Welcome, Jordan K-8 reviewers!
Welcome, Jordan K-8 reviewers!
Welcome to Transitional Kindergarten
Amplify Science California jump-starts a lifelong love of science with developmentally and pedagogically appropriate instruction featuring:
- Real-world problems and scientific phenomena.
- An experiential approach with lots of hands-on.
- Explicit support for building oral language and early literacy skills.
What students learn
Our program is comprised of three units: one life science, one physical science, one Earth science.
As students take on the role of a scientist or engineer to figure out real-world phenomenon, each unit:
- Sparks curiosity and engagement.
- Encourages students to wonder, think, and talk.
- Builds a solid foundation for future success with science.
Look below for a summary of each unit.
Unit 1
Unit: Wondering About Noises in Trees
Student role: Life scientists
Phenomenon: Strange noises appear to be coming from the trees outside.
Unit 2
Unit: Wondering About Buildings
Student role: Building engineers
Phenomenon: One class made a play city. Some of the buildings stayed up, while others fell down.
Unit 3
Unit: Wondering About Puddles
Student role: Weather scientists
Phenomenon: Puddles exist in some places but not in other places along a girl’s walk to school
Program structure
To meet the unique needs of little learners, our program follows a unique structure.
Each unit:
- Begins with an Introductory Activity that
introduces the phenomenon. - Includes a series of three Explorations that are comprised of a Kickoff Discussion, four activities, and a Shared Drawing and Discussion.
- Ends with a Culminating Activity that consolidates students’ understanding.
Each activity is designed to span 15 minutes. Depending on how the program is implemented, an entire unit generally takes 4–6 weeks.
How teachers teach
Tom Teacher feels confident delivering 3-D instruction with our resources by his side. Watch this video to learn more. >
When you’re ready, scroll down to take a closer look at sample resources.
Printed Teacher’s Guide
Our unit-specific Teacher’s Guides are chock full of helpful resources, including scientific background knowledge, planning information and resources, detailed lesson plans, tips for delivering instruction, differentiation strategies, additional classroom resources, and copymasters.
Big Books
Big Books contain vivid photographs and are used to introduce topics, facilitate group discussions, and support students’ firsthand investigations. Each Big Book is an integral part of instruction and is used multiple times for multiple purposes across a unit.
Science Questions
Each unit includes three printed Science Question cards, one for each Exploration of the unit. The cards can be posted on classroom walls and support the class as they are introduced to and revisit the focus of their investigations over the course of an Exploration and, ultimately, the unit.
Vocabulary and Picture Cards
Each unit includes six or seven printed Vocabulary Cards and a set of colorful Picture Cards that can be posted on classroom word walls and concept walls. Cards are used for a variety of purposes, including gathering evidence, building background knowledge, and introducing the focal phenomenon.
Resources
S1-02: Community and joy within K–8 science instruction: Desiré Whitmore
In this episode, we join Eric Cross as he sits down with physicist and science education specialist, Desiré Whitmore. Listen in as Desiré explains her work at the Exploratorium, a public learning laboratory. Eric and Desiré discuss finding passion in science, the importance of meeting students we’re they’re at, and K–8 science instruction with real-life connections. Desiré chats with Eric about her work on supporting the science of teaching science content at the Exploratorium museum.
Explore more from Science Connections by visiting our main page.
Desiré Whitmore (00:00):
I think it’s really amazing when we can realize as teachers, like, no, our job is not to just enforce rules on our students, right? Our job is to help students to achieve more learning.
Eric Cross (00:37):
Welcome to Science Connections. I’m your host, Eric Cross. My guest today is Desiré Whitmore. Desiré has held positions as a science curriculum specialist with Amplify Science, a professor of laser and photonics technology at Irvine Valley College, and is now the senior physics educator in the Teacher Institute at the Exploratorium in San Francisco. Her current work is focused on providing support and professional development to middle and high school science teachers to help them teach through inquiry. In this episode, we discussed Desiré’s pathway into physics, the impact of educators in her life, and the importance of representation for students in the classroom. I’m so excited for you to meet my physicist friend, Dr. Desiré Whitmore. All right. So just like a superhero, STEM superhero, you have an origin story and so—
Desiré Whitmore (01:36):
How long is this podcast gonna be? ‘Cause, you know, I can talk for days, so you—
Eric Cross (01:40):
I know, I know! But it’s, it’s…so, OK. We can give us a highlight. So, you know, 30 minutes. But what would be the origin story? You can start from any point in time, but what’s that journey like?
Desiré Whitmore (01:51):
I’m gonna start at the beginning, when I was really young, just because I think it’s important. Neither of my parents were college-educated. My mother didn’t finish high school. My father went back and got a GED later. But my father’s grandmother, her name was Claudia Pairs, and she was a teacher, right? So when I was a kid, she actually kind of raised me from, I don’t know, until I was around seven or eight. And so she was very important in who I became, I think because she taught me that college is important and she taught me to think. She taught me to ask questions. She taught me how to ask questions. Just the Exploratorium likes to do. Which is why I fit so well here. She taught me to always wonder and always think about things. And I remember as a kid, she taught me to count and read and write when I was, like, three. And she would always have bubbles at her house. And I was obsessed with bubbles. I thought bubbles were the coolest thing in the world. And just how you can take your breath and create this thing that now you can see, and it’s your breath, right? It’s your breath inside of a bubble and it’s flying around and it has all these cool colors, and then it would fly up and then eventually just pop. And you’re like, where did it go? Now my breath is just up there. Not understanding, as a kid, but my breath is always everywhere. I didn’t understand any of that, but I understood that my breath was inside of a bubble. That’s my earliest memory of thinking about science, was from that. And she was not a science teacher. She was—I don’t even know what she taught. I think she was an elementary school teacher, maybe. She died when I was 12. So I don’t have super-strong memories or of understanding who she was, only that she raised me and what she taught me as a kid. But that in itself really helped me because then when I was in the environment that I was in at home with my parents, which was not at all the environment she provided for me, I always had the things she taught me in my head, right? So I was always asking questions. My mother hated it. I was always taking things apart and putting them back together. So I used to take apart TVs and VCRs and vacuum cleaners and telephones, and my mother’s like, “Oh my God, I’m gonna murder you.” And she tried a couple times, too.
Eric Cross (04:25):
Did you ever put ’em back together and realize you had extra parts? You’re like, oh, hi.
Desiré Whitmore (04:29):
Oh yeah. All the time. Yeah. Yeah. VCRs have a lot of extra pieces. You’re like, “What do you even…it still works. It’s fine.” <laugh> You know? And vacuum cleaners too. They had a lot of extra parts, <laugh> all the time. And TVs. I should not have been playing with TVs. But like I said, I didn’t have a lot of parental, guidance as a child. So, like, whatever—I’m opening up TVs.
Eric Cross (04:54):
There’s a lot of open inquiry going on in your household. Yeah. Unsupervised.
Desiré Whitmore (04:59):
Unsupervised. But I didn’t know what it was or what it meant as a kid. I mean, I used to put things in the microwave. I did so many microwave experiments as a child, trying to cook different foods or melt different things. And so I think those kinds of experiences, where I was allowed to just be curious, kind of shaped who I am today. And then I kind of got into…you know, when I was in school, I loved math. In 10th grade, I had my first Black teacher, he was my chemistry teacher. His name was Mr. Strickland. And I was like, chemistry is cool, dude. And he was not the best teacher, but he was fun. Like you were saying, he was me, and he was talking to us the way I speak. And he was so like, just kind of chill and happy-go-lucky, I guess. But he wasn’t…he hadn’t taught chemistry in a long time. So he wasn’t a very good teacher. And me and one other kid in the class were in love with chemistry. And so we would read the book and do all the homework and he’d be in class lecturing and we’re like, “That’s not right, Mr. Strickland, like, what are you talking about?” And then he’d be like, “Oh, really, Desiré? Do you wanna teach the class, then?” And I’d be like, “Yeah.” And so I would go up and I would teach my chemistry class in high school, because the teacher was trying to make an example out of me. But he was also, I think, willing to be like, “I really don’t know.” And I really appreciated that. That he wasn’t just like, “I know all of the answers and you’re wrong.” Like, he wasn’t being a jerk, right? Like, the fact that I said, “Yes, I do wanna teach it,” and he actually let me do it? That’s pretty dope. And then I liked physics in my senior year in high school, but I didn’t think it was where I was gonna go or anything. I loved music and I loved math. Those were my two subjects.
Eric Cross (06:51):
What was it about math that resonated with you?
Desiré Whitmore (06:55):
I think it helped me understand the world a lot better. I didn’t have strong science teachers, I guess, growing up. It was a lot of reading out of books or watching laser discs in class. That’s how old I am.
Eric Cross (07:12):
Laser discs.
Desiré Whitmore (07:13):
Laser discs. And you know, so there wasn’t a lot of…I moved around a lot as a kid. I didn’t have this straight curriculum. You know, in one year, in the third grade, I went to three different schools.
Eric Cross (07:25):
Mm. Oh wow.
Desiré Whitmore (07:26):
It was kinda hard for me to latch onto school. But with math, because I could look at math and actually understand the world in it, I could see how math can be used to describe how things work.
Eric Cross (07:40):
I almost imagine, especially with so much transition in your life, it helped make sense of things. You had a lot of transition going on, but you were able to understand the world through the process of math. And then this early exposure, it kind of reminds me my own story too. Because there were these books that would do these cross sections of a cruise ship or a machine; that’s what got me really into engineering. Kind of How Stuff Works. I would watch that on Nova, How Stuff Works. I’d always be fascinated. Even Sesame Street had a segment where they would show you crayons and how the dye was added. You remember that?
Desiré Whitmore (08:19):
Yep. Yeah.
Eric Cross (08:20):
Young Desiré, doing photronics…photronics?
Desiré Whitmore (08:24):
Photonics.
Eric Cross (08:24):
Photonics. Photonics at home with the microwave and all these other things.
Desiré Whitmore (08:29):
Sure. How ’bout that.
Eric Cross (08:30):
<laugh> Right. And then loving math. So, early, I could see this combination, sort of this alchemy, happening inside you. And then, how did that lead to you becoming a physicist?
Desiré Whitmore (08:46):
It’s not as straightforward as it seems it should be. It’s obvious to everyone. <laugh>. But it wasn’t obvious to me. ‘Cause I wanted to be a lawyer. You know, because my parents weren’t educated, they didn’t really know…both of my parents and their subsequent spouses when they broke up—so my parents and my stepparents—are all bus drivers. And so they don’t know what options are. Right? So for them it’s like, “You have to be—you can be a doctor. You can be a lawyer. ‘Cause you’re smart. I know you’re smart, so you’re gonna be one of those things.” And I was like, “I don’t wanna be a doctor. That’s not actually interesting to me.” I did wanna be a teacher when I was younger, because I knew that my grandmother was one. But yeah, I went in and I was like, “I’m gonna be a lawyer. I’m gonna be a lawyer.” And then I go to college and I was like, ‘Eh, I don’t. I hate writing.” <Laugh> Like, I love reading, but I don’t writing. So I don’t think I wanna be a lawyer. I love music and I love math. I was originally going to major in music and math, but then I went to community college because I missed my opportunity to go to university for…long story. And so I’m at community college and I was like, “You know what? I’m gonna just do something new. I’m gonna be a marine biologist.” So my major was marine biology, and then they’re helping me pick out my classes. And they had zero math there. And I was like, “Pardon me. I think there’s a mistake, but I’m not taking any math.” And they were like, “No, you’re done with all your math. For marine biology, you only need calculus. And you took all of that in high school, so you’re done.” And I was like, “No, this is not gonna work for me, dude.” So I continued taking calculus anyway and moving on in math. And then I realized that biology wasn’t what I needed, but I did love my chemistry and I loved my physics classes. So I asked those teachers—chemistry, physics, and math teachers in community college, my professors—”I don’t wanna be a marine biologist and I don’t wanna be a lawyer. What do I do? What do you think I could study? I really like chemistry and math and physics.” And so all of them, all three of these professors told me, “Oh, it sounds chemical engineering would be good for you, so you should be a chemical engineer.” And I was like, “OK, cool. No problem.” That’s what I did. So I got my degree in chemical engineering. Right. And I finished community college, studying chemical engineering. I was like, “This is really cool. This is a lot of fun. I love engineering.” And then I transferred to UCLA as a chemical engineering major. And I was like, “I hate this.” <Laugh>. “I hate it a lot.” It was just…
Eric Cross (11:07):
What was it about chemical engineering that you were just not feeling anymore? What was it that just made you go, “nope”?
