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.

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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!

S1-05: How does coding fit in the science classroom? A conversation with Aryanna Trejo of Code.org

Podcast cover titled "Science Connections" featuring Aryanna Trejo, Season 1, Episode 5. It includes abstract illustrations of a globe and telescope, discussing coding in the science classroom.

In this episode, Eric sits down with Aryanna Trejo, a professional learning specialist of Code.org. Aryanna shares her journey from working as an elementary teacher in New York City and Los Angeles to teaching other educators at Code.org. Eric and Aryanna chat about computer literacy within the science classroom, problem-solving skills, and ways to model productive struggle for students. Aryanna also shares ways to teach coding and computer literacy in schools, no matter the classroom’s technology level. Explore more from Science Connections by visiting our main page.

Download Transcript

Aryanna Trejo (00:00):

I would hear teachers saying things like, “Well, I just can’t do coding; this is too hard for me; the time has passed.” And I would ask them, “Would you say that to your student about math or English?” And they would always sheepishly go, “No.” And I’d say, “Well, be as kind to yourself as you would be to your student.”

Eric Cross (00:19):

Welcome to Science Connections. I’m your host, Eric Cross. My guest today is Aryanna Trejo. Aryanna is a member of the professional learning team at Code.org. Before joining Code.org, Aryanna led computer science professional development for elementary school teachers, and served as an instructional coach for new educators. She also taught fourth and fifth grade in both New York City and in Los Angeles. In this episode, we discuss Aryanna’s journey to Code.org, where she helps educators connect coding to real life, how to use a rubber duck to solve problems, and how coding and computer science principles can be taught to students in areas without access to the internet…or even a computer. I hope you enjoy my conversation with Aryanna Trejo. So I was born and raised here, and I saw that you went to UC San Diego.

Aryanna Trejo (01:11):

I did, I did. I actually just put a deposit down on an apartment in University Heights, ’cause I’m moving back.

Eric Cross (01:16):

You’re coming back?

Aryanna Trejo (01:17):

I’m coming back. Yeah.

Eric Cross (01:19):

So if you need a classroom to visit….

Aryanna Trejo (01:21):

I would love to do more classroom observations!

Eric Cross (01:24):

Are we doing this? Let’s do—we’re making this happen.

Aryanna Trejo (01:26):

We are. Yeah. So I’ll be there. I’m moving there in April. I actually grew up in Orange County too, so I’m like a very diehard SoCal person.

Eric Cross (01:35):

So I feel like I know the answer to, hopefully—Tupac or Biggie? ‘Cause you’re on the East Coast, and you’re on the West Coast.

Aryanna Trejo (01:40):

Yeah. I like Tupac, but I have more Biggie songs committed to memory. Which is not a lot. I have “Juicy” and “Hypnotized” memorized.

Eric Cross (01:53):

All right. So you’re just memorizing, and you have the Biggie songs memorized, but not the Tupac ones.

Aryanna Trejo (01:58):

No, but I do love Tupac songs. You know, it’s like, Biggie has the flow, but Tupac has the lyrics. Nobody’s—they both have something really amazing about them.

Eric Cross (02:06):

You know, I can respect that you broke it down into both of their strengths.

Aryanna Trejo (02:11):

Thanks for buttering me up before this interview. And not….

Eric Cross (02:15):

<laugh> Oh, we already started.

Aryanna Trejo (02:16):

Huh? We already started?

Eric Cross (02:17):

We’re already started. Yeah. We’re already into this.

Aryanna Trejo (02:19):

We’re into it.

Eric Cross (02:21):

You were in the classroom, fourth and fifth grade, and you were doing TFA.

Aryanna Trejo (02:26):

I did. I did Teach For America. I was 2012, New York City Corps. Right after graduation. ‘Cause I graduated UC San Diego in 2012. So graduation was on June 17th, and I touched down at JFK on June 19th.

Eric Cross (02:40):

Even though I wasn’t in TFA, I know a lot of the fellows that are in it. And there’s just some phenomenal teachers in there. How long were you doing elementary school when you were teaching?

Aryanna Trejo (02:49):

Yeah, I taught for—well, I did, three years of teaching fourth grade. Then there happened to be an instructional coach opening in my fourth year. I took that, did some instructional coaching within the same network, and then I moved back to LA and I taught fifth grade for a year.

Eric Cross (03:11):

  1. And what was it like now? Did you go to Code.org right after the classroom?

Aryanna Trejo (03:17):

No, I didn’t. No. I transitioned after teaching fifth grade for a year in downtown Los Angeles, in the Pico-Union neighborhood. I ended up getting this email out of the blue from someone who had actually found me through the Teach for America job site. ‘Cause I was hitting the pavement; I was really looking to transition out of the classroom. And she invited me to interview with this company called 9 Dots. And they taught computer science to kids K–6 throughout Los Angeles and Compton. And I was like, “Sure, no problem. Let’s do it.” So I interviewed, I got the job, and yeah, that’s how I transitioned to 9 Dots. And then after almost four years there, I transitioned to Code.org, with the same person. Actually, she moved over to Code.org first, and then she helped me get this job.

Eric Cross (04:07):

Oh, that’s happened a lot—like, that relationship kinda carries over.

Aryanna Trejo (04:11):

Yeah. We’re meant to be coworkers.

Eric Cross (04:13):

Yeah. Are you still? Is she still there? Are you both still together?

Aryanna Trejo (04:17):

Yeah, we’re on the same team and it’s nice. I saw her last night for Happy Hour, with another coworker who’s in LA. So we’re tight. And she’s a wonderful, wonderful mentor to me.

Eric Cross (04:28):

That’s great. Did you have computer-science background, when you were doing elementary school teaching? Did you have—

Aryanna Trejo (04:34):

No. <laugh> Not at all. When I was teaching in New York City, I had like four desktop computers in my classroom, and we rarely used them. Which was such a shame. And then when I moved to Los Angeles and taught fifth grade there, we were a one-to-one school, and the joys of that are just amazing. It was just really wonderful to, you know, get the students used to typing on the computer, using different software to submit their assignments. Getting creative—as creative as you can get—with Google Slides. You know, to show off what they know. And stuff like that. That’s all I had, though. And you know, when I transitioned to 9 Dots I was like, “Sure, why not? Let’s give a shot.” And I learned a lot. It was really interesting, yeah.

