classroom table under a "CKLA Skills" sign, guiding them through successful CKLA implementation.

Literacy Essentials, Episode 4

Science of Reading Essentials: The science of learning

On this Science of Reading Essentials episode, we're taking a deeper dive into the science of learning to explore how memory, cognitive load, and knowledge building can transform your literacy instruction. On this synthesis episode, host Susan Lambert, Ed.D., weaves in the insights of our expert guests—Natalie Wexler; Nathaniel Swain, Ph.D.; Hugh Catts, Ph.D.; Daniel Willingham, Ph.D.; Peter C. Brown; Jamey Peavler, Ed.D.; and David Rapp, Ph.D. With their insights, Susan reflects on how memory works and why understanding its processes is foundational to effective teaching; why cognitive load theory and background knowledge are game-changers for literacy instruction; and which evidence-based strategies—like retrieval practice, spaced repetition, and mixed practice—make learning stick.

Meet Our Guest(s):

Portrait of a woman with short, curly blonde hair, light skin, and a white top, looking at the camera with a neutral expression—an image that could illustrate modern perspectives in literacy instruction or the science of learning.

Natalie Wexler

Natalie Wexler is the author of multiple books, including Beyond the Science of Reading: Connecting Literacy Instruction to the Science of Learning and The Knowledge Gap: The Hidden Cause of America’s Broken Education System—and How to Fix It; and is the co-author, together with Judith C. Hochman, Ed.D., of The Writing Revolution: A Guide to Advancing Thinking Through Writing in All Subjects and Grades. She has a free Substack newsletter called Minding the Gap, and she was the host of the Knowledge Comprehension podcast, Season 1. More information is available on her website, www.nataliewexler.com.

A man with short brown hair and a beard, wearing a light blue collared shirt, poses in front of a blurred background, reflecting his passion for reading comprehension and literacy instruction.

Nathaniel Swain, Ph.D.

Nathaniel Swain is a teacher, instructional coach, and writer. He produces a blog for teachers called Dr. Swain’s Cognitorium and is cohost of the Chalk Dust podcast with Rebecca Birch. Nathaniel works directly with schools and systems through an online learning platform called Luminary.

He founded a community of educators committed to the science of learning, called Think Forward Educators. He also has a best-selling book, Harnessing the Science of Learning: Success Stories to Help Kickstart Your School Improvement.

A bald older man with a white goatee and mustache, wearing a dark collared shirt, smiles at the camera against a plain gray background—exuding warmth often found in dedicated literacy instruction professionals.

Hugh Catts, Ph.D.

Hugh Catts’ research interests include the early identification and prevention of reading and disabilities. He is a former board member of the International Dyslexia Association and former president of the Society for the Scientific Study of Reading. He has received the Samuel T. Orton Award, the International Dyslexia Association’s highest honor, and the Honors of the Association award from the American Speech-Language-Hearing Association, for his career contributions in these disciplines. His current research concerns the early identification of reading and language difficulties and the nature and assessment of reading comprehension problems.

A bald man with red-framed glasses and a brown jacket stands in front of a brick wall, embodying the spirit of literacy instruction as he looks at the camera.

Daniel Willingham, Ph.D.

Daniel Willingham is a professor of psychology at the University of Virginia, where he has taught since 1992. Until about 2000, his research focused solely on the brain basis of learning and memory. Today, all of his research concerns the application of cognitive psychology to K–12 education. He is the author of several books, including the best-selling Why Don’t Students Like School? and Outsmart Your Brain. His writing on education has appeared in 23 languages. In 2017, he was appointed by President Barack Obama to the National Board for Education Sciences.

An older man with white hair and a beard, wearing a blue checked shirt, stands outdoors near a body of water with trees in the background, perhaps reflecting on reading comprehension or the science of learning.

Peter C. Brown

Peter C. Brown is a bestselling writer and novelist, retired from a career as a management consultant. He is the lead author of Make It Stick: The Science of Successful Learning. Make It Stick has been translated into 17 foreign languages and received international acclaim for changing the way we understand learning.

Jamey Peavler, Ed.D.