Desiré Whitmore (11:12):
It didn’t—at least the way it was taught to me—it wasn’t as as…exploratory, I guess. There wasn’t a lot of theory in it. There was just a lot of “OK, pull out a ruler and you’re gonna draw a thing and then this is how you’re gonna build a reactor.” And it didn’t seem very scientific to me. The science was missing. And don’t get me wrong, I understand, now that I have a degree in chemical engineering, that it’s not that chemical engineering is not scientific. But it’s that you build up the science and then you don’t focus on it. You focus on the engineering aspect of it. Which is, you have the science and the scientists will work on that aspect. But then how can WE do kind of larger batch chemistry. And for me, that was just less interesting. It was a lot of pushing buttons and just plug-and-play equations stuff. Instead of diving into first principles of why things happen in chemical engineering. There was no “why things happen”; it was “this is what happens, so this is the next step.”
Eric Cross (12:25):
You had to go so far into your academic career to realize that this is what chemical engineering is. And we were talking about representation, and not having examples or parents; your families were bus drivers. My mom was a receptionist and executive assistant, things like that. And I was the first of many, like you…we kind of had to go through and invest all this time and money to finally get to this place to realize, “This ain’t it.”
Desiré Whitmore (12:58):
This is not for me, yeah.
Eric Cross (12:59):
This is not for me. That was a long journey to get to that point.
Desiré Whitmore (13:03):
It was. Especially because I went through community college and I took a long time in community college, ’cause I was working full-time. So I was working full-time, going to community college. Took me a while. And then I finally get to UCLA. I’m like, “Yeah, I’m finally gonna get my degree and go make money!” And then I was like, “Ooh, no.” I mean, I could go and make money, don’t get me wrong. I could have graduated and made a ton of money. But I was not happy at all and I did not enjoy what I was doing. So, while I was in undergrad, I realized I don’t wanna do chemical engineering anymore. But what do I wanna do? But then I was taking…I took a quantum mechanics class. And that class blew my whole mind. And I was like, “This is the coolest thing that I’ve ever learned in my life, and this is what I wanna do.” And so I went and talked to my professor and I was like, “Can I work for you? Can I do research? Because this is amazing and I wanna do this.” I felt it was too late for me. I had been in school for so long and I was already kind of burnt out. So I was, “I’m not going to change my major. That’s just outta the question for me right now. It costs so much money for this degree and I don’t have—I’m not just gonna waste my time and keep working all these jobs.” So I had three jobs in college. And it was like, I worked at Radio Shack, I did research for this professor, and I worked in the library, the chemistry and physics library.
Eric Cross (14:28):
I love the fact that we’ve talked about laser discs; you said Radio Shack; and we talked about the analog internet of the encyclopedia salespeople. And I know all of those things. And I’ve been through all of those things together.
Desiré Whitmore (14:43):
Just in case people don’t know how old I am. <Laugh>
Eric Cross (14:47):
For our listeners who are way younger, yeah, this is how we grew up. This is how we—these things are extinct now. There’s this element of this kind of cultural connection. I think that we experience that. It kind of it flies under the radar. People don’t really realize it until you’re in an environment that’s different from what you’re used to. And you realize that, “Oh wow. this is not what I’m used to.” And the things that I’m finding funnier, the things that I connect with, it’s not what everybody else connects with. And as a teacher, it’s the same thing, right? Like, we go in the classroom and you know, you and I are rapping about laser discs and Radio Shack and I’m trying to talk to my kids about it. And they’re like, “Yo, Cross, what is that? Are you gonna give us a history lesson? What are these things?”
Desiré Whitmore (15:35):
Yeah.
Eric Cross (15:36):
And I found myself having to stay connected to pop culture, because I teach 12- and 13-year-olds all day. And it’s great for keeping things relevant for my students. But when I talk to my friends that are my peers, they’re like, unless they’re a teacher, they’re like, “I got no idea what you’re talking about.”
Desiré Whitmore (15:55):
Yeah. I have a friend who’s also a middle-school teacher and she’s always coming to me with all this. I’m like, “What are you talking about?” She did the Glow-up Challenge, but she did the Glow-down Challenge. So she invented a new thing. She’s like, “No, I couldn’t do Glow Up ’cause that’s too much. So I did the Glow-Down Challenge.” And it’s the cutest thing ever. And the students think it’s amazing. And I’m like, “That’s awesome. But I have no idea what the point of that is.” <Laugh>
Eric Cross (16:21):
And there’s this theme, too, that when we talk about teaching kids STEM, there’s this soft part of it, this relational piece of it that you mentioned, of this connective aspect that in a certain way kind of even superseded the content knowledge that your teacher even had at that point, where you’re going up and teaching the class. But just the fact that someone looked like you or spoke like you or connected with you in a certain way made a big difference to who you are as…well, the trajectory of where you went.
Desiré Whitmore (16:57):
Yeah.
Eric Cross (16:57):
“I like chemistry. It resonates with me.” And it’s something I think can get lost. And I think just to kind of a good segue, I use Amplify my classroom, and one of the reasons why is because of the representation that is in these videos. And you were part of crafting this for…was it the fifth grade?
Desiré Whitmore (17:21):
I mean, it was K–8. So I was—
Eric Cross (17:23):
OK, so you were doing the whole thing.
Desiré Whitmore (17:24):
Yeah, I was a part of the K–8 science team. My title was science curriculum specialist. But in reality I was hired to do the engineering internships, mostly. Which are middle school. And to be a sim developer. So sims K–8. I worked on several of them in both middle school and elementary. Yeah.
Eric Cross (17:47):
What was that like for you? When you were designing curriculum? ‘Cause as a teacher, it’s, you know, I think with teachers it’s kind of…I would consider myself, if I was gonna use hip hop as a metaphor, I’m more of a DJ than an MC. Where I wanna remix things that exist, versus, I don’t wanna write the lyrics in freestyle. So I don’t want to go and write the curriculum completely; I wanna take something that’s solid and then I want to go ahead and remix it. You are great at both. What was the process for you, being on that team, designing? How did you go about making, “OK, we’re gonna create this experience for kids”?
Desiré Whitmore (18:25):
It was, it was amazing. I learned so much, so much. It was the best job I had before I came to the Exploratorium. The process was amazing, because it wasn’t just me, right? It wasn’t just me. It was a whole team. And each unit had its own team. So we had a scientist, which I was the scientist we had. So we had a scientist; we had a literacy specialist, because it was really important to increase science literacy so that students understand not just that science exists, but “What are the terms that are used in science and how can I speak and act a scientist? What are the things that scientists actually do in their real life?” Then we had an assessment specialist and then we had a simulation specialist. And so, on the units that I was on, sometimes I was both the sim developer and the scientist, or sometimes I was just the sim developer and I got to work alongside another scientist, which was always fun. And so it was really nice, because I was working alongside master teachers. People who had been teaching for years, and they were able to help me better understand. ‘Cause I’ll come in and I’ll be like, “Yeah, there’s a unit on light waves, let’s come in and teach this unit on light waves!” <laugh> I was the sim developer and scientist on that unit, and there was another scientist working on the unit, but they were like, “Well, Desiré literally builds lasers, so I think she should be the science developer.” So we kinda had two science developers on that one, which was fun. But I come in and she’ll come in and she’ll be like, “Yeah, I think this is where we wanna go and this is what we wanna teach.” I’m like, “No way! Like, that’s not accurate, right?” And so I can come in, but then I’m coming in with all this crazy lingo, right? I’m up here. But then also I have taught kids about lasers and optics and photonics my whole career. So I’m also very capable of bringing it down to where kids need it to be. What I don’t know is how effective that is, right? When to do it and when not to do it. When to bring the level up; when to bring the level down. And so working alongside these other teachers and assessors really helped me to do that. And so for me it was just two years of deep learning experience. I learned—every single day at work, I learned something new. Which is something that I value and I’ve wanted in my career, my whole life. We made active decisions in that room. Like, “We want to interview scientists who are scientists of color or who have different abilities or who have different representations in all kinds of ways.” Right? And then we also have these fake internships, or not even the internships, but just in the general units. And we actively wrote scripts for those. And we actively wrote in those scripts, like, “This is a Black woman. This is an Indian woman. This is a Jewish man in a wheelchair.” Like, we specifically dictated exactly who we wanted in these videos, because we knew that representation was super-important and we knew that we wanted students to be able to connect.
Eric Cross (21:35):
Right. One of the things, I appreciate what I’m hearing a lot in that is the amount of intentionality that went into this. But even now as you’re reliving it, you’re still almost iterating on how could we improve it or how can we make it different or reach more people. And I think that goes towards when we’re talking about including more people and inclusion. Like, it’s not a binary thing. You’re always modifying; you’re always iterating; you’re always redesigning and improving to be more inclusive, to reach more students. Because you know, to your point, part of it is, “Yes, we wanna do this really awesome science curriculum,” but the other part of it is there’s more to it than just your content. And I think now more than ever…I use—we just finished the food bar unit. Metabolism. And in there there’s a simulator. They always ask me when I show the videos, “Are these, are these real people? Are these real situations?” And I tell ’em, “Well, the story is real, but these are all fictional actors. But what’s actually happening happens. It’s real.” And they get really into it. And I think one of the other things is with your simulations—especially the engineering units—there’s no one right answer. And so my students who want to go, “Mr. Cross, I wanna make the best bar! Perfect 10, best taste, cheapest!” And I’m like, “All right, good luck!”
Desiré Whitmore (23:06):
Yeah. Go do that.
Eric Cross (23:09):
Casue there’s something called trade-offs! It could happen! And they’re like, they’re trying. They get into the code. They try to open up the Inspect Element, when they feel like hackers.
Desiré Whitmore (23:17):
Yeah, they do. But these kids like, they’re so smart and they’re so resourceful. And I’m just thinking like, maybe that’s how we challenge them more, right? Sometimes we can give them these kinds of things where it’s like, “Go and create a program, ’cause that’s the level you’re at <laugh>. Go and create this program to do something similar that’s related to the work that we’re doing.”
Eric Cross (23:38):
I’ve had some of my own students redesign—I have one student who redesigns every assessment I give him. I give the project; I give the options for the final goal; and he always chooses—if I give three options, he always chooses option four. If I choose two options, he’s choosing option three. And so he’ll go into Google Sheets, he’ll pull all the data and then he’ll construct his own kind of spreadsheet with all the probabilities of different things.
Desiré Whitmore (24:06):
You tell this kid to make a GitHub right now <laugh> so that he can get a job as soon as he’s done with high school. <laugh>.
Eric Cross (24:12):
He’s amazing. And we did this one project where students had to design a Netflix show to show their understanding of metabolism. And they had to do four episodes. So I gave him a template. It’s not from me; it’s from, I think, EdTechPicks.org or something. And it looks like the whole Netflix splash page. They took photos, did the whole deal. He created NOTflix. Everyone else did Google Slides. His Google Slides was interactive. So when you clicked on different boxes, it actually took you to the next splash page of that show. I mean, it was….
Desiré Whitmore (24:48):
That’s fantastic.
Eric Cross (24:49):
It was, it was. I recorded his presentation. It was brilliant.
Desiré Whitmore (24:53):
But that’s amazing. And that speaks to your strengths as a teacher and why you’re an amazing teacher. Because you see the students and what they’re trying to do and you work with them; you meet them where they are. Right? There are so many teachers who would just be frustrated with that student. And it’d be like, “No, these are not your options. Your option was to do what I told you to do.” And there are many teachers who would do that. And I think it’s really amazing when we can realize as teachers, “No, our job is not to just enforce rules on our students. I mean, that is part of the job, because that’s what school was when it was created. But our job is to help students to achieve more learning in what we’re trying to do. And so the fact that you are so good with this student and that you encourage him to go above and beyond when he can, I think it’s so amazing.
Eric Cross (25:49):
Well, that brings me to my favorite group, organization, and the phase of your career of where you are now: The Exploratorium. And I wanted to kind of rap, talking about what you do now. Because the Exploratorium—I tell people, they go, what is that place? And maybe you can tell us what it is and then what you do. But for me, I’ll just tell everybody: It’s Disneyland for science teachers. And I love going there. I not only love going there because of what I receive from it professionally. Many of the PDs, I don’t even call ’em PDs—just communal learning experiences, that I’ve had that have been led by you and Lori and, and Tammy and the rest, and everybody that’s there have been incredible. And I have so much fun. Emotionally, I get excited when I go. When I’m on the plane, I’m like, “Here we go!” And then we go and we’re making fudge or we’re blowing darts with marshmallows across the room in the theme of Boba Fett. There’s just these rad things that are going on there. And it’s not like anything I’ve ever experienced before. So maybe we can close with talking about what the Exploratorium is, what you do there, for people who’ve never been and have been a part of it.