Eric Cross (05:26):

And so now at Code.org you are…well, so my journey with Code.org, I’ve been in the classroom for eight years. Still in the classroom as of…an hour ago, I was there. <Laugh> And I use Code.org, and I feel like I’ve checked it periodically, and I feel like it’s evolved over the gaps. And I’ve seen it. It’s become more robust in the things that they offer, over the years I’ve been an educator. Just to kind of…could you give a thumbnail sketch? Like, what is Code.org? Who’s it for? Who’s the target audience? What resources are there?

Aryanna Trejo (06:00):

Yeah. So it’s for everyone. It is a nonprofit that provides curriculum and training and a platform for teachers and students. We provide curriculum for K through 12. It’s completely free. And it comes with lesson plans, slideshows, all that. We focus specifically on underrepresented groups. So we have targeted measures for Black students, for Native American students, for students who identify as female. That’s a huge part of our mission. But we’re really working to expand access to computer science to as many students as we can.

Eric Cross (06:41):

One of the things I’m hearing in your story is you were teaching in Compton; you were in Bronx, New York. One of the reasons why I got into the classroom is because of educators, and the impact they made on me in exposing me to science and technologies I’d never had access to. And that intentionality, that you’re going about it…are there…not just the code, but how you bring that across to different groups…are there strategies, or are there ways to connect this idea of coding to diverse groups and diverse audiences? Or is it kind of, the curriculum applies for everyone? ‘Cause in science, when I’m teaching, I’m always trying to make what I’m doing relevant to the backgrounds of my students.

Aryanna Trejo (07:28):

Sure.

Eric Cross (07:28):

So I’m teaching biology, and I’m trying to make this kind of connection. Sometimes it’s more organic; sometimes it feels kind of forced. Because it’s just not always a nice fit. But it sounds like Code.org is really about inclusion. And in the numbers that I’ve seen for representation, in especially computer science software engineers, the groups that you’re focusing on are not necessarily represented in the professional workforce. At least disproportionately.

Aryanna Trejo (07:54):

Yeah, absolutely. Yeah, that’s correct.

Eric Cross (07:57):

And so how do you go about being intentional about reaching groups that we don’t see in, you know, the Silicon Valley software engineers? How do you start that? Like, at a young age, do you look for specific schools in specific areas to say, “We are going to bring this to the school. We’re going out to these populations of the cities”? Because we’re just not seeing…you know, on the map, we’re not seeing anybody really doing anything with coding here. Or we’re not seeing the numbers come out of these areas, out of these cities, of students who are going into STEM or going into computer science fields.

Aryanna Trejo (08:41):

Yeah. I don’t necessarily work on the recruitment side of it, is the issue, in my position. But I do work on the professional learning, that is brought out to teachers. And we have a huge focus on equity throughout the workshops that we create from K–12. It’s something we’re really passionate about. We definitely aim to prepare teachers to teach computer science. That’s a huge part of it. Knowing the content, but also thinking through, “What does recruitment look like at your school to make sure that the demographics of your classroom match the demographics of your entire school?” Also, thinking through, “How can we make sure that female students feel included in your classroom? How can we make sure that we are, giving students creativity to think about, or we are setting students up to be creative and think about the problems that are in their community, and how they can use computer science to solve them, or at least work towards them?”

Eric Cross (09:39):

So solving real-world problems and that inclusion aspect…are there things like…you were saying “female or students who identify as female”…are there things that teachers can do to ensure that they’re being more inclusive? Or to recruit, or encourage more female students to take part? One of the things I was thinking of, that I’ve seen, is I’ve seen coding kind of camps.

Aryanna Trejo (10:06):

Sure.

Eric Cross (10:08):

That were specifically for a female audience. And that seemed to help with recruitment. Is that something that you see on your side?

Aryanna Trejo (10:16):

That’s not something that we set up, no. But the curriculum that I work with is CS Principles. And it’s offered as an Advanced Placement course, as well as an AP class. So that’s a curriculum that’s designed for students who are in grades 10 through 12. And so at that point, we can really talk to teachers and ask them what the recruitment strategy is. But in terms of strategies that teachers can use to recruit those students…I mean, I’ve heard over and over from lots of different teachers who identify as female that they didn’t think that computer science was for them, until they saw a role model in that position. And so just being a role model for those students is really wonderful.

Eric Cross (11:00):

And I see it too, with—like, we do “Draw a Scientist” activity, which is like a popular science thing—

Aryanna Trejo (11:05):

Sure, yeah, I’m familiar.

Eric Cross (11:05):

But it’s the same thing, right? Like, it fleshes out. My students don’t draw themselves as scientists. They draw what they perceive, based on what television says. I imagine with computer science, it’s probably really similar, when you think about “What’s a software engineer look like?” Do students tend to draw themselves? Or is it even a mystery? Because I don’t even know what a software engineer looks like.

Aryanna Trejo (11:28):

Yeah, absolutely. Well, one of the things we love to do with our professional learning workshops is talk about understanding yourself, your identities, how they show up in the classroom as biases. And, you know, things like stereotype threat. We see that as really important to understand, and think through, and consider, before you step into the classroom. So that you’re not, you know, coddling certain groups of students because you don’t believe that they are able to be successful in computer science. Holding all the students to the same expectations and believing that they can succeed. And computer science, I think a lot of the times people have this conception of it being this utopian, bias-less, technocratic field. When in reality, everything has bias. And people talk about algorithmic bias and facial recognition, but also the people who created computers and computer languages have their own bias that comes through. And I think it’s really important to show students that. So that they can, one, know what they’re working with, and two, make sure that they can create products that reduce that bias.

Eric Cross (12:50):

It’s like…it’s not objective, just because we’re creating software. Like, once it gets to a point of being so sophisticated…I think, like, AI software, right? With facial recognition? And we’re seeing more and more articles come out about, you know, predicting trends based on historical data.

Aryanna Trejo (13:12):

Sure.