Jamey Peavler is a co-director of and full-time instructor in the Graduate Reading Science program at Mount St. Joseph University. Before joining Mount St. Joseph, Jamey served as director of training for the M.A. Rooney Foundation. In addition, she works for the National Council for Teacher Quality (NCTQ) as a higher-education textbook and teacher licensure reviewer. Her research interests include instructional design, the impact of spaced practice and interleaving to support effortful retrieval and retention of information, the role of oral language and syntactic awareness on comprehension and written expression, and foundational skills for supporting literacy in the early childhood setting.

A woman with long brown hair is smiling at the camera, surrounded by books and plants blurred in the background—a perfect scene for anyone passionate about reading comprehension and the science of learning.
A man with short gray hair, a beard, and glasses, known for his work in literacy instruction, is wearing a purple checkered shirt and smiling slightly against a plain white background.

David Rapp, Ph.D.

David Rapp is the Walter Dill Scott Professor of Education, Social Policy, and Psychology at Northwestern University. His research examines language and memory, focusing on the cognitive mechanisms responsible for successful learning and knowledge failures. This has included investigations into the influence of inaccurate information on comprehension, the evaluation of technologies that support formal and informal learning, and the iterative development of tools and curricula intended to support literacy. Rapps’ projects have been funded by the National Science Foundation, the U.S. Department of Education, the National Institute on Aging, and Meta.

Meet our host, Susan Lambert, Ed.D.

Susan Lambert is chief academic officer of literacy at Amplify and host of Science of Reading: The Podcast. Throughout her career, she has focused on creating high-quality learning environments using evidence-based practices. Lambert is a mom of four, a grandma of four, a world traveler, and a collector of stories.

As the host of Science of Reading: The Podcast, Lambert explores the increasing body of scientific research around how reading is best taught. A former classroom teacher, administrator, and curriculum developer, she’s dedicated to turning theory into best practices that educators can put right to use in the classroom, and to showcasing national models of reading instruction excellence.

Person with short blonde hair, glasses, and earrings, wearing an orange jacket, smiling in front of a plain gray background—committed to literacy education and fostering background knowledge for all learners.

Quotes

“To build a meaningful memory of something that you can hold on to and use, you have to think about it.”

—Hugh Catts

“Memory is a cognitive process. It's the way the brain encodes, stores, and retrieves information.”

—Susan Lambert

“You can't learn something new if it doesn't connect to something you already know.”

—Peter C. Brown

“The catch about writing is it's hugely important. It can help cement knowledge and long-term memory, deep knowledge, et cetera.”

—Natalie Wexler

“When we have knowledge in our long-term memory, all of these limitations suddenly disappear.”

—Nathaniel Swain

“We can only work with a limited set of information and when there's too much happening in our working memory, we experience cognitive overload. Essentially, our system is overloaded and we shut down.”

—Susan Lambert

“Essentially, memory is what enables us to retain knowledge, skills, and experiences, forming the foundation for all learning and cognition.”

—Susan Lambert

“The resonance model of comprehension suggests when someone asks a question, lots of ideas get activated automatically in memory.”

—David Rapp

“Your mind is very good at bringing up from memory the necessary facts, the facts that will help you given the context.”

—Daniel Willingham

“A lot of our students that are having difficulty are experiencing cognitive overload. So the first thing we need to think about is how are we gonna minimize that for them?”

—Jamey Peavler

Season 3, Episode 2

Mathematizing children’s literature with Allison Hintz and Antony Smith

In this episode, Mathematizing Children’s Literature authors Allison Hintz and Antony Smith join Bethany Lockhart Johnson and Dan Meyer to discuss what would happen if we were to approach children’s literature, and life, through a math lens – and how we can apply those techniques to classroom teaching.

Two portraits in circular frames: a smiling woman with blonde hair and a man mathematizing beards in a store. The background graphic features shirt icons in blue and orange triangles.

Meet Our Guest(s):

Two people appear in separate circular frames; the woman is smiling and wearing headphones, while the man stands in front of bookshelves, perhaps discussing Mathematizing Children’s Literature.

Allison Hintz and Antony Smith

Dr. Allison Hintz’s research and teaching are in the area of mathematics education. Her focus on mathematics came about during her years as a fifth grade teacher – it was alongside her students that she developed her own positive identity as a mathematician! Today she studies teaching and learning, specifically facilitating engaging discussion. Her research and teaching happen in partnership with educators and children in formal and informal settings and focuses on beliefs and practices that support all children in lively mathematics learning. She is a co-author, with Elham Kazemi, of Intentional Talk: How to Structure and Lead Productive Mathematical Discussions.