Desiré Whitmore (27:19):
I’m gonna give you what my definition of the Exploratorium is.
Eric Cross (27:21):
That’s what we want.
Desiré Whitmore (27:22):
So, the actual definition is, we are a public learning laboratory. We are known as the Museum of Art, Science and Human Perception. Cool. But, like, what does that all mean? Right? And I think your description of the Disneyland for science teachers, I think that’s a perfect description. ‘Cause for me, I tell people like, “Oh, I wanna go to the happiest place on earth.” And for me, that is the Exploratorium. And yes, I work there, and yes, it’s still true for me. So the Exploratorium is this huge museum. It’s an interactive science museum. And art—we have a lot of art. And it’s all about learning through doing. It’s not about learning science by going up to an exhibit and reading the little paper next to it. It’s like, no, you go up to an exhibit and you interact with it and you teach yourself science. The goal of the Exploratorium is really to help people understand that learning science, doing science, isn’t reserved for only scientists. Doing science is something that everyone in the world should and does do. And so helping people understand that everything we do is science is kind of the point of the Exploratorium to me.
Eric Cross (28:35):
Even the building itself…one of the other cool things too is, for people that don’t know, it’s the size of Costco or two.
Desiré Whitmore (28:43):
Yeah. Yeah.
Eric Cross (28:44):
It’s immense! And even the building itself teaches. Like, you have that whole workshop, dead-center in the middle of the floor where they’re designing things. It’s like inside-out. And then I remember going to the one experience where I think it was Eric who showed us that it’s one of the few facilities that is actually cooled by the Bay water. And there’s only a couple of those in the state that can do that. And it has a platinum rating, something wild that. So even just the building itself…everything that if they can extract every ounce of science teaching in that, it’s in there. And you are in a very important program for me. And can you talk a little bit about maybe what you’re doing in T.I.?
Desiré Whitmore (29:33):
So I am in the Teacher Institute. I’m a physicist in the Teacher Institute. And the Teacher Institute is a group of teachers and scientists. And our job is to basically support middle school and high school science teachers and teacher leaders in the state of California, but science teachers around the world, in their pursuit of science teaching. And by support, I mean we provide professional development. We provide other things, communities of practice, and we go and do workshops in certain places. We go to India to teach Tibetan monks and nuns science. And we go to Costa Rica to teach teachers all over the country of Costa Rica about science. And so our job is really, to help science teachers feel more secure in their science teaching and help to retain them in the field, because a good science teacher is so important in helping our students thrive. And so our job—and we take this very seriously—is to help science teachers thrive. And we are made up of PhD scientists and veteran classroom teachers. So we have on the one side teachers who have been teaching middle school or high school for years. One of my coworkers, Zeke, who I work with the most, he was a high school physics and environmental science teacher for 21 years before coming to the Exploratorium. And then me, I was never a classroom teacher. I was a professor; I was a physics professor at a community college, and I was a researcher. So my deep knowledge of physics and current knowledge of physics—or knowledge of current physics—combined with Zeke’s extremely experienced pedagogy is really how we work together as a team. And it’s not just Zeke, right? We’ve got a geologist on the team, Eric Muller. We’ve got Tammy, who’s a middle-school bio teacher. We’ve got, Julie Yu, who is a chemical engineer, PhD, and also a prior middle school teacher, former middle school teacher. We’ve got Hilleary Osheroff, who was a PhD biologist who used to work at the American Museum of Natural History. We’ve got Lori Lambertson, who was a middle-school math teacher. And so, you know, we all come together to bring our experiences both in and out of the classroom and in and out of the research lab to provide teachers with the best inquiry-driven stuff we can. And we’re very—we’re so equity-focused, because we believe that that’s important, right? We know that the impact of our work is, I think, why most of us are here. It’s why I’m here. In undergrad, my grad school, and my postdoc, I would go into classrooms. I would go into science museums and teach science to people. And I probably reached out to maybe…over that whole time, I would say a couple thousand people, right? Maybe a couple thousand people total. That’s great. But over 15 years of reaching out and only reaching a couple thousand people, that’s rough, right? And now I’m at the Exploratorium, and I know that if I reach one teacher, right? If I can teach one teacher…let’s say you. How many students do you have in your classes a year?
Eric Cross (33:11):
Two hundred a year.
Desiré Whitmore (33:12):
You have 200 students a year that you teach. So if you teach for 10 years, that’s 2000. That’s 2000 students. So I have, by teaching you today, assuming that I’m actually teaching you something that’s gonna be useful for you—
Eric Cross (33:29):
You do! And you are!
Desiré Whitmore (33:30):
You are going to be impacting these 2000 students over the next 10 years. And of course you’re gonna be in teaching for much longer than that. But let’s just say in 10 years, that payoff is so much higher, right? And you’re one teacher. But I have 30 of you in my workshop! And so if all of these 30 teachers each teach 2000 kids over the next 10 years, then I’m actually doing something. I’m actually changing the way that students see science, through changing the way that you see science. Right? And so I take my job very seriously, as we all do. Like, we’re so invested in our teachers. And it’s not that we don’t care about students, ’cause we absolutely do. But we understand that without good teachers, students aren’t going to be able to thrive, as often as they would otherwise. I was able to do it somehow. But I’m one. There are so many other kids who could have gone into science who didn’t because they felt they never connected to it. So our job is to try to help teachers connect to it. And an important part of that is allowing you all to experience science as a learner. We want you to play and have joyful experiences. We want you to enjoy science and to try to think about it from the perspective of your students. Walk in their shoes. So that when you then go back to your classroom, you are able to think about like, “Oh yeah, you know, my students totally asked the same question that I asked, or that another teacher asked in the workshop because they had the foresight to think about that’s what my students would ask.” Right?
Eric Cross (35:02):
Well, I think it’s really effective to create empathy for the learner. Because I find myself in that position. I don’t know if some kind of memory displacement field happens to me when I sit in those workshops, but Hillary will ask a question that I know the answer to and I’m like, “I don’t want to answer the question. I don’t—I might be wrong.” And I teach the subject! And I embody what it’s like to be a student. And when I leave, I might have to go back and reference exactly what the lesson was, but I remember how I felt when I didn’t know. And very rarely as teachers do we get put in positions like that. And so it helps me be in the position of my students emotionally, of what it’s like. Even even the intentionality of how do you ask questions and not showing an affect on your face when somebody says the right answer or the wrong answer.
Desiré Whitmore (35:55):
Well, I’m still learning that. I’m not great at it. Julie is the mast.
Eric Cross (35:59):
Julie’s got it nailed.
Desiré Whitmore (36:00):
I’m still trying to learn from her. She’s amazing. And I really would like to get there one day. But I’m still not there. I’ll be like, “Oh! Oh! Well, that’s…”. I have a terrible poker face. So I’ll be like, “Oh yeah, but you think that? Maybe…”. That’s a piece of it that’s really important, right? It’s this not giving away the answer, even when you have the right answer. Allowing people to ask the questions and explore and become invested in the problem, before giving away the answer. That’s something that I learn here at the Exploratorium. And like I said, I learn every day. And it’s something that I think is so important for us as teachers to learn and try to implement. Because oftentimes you’ll come and you’ll have students who are like, “I’m too stupid. I don’t know the answer.” And then somebody else will say the answer, and then the student is like, “Yeah, I was right. I’m too stupid.’” But it’s like no! But if you have that student actually think about it, then the student—once they do hear the right answer—they might be like, “Oh yeah, that would make sense.” Instead of “I’m stupid.” It’s like, no, this is, “I explored this and I figured it out on my own.”
Eric Cross (37:08):
Things keep coming back to how this experience and the process of them learning science even outweighs the content of it. ‘Cause the content is almost easier to share, it’s easier to get, you can look it up really quickly. But in your story and in many other people’s stories, the exposure, the experience, how they’re going through that process—I know that’s something that I’ve learned a lot in just watching. Not teaching science, but actually the science of teaching. Sitting in the workshops and watching how we’re treated as students, how you interact with us, and then being able to take that back to the classroom. And just to add onto the value that it’s created, I think one thing that it’s also done is given us community. And in addition to being able to impact students, it’s also been able to build resilience in teachers. Because we as teachers can feel very isolated. And especially now when things are incredibly difficult, and every teacher’s experiencing Covid and shutdowns and low staffing across the country in different ways, when you don’t feel you have community or people that you can connect with, it just makes everything feel exponentially harder. And you’ve done a great job at being able to build community with us in our community of practice. The Exploratorium has been able to do that. And it’s something that I’m super-grateful for probably more than anything else is that through these last two years, being able to connect really made me feel like, “OK, we’re gonna be able to do this.” And it’s not just about Cross or my other teacher in eighth grade or my sixth grade teacher who’s doing this. That message, I think, is really, really important. I wanna ask this: Was there a teacher or an experience that impacted you or inspired you throughout your educational career? You know, kindergarten all the way to college? Was there a moment or a person or anything that that really stuck with you, that you felt maybe influenced who you became? Met you where you were at? I know you mentioned your chemistry teacher at that point, but is there anyone else, or was it that person that was really the person who sticks out for you?
Desiré Whitmore (39:21):
There actually have been a few. Of course, the first is my great-grandmother, Claudia Pairs. But I think in the fourth and fifth grade I had the same teacher. She stayed with us going from fourth to fifth grade. And fourth grade was a new school for me. New town. I was the only Black child in the school, me and my sister. And my teacher recognized that I had no real help at home, I guess? And she really kind of…she saw that I was really smart. She would give me extra assignments when she could tell I was bored. It meant that someone outside of my house cared about me in a way that I didn’t feel cared about at home. Her name is Ms. Comet. Mrs. Comet.
Eric Cross (40:11):
Like…comet?
Desiré Whitmore (40:13):
Yeah. Mrs. Fran Comet. And I’ve tried looking her up as an adult and I can’t find her. But I work with so many teachers, and I know how hard teaching is and how degrading it can be…or demoralizing, I guess, to not be appreciated. And so I know what it feels to me when a student has reached out and shown me like, “Hey, I’m now in dental school,” or “I’m now getting a PhD in science,” and I’m just like….
Eric Cross (40:40):
I got a message this morning on Instagram from a student. And none of my students use their real names in their Instagram handles. So I got a message from Moonshine. <Laugh> And I was a seventh grade teacher. And through deduction, deductive reasoning, I figured out who it was. This person’s now in college and they responded in that…you know, you get one of those every once in a while. And I feel it just fills your tank. It’s just so important that we—it’s funny because, kind of to your point, we don’t realize who or how we’re making impacts on people. And in what ways. We just know that we are. And I tell other teachers, I said, “You have one of the few professions where you fall asleep worrying about other people’s kids.” And it’s the words that we speak, the things that we do, people are always watching. I know, no pressure, right!? Hopefully, someone listening can find Ms. Comet.
Desiré Whitmore (41:37):
Ms. Comet. Teacher at Buena Vista Elementary School back in the ’80s. But your talk about this impact, it reminds me of the thing I wanted to say, but I didn’t. But I’m gonna tell you right now. I mentioned how science was not a priority when I went to school, in my hometown. That’s Lancaster, California. But recently I got a phone call from a family friend and she was so excited. And she called me to tell me that her daughter was super-excited when she picked her up from school. Because I was in her classroom. She said, “Auntie Desiré was in my class today! And she works on lasers! And she does spectroscopy! And I wanna learn about spectroscopy now. So can we call Auntie Desiré?” And I was like, “Wait, what?” My friend was kind of confused. She’s like, “Desiré didn’t tell me she was in town.” She had no idea why her daughter was saying I was in her classroom, ’cause I was not physically there. And then I had to put the pieces together and I was like, “Oh my God, your daughter’s in eighth grade already.” It made me feel really old, ’cause I know this girl from a little baby. But I was like, “Oh my God, that’s the eighth grade unit on light waves for Amplify that I wrote, and I’m featured as the scientist.” Because we have real scientists in the units. And they featured me in that one, in my laser lab. And so this little girl who knows me really well, who lives in my hometown, is seeing representation in science. She doesn’t necessarily know I’m a scientist. She knows that—I don’t know what she knows about me. She just knows I’m Auntie Desiré and, you know, I like gumbo at Christmas. That’s what she knows about me. <Laugh>. And so she comes back and she’s so excited ’cause now she knows so much more about me. And she knows that if I can do it and I came from where she’s at, she can do it too. And she was super-excited. And I was just…it brought me to tears. I was just crying in the car. I was driving <laugh> at the time and I was like, “This is amazing. Work that I did is teaching you and all of your friends in this tiny little town that you live in. And that to me is so important because now this little girl knows that, like, she knows me as just a normal human right. Who likes Star Trek and Star Wars and The Owl House. And now she’s over here like, “Oh my gosh, this normal human wrote the science curriculum that I’m learning from.” Which I think is just so fantastic. And it really brought home for me kind of the importance of my work and why I’m doing what I’m doing. And that’s pretty awesome. And I get messages from Instagram, you know, from teachers who are like, “Hey, did you work on this? ‘Cause you were featured in the video, but did you write this light waves unit?” And I’m like, “Yeah.” And they’ll tell me, “I have students, this is their favorite unit. I’ve gotten notes from students saying, ‘This was my favorite unit in all of middle school.’” And I’m like, “Ohhhhhh!”<Laugh>
Eric Cross (44:33):
That story just gives me chills. Because I just can imagine how surreal that must feel. And you’re directly making that impact on those kids. And I’m glad that you shared that story so that everyone can hear it, because it’s a powerful story and I lived—I feel I was living it through you, just now, as you were discussing it.