Eric Cross (13:13):

But then, the trends and things that they’re seeing tend to target things that have happened in the past. But it also doesn’t take into consideration a lot of other factors that can lead to certain groups or populations being identified. And I’ve seen some articles lately about how your code is really just representation of what you put into it. And like you just said, your bias—if you have that, conscious or unconscious—you’re gonna put that into your code. And the input is gonna be an impact, is gonna impact the output.

Aryanna Trejo (13:44):

Yeah, absolutely. Or even just—and I’m ashamed to say this, ’cause this is an idea that came to me just recently, through an article that I read—but computers themselves have bias. The hardware assumes that you have vision, that you can see the screen, that you are able-bodied, that you can use your hands to work the keyboard, the mouse, et cetera, and that you don’t have to use assistive technology. You know, there are small things like that, where we think that technology, like I said, is this utopian, futuristic science…but there are biases throughout.

Eric Cross (14:19):

You’re absolutely right. I’ve never even—I’ve never even considered that. Even though I do use assistive tech, and figure it out, I’ve never thought from the ground up, the process is built for an able-bodied, sighted, hearing person.

Aryanna Trejo (14:31):

Exactly.

Eric Cross (14:32):

To be able to engage with the hardware. And then these other things, these tertiary things that we kind of add on, so that you can do this, but it’s not designed from the ground up for people who are, you know, different audiences, physically. So I’m glad you brought that up, though. Now I’ve seen—and I haven’t done this—but I know Hour of Code is a big thing. And this is something that’s ongoing. Can you talk a little bit about what Hour of Code is? I know it’s, it’s a big thing for the classroom teachers.

Aryanna Trejo (15:08):

Yeah. So Hour of Code is really exciting, and it’s just blossomed from something small to something tremendous. This year is gonna be the 10th Hour of Code. So what it is, is it happens during CS Education Week in December, during Grace Hopper’s—or to honor Grace Hopper’s birthday. She was a computer scientist and Navy Admiral. And basically the aim of it is to get as many students on the computer doing an hour of code, and demystify what coding is. You know, to do seed-planting. To show teachers that this is something that you can facilitate for your students. And also to show students like, “Hey, computer science is something you can absolutely do. Not just for an hour, but more if you want.” So, yeah. Now it’s worldwide, and it’s really exciting.

Eric Cross (15:58):

That’s awesome. And I think about teachers and I still hear the apologetic—when I’m helping teachers in the classroom with education technology—the self-deprecating “I’m a dinosaur; I’m not good with tech,” which is never true. Like, they’re better than they even realize. And I feel like sometimes there’s still a stigma, too. It’s like <laugh> The Simpsons’ Comic Book Store Guy. The condescending tech support person—

Aryanna Trejo (16:27):

Sure.

Eric Cross (16:28):

—who has that tone. And so I feel like some people have been so negatively impacted by that person. So I know when I’m helping people, I actually try to go full-spectrum the other side. But I’m thinking about teachers’ barrier to entry. Sometimes code is like, “Whoa.” And I don’t teach computer science. Do you see those barriers to entry, or at least the perception of them? And then, what’s the reality for like someone listening, and going, “I’m a fourth grade teacher,” or “I’m a humanities teacher in ninth grade.” What’s the perception that you see, versus reality, with the teachers that you train? Is it much more accessible than we think? Or is there a level of sophistication that you have to have coming into it?

Aryanna Trejo (17:10):

No, not at all. I know computer science, and that says a lot! <Laugh> You know, I know my own corner of computer science. And you know, that’s me being self-deprecating, too. But I think learning computer science has helped me in so many different ways that I wasn’t expecting. I recently took the GRE in hopes of, you know, getting back into grad school. And I think just the way that computer science teaches you to search for bugs in your code, or errors, and kind of tirelessly look at a problem from multiple different angles, I was able to carry that into the math that I was doing. And I noticed just a huge difference in the way that I approached it, and the way that I was open to it. But you asked a great question, in regards to the barriers to technology. In my position at 9 Dots, I was working directly with teachers to lead professional development with them. Sometimes it would be a full day; sometimes it would be an hour after school. And the one thing that I always had in my back pocket that was really useful is that I would hear teachers saying things like, “Well, I just can’t do coding; this is too hard for me; the time has passed.” And I would ask them, “Would you say that to your student about math or English?” And they would always sheepishly go, “No.” And I’d say, “Well, be as kind to yourself as you would be to your student.” You know, it takes some patience and nobody’s gonna get it perfect 100 percent of the time. Have I banged my head against the wall trying to solve one tiny little syntax error in my code? Absolutely! But it feels absolutely phenomenal to fix that. And I was an English major in undergrad, and I had never done computer science before. So it’s something that becomes really satisfying.

Eric Cross (19:07):

Yeah, I imagine. I had someone—a trainer or a presenter—one time bring up the fact that our students rarely get to see us learn in real time.

Aryanna Trejo (19:19):

Yeah.

Eric Cross (19:19):

So we don’t get to ever really model failure. I mean, unless we’re in a classroom situation <laughs> in our failures, with classroom management. Then they see it, they see it! But they don’t get to see us model learning failure. And I don’t mean like failure—and yes, I know, “first attempt is learning,” and “no such thing as failure”—that’s not what I’m talking about. But just when we’re not successful with our code, and then we experience real-time frustration.

Aryanna Trejo (19:42):

Yep.

Eric Cross (19:42):

And they said that is actually a great learning experience for your students to watch you go through productive struggle. And that was really liberating for me. Because now I’m in the classroom, and I’m trying to go through it with my students, and the beautiful thing was, they started helping me. We were all trying to solve the problem. And then we had this authentic problem-solving experience. I think it was like a Scratch program, where we were trying to solve, trying to embed it somewhere, or something. And then, in the background of the class: “Mr. Cross! I got it! I figured it out!” And it was this really neat bonding experience. And I felt that—your ears get red, and you get hot, ’cause you’re not—

Aryanna Trejo (20:19):

Oh yeah.

Eric Cross (20:20):

You don’t know it! And you’re in front of 36 kids! And I said, “OK, I need to tell them how I feel.”

Aryanna Trejo (20:25):

Yeah.