Antony T. Smith is an associate professor of literacy education at the University of Washington, Bothell. He works alongside teachers to create engaging literacy-mathematics learning experiences through exploring and discussing children’s literature. He is committed to the concepts of motivation, engagement, challenge, and creativity in literacy teaching and learning.

Meet our hosts: Bethany Lockhart Johnson and Dan Meyer

Bethany Lockhart Johnson is an elementary school educator and author. Prior to serving as a multiple-subject teacher, she taught theater and dance, and now loves incorporating movement and creative play into her classroom. Bethany is committed to helping students find joy in discovering their identities as mathematicians. In addition to her role as a full-time classroom teacher, Bethany is a Student Achievement Partners California Core Advocate and is active in national and local mathematics organizations. Bethany is a member of the Illustrative Mathematics Elementary Curriculum Steering Committee and serves as a consultant, creating materials to support families during distance learning.

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is currently the Dean of Research at Desmos, where he explores the future of math, technology, and learning. Dan has worked with teachers internationally and in all 50 United States and was named one of Tech & Learning’s 30 Leaders of the Future.

Two people smiling at the camera, each in a separate circular frame, with geometric shapes decorating the background—perfect for a math teacher lounge or highlighting fresh math teacher resources.

Quotes

We started asking ourselves, “what would happen if we considered any story a chance to engage as mathematical sensemakers.”

—Allison Hintz

Stay connected!

Season 6, Episode 2

Assessing math fluency

Join Math Teacher Lounge as we continue our season-long deep dive into math fluency. Tune in to our latest episode where we sat down with Valerie Henry, Ed.D. to discuss how we can redesign assessments of math fluency to provide teachers with better data and students with better learning.

Listen today and don’t forget to grab your MTL study guide to track key strategies and make the most of this episode!

Elderly woman with glasses smiling at the camera, framed by a circle with a geometric patterned border on a garden background, exemplifying what is math fluency.

Meet Our Guest(s):

An older adult with short gray hair and glasses, wearing a blue fleece, sits outdoors with greenery in the background, perhaps pondering what is math fluency or reflecting on lifelong learning.

Valerie Henry Ed.D.

Valerie Henry, Ed.D. has been a math educator since 1986. She taught middle school math for 17 years and has worked as a lecturer at UC Irvine since 2002. After doing her 2004 dissertation research on addition/subtraction fluency in first grade, Valerie created FactsWise, a daily mini-lesson approach that simultaneously develops  fluency,  number sense and algebraic thinking. Thousands of teachers have used Valerie’s  books, classroom videos, screencasts, and online courses for addition/subtraction and multiplication/division to integrate fluency into their daily routines.

Valerie has provided curriculum and math professional development for K-12 teachers throughout her career, working with individual schools, districts, county offices of education, Illustrative Mathematics, the SBAC Digital Library, and the UCI Math Project. She has  an Ed.D. from UCLA/UCI and a bachelor of arts degree in mathematics from UC Davis, is credentialed in both Multiple and Single Subject mathematics and received National Board Certification in early adolescent mathematics.

Meet our hosts: Bethany Lockhart Johnson and Dan Meyer

Bethany Lockhart Johnson is an elementary school educator and author. Prior to serving as a multiple-subject teacher, she taught theater and dance, and now loves incorporating movement and creative play into her classroom. Bethany is committed to helping students find joy in discovering their identities as mathematicians. In addition to her role as a full-time classroom teacher, Bethany is a Student Achievement Partners California Core Advocate and is active in national and local mathematics organizations. Bethany is a member of the Illustrative Mathematics Elementary Curriculum Steering Committee and serves as a consultant, creating materials to support families during distance learning.

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is currently the Dean of Research at Desmos, where he explores the future of math, technology, and learning. Dan has worked with teachers internationally and in all 50 United States and was named one of Tech & Learning’s 30 Leaders of the Future.

Two people smiling at the camera, each in a separate circular frame, with geometric shapes decorating the background—perfect for a math teacher lounge or highlighting fresh math teacher resources.

Quotes

“Putting a number on a piece of paper doesn’t help me know what to do next with my students. But, listening and engaging with them does let me know what the next thing I can do to help them should be."

—Dr. Valerie Henry

Stay connected!