Desiré Whitmore (44:54):
Yeah.
Eric Cross (44:54):
And I feel that way in the classroom to a small degree, because I get to have—when my students create posters of scientists that we don’t typically see, I’ve got you on my list of scientists, and I’m they’re like…And I’m like, “I can call her!” Like, “Mr. Cross, you KNOW her?!” I’m like, “Yeah, she’s a friend of mine! I was talking to her the other day!” And they’re like, “Whoa. She works with lasers?!”
Desiré Whitmore (45:17):
<Whispers> I do.
Eric Cross (45:18):
Desiré. I’ve held you for so long and—
Desiré Whitmore (45:23):
Yes, I’m sorry! I told you, I talk so much! I’m a teacher!
Eric Cross (45:26):
No! No, no, no, no. It was great! I wanna honor your time. Can you tell everybody where they can find out more about you again?
Desiré Whitmore (45:33):
So first off, you can find me on Twitter at Darth Science, D A R T H S C I E N C E, and you can also find me at Instagram at Dr. Laser Chick: D R dot laser chick. Even though I don’t post on Instagram that much. I also have a website, which is laser chick dot net. I’m still working on it. It’s not the best website yet. But, you know, it’ll, it’ll be better in the future.
Eric Cross (46:02):
Would you be willing to come back later on in the year and do a part two?
Desiré Whitmore (46:07):
Oh, for sure. Yeah. So I can actually finish telling you the story of how I got into physics! ‘Cause I totally didn’t. ‘Cause I’m all over the place.
Eric Cross (46:15):
So, everybody, cliffhanger! Next time she comes back, she’ll continue to tell us the story. Desiré, thank you so much.
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Meet the guest
A Southern California native, Desiré earned an associate of science from Antelope Valley College, a bachelor of science in chemical engineering from UCLA, and a master of science and Ph.D. in chemical and material physics from UC Irvine. Her research focused on developing very fast laser and microscope systems that could capture molecules vibrating and rotating in real time. She was a postdoctoral fellow at UC Berkeley, where she designed and built attosecond lasers (the fastest laser pulses, which emit x-ray light, ever measured). At the Lawrence Hall of Science she wrote an all-digital K–8 science curriculum (Amplify Science), which aligned to the NGSS, with the Learning Design Group (LDG). Desiré left LDG to teach hands-on laser technology and physics courses at Irvine Valley College before joining the TI staff. She is the proud mom of Stella, a four-year-old boxer-pit mix. In her spare time, Desiré is restoring her 1967 VW bug.
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!
Winter Wrap-Up 03: Ideas to build math fluency
Join us for the third episode in our Winter Wrap-Up! In this episode from season 3 of Math Teacher Lounge: The Podcast, we sit down with Dr. Valerie Henry to talk about math fluency and what that means for students. Listen as we dig into the research, hear Val’s three-part definition of fluency, and explore her five principles for developing it.
Explore more from Math Teacher Lounge by visiting our main page.
Dan Meyer (00:03)
Hey folks. Welcome back. This is Math Teacher Lounge, and I am one of your hosts, Dan Meyer.
Bethany Lockhart Johnson (00:07):
And I’m your other host, Bethany Lockhart Johnson. Hi, Dan.
Dan Meyer (00:11):
Hey, great to see you. We have a big one this week to chat about and some fantastic guests. We are chatting about fluency, which is the sort of word and concept that I feel like people have very, very non-neutral associations with it. A lot of them are very negative, for a lot of people.
Bethany Lockhart Johnson (00:26):
I saw you frown a little. What’s up with that, Dan? You kind of, like, shrank.
Dan Meyer (00:30):
I have strong feelings about it. You know, there’s lots of ways that people go about helping people become fluent in mathematics. And a lot of them are harmful for students, and ineffective. And it got me thinking about fluency as it exists outside of the world of mathematics, where we have a lot of very clear images of it. We’re getting fluent in things all the time. Like, as humans. Human development is the story of fluency. And I just was wondering….Bethany, would you describe yourself as fluent at something outside of the world of mathematics? What is that? How’d you get fluent at it? What was the process?
Bethany Lockhart Johnson (01:05):
Hmm, I think I’m a pretty fluent reader. I read all the time. I’m a happier person if I’ve read that day. I once saw this poster in a classroom; it said “10 Ways to Become a Better Reader: Read, Read, Read, Read, Read…you know, 10 times. Get it? Reading? You get better at reading by reading! So I would say reading. And it’s been kind of cool—I have a one-year-old who, it’s been really exciting slash overwhelmingly anxiety-producing to see him get very fluent with walking slash running, ’cause he’s getting faster every day. And it’s kind of fun. When I think of what’s something somebody’s trying to get fluent with…walking! He’s trying to be more fluid. He’s practicing transitions. He doesn’t wanna hold my hand while he traverses rocky terrain. He’s getting better at it. He’s practicing. What about you? What’s something…?
Dan Meyer (02:08):
I think about driving a lot. I’m a very fluent driver and I think a lot about when I was first a driver, you know? And how l have my hands on 10 and 2, vice grip, and do not talk to me; do not ask me anything; don’t ask me my NAME. I need to focus so hard. And then a year later, you know, I’m driving with one hand, smash the turn signal, take a sip off of whatever, change the CD. And then it’s no big deal.
Bethany Lockhart Johnson (02:38):
Wait, did you pass the first time? Your test?
Dan Meyer (02:40):
Yeah, I don’t like to brag about it. <laugh> But I do all the time. <laugh> But I got a hundred on my driving test. I don’t care who knows it. And I hope it’s everybody. But I guess all of this is just to say there are areas of life where fluency feels natural, with the case of walking. There’s areas of life where fluency feels motivating, with like driving—I wanna be able to switch the CD out or whatever. And there’s areas where fluency feels terrifying and hard to come by, like mathematics, sometimes. So we have a set of guests here. Our first guest will help us figure out what do we mean by fluency? And what’s the research say about what fluency is and how students develop it in mathematics? And then our other guests will help us think about what it looks like in practice in the classroom. What are some novel, new ways to work on fluency? So first up we have Val Henry, Dr. Val Henry.
Bethany Lockhart Johnson (03:32):
So we knew we needed help with the fluency definition, because when we think about it, it’s kind of big, right? And we wanted to look at what research about fluency really says. So we called on Valerie Henry. Val is a nationally board-certified teacher, taught middle school for 17 years, and since 2002 has worked with undergraduates graduates, credential candidates as a lecturer at the University of California, Irvine, one of my alma maters. So after doing her dissertation on addition and subtraction fluency in first grade, Val created a project to study ways to build addition and subtraction and multiplication and division fluency while also developing number sense in algebraic thinking. And the pilot grew and grew over the last 18 years into a powerful daily mini-lesson approach to facts fluency called FactsWise. And when we thought of fluency, the first person I thought of was Val. Welcome, Val Henry, to the Lounge! I’m so excited to have you here. Welcome.
Valerie Henry (04:36):
Thanks, Bethany. And thanks to you, Dan. It’s great to be here today.
Dan Meyer (04:41):
Great to have you; help yourself to whatever you find in the fridge. The names that people write down on those things in the bags are just recommendations. It’s potluck-style here. I’m curious, Val, if you’re, like, on an airplane, someone asks you what you do, and you say you study fluency…what is the layperson’s definition of what does it mean to be fluent in mathematics? And if you can give a brief tour through what the research says about what works and what doesn’t that would really help us orient our conversation here.
Valerie Henry (05:12):
The first thing I have to do when I talk to somebody on a plane is define the idea of fluency. And I often use an example of tying your shoelaces. Because that works with first graders as well as adults. This idea that when we first start trying to put our shoes on and get those shoelaces tied, somebody tries to, first of all, just do it for us. But then of course maybe tries to teach us the bunny-ears approach. And we struggle and struggle as little kids and eventually either the bunny-ears approach or something else starts to work for us. But we still have to pay attention to it. We have to think hard and it’s not easy. And then over time we get to the point where we basically don’t even think about it. When I tie my shoes in the morning. I’m not thinking about right-over-left and left-over-right and all of those things. I just do it. And so that’s a good, easy example of becoming fluent with something. I think what we’re talking about today though, is the basics, the adding and subtracting that we hope kids are going to have mastered maybe by second grade, and the multiplication and division facts that we wanna maybe have mastered by third, maybe fourth grade. So now what does that mean to become fluent with those basics? I have a three-part definition that seems to match up really nicely with the common core approach to fluency. Which is, first of all, we want the answers to be correct. And then second, we want the answers to be easy to know. And so what does that mean? Well, to me, it means without needing to count,
Bethany Lockhart Johnson (07:12):
You mean without having to kind of muscle through it? Or say more about you mean.
Valerie Henry (07:16):
Well, I guess what I mean is that when you watch a young child try and solve something even as simple as two plus three, they might put up two fingers and then go 3, 4, 5 with three more fingers winding up on their hand, one or the other of their hands. While they’re doing that, they don’t really have a sense of whether even their answer is right or not, quite often. Especially when you get to the larger adding and subtracting problems, you can see a lot of errors happening as they’re trying to count. And it’s taking up cognitive energy to do that counting process, especially as you get to the larger quantities. So my definition of fluency now is “getting it right without needing to do that hard work like counting.” Now, some people might say, well, we just want them to have ’em memorized. But in my research, I’ve learned that a lot of very fluid adults don’t always have every fact memorized. In fact, if you ask a room full of adults, what’s seven plus nine, you might learn that they can all get it correct quickly, quickly…but they don’t all have it memorized. And so when you ask them, “How did you get that?” Many of them will say, “Well, I just gave one from the 7 to the 9 and I know that 10 plus 6 is 16.”
Bethany Lockhart Johnson (08:53):
That’s such an important distinction. My brain literally just did that actually!
Valerie Henry (08:58):
<laugh> Right? <laugh> But you’re fluid with it, because it doesn’t take you much cognitive energy at all.
Bethany Lockhart Johnson (09:05):
Right.
Valerie Henry (09:07):
So now we have “correct without needing to put that cognitive energy,” which usually means that you’re counting. And then the third thing is “relatively quickly,” so that you’re not spending 15 seconds trying to figure it out. Even that part-whole strategy approach can be done really quickly, almost instantaneously. Or it can take a long time. So if a student can get the answer correct within, you know, three or four seconds— is I’m pretty generous—I figure that they’re pretty darn fluent with that fact. So that’s my three-part definition of these basics, fluency.
Dan Meyer (09:55):
I love the distinction between getting it correct and getting it quick. It’s possible to be quick with wrong answers. It’s possible to be like, “Those are separate components there.” And I echo Bethany’s appreciation for this third option in between knowing it instantaneously through memorization and muscling through it. But there’s like a continuum there of how much energy it took you to come up with it that all feels extremely helpful.
Valerie Henry (10:21):
And you know, one of the things that I’ve noticed is that when kids are pressured to come up with those instantaneous answers, they often default to guessing and get it wrong.
Bethany Lockhart Johnson (10:30):
Mm, yeah.