Eric Cross (20:26):

So I said, “Now I feel really frustrated.” Like, “I want to go through this, and here’s my thoughts.” ‘Cause I knew that it would be helpful if they saw and would hear my thoughts. So I just did a quick think-aloud and I said, “In my head, <laugh> I want to just quit,” I said, “But I realize that this is the part where my learning’s happening. So I just want you all to hear what’s going on in my brain.” And now I feel like when I’m doing coding with my students, and it’s just basic coding, I feel much more comfortable, like, not knowing. But I needed someone to release me from that “I have to be the expert in everything” to do it.

Aryanna Trejo (21:06):

And teachers are used to being the experts. Right? And they should be. And coding is just such a different landscape. But I think once you kind of give over to the power of tinkering, I think it’s really gratifying. I love being able to…you can revise a sentence, and then read your paragraph back to yourself in English, and say, “OK, I get it.” But there’s something so gratifying about changing a line of code or a block and then being able to hit play and watch your program come to life, and say, “Hmm, that’s not quite what I wanted. Let’s try something different.”

Eric Cross (21:39):

I love your connection to tinkering. ‘Cause—I had never thought about it—’cause I love tinkering with my hands. But I always think about physical things. But coding is exactly that. It’s tinkering.

Aryanna Trejo (21:47):

It’s exactly that.

Eric Cross (21:47):

That’s exactly what it is.

Aryanna Trejo (21:49):

And a lot of it is, for me, especially when I’m trying something new, it’s guess-and-check. It’s like, “OK, that didn’t work. What if I add a semicolon here? Will it finally work? Or what if I add a ‘for’ loop? Will this get me what I want?” And it’s wonderful because you have that with students as well. Like, you have that record of their thinking, and you can ask them to go step-by-step and tell you, you know, “First, I added this, because I wanted the program to do this,” and so on and so forth. And so you have that record, but you can always get rid of it. Students often wanna get completely get rid of it. That’s something that I’ve noticed a lot as I’ve taught computer science. But, once you can get them to target the specific parts of the program, tinker with that, and continue, that’s a really wonderful learning space. There was also something you said about modeling failure. I love the fact that in computer science you can model failure for your students. You said to your students, “I’m getting frustrated.” I love that, because I never got that in math. Nobody ever showed me what it was like to be frustrated with graphing a parabola. Right? Like, my math teachers were always like, “Doot, doot, doot, here you go, you’re done!” <Laugh> And I would get so frustrated, because it didn’t come that easily to me. And I think there’s two parts to that. So there’s modeling the learning and the thinking and the productive struggle, but also there’s the identity of being a computer scientist and modeling what that looks like. So for me, when I get really frustrated with a program, I walk away. I take five minutes. I take a deep breath. I say, “I’m not gonna think about it in these five minutes.” And I come back to it. And I think once you start teaching computer science, you can facilitate that for students. And there’s so many different strategies that they can pick up. They can pick up rubber ducking, which is where they pick up a rubber duck or a similar object, and they talk to it as if they were a partner and talk through their code. And oftentimes, as you’re rubber ducking, you’re gonna find that error, because you’re explaining it to someone who’s a stand-in for a novice. And rubber ducking is a well-known strategy for computer scientists who make it their career. You know, there’s pair programming. Some students love pair programming; some students hate it. But the students start to build this identity about how they problem-solve. And how they approach failure. And I just love that.

Eric Cross (24:31):

I’m writing this down. Because the rubber-ducking strategy, I love. I just imagine my seventh graders, a bunch of 13-year-olds with, like, rubber on the desk. And not necessarily in coding, but I was thinking in my science class. And they’re working through a challenge, and they’re all looking at this duck, and they’re talking to it. But I just love the the idea of externalizing your thought process and talking through it yourself so that you can hopefully arrive at a conclusion. But it’s such a great practice, and this is something that’s been around for a long time, apparently. So.

Aryanna Trejo (24:59):

Yeah. Yeah. It’s a real thing. And you know, you can go low-fi. It doesn’t have to be a rubber duck. You can have students talk to their pencils or their imaginary friends. That’s not the issue; the issue is, you know, talking to somebody.

Eric Cross (25:10):

I know you support teachers. But I just wanted to…I was just curious about your typical day, what that’s like. And then what you do, how you support ’em.

Aryanna Trejo (25:15):

So, at my previous job at 9 Dots, I was in there with the teachers in the classrooms. I was coaching our internal staff who went out to co-teach with teachers. And I loved that. And I had such a great impact on a local scale. But now at Code.org, I have a much broader impact. But I don’t get to interface with—that’s such a tech-y word!—I don’t get to interact with—

Eric Cross (25:42):

You work at Code.org! You get to—

Aryanna Trejo (25:42):

I know! But I’m a teacher at heart, forever, right? That’s my identity that I forged when I was 22 years old. And a typical day looks like opening up my computer, taking a look at my calendar. I often have meetings to talk about, different things that we’re doing to support our facilitators who go out to our teachers and lead their workshops for them. I recently worked on a product that was designed for CS principles, teachers, to onboard to the course if they weren’t able to get into an in-person workshop. And it’s completely self-paced, so it gives teachers an on-ramp into the course. And now I’m working on some in-person workshop agendas. So I feel really wonderful that my work is going out to thousands of teachers. But at the same time, I really, really miss talking to teachers. Because that’s something that energizes me so much.

Eric Cross (26:46):

When should students start learning computer science? I feel like we see it in this kind of narrow lane. Like, this is computer science if you make an app. Can it be more than that? As far as like the benefit of computer science? And—I guess two-part question—when should students, one, start being exposed to it? And then two, what are some of the benefits beyond just, “I wanna just make an app”?

Aryanna Trejo (27:08):

I taught coding to kindergartners. It can start as early as you as you want it to. And it doesn’t necessarily need to be on the computer. A lot of students that I worked with didn’t have computers at home, were interacting with computers for the first time. And that’s a huge barrier, of course, to a lot of teachers. But there are so many unplugged lessons that you can do to start to start to have students think about algorithms, which is just a series of steps to complete to solve a problem. As long as a student can use a computer, I think they can do computer science. There are products out there like codeSpark, where students—and Code.org has these products too—where students are moving an avatar around a board, kind of like a quadrant to…you know, they feed the directions to a computer and then the computer enacts it for them. And with that, they can learn algorithms. You know, that is computer science. And a lot of people don’t see it that way, but it really is. And it starts to set students up for more complex thinking as they move on.