Valerie Henry (10:30):
So that’s one of the things that I’ve learned is that as we’re trying to help students develop fluency, it’s important to start with building their conceptual understanding of what it means to do, you know, 3 times 9 and what the correct answer is, maybe using manipulatives or representations of some sort. Not skip-counting! I really have found that skip-counting just perpetuates itself in many students’ minds and that they never stop skip-counting, which means they’re putting in not very much mental energy if it’s 2 times 3 but a ton of mental energy if it’s 7 times 8. Because frankly, it’s really hard to skip count by sevens. And by eights.
Bethany Lockhart Johnson (11:18):
I can get to 14 and then I’m like, wait, wait, what was next? Right? No, no, no…21! What do you feel are some misconceptions that maybe teachers, maybe parents have about fluency in math?
Valerie Henry (11:30):
I think maybe one of the first ones is that if students count or skip-count, their answers repetitively over and over and over and over, that they’re bound to memorize them. And the study that I did back in 2004, I actually had a school that had decided that they were going to do time tests with their students every day, all year. And that undoubtedly by the end of the year, those students would be fluent.
Bethany Lockhart Johnson (12:06):
And to clarify by time test, you mean like, sit down, pencil, paper, ready, go, worksheet kind of thing.
Valerie Henry (12:15):
Yes.
Bethany Lockhart Johnson (12:16):
Some of us might remember quite vividly.
Valerie Henry (12:18):
<laugh> Very vividly. And you know, you have to get it done within a certain amount of time. So they made it fun for the students. Apparently the students enjoyed it. I was a little leery about that, but in the end, when I went and checked on the students and I did one-on-one assessments with half of the students in every class that were randomly selected so that I could get a sense of where they were with their fluency—and these were first graders—they basically had nothing memorized. They were simply counting as fast as they possibly could. And, you know, mostly getting the right answers. But they had not memorized. So that’s one of the myths, I think, is that repetitive practice of counting gets you to memorization.
Bethany Lockhart Johnson (13:10):
If I put it in front of you enough times, you’ll become fluent.
Valerie Henry (13:14):
Right, right. Now these students didn’t really get any instruction, any help learning these. They just simply tested over and over and over. So that’s another thing that I think is a misconception. It’s that if we test students, but don’t really teach them fluency, then they’re going to become fluent. If we just test them every Friday or that kind of thing. And that they’ll learn them at home. But really what that means is a few lucky kids who have parents who have the time and the energy and the background to know how to help will take that job on at home. Not that many students are really that fortunate.
Dan Meyer (14:01):
It’s almost like the traditional approach, or the approach you’re describing, confuses process and product. It says, “Well, the product is that eventually fluent students will be able to do something like this, see these problems and answer them, answer them quickly,” and says, “Well, that must be the process then as well; let’s give them that products a whole lot.” But as I hear you describe fluency with bunny ears on shoelaces, there’s these images and approaches and techniques that require a very active teacher presence to support the development of it. That’s just kind of interesting to me.
Valerie Henry (14:35):
My initial project, the pilot project that I tried, was to simply ask teachers to follow five key principles. And the first one was to do something in the classroom every day for—I told them, even if you’ve only got five or 10 minutes, work on fluency for five or 10 minutes a day, and let’s see what happens. So that was one key element was just to teach it and to give students opportunities to get what the research calls for when you’re trying to memorize, which is actually immediate feedback. When I talk about immediate feedback with my student teachers, I say, “I’m talking about within one or two seconds of trying a problem, and then sort of immediately knowing, getting feedback of whether you got the answer right or not so that your brain can kind of gain that confidence. ‘Oh, not only did I come up with an answer, but somebody’s telling me it’s the correct answer.’”
Dan Meyer (15:38):
There’s a lot of apps now in the digital world that offer students questions about arithmetic or other kinds of mathematical concepts and give immediate feedback of a sort: the feedback of “You’re right; you’re wrong” sort. Is that effective fluency development, in your view?
Valerie Henry (15:57):
I haven’t heard and I haven’t seen them being super-effective. The ways I think about this are “Immediate feedback isn’t the only thing we need.” Probably one of the biggest things that we need is for students to develop strategies. And this is one of the other things I’ve learned from international research, from countries that do have students who become very fluent very early, is that they don’t shoot straight for memorization, but they go through this process of taking students from doing some counting and then quickly moving them to trying to use logic. So, “Hey, you really are confident that 2 + 2 is 4; so now let’s use that to think about 2 + 3.” Actually, as an algebra teacher, I would much rather have students that have a combination of memorization and these strategies, than students who’ve only memorized. Isn’t that interesting that my most successful algebra students were good strategy thinkers. Not just good memorizers.
Bethany Lockhart Johnson (17:09):
So you mentioned there were five that kind of helped root this idea in like, “What can teachers do? What is the best thing that teachers can do to support with fact fluency?” So, everyday was key.
Valerie Henry (17:22):
Then the next principle that I really focus on is switching immediately to the connected subtractions so that students—
Bethany Lockhart Johnson (17:33):
Not waiting until you’ve gotten all the way through addition. But making “Ooh!”
Valerie Henry (17:38):
Totally. And I didn’t do that the first year. And when we looked at the results of the assessments at the end of the year, we realized that our students were so much weaker in subtraction than addition. So the following pilot year, we tried this other approach of doing subtraction right after the students had developed some fluency with that small chunk of addition. And we got such better subtraction results.
Bethany Lockhart Johnson (18:11):
What are the other principles?
Valerie Henry (18:13):
The biggest one is to use these strategies. So the strategies makes the third. And then the fourth I would say is to go from concrete to representational to abstract.
Bethany Lockhart Johnson (18:27):
Don’t put away those manipulatives. Don’t put away those tools.
Valerie Henry (18:31):
Oh, so important to come back to them for multiplication and division. And my fifth principle is to wait on assessment. To use it as true assessment, but not race to start testing before students have had a chance to go through this three-phase process. Which is conceptual understanding with manipulatives; building strategies, usually with representations; and then working on building some speed until it’s just that natural fluency.
Bethany Lockhart Johnson (19:07):
I wanna say thank you so much for offering your really learned perspective, because you have not only done the research, but seen it in action and seen how shifting our notions of fluency and what fluency can be and what a powerful foundation it can be for all mathematicians. Really, that shift is so powerful. And I appreciate you sharing it with our listeners and with us. So we’re so excited that we got to talk with you today, Val—
Dan Meyer (19:35):
Thank you, Dr. Henry.
Valerie Henry (19:37):
You’re welcome!
Dan Meyer (19:41):
With us now we have Graham Fletcher and Tracy Zager, a couple of people who understand fluency at a very deep and classroom level. I wanna introduce them and get their perspective on what we’re trying to solve here with fluency. So Graham Fletcher has served in education in a lot of different roles: as a classroom teacher, math coach, math specialist, and he’s continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary math. He’s the author, along with Tracy, of Building Fact Fluency, a fluency kit we’ll talk about, and openly shares so much of his wisdom and resources at gfletchy.com. Tracy Johnson Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of this toolkit, Building Fact Fluency, and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books for teachers at Stenhouse Publishers, including, yours truly. Thank you for all that insight, Tracy, and support on the book.
Bethany Lockhart Johnson (20:49):
Dan and I were talking at the beginning of the episode about things we feel like, “Hey, I’m fluent in that. I’m fluent in that.”
Dan Meyer (20:55):
Just very curious: What’s something you would like to get fluent in outside of the world of mathematics, let’s say?
Tracy Zager (21:00):
I’ll say understanding the teenage brain, as the parent of a 13-year-old and 15-year-old. That’s the main thing I’m working on becoming fluent in!
Bethany Lockhart Johnson (21:10):
Ooh!
Dan Meyer (21:13):
A language fluency, perhaps. All right, Graham. How about you?
Graham Fletcher (21:16):
For me typing, it’s always been an Achilles heel of mine. So voice-to-text has been my friend. But it’s also been my nemesis in much of my texting here and working virtually over the last couple years. So yeah, typing.
Dan Meyer (21:33):
Do you folks have some way of helping us understand the difference in how fluency is handled by instructors and by learners?
Tracy Zager (21:40):
I would say that the lay meaning of fluency is definitely a little different than what we mean in the math education realm. When we’re talking about math fact fluency, which is just one type of fluency. So you gotta think about procedural fluency and computational fluency; there are lots of types of fluency in math. And Graham and I had the luxury of really focusing in specifically on math fact fluency. We’re looking at kind of a subset of the procedural fluency. So the words you hear in all the citations are accurate, efficient, and flexible. There’s this combination of kids get the right answer in a reasonable amount of time and with a reasonable amount of work and they can match their strategy or their approach to the situation. That’s where that flexibility comes in. And there’s like lots more I wanna say about that about sort of…I think one issue that comes up around fluency is that people are in a little bit of a rush. So they tend to think of the fluency as this automaticity or recall of known facts without having to think about it. And that is part of the end goal, but that’s not the journey to fluency. So this is one of the things that Graham and I thought about a lot was the path to fluency. The goal here it’s that student in middle school who’s learning something new doesn’t have to expend any effort to gather that fact. And they might do it because they’ve done it so many different ways that they’ve got it, and now they just know it, or they might be like my friend who’s a mathematician who still, if you say, “Six times 8,” she thinks in her head, “Twelve, 24, 48…” and she does this double-double-double associative property strategy. And it’s so efficient, you would never know. And that’s totally great. That’s fine. That’s not slowing her down. That’s not providing a drag in the middle of a more complex problem or new learning. So we’re really focused on having elementary school students be able to enter the middle and high school standards without having that pull out of the new thinking.
Graham Fletcher (23:53):
And as I think about that, I think about how so many students will memorize their facts, but then they haven’t memorized them with understanding. So that when they move into middle school and they move into high school, it’s almost like new knowledge and new understanding that’s applied from a stand-alone skill.
Bethany Lockhart Johnson (24:10):
So something that felt really unique to me, Graham, as I was diving into the toolkit, is your use of images, Tracy, Graham, is the way that you use images to help students notice and wonder to start making sense of these quantities and the decomposition of numbers using images. Can you talk a little bit about how images played a part in the way that you think about this building a fact fluency?
Graham Fletcher (24:41):
What I realized is so many times when we approach math with just naked numbers with so many of our elementary students, the numbers aren’t visible. The quantities. They can’t see them; they can’t move them. They’re just those squiggly figures that we were talking about earlier on. So how is it that we make the quantities visible, to where students feel as if they can grab an apple and move it around? Because a lot of times we start with the naked numbers and then if kids don’t get the naked numbers, then we kind of backfill it. But what would happen if we start with the images? And then from there, these rich, flourishing mathematical conversations develop from the images. And I think that was the premise and the goal of the toolkit.
Tracy Zager (25:22):
When you look at how fact fluency has traditionally been taught, it’s all naked numbers. And sometimes we wrote ’em sideways. Like, that’s it. That was our variety of task type. Right? Sometimes it’s vertical; sometimes it’s horizontal. And that was it. And I’ve just known way too many kids who couldn’t find a hook to hang their hat on with that. It didn’t connect to anything. And so part of why I knew Graham was the perfect person for this project was his strength in multimedia photography, art, video. And so we started from this idea of contexts that for each lesson string in the toolkit, there’s some kind of context. An everyday object, arranged in some kind of a way that reveals mathematical structure and invites students to notice the properties. So we start with images of everyday objects: tennis balls, paint pots…um, help me out; here are a million of them. Crayons—
Bethany Lockhart Johnson (26:18):
Crayons, markers.
Tracy Zager (26:18):
Shoes, right? Sushi, origami paper, all kinds of things in the different toolkits. So there’s a series of images or a three-act task or both around those everyday objects, and then story problems grounded in that context. And then there are images with mathematical tools that bring out different ideas, but relate in some way to the image talks. And we do all of that before we get to the naked number talk. Which we do, and by the time you get to the number talk, it’s pretty quick, ’cause they’ve been reasoning about cups of lemonade. And now when you give them the actual numerals, they’re all over it.
Bethany Lockhart Johnson (27:03):
I have to say too, as somebody who—particularly in middle school—navigated math anxiety, we recently talked with Allison Hintz and Anthony Smith about their amazing book Mathematizing Children’s Literature.
Tracy Zager (27:14):
Yay!
Bethany Lockhart Johnson (27:14):
And I was explaining, like, if I sat down at the beginning of a math class and my teacher opened a picture book and said, “We’re gonna start here,” I felt my whole body relax. And if we start with this image, if we start with just looking at an image and making sense of an image, I feel like that could be such a powerful touchstone for all the work you do from there.