Eric Cross (28:13):

One of the biggest underserved communities, geographically, are students in rural areas.

Aryanna Trejo (28:20):

Yep.

Eric Cross (28:21):

They can be reservations; they can be places just not an urban area. Is there a way to serve our communities of students and bring these skills in an unplugged way?

Aryanna Trejo (28:32):

Yeah. Yeah. If you typed in “unplugged computer science lessons” to Google, you’ll have a ton of hits. And there are so many students out there—not just in rural areas. But there’s incarcerated students. It hurts my heart to even say those words, but in urban areas too. Like in my classroom, where I only had four desktop computers. Access is a real struggle. And there’s things, like I said, instead of moving an avatar around a grid on the computer, I used to have an actual mat that I would take out to my kindergarten classrooms, lay it out, and it would have a grid on it. And we’d have one of the students act as the avatar and the rest of the students would give them directions to get to a different point on the grid. And there, you’re building an algorithm or just a series of steps. Like I said, it’s not some fancy term to solve a problem. And there’s multiple ways to solve that problem, too. And I think investigating that can be a really good way to stretch those lessons.

Eric Cross (29:32):

It almost sounds like an oxymoron, but this low-tech computer science strategy. Develop these skills and then transfer that once you have access to the tools.

Aryanna Trejo (29:39):

Yeah. Yeah. Absolutely. And I think it’s a good way for students who need kinesthetic means to start to understand something, or just different learning styles, to start transferring that over.

Eric Cross (29:53):

I probably have students in the classroom where those kinesthetic moving things would help be a great way—or WILL be a great way—for them to learn the principles and the fundamentals of coding. Instead of only giving the option to just do the computer, actually giving them some choice. Or giving them a way to be able to manipulate things. We’re still in the system of education that’s still very siloed. It’s been the same way for a hundred years. We got math and then we got science and we got English. I’m wondering, how can a teacher fit this into their daily lessons? And then, do you have any experiences or stories or things that you’ve seen, just really creative ways that you’ve seen teachers incorporate this? Outside the norm of, “This is a computer science class; we’re just gonna code.” But have you seen it branch out? In the trainings that you’ve done?

Aryanna Trejo (30:40):

I’ve seen examples of that. I’ve seen a teacher use Scratch to demonstrate different climates of California, and show the different climates. This past year for Hour of Code, my friend Amy—the one who helped me move to 9 Dots and at Code.org—she created this incredible tutorial called Poetry Bot. And it was a way to get students to match the mood of the poem to some of the elements that were happening in the stage. So they would have different backgrounds show up at different parts of the poem. When the words would show up, they would have different sprites show up. They would have, sometimes, sounds. Or the text would show up with different animations. So there are cross-curricular opportunities everywhere, if you can be creative enough to find them, or if you beg, borrow, steal from other educators who are doing this incredible work out there.

Eric Cross (31:36):

Yeah. I say this all the time, but I’m an educational DJ, not an MC.

Aryanna Trejo (31:44):

Oh yeah.

Eric Cross (31:45):

So MCs write their lyrics and DJs remix with things that other people have done.

Aryanna Trejo (31:48):

Absolutely.

Eric Cross (31:48):

I was like, I’m a DJ. I was like, all day. Sometimes I’ll write a lyric, once or twice, but most of the time I’m remixing things. So teachers, if you’ve been out there and you got an awesome interdisciplinary thing, or you’ve incorporated coding and it’s something that’s traditionally not seen, please send it to us. Share it with us.

Aryanna Trejo (32:03):

Yeah. And there are so many different places where you can find that. We have a forum for Code.org, but there’s also CSTA, the Computer Science Teachers Association. You can join your local chapter and get to know other computer science teachers out there.

Eric Cross (32:19):

I guess…to wrap up, I’ve been using Scratch programming, the MIT website. My students do the basic animated name, CS First, stuff. But over the years, I’ve noticed that my students are coming in with a higher level of sophistication in Scratch to where now the differentiation…some of my students are just doing very basic…and then I have other students who’ve created full-on video games with complex…like, you look at their Scratch page and it’s just an amazing amount of blocks and integrations and things that they have. Is there anything on Code.org that could be a next step? That takes them beyond, maybe like the visuals? And if so, what would be a good next step, to take students to advance them to another platform? There’s so many coding languages out there, I feel like. Or I might not even be thinking about that the right way.

Aryanna Trejo (33:20):

No, I think you are. You know, we have three different curricula out on our website right now. We have CS Fundamentals, which is probably more in line with what you’re talking about. We have a free CS Discoveries curriculum, and that is designed for, grades, I believe, 6 through 10. And that would be a really good entry point, for both teachers and for students.

Eric Cross (33:44):

There’s a lot of new stuff that I hadn’t seen yet, a few years ago.

Aryanna Trejo (33:49):

Yeah.

Eric Cross (33:49):

So I was really excited.

Aryanna Trejo (33:50):

One thing that I do know is that CS Discovery has just added an artificial intelligence slash machine-learning unit, that you can just pick up and give to your students. You don’t have to go in order with CS Discoveries, like you do with CS Principles. And I’ve gone through some of those lessons. They are really rad. And I would’ve loved to have learned that when I was in middle school or high school. So yeah, we’re constantly thinking of how we can make things one, relevant to our students, and two relevant to what’s going on in the world.

Eric Cross (34:20):

So would I be overselling it if I said, “If you go through this, you’ll be able to create an AI or a neural net to do all your homework”?

Aryanna Trejo (34:26):

You would be overselling it.

Eric Cross (34:27):

I would be? OK. So what I’ll do is, I’ll wait until the end of the school year, and then introduce it, and then by the time they’ve realized it’s not true, they’ll be eighth graders.

Aryanna Trejo (34:35):

There you go. Good old bait-and-switch.