Tracy Zager (27:41):
That’s core. That’s a core design principle, is that invitational access. There are no barriers to entry. There’s nothing to decode. There’s nothing formal. We’ve been learning from Dan for years about this, right? Of starting with the informal and then eventually layering in the formal. I was in a class in Maine where they were doing an image talk and it’s these boxes of pencils. It’s a stack of boxes of pencils and they’re open and you can see there are 10 pencils in each box. And so there are five boxes of pencils each with 10 pencils in it. And then the next image is 10 boxes of pencils and each box is half full. So now it’s 10 boxes each with five. And the kids are talking and talking and then the third image, I think there are seven boxes each with 10 pencils in it. And she said, “What do you think the next picture’s gonna be?” And this girl said, “You just never know with these people!” <laugh> I dunno!”
Bethany Lockhart Johnson (28:37):
That’s kinda true. Knowing you both, it’s kinda true.
Tracy Zager (28:42):
Like if it’s seven boxes with 10 in it, one kid said, I think it’s gonna be 14 boxes of five. And other kids are like, I think it’s gonna be 10 boxes with seven. And they start talking about which of those there are and the relationships between—
Bethany Lockhart Johnson (28:58):
But they’re making sense of numbers!
Tracy Zager (28:59):
Totally. So all the kids felt invited. They can offer something up. They’re noticing and wondering about that image. They’re talking about it in whatever informal language or home language that they speak. And that was core to us. That was a huge priority, because honestly, one of the motivations to talk about fluency is that it’s always been this gatekeeper. It has served to keep kids out of meaningful math. Particularly kids from marginalized or historically excluded communities. So they’re back at the round table, doing Mad Minutes, while the more advantaged kids are getting to do rich problem solving. And so, we thought, what if we could teach fact fluency through rich problem solving that everybody could access? That was like square one for us.
Bethany Lockhart Johnson (29:45):
That’s huge.
Dan Meyer (29:46):
That’s great to hear. What’s been helpful for me is to understand that students who are automatic, that’s just kind of what’s on the surface of things. And that below that might be some really robust kind of foundation or scaffolding that bleeds to a larger building being built, or it might be just really rickety and not offer a sturdy place to build farther up. It’s been really exciting to hear that. I wonder if you’d comment for a moment about, in the digital age and—I’m at Desmos and our sponsors are Amplify and we all work in the digital world quite a bit. There are a lot of what report to be solutions to the fluency issue, to developing fluency in the digital world. Just lots and lots of them. Some that are quite well used, others that are just like X, Y, or Z app on the market. You can find something. Do you have perspectives on these kinds of digital fluency building apps? Like, what about them works or doesn’t work? Let us know. Graham, how about you? And then Tracy, I’d love to hear your thoughts too.
Graham Fletcher (30:47):
Yeah, I think that’s a great question, ’cause there’s a lot of shiny bells and whistles out there right now that can really excite a lot of teachers. But I always come back to what works for me as a classroom teacher is probably gonna work in a digital world as well. So what are the things that I love and honor most about being in front of students, and how can I capture that in that virtual world? I think one of the things that really helps students make connections is coherence. I think coherence, especially when you leave students for—you don’t get to talk with them after the lesson is done—so I think about how we can purposefully sequence things through a day-to-day basis. I think coherence is something that gets really lost when we talk about fluency, especially with whether it be digital or whether it be print, because what ends up happening is we say, “OK, we have all these strategies we need to teach,” and it becomes a checklist. So how is it that we can just provide students the opportunity to play around in a space, whether it be digital or in person, but in a meaningful way that allows them the time and the space and that area to breathe and think, but be coherent. And connecting those lessons along the way. And I think coherence is one thing that a lot of the times it’s harder to—when we’re in the weeds, it’s so hard and difficult to zoom back out and say, “Do all these lessons connect? How do they intentionally connect? And how do they purposefully connect?” And without coherence, everything’s kind of broken down into that granular level. So when looking at—I think about Desmos and I think about the Toolkit and I think about how Tracy and I talked a lot about, “Well, this, does it connect with the context problem, does it connect with the image talk, or the lessons? Like, how does it all connect and how are we providing students an opportunity to make connections between the day-to-day instruction and lessons that we tackle?”
Tracy Zager (32:44):
I’m reminded of a conversation that Dan, you and I had a long time ago, in Portland, Maine, in a bar. I’ll just be honest. <laugh> And we were talking about how, in the earlier days of Desmos, you were stressed out by what you saw, which was kids one-on-one, on a device, in a silent room. And you were like, no, this is not it. This is not what technology is here to serve. We can do so many things better using technology appropriately, but we can’t lose talk and we can’t lose relationships and we can’t lose formative assessment and teachers listening to kids and kids listening to each other and helping each other understand their thinking. Right? So when I think about the tech that’s out there for fact fluency, most of it is gonna violate all rules I have around time testing. So that a whole bunch of it, I would just toss on that premise. They’re really no different than flashcards. It’s just flashcards set in junkyard heaps. Or, you know, underground caverns. Or with a volcano or whatever. It’s the same thing. There are some lovely visuals—I’m thinking of Berkeley Everett’s Math Flips. Those are really pretty. Mathigon has some really nice stuff that’s digital. And I think that those resources invite you to kind of ponder and notice things and talk about them. All the tools that we design in the toolkit are designed to get people talking to each other, and give teachers opportunities to pull alongside kids and listen in and understand where they are. For example, our games, we didn’t design the games to be played digitally, even though you could, and people did during COVID, because we want kids on the rug, next to each other, on their knees; I’ve seen kids like across tables. I was in a school recently where a kid was like, “I hope you believe in God, ’cause you’re going…!” You know what I mean? <laugh>. Like they’re all pumped up.
Bethany Lockhart Johnson (34:41):
They’re invested!
Tracy Zager (34:45):
They’re psyching each other up and down and they’re interacting and it’s social and the teacher’s walking around and she’s listening to the games. And they don’t actually need any bells and whistles. They need dice and they need counters and they need this game that is actually a game. In all of our conversations, games have to actually be games. Games cannot be “roll and record.” Games have to involve strategy. They have to be fun. So in designing those games, we didn’t feel like it brought any advantage to make that a digital platform. But things that did bring advantages digitally, like the ability to project these beautiful images or to use short video in the classroom, that really was a value-add that enabled us to do something different in math class than we had done before, and to get kids talking in a different way than they ever had before. When I think about fluency, historically, if you say like, “OK, it’s time to practice our math facts,” you hear a lot of groans. And when I see a Building Fact Fluency classroom and I say, “OK, it’s BFF time!” There’s like a “YEAAAAHHH!” You know? And so that’s what we’re after.
Graham Fletcher (35:47):
It’s all about kids, really, for us. And I think at the heart of it, we made all the decisions with teachers and kids at the forefront of it.
Tracy Zager (35:55):
I know of high schoolers who are newcomers, who have experienced very little formal education, and speak in other languages, are using it as high schoolers, because it involves language and math and all the deep work in the properties and it’s accessible, but it’s also not at all condescending or patronizing. Like we designed it to be appropriate for older kids. So that’s just something that I think we’re both really proud of. One thing we thought a lot about, especially in the multiplication-division kit is how a classroom teacher could use it and a coordinating educator in EL, Title, special education, intervention could also use it because there’s so much in it, that students could get to be experts, if they got extra time in it, using something that’s related and would give them additional practice. So they could play a game a little bit earlier than the rest of the classes. And they could come in already knowing about that game, or they could do a related task. We have all these optional tasks that no classroom teacher would ever have time to teach it all. So the special educator could use it and have kids doing a Same and Different or a True/False, or some of the optional games. And then the work in both special education and general education could connect.
Dan Meyer (37:20):
I just wanna say that this is an area that for so many students, as you’ve said, Tracy, it presents a barrier. It’s a very emotionally fraught area of mathematics. And we really appreciate the wisdom you brought here. And just the care you’ve brought to the product itself. Your knowledge of teaching, knowledge of math, and yeah, especially a love for students feels like it’s really infused throughout Building Fact Fluency. If our listeners want to know more outside of this podcast, outside of the product itself, where can they find your words, your voice? Where you folks at these days? Tell ’em, Graham would you?
Graham Fletcher (37:57):
You can find us at Stenhouse, Building Fact Fluency. And then Tracy and I, currently playing around, sharing ideas a lot on Twitter, under the hashtag #BuildingFactFluency. That’s kind of where we can all come together and share ideas. And then also on the Facebook community, where there’s lots of teachers sharing ideas.
Bethany Lockhart Johnson (38:19):
If you were to ask our listeners like, “Hey, if you wanna keep thinking about this, here’s something you could try or here’s something you could go do,” what could be a challenge that we could share that could help us continue this conversation?
Graham Fletcher (38:35):
Online you can actually download a full lesson string. And a lesson string is a series of activities and resources that are purposefully connected. You can pick one or two of those from the Stenhouse web site, Building Fact Fluency. You can try the game. You can try one of those strategy-based games. You can try an image talk and just see how it goes. And just share and reflect back, whether on Twitter or on Facebook. But it’s kind of there, if you wanna give it a whirl. And as Tracy was sharing, even if you’re a middle-school teacher or a high-school teacher, we really tried to think about those middle-school and high-school students keeping it grade level-agnostic. Just so every student has those opportunities for those mathematical conversations. So download a lesson string and give it a whirl, and we’d love to hear how it goes.
Dan Meyer (39:25):
Bethany and I will be working the same challenge with people in our life.
Bethany Lockhart Johnson (39:29):
Yes.
Dan Meyer (39:29):
Enjoying some fact fluency with people in our homes, perhaps. We’ll see. And we’ll be sharing the results in the Math Teacher Lounge Facebook group. Graham and Tracy, thanks so much for being here. It was such a treat to chat with you both.
Bethany Lockhart Johnson (39:42):
I love learning with you and just helping to shift this idea of fluency into something that can be accessible and powerful and positive.
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Meet the guest
Valerie Henry has been a math educator since 1986. She taught middle school math for 17 years and has worked as a lecturer at University of California Irvine since 2002. After doing her 2004 dissertation research on addition/subtraction fluency in first grade, Valerie created FactsWise, a daily mini-lesson approach that simultaneously develops fluency, number sense, and algebraic thinking. Additionally, she has provided curriculum and math professional development for K-12 teachers throughout her career, working with individual schools, districts, county offices of education, Illustrative Mathematics, the SBAC Digital Library, and the UCI Math Project.
About Math Teacher Lounge: The podcast
Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.
Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!
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S3 – 04. Ideas to build math fluency with Valerie Henry, Graham Fletcher, and Tracy Zager
Fluency in math can oftentimes be associated with negative experiences with its development— timed worksheets, for example. Bethany and Dan are joined by three guests to better understand fluency and how to make its approach fun. Dr. Val Henry shares her three-part definition of fluency and her five principles for developing it. Additionally, Tracy Zager and Graham Fletcher join Bethany and Dan to better understand fluency through a lens of equity and using multimedia as a tool.
Explore more from Math Teacher Lounge by visiting our main page.
Dan Meyer (00:03)
Hey folks. Welcome back. This is Math Teacher Lounge, and I am one of your hosts, Dan Meyer.
Bethany Lockhart Johnson (00:07):
And I’m your other host, Bethany Lockhart Johnson. Hi, Dan.
Dan Meyer (00:11):
Hey, great to see you. We have a big one this week to chat about and some fantastic guests. We are chatting about fluency, which is the sort of word and concept that I feel like people have very, very non-neutral associations with it. A lot of them are very negative, for a lot of people.
Bethany Lockhart Johnson (00:26):
I saw you frown a little. What’s up with that, Dan? You kind of, like, shrank.
Dan Meyer (00:30):
I have strong feelings about it. You know, there’s lots of ways that people go about helping people become fluent in mathematics. And a lot of them are harmful for students, and ineffective. And it got me thinking about fluency as it exists outside of the world of mathematics, where we have a lot of very clear images of it. We’re getting fluent in things all the time. Like, as humans. Human development is the story of fluency. And I just was wondering….Bethany, would you describe yourself as fluent at something outside of the world of mathematics? What is that? How’d you get fluent at it? What was the process?
Bethany Lockhart Johnson (01:05):
Hmm, I think I’m a pretty fluent reader. I read all the time. I’m a happier person if I’ve read that day. I once saw this poster in a classroom; it said “10 Ways to Become a Better Reader: Read, Read, Read, Read, Read…you know, 10 times. Get it? Reading? You get better at reading by reading! So I would say reading. And it’s been kind of cool—I have a one-year-old who, it’s been really exciting slash overwhelmingly anxiety-producing to see him get very fluent with walking slash running, ’cause he’s getting faster every day. And it’s kind of fun. When I think of what’s something somebody’s trying to get fluent with…walking! He’s trying to be more fluid. He’s practicing transitions. He doesn’t wanna hold my hand while he traverses rocky terrain. He’s getting better at it. He’s practicing. What about you? What’s something…?