Eric Cross (34:37):

You’re amazing. Thank you for serving teachers, and for being part of such a great organization that puts out great stuff. So much free curricula for teachers to be able to use. Especially nowadays we hunt and scour the internet for those types of things. And to be able to bring computer literacy into the classroom, and with your focus of serving communities of underrepresented groups, it feels good to know that not only is it high-quality material, but it’s also trying to raise everyone up. Because ultimately when we have more people trying to solve a common problem, we come up with better solutions. And I was talking to somebody who was a materials engineer somewhere in Europe, and he said one of the things about the U.S., As he was critiquing me on this flight, critiquing the U.S., He said, “One of the things about your country is that you have a heterogeneous group of people who, in a group, when you have multiple perspectives attacking a problem, you come up with more novel solutions.” He says, “That’s one of the great things, is that there’s not necessarily just a hive mind.” And I think that that’s one of the great things. We uplift different communities, and we uplift women, people of color, people who, have backgrounds that parents didn’t go to college but have these amazing qualities and strengths. And we put everybody focusing on the same issue. We come up with novel solutions that we wouldn’t have come up with if only select groups were trying to look at it and solve it. And so—.

Aryanna Trejo (36:22):

Yeah.

Eric Cross (36:23):

And we couldn’t do that without organizations like yours, that help empower teachers. So.

Aryanna Trejo (36:27):

Yeah! You really said it.

Eric Cross (36:29):

You’re coming to my classroom when you’re back in San Diego?

Aryanna Trejo (36:31):

Yeah! I totally will. Yeah. Let’s make it happen.

Eric Cross (36:34):

Last question. If you think back in your schooling, your own schooling, K through college, is there a person or a teacher that had a big impact on you? Or a learning experience that had an impact on you? And it could be, you know, positive or negative. But something that impacted you, even to this day, that stands out to you, that you remember?

Aryanna Trejo (36:56):

This is a big diversion from the topics that we’re talking about. But in grades 10 through 12, my drama teacher, Mr. Byler, who I still talk with, was such a huge impression on me. Really wonderful. And I couldn’t tell you the teaching moves that he did that were wonderful. I don’t know much about his management. But I can tell you that he gave me space to be confident, and grow into myself, through drama productions. They were high school productions, so they weren’t amazing. But I just really came into myself in high school, because I had the confidence to get on stage. And he was just such a wonderful mentor to all of us. So, props to Mr. Byler.

Eric Cross (37:39):

Shout out to Mr. Byler for creating space for Aryanna to fly! Thanks for making time, after your workday, to talk with us and to share Code.org with teachers.

Aryanna Trejo (37:54):

Of course. Happy to.

Eric Cross (37:59):

Thanks so much for joining me and Aryanna today. We want to hear more about you. If you have any great lessons or ways to keep student engagement high, please email us at stem@amplify.com. Make sure to click subscribe wherever you listen to podcasts. And join our brand new Facebook group, Science Connections: The Community for some extra content.

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 Aryanna Trejo says about science

“I would hear teachers saying things like, ‘Well I just can’t do coding, it’s just too hard for me.’ And I would ask them…Would you say that to your student about math or English? Be as kind to yourself as you would be to your student.”

– Aryanna Trejo

Professional Learning Specialist, Code.org

Meet the guest

Aryanna is a member of the Code.org Professional Learning Team. Before joining Code.org, Aryanna led computer science professional development for K-6 teachers and served as an instructional coach for new educators. She also taught fourth and fifth grade in New York City and Los Angeles. In her spare time, Aryanna loves taking advantage of the California sunshine, creating wheel-thrown pottery, and hanging out with her dog Lola.

Person with curly hair smiling, standing in front of a brick wall. Circular frame with decorative star in the corner.

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. Listen here!

Committed to reading equity

We believe that all students have the right to read complex texts and engage in rich classroom discussions. They should also see themselves reflected and experience new worlds through reading.

This commitment guides our text selection, unique artwork, and dedication to reaching every student where they are.

A student with curly hair reads a book in a classroom, while other students are visible in the background, sitting at desks.

Text selection

Texts in the Amplify ELA curriculum cover a wide range of topics, themes, and genres, with differentiated supports that ensure that all students can work through each reading and lesson. Taken as a whole, the texts show students a diverse picture of the world, while fostering a lifelong love of reading.

Illustration of diverse people and landscapes, featuring native designs, botanical elements, and a silhouetted airplane against a script background.
A painted scene shows a blue sky with scattered white dots resembling stars and red clouds, against a backdrop of dark and light color gradients.

In the Liberty & Equality unit, students reflect on the harrowing journeys and avenues to freedom that enslaved African-Americans were forced to forge.

Character & Conflict

Students read A Raisin in the Sun, a play that focuses on the impact of poverty and racial tensions on family relationships and identity within an African-American family.

Summer of the Mariposas

In the Summer of the Mariposas unit, students dive into a retelling of the Odyssey through a contemporary Hispanic lens as they explore sibling and extended-family relationships.

A pencil sketch of an airplane is shown on a textured background with orange and yellow watercolor paint.

In the Perspectives and Narrative unit, students explore a coming of age moment for an adolescent daughter of immigrant parents.

Red Scarf Girl

In the Red Scarf Girl and Narrative unit, students learn about a key historic moment in Asian and world history, while making connections to relatable themes like authority figures imposing rules on children, and family and peer loyalties standing at odds.

Mysteries & Investigations

In the Mysteries & Investigations unit, many of the texts present an ethnically and culturally diverse group of characters, including many pre-teen or teen protagonists rebelling against authority, navigating their relationships with their peers and families, and figuring out their unique identities.

Created with diverse perspectives

With our new illustrations, time spent in our classrooms will feel relevant and relatable to every student. We’ve brought together an art team with unique perspectives and visual styles so that their diversity can shine along with the
complex texts in our curriculum, and illuminate their relationship with our literature. Everyone deserves to see themselves as the hero of a story. It is our hope that our students will find themselves within our program, and will be ever more curious in their learning, and engaged in their reading.

https://youtu.be/_FLV_Le7Zoc
A person sits at a desk with art supplies, flowers, and plants, speaking on camera. An orange play button overlays the image, indicating a video. A colorful artwork hangs on the wall behind them.

Dive into the world of Mysteries &
Investigations with Dr. Womack,
the illustrator who may have once
become a scientist…

A person sits on a couch in a room decorated with colorful artwork and a wooden sculpture; a play button icon is overlaid at the center.

Meet Tre, a seeker and traveller that became homies Fredrick Douglass through illustrating his narrative for our program…

A woman with long dark hair in a red top sits indoors near a window with yellow flowers and colorful decorations; a play button overlay is at the center.

There’s no one way to be a maker, and Jackie certainly has made a lot of things. Check out the weird and mysterious world of her miniatures…

A person with curly hair and hoop earrings speaks indoors, with colorful posters and decorations visible in the background. An orange play button overlays the image.

She’s been drawing characters and comics ever since middle school. Now see the drama of Edel’s work in the mythos of the Greeks…

A woman stands in front of a wall covered with colorful artwork. An orange play button icon is overlaid on the center of the image.

Travel through countries and narratives with Caroline, as she shares her delicate watercolors for illustrating the hero’s journey…

A man with short brown hair and a beard sits at a desk near a window, with artwork displayed on the wall behind him. An orange play button is centered over the image.

The haunting work that Patrick creates will leave you feeling a sense of melancholy and longing, but not without hope for the future…

A woman in a red blazer sits in an office with open books and art prints on the wall. An orange play button is overlaid in the center of the image.

She’s been drawing characters and comics ever since middle school. Now see the drama of Edel’s work in the mythos of the Greeks…

A man in a light blue shirt speaks while seated in a creative workspace with colorful artwork and sketches displayed on the wall behind him.

As a latino American, Eddie is an illustrator, a father, and a teacher. He is working in collaboration with Poetry in America to use his heritage as inspiration…

A woman sits in front of a wall covered with colorful educational posters, partially obscured by a large play button icon in the center.

Listen to a word from Tory, the Art Director at Amplify, on how the vision
was set for the project and how she brought the team together that would get to illustrate ELA…

Fanart

Here is a library of all the inspiring art that our beloved fans have submitted for our program. Do you or your students have a favorite literary character from our program? Send us your fanart to be shared with our community here!

A collage of various portrait illustrations and drawings, including stylized faces, historical figures, animals, and astronauts, in both color and black and white.

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.

Stay connected!

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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!

The importance of reading fluency in effective literacy instruction

There’s a difference between the ability to sound out words on a page and the ability to truly understand their meaning. That difference? Reading fluency. 

Fluency is one of the five foundational reading skills. (The other four, as you likely know, are  phonological awareness, phonics, vocabulary, and comprehension.) Fluency connects readers not just to words, but to emotions and expressions, characters and connotations. And it’s also where reading really starts to foster joy. 

In this post, we’ll explore what fluency is, why it matters, and how to successfully incorporate it into your literacy instruction. 

Defining fluency

The International Literacy Association defines reading fluency as “reasonably accurate reading, at an appropriate rate, with suitable expression, that leads to accurate and deep comprehension and motivation to read.” 

In other words, fluency is not just reading fast. And it goes beyond merely decoding words, to developing a deep understanding of what they’re trying to say. Fluency allows readers to connect ideas, recognize patterns, and infer meanings. 

“I call fluency the bridge to comprehension,” says Kent State literary education professor Tim Rasinski, discussing the topic on Amplify’s Science of Reading: The Podcast

Why fluency in reading matters

Rasinski is also director of Kent State’s award-winning reading clinic, and in his podcast episode, he describes encountering students as old as grade 5 who have decoding skills, but not fluency. “[These students] can sound words out, but if you were to hear them read orally, it would be slow, laborious reading in a monotone,” he says. According to Rasinski, these students aren’t getting “much joy and satisfaction, or even comprehension” from their reading. 

While oral expression in reading is not the ultimate goal, it is an indicator. “The way you read orally reflects the way you read silently,” Rasinski says. “Most of us would say when we read silently we ‘hear’ ourselves with our internal voice.” 

When readers develop fluency, they also develop: 

  • Comprehension. As decoding becomes more effortless, readers can focus on understanding meaning. Fluent readers recognize words automatically, allowing them to dedicate cognitive resources to complex sentence structures and connections among ideas. They grasp both main points and nuances. All told, they get what they’re reading. 
  • Confidence. Fluent readers are more likely to feel accomplished, proud, and motivated with regards to their reading abilities. And it’s a virtuous cycle: As their confidence grows, they’re more likely to engage in and enjoy reading—and continue to improve. 
  • Vocabulary. Fluency plays a significant role in vocabulary acquisition and language development. Fluent readers encounter a larger variety of words in context. This exposure enhances their language and communication skills across academic topics and life experiences. 
  • Academic success. Fluency helps students read to learn. As students advance through school, fluency becomes increasingly important for comprehension and analysis of more advanced and content-rich texts.
  • Emotional connection. Fluency enables readers to connect with the characters, emotions, experiences, and implications in a given text. That’s what makes reading immersive and enjoyable—in the moment and for a lifetime. 

The fluency journey: learning and assessment

The Science of Reading tells us that foundational reading skills must be taught explicitly and systematically, and fluency is no exception. Developing reading fluency is a gradual process that requires consistent practice and exposure to different types of texts. There are several stages and skills that support the development of reading fluency. 

  • Fluency starts with accuracy in decoding. As students practice and improve their phonics skills, they can accurately recognize and decode more and more words. This helps them move from laborious reading toward more efficient reading.
  • Speed comes as a result of accuracy. As students become more accurate in decoding, they can read words more quickly. Accuracy helps reduce the time it takes to identify and process each word, allowing for a smoother and faster reading experience.
  • Fluency practice helps with automaticity. And the more students develop both accuracy and speed, the more they develop automaticity. 

As you may know, there’s a tool called Oral Reading Fluency (ORF) that reading professionals use as a quick-read thermometer of sorts to measure reading speed and accuracy. It’s a simple assessment, measuring how many words a student reads correctly in an unpracticed passage. It’s considered one of the best indicators of a student’s reading progress. 

“It works! It has validity. It gives us good, useful information,” says researcher, educational consultant, and author Dr. Jan Hasbrouck on Science of Reading: The Podcast. That’s why it’s widely used—but, she adds, it’s also widely misunderstood. 