Dan Meyer (02:08):
I think about driving a lot. I’m a very fluent driver and I think a lot about when I was first a driver, you know? And how l have my hands on 10 and 2, vice grip, and do not talk to me; do not ask me anything; don’t ask me my NAME. I need to focus so hard. And then a year later, you know, I’m driving with one hand, smash the turn signal, take a sip off of whatever, change the CD. And then it’s no big deal.
Bethany Lockhart Johnson (02:38):
Wait, did you pass the first time? Your test?
Dan Meyer (02:40):
Yeah, I don’t like to brag about it. <laugh> But I do all the time. <laugh> But I got a hundred on my driving test. I don’t care who knows it. And I hope it’s everybody. But I guess all of this is just to say there are areas of life where fluency feels natural, with the case of walking. There’s areas of life where fluency feels motivating, with like driving—I wanna be able to switch the CD out or whatever. And there’s areas where fluency feels terrifying and hard to come by, like mathematics, sometimes. So we have a set of guests here. Our first guest will help us figure out what do we mean by fluency? And what’s the research say about what fluency is and how students develop it in mathematics? And then our other guests will help us think about what it looks like in practice in the classroom. What are some novel, new ways to work on fluency? So first up we have Val Henry, Dr. Val Henry.
Bethany Lockhart Johnson (03:32):
So we knew we needed help with the fluency definition, because when we think about it, it’s kind of big, right? And we wanted to look at what research about fluency really says. So we called on Valerie Henry. Val is a nationally board-certified teacher, taught middle school for 17 years, and since 2002 has worked with undergraduates graduates, credential candidates as a lecturer at the University of California, Irvine, one of my alma maters. So after doing her dissertation on addition and subtraction fluency in first grade, Val created a project to study ways to build addition and subtraction and multiplication and division fluency while also developing number sense in algebraic thinking. And the pilot grew and grew over the last 18 years into a powerful daily mini-lesson approach to facts fluency called FactsWise. And when we thought of fluency, the first person I thought of was Val. Welcome, Val Henry, to the Lounge! I’m so excited to have you here. Welcome.
Valerie Henry (04:36):
Thanks, Bethany. And thanks to you, Dan. It’s great to be here today.
Dan Meyer (04:41):
Great to have you; help yourself to whatever you find in the fridge. The names that people write down on those things in the bags are just recommendations. It’s potluck-style here. I’m curious, Val, if you’re, like, on an airplane, someone asks you what you do, and you say you study fluency…what is the layperson’s definition of what does it mean to be fluent in mathematics? And if you can give a brief tour through what the research says about what works and what doesn’t that would really help us orient our conversation here.
Valerie Henry (05:12):
The first thing I have to do when I talk to somebody on a plane is define the idea of fluency. And I often use an example of tying your shoelaces. Because that works with first graders as well as adults. This idea that when we first start trying to put our shoes on and get those shoelaces tied, somebody tries to, first of all, just do it for us. But then of course maybe tries to teach us the bunny-ears approach. And we struggle and struggle as little kids and eventually either the bunny-ears approach or something else starts to work for us. But we still have to pay attention to it. We have to think hard and it’s not easy. And then over time we get to the point where we basically don’t even think about it. When I tie my shoes in the morning. I’m not thinking about right-over-left and left-over-right and all of those things. I just do it. And so that’s a good, easy example of becoming fluent with something. I think what we’re talking about today though, is the basics, the adding and subtracting that we hope kids are going to have mastered maybe by second grade, and the multiplication and division facts that we wanna maybe have mastered by third, maybe fourth grade. So now what does that mean to become fluent with those basics? I have a three-part definition that seems to match up really nicely with the common core approach to fluency. Which is, first of all, we want the answers to be correct. And then second, we want the answers to be easy to know. And so what does that mean? Well, to me, it means without needing to count,
Bethany Lockhart Johnson (07:12):
You mean without having to kind of muscle through it? Or say more about you mean.
Valerie Henry (07:16):
Well, I guess what I mean is that when you watch a young child try and solve something even as simple as two plus three, they might put up two fingers and then go 3, 4, 5 with three more fingers winding up on their hand, one or the other of their hands. While they’re doing that, they don’t really have a sense of whether even their answer is right or not, quite often. Especially when you get to the larger adding and subtracting problems, you can see a lot of errors happening as they’re trying to count. And it’s taking up cognitive energy to do that counting process, especially as you get to the larger quantities. So my definition of fluency now is “getting it right without needing to do that hard work like counting.” Now, some people might say, well, we just want them to have ’em memorized. But in my research, I’ve learned that a lot of very fluid adults don’t always have every fact memorized. In fact, if you ask a room full of adults, what’s seven plus nine, you might learn that they can all get it correct quickly, quickly…but they don’t all have it memorized. And so when you ask them, “How did you get that?” Many of them will say, “Well, I just gave one from the 7 to the 9 and I know that 10 plus 6 is 16.”
Bethany Lockhart Johnson (08:53):
That’s such an important distinction. My brain literally just did that actually!
Valerie Henry (08:58):
<laugh> Right? <laugh> But you’re fluid with it, because it doesn’t take you much cognitive energy at all.
Bethany Lockhart Johnson (09:05):
Right.
Valerie Henry (09:07):
So now we have “correct without needing to put that cognitive energy,” which usually means that you’re counting. And then the third thing is “relatively quickly,” so that you’re not spending 15 seconds trying to figure it out. Even that part-whole strategy approach can be done really quickly, almost instantaneously. Or it can take a long time. So if a student can get the answer correct within, you know, three or four seconds— is I’m pretty generous—I figure that they’re pretty darn fluent with that fact. So that’s my three-part definition of these basics, fluency.
Dan Meyer (09:55):
I love the distinction between getting it correct and getting it quick. It’s possible to be quick with wrong answers. It’s possible to be like, “Those are separate components there.” And I echo Bethany’s appreciation for this third option in between knowing it instantaneously through memorization and muscling through it. But there’s like a continuum there of how much energy it took you to come up with it that all feels extremely helpful.
Valerie Henry (10:21):
And you know, one of the things that I’ve noticed is that when kids are pressured to come up with those instantaneous answers, they often default to guessing and get it wrong.
Bethany Lockhart Johnson (10:30):
Mm, yeah.
Valerie Henry (10:30):
So that’s one of the things that I’ve learned is that as we’re trying to help students develop fluency, it’s important to start with building their conceptual understanding of what it means to do, you know, 3 times 9 and what the correct answer is, maybe using manipulatives or representations of some sort. Not skip-counting! I really have found that skip-counting just perpetuates itself in many students’ minds and that they never stop skip-counting, which means they’re putting in not very much mental energy if it’s 2 times 3 but a ton of mental energy if it’s 7 times 8. Because frankly, it’s really hard to skip count by sevens. And by eights.
Bethany Lockhart Johnson (11:18):
I can get to 14 and then I’m like, wait, wait, what was next? Right? No, no, no…21! What do you feel are some misconceptions that maybe teachers, maybe parents have about fluency in math?
Valerie Henry (11:30):
I think maybe one of the first ones is that if students count or skip-count, their answers repetitively over and over and over and over, that they’re bound to memorize them. And the study that I did back in 2004, I actually had a school that had decided that they were going to do time tests with their students every day, all year. And that undoubtedly by the end of the year, those students would be fluent.
Bethany Lockhart Johnson (12:06):
And to clarify by time test, you mean like, sit down, pencil, paper, ready, go, worksheet kind of thing.
Valerie Henry (12:15):
Yes.
Bethany Lockhart Johnson (12:16):
Some of us might remember quite vividly.
Valerie Henry (12:18):
<laugh> Very vividly. And you know, you have to get it done within a certain amount of time. So they made it fun for the students. Apparently the students enjoyed it. I was a little leery about that, but in the end, when I went and checked on the students and I did one-on-one assessments with half of the students in every class that were randomly selected so that I could get a sense of where they were with their fluency—and these were first graders—they basically had nothing memorized. They were simply counting as fast as they possibly could. And, you know, mostly getting the right answers. But they had not memorized. So that’s one of the myths, I think, is that repetitive practice of counting gets you to memorization.
Bethany Lockhart Johnson (13:10):
If I put it in front of you enough times, you’ll become fluent.
Valerie Henry (13:14):
Right, right. Now these students didn’t really get any instruction, any help learning these. They just simply tested over and over and over. So that’s another thing that I think is a misconception. It’s that if we test students, but don’t really teach them fluency, then they’re going to become fluent. If we just test them every Friday or that kind of thing. And that they’ll learn them at home. But really what that means is a few lucky kids who have parents who have the time and the energy and the background to know how to help will take that job on at home. Not that many students are really that fortunate.
Dan Meyer (14:01):
It’s almost like the traditional approach, or the approach you’re describing, confuses process and product. It says, “Well, the product is that eventually fluent students will be able to do something like this, see these problems and answer them, answer them quickly,” and says, “Well, that must be the process then as well; let’s give them that products a whole lot.” But as I hear you describe fluency with bunny ears on shoelaces, there’s these images and approaches and techniques that require a very active teacher presence to support the development of it. That’s just kind of interesting to me.
Valerie Henry (14:35):
My initial project, the pilot project that I tried, was to simply ask teachers to follow five key principles. And the first one was to do something in the classroom every day for—I told them, even if you’ve only got five or 10 minutes, work on fluency for five or 10 minutes a day, and let’s see what happens. So that was one key element was just to teach it and to give students opportunities to get what the research calls for when you’re trying to memorize, which is actually immediate feedback. When I talk about immediate feedback with my student teachers, I say, “I’m talking about within one or two seconds of trying a problem, and then sort of immediately knowing, getting feedback of whether you got the answer right or not so that your brain can kind of gain that confidence. ‘Oh, not only did I come up with an answer, but somebody’s telling me it’s the correct answer.’”
Dan Meyer (15:38):
There’s a lot of apps now in the digital world that offer students questions about arithmetic or other kinds of mathematical concepts and give immediate feedback of a sort: the feedback of “You’re right; you’re wrong” sort. Is that effective fluency development, in your view?
Valerie Henry (15:57):
I haven’t heard and I haven’t seen them being super-effective. The ways I think about this are “Immediate feedback isn’t the only thing we need.” Probably one of the biggest things that we need is for students to develop strategies. And this is one of the other things I’ve learned from international research, from countries that do have students who become very fluent very early, is that they don’t shoot straight for memorization, but they go through this process of taking students from doing some counting and then quickly moving them to trying to use logic. So, “Hey, you really are confident that 2 + 2 is 4; so now let’s use that to think about 2 + 3.” Actually, as an algebra teacher, I would much rather have students that have a combination of memorization and these strategies, than students who’ve only memorized. Isn’t that interesting that my most successful algebra students were good strategy thinkers. Not just good memorizers.
Bethany Lockhart Johnson (17:09):
So you mentioned there were five that kind of helped root this idea in like, “What can teachers do? What is the best thing that teachers can do to support with fact fluency?” So, everyday was key.
Valerie Henry (17:22):
Then the next principle that I really focus on is switching immediately to the connected subtractions so that students—
Bethany Lockhart Johnson (17:33):
Not waiting until you’ve gotten all the way through addition. But making “Ooh!”
Valerie Henry (17:38):
Totally. And I didn’t do that the first year. And when we looked at the results of the assessments at the end of the year, we realized that our students were so much weaker in subtraction than addition. So the following pilot year, we tried this other approach of doing subtraction right after the students had developed some fluency with that small chunk of addition. And we got such better subtraction results.
Bethany Lockhart Johnson (18:11):
What are the other principles?
Valerie Henry (18:13):
The biggest one is to use these strategies. So the strategies makes the third. And then the fourth I would say is to go from concrete to representational to abstract.
Bethany Lockhart Johnson (18:27):
Don’t put away those manipulatives. Don’t put away those tools.
Valerie Henry (18:31):
Oh, so important to come back to them for multiplication and division. And my fifth principle is to wait on assessment. To use it as true assessment, but not race to start testing before students have had a chance to go through this three-phase process. Which is conceptual understanding with manipulatives; building strategies, usually with representations; and then working on building some speed until it’s just that natural fluency.