It is a reliable and helpful measure of fluency in terms of reading rate and accuracy, she says. At the same time, “It was unfortunate to put the label ‘fluency’ on it,” she says. “We reading teachers think of fluency as something much more multifaceted and complex that at minimum includes prosody, or expression. It is accuracy, rate, expression, metacognition, background knowledge—it’s all of this stuff that really experienced reading teachers think of as fluency.” 

Fluency best practices for literary instruction

Automaticity frees up cognitive space for comprehension, but fluency isn’t just about reading fast—it’s also about making meaning, which is where prosody comes in. 

Prosody refers to the rhythm, intonation, and expression used by someone reading aloud. 

But it’s not just for the natural performers in the classroom. Prosody can be influenced. How do we help students develop that external, and internal, prosodic voice? 

Through targeted read-aloud practice. By explicitly teaching students about prosody and providing systematic practice opportunities, educators can nurture fluency and comprehension simultaneously—a connection to overall reading success that is well-supported by evidence-based research. 

Some fluency strategies include: 

  • Reader’s Theater in the classroom: Students don’t have to be skilled actors to take on roles and read from scripts. Theater activities allow them to practice recognition and expressions of drama and emotion as they bring the lines to life. 
  • Assisted reading: When students read aloud simultaneously with a more fluent reader, they practice their own skills while also hearing someone else make meaning of the same text. This can also take the form of choral reading, i.e., students reading aloud as a group, focusing on using appropriate intonation and expression. Reading together allows them to practice prosody in a supportive and collaborative environment.
  • Consistent reinforcement and rewards: Rasinski works with students on snippets of text, first with prosody modeled by teachers, then practiced alone and together (repeated reading), then performed for each other or even parents or other adults who offer praise. This regular practice helps boost the confidence and motivation that assists students in developing fluency. “We want children to experience reading success every single day,” says Rasinski. 

More to explore

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.

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

Season 1, Episode 2

Teaching for life, starring Eric Jones

Today on Beyond My Years, host Ana Torres becomes a student of Eric Jones, an educator who came out of retirement at 80 years of age to help with a national teacher shortage—thus becoming the oldest paid teacher in Britain. Eric shares his insights with Ana about building a collaborative classroom and what it means to teach children, not content. He also reflects on how the trajectory of his life changed when one man recognized and encouraged his desire to be a teacher. Eric delves into how attending school in the ’50s shaped his teaching style, his experience of retiring before the smartphone era only to return when every student has one, and how his anti-bullying efforts contributed to the passing of a national law. He also discusses why his love for teaching has lasted a lifetime. Taking all those lessons back to the classroom, Eric Cross and Ana then discuss how they would apply the tenets of respect and collaboration in their own classrooms.

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Meet Our Guest(s):

A middle-aged man with short brown hair, glasses, and a pink collared shirt sits in front of a wooden background, looking at the camera as he hosts his teaching podcast.

Eric Jones

Eric Jones, born in 1941 during World War II, was determined to become a teacher. A chance encounter with a teaching college lecturer inspired him to follow his passion, leading him to qualify as a teacher in 1969 and earning a Bachelor of Education (Hons) in 1977. Eric dedicated over 30 years to teaching, holding positions such as head of school, head of department, and deputy head at a large inner-city school in London. He briefly retired in 1993 but continued to volunteer with teenagers in drama activities and tutoring for acting exams. In 2020, Eric wrote his first novel, Finding a Sovereign.

During an impending teaching shortage in 2022, Eric volunteered when the government asked for retired teachers to help keep schools running. Since then, he’s been teaching 1–2 days per week in local high schools. Over the years, Eric has contributed significantly to anti-bullying initiatives, co-authoring guides and speaking at conferences and media outlets. He’s won numerous awards and nominations, including a nomination by the Wychavon District Council for an arts recognition award, as well as a nomination for Best Musical in the West Midlands for a theater production he directed.

Meet our host, Ana Torres.

Ana has been an educator for 30 years, working in both the K–8 and higher education sectors. She served as an administrator and instructor at various public and private colleges and universities and as a bilingual and dual language teacher, dual language math and reading interventionist, dual language instructional coach, assistant principal, and principal in K–8 schools. Ana is currently the Senior Biliteracy and Multilingual Product Specialist on Amplify’s Product Specialist team, and delivers literacy and biliteracy presentations across the nation. Ana’s passion and advocacy for biliteracy and multiculturalism has led her to educate leaders, teachers, and parents about the positive impact of bilingualism and biliteracy in our world.

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Meet our Classroom Insider, Eric Cross.

Eric Cross is a middle school science teacher who hopes to someday be a lifelong educator, like the guests on Beyond My Years! In each episode, Eric connects with host Ana Torres to discuss her guests’ best insights gleaned from their long and rewarding careers in the classroom. Then, Eric talks about bringing some of their wisdom into his current classroom and busy life.

Quotes

“He said to me, ‘You want to be a teacher, don’t you?’…I said, ‘Well, yeah, I’d love to, but I didn’t get enough qualifications when I left school. So I don’t think I’d ever really be qualified.’ And he said the magic words, ‘What are you waiting for?’”

—Eric Jones

“What I would say to young teachers is this: ‘Don’t teach science. Don’t teach maths. Don’t teach French. Don’t teach geography. Teach children.’”

—Eric Jones

“You’ve got to love teaching; you’ve got to love the kids; and you’ve really got to want to do it. Almost, dare I say, in your blood.”

—Eric Jones

“At the end of my 10 or 12 years of touring around and nattering on about bullying and trying to sort of quantify it in some way so that we could teach specifics…there is now a law in Britain that says every school must have an anti-bullying policy.”

—Eric Jones

“I like teaching kids things they didn’t know before and now they’re excited about. I love the idea that they will then move on into realms of industry and economics success that I would never dream of.”

—Eric Jones

“I’m in the education business. I’m not in the vengeance business. And if a boy doesn’t know how to use a knife and fork, I’ll teach him. If an infant doesn’t know how to tie shoelaces, I’ll teach him. If a child doesn’t know how to behave in society, I’ll teach him. Pleasantly, and productively, and creatively, and positively, I will teach him if that’s what he needs to learn.”

—Eric Jones