Bethany Lockhart Johnson (19:07):
I wanna say thank you so much for offering your really learned perspective, because you have not only done the research, but seen it in action and seen how shifting our notions of fluency and what fluency can be and what a powerful foundation it can be for all mathematicians. Really, that shift is so powerful. And I appreciate you sharing it with our listeners and with us. So we’re so excited that we got to talk with you today, Val—
Dan Meyer (19:35):
Thank you, Dr. Henry.
Valerie Henry (19:37):
You’re welcome!
Dan Meyer (19:41):
With us now we have Graham Fletcher and Tracy Zager, a couple of people who understand fluency at a very deep and classroom level. I wanna introduce them and get their perspective on what we’re trying to solve here with fluency. So Graham Fletcher has served in education in a lot of different roles: as a classroom teacher, math coach, math specialist, and he’s continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary math. He’s the author, along with Tracy, of Building Fact Fluency, a fluency kit we’ll talk about, and openly shares so much of his wisdom and resources at gfletchy.com. Tracy Johnson Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of this toolkit, Building Fact Fluency, and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books for teachers at Stenhouse Publishers, including, yours truly. Thank you for all that insight, Tracy, and support on the book.
Bethany Lockhart Johnson (20:49):
Dan and I were talking at the beginning of the episode about things we feel like, “Hey, I’m fluent in that. I’m fluent in that.”
Dan Meyer (20:55):
Just very curious: What’s something you would like to get fluent in outside of the world of mathematics, let’s say?
Tracy Zager (21:00):
I’ll say understanding the teenage brain, as the parent of a 13-year-old and 15-year-old. That’s the main thing I’m working on becoming fluent in!
Bethany Lockhart Johnson (21:10):
Ooh!
Dan Meyer (21:13):
A language fluency, perhaps. All right, Graham. How about you?
Graham Fletcher (21:16):
For me typing, it’s always been an Achilles heel of mine. So voice-to-text has been my friend. But it’s also been my nemesis in much of my texting here and working virtually over the last couple years. So yeah, typing.
Dan Meyer (21:33):
Do you folks have some way of helping us understand the difference in how fluency is handled by instructors and by learners?
Tracy Zager (21:40):
I would say that the lay meaning of fluency is definitely a little different than what we mean in the math education realm. When we’re talking about math fact fluency, which is just one type of fluency. So you gotta think about procedural fluency and computational fluency; there are lots of types of fluency in math. And Graham and I had the luxury of really focusing in specifically on math fact fluency. We’re looking at kind of a subset of the procedural fluency. So the words you hear in all the citations are accurate, efficient, and flexible. There’s this combination of kids get the right answer in a reasonable amount of time and with a reasonable amount of work and they can match their strategy or their approach to the situation. That’s where that flexibility comes in. And there’s like lots more I wanna say about that about sort of…I think one issue that comes up around fluency is that people are in a little bit of a rush. So they tend to think of the fluency as this automaticity or recall of known facts without having to think about it. And that is part of the end goal, but that’s not the journey to fluency. So this is one of the things that Graham and I thought about a lot was the path to fluency. The goal here it’s that student in middle school who’s learning something new doesn’t have to expend any effort to gather that fact. And they might do it because they’ve done it so many different ways that they’ve got it, and now they just know it, or they might be like my friend who’s a mathematician who still, if you say, “Six times 8,” she thinks in her head, “Twelve, 24, 48…” and she does this double-double-double associative property strategy. And it’s so efficient, you would never know. And that’s totally great. That’s fine. That’s not slowing her down. That’s not providing a drag in the middle of a more complex problem or new learning. So we’re really focused on having elementary school students be able to enter the middle and high school standards without having that pull out of the new thinking.
Graham Fletcher (23:53):
And as I think about that, I think about how so many students will memorize their facts, but then they haven’t memorized them with understanding. So that when they move into middle school and they move into high school, it’s almost like new knowledge and new understanding that’s applied from a stand-alone skill.
Bethany Lockhart Johnson (24:10):
So something that felt really unique to me, Graham, as I was diving into the toolkit, is your use of images, Tracy, Graham, is the way that you use images to help students notice and wonder to start making sense of these quantities and the decomposition of numbers using images. Can you talk a little bit about how images played a part in the way that you think about this building a fact fluency?
Graham Fletcher (24:41):
What I realized is so many times when we approach math with just naked numbers with so many of our elementary students, the numbers aren’t visible. The quantities. They can’t see them; they can’t move them. They’re just those squiggly figures that we were talking about earlier on. So how is it that we make the quantities visible, to where students feel as if they can grab an apple and move it around? Because a lot of times we start with the naked numbers and then if kids don’t get the naked numbers, then we kind of backfill it. But what would happen if we start with the images? And then from there, these rich, flourishing mathematical conversations develop from the images. And I think that was the premise and the goal of the toolkit.
Tracy Zager (25:22):
When you look at how fact fluency has traditionally been taught, it’s all naked numbers. And sometimes we wrote ’em sideways. Like, that’s it. That was our variety of task type. Right? Sometimes it’s vertical; sometimes it’s horizontal. And that was it. And I’ve just known way too many kids who couldn’t find a hook to hang their hat on with that. It didn’t connect to anything. And so part of why I knew Graham was the perfect person for this project was his strength in multimedia photography, art, video. And so we started from this idea of contexts that for each lesson string in the toolkit, there’s some kind of context. An everyday object, arranged in some kind of a way that reveals mathematical structure and invites students to notice the properties. So we start with images of everyday objects: tennis balls, paint pots…um, help me out; here are a million of them. Crayons—
Bethany Lockhart Johnson (26:18):
Crayons, markers.
Tracy Zager (26:18):
Shoes, right? Sushi, origami paper, all kinds of things in the different toolkits. So there’s a series of images or a three-act task or both around those everyday objects, and then story problems grounded in that context. And then there are images with mathematical tools that bring out different ideas, but relate in some way to the image talks. And we do all of that before we get to the naked number talk. Which we do, and by the time you get to the number talk, it’s pretty quick, ’cause they’ve been reasoning about cups of lemonade. And now when you give them the actual numerals, they’re all over it.
Bethany Lockhart Johnson (27:03):
I have to say too, as somebody who—particularly in middle school—navigated math anxiety, we recently talked with Allison Hintz and Anthony Smith about their amazing book Mathematizing Children’s Literature.
Tracy Zager (27:14):
Yay!
Bethany Lockhart Johnson (27:14):
And I was explaining, like, if I sat down at the beginning of a math class and my teacher opened a picture book and said, “We’re gonna start here,” I felt my whole body relax. And if we start with this image, if we start with just looking at an image and making sense of an image, I feel like that could be such a powerful touchstone for all the work you do from there.
Tracy Zager (27:41):
That’s core. That’s a core design principle, is that invitational access. There are no barriers to entry. There’s nothing to decode. There’s nothing formal. We’ve been learning from Dan for years about this, right? Of starting with the informal and then eventually layering in the formal. I was in a class in Maine where they were doing an image talk and it’s these boxes of pencils. It’s a stack of boxes of pencils and they’re open and you can see there are 10 pencils in each box. And so there are five boxes of pencils each with 10 pencils in it. And then the next image is 10 boxes of pencils and each box is half full. So now it’s 10 boxes each with five. And the kids are talking and talking and then the third image, I think there are seven boxes each with 10 pencils in it. And she said, “What do you think the next picture’s gonna be?” And this girl said, “You just never know with these people!” <laugh> I dunno!”
Bethany Lockhart Johnson (28:37):
That’s kinda true. Knowing you both, it’s kinda true.
Tracy Zager (28:42):
Like if it’s seven boxes with 10 in it, one kid said, I think it’s gonna be 14 boxes of five. And other kids are like, I think it’s gonna be 10 boxes with seven. And they start talking about which of those there are and the relationships between—
Bethany Lockhart Johnson (28:58):
But they’re making sense of numbers!
Tracy Zager (28:59):
Totally. So all the kids felt invited. They can offer something up. They’re noticing and wondering about that image. They’re talking about it in whatever informal language or home language that they speak. And that was core to us. That was a huge priority, because honestly, one of the motivations to talk about fluency is that it’s always been this gatekeeper. It has served to keep kids out of meaningful math. Particularly kids from marginalized or historically excluded communities. So they’re back at the round table, doing Mad Minutes, while the more advantaged kids are getting to do rich problem solving. And so, we thought, what if we could teach fact fluency through rich problem solving that everybody could access? That was like square one for us.
Bethany Lockhart Johnson (29:45):
That’s huge.
Dan Meyer (29:46):
That’s great to hear. What’s been helpful for me is to understand that students who are automatic, that’s just kind of what’s on the surface of things. And that below that might be some really robust kind of foundation or scaffolding that bleeds to a larger building being built, or it might be just really rickety and not offer a sturdy place to build farther up. It’s been really exciting to hear that. I wonder if you’d comment for a moment about, in the digital age and—I’m at Desmos and our sponsors are Amplify and we all work in the digital world quite a bit. There are a lot of what report to be solutions to the fluency issue, to developing fluency in the digital world. Just lots and lots of them. Some that are quite well used, others that are just like X, Y, or Z app on the market. You can find something. Do you have perspectives on these kinds of digital fluency building apps? Like, what about them works or doesn’t work? Let us know. Graham, how about you? And then Tracy, I’d love to hear your thoughts too.
Graham Fletcher (30:47):
Yeah, I think that’s a great question, ’cause there’s a lot of shiny bells and whistles out there right now that can really excite a lot of teachers. But I always come back to what works for me as a classroom teacher is probably gonna work in a digital world as well. So what are the things that I love and honor most about being in front of students, and how can I capture that in that virtual world? I think one of the things that really helps students make connections is coherence. I think coherence, especially when you leave students for—you don’t get to talk with them after the lesson is done—so I think about how we can purposefully sequence things through a day-to-day basis. I think coherence is something that gets really lost when we talk about fluency, especially with whether it be digital or whether it be print, because what ends up happening is we say, “OK, we have all these strategies we need to teach,” and it becomes a checklist. So how is it that we can just provide students the opportunity to play around in a space, whether it be digital or in person, but in a meaningful way that allows them the time and the space and that area to breathe and think, but be coherent. And connecting those lessons along the way. And I think coherence is one thing that a lot of the times it’s harder to—when we’re in the weeds, it’s so hard and difficult to zoom back out and say, “Do all these lessons connect? How do they intentionally connect? And how do they purposefully connect?” And without coherence, everything’s kind of broken down into that granular level. So when looking at—I think about Desmos and I think about the Toolkit and I think about how Tracy and I talked a lot about, “Well, this, does it connect with the context problem, does it connect with the image talk, or the lessons? Like, how does it all connect and how are we providing students an opportunity to make connections between the day-to-day instruction and lessons that we tackle?”
Tracy Zager (32:44):
I’m reminded of a conversation that Dan, you and I had a long time ago, in Portland, Maine, in a bar. I’ll just be honest. <laugh> And we were talking about how, in the earlier days of Desmos, you were stressed out by what you saw, which was kids one-on-one, on a device, in a silent room. And you were like, no, this is not it. This is not what technology is here to serve. We can do so many things better using technology appropriately, but we can’t lose talk and we can’t lose relationships and we can’t lose formative assessment and teachers listening to kids and kids listening to each other and helping each other understand their thinking. Right? So when I think about the tech that’s out there for fact fluency, most of it is gonna violate all rules I have around time testing. So that a whole bunch of it, I would just toss on that premise. They’re really no different than flashcards. It’s just flashcards set in junkyard heaps. Or, you know, underground caverns. Or with a volcano or whatever. It’s the same thing. There are some lovely visuals—I’m thinking of Berkeley Everett’s Math Flips. Those are really pretty. Mathigon has some really nice stuff that’s digital. And I think that those resources invite you to kind of ponder and notice things and talk about them. All the tools that we design in the toolkit are designed to get people talking to each other, and give teachers opportunities to pull alongside kids and listen in and understand where they are. For example, our games, we didn’t design the games to be played digitally, even though you could, and people did during COVID, because we want kids on the rug, next to each other, on their knees; I’ve seen kids like across tables. I was in a school recently where a kid was like, “I hope you believe in God, ’cause you’re going…!” You know what I mean? <laugh>. Like they’re all pumped up.
Bethany Lockhart Johnson (34:41):
They’re invested!
Tracy Zager (34:45):
They’re psyching each other up and down and they’re interacting and it’s social and the teacher’s walking around and she’s listening to the games. And they don’t actually need any bells and whistles. They need dice and they need counters and they need this game that is actually a game. In all of our conversations, games have to actually be games. Games cannot be “roll and record.” Games have to involve strategy. They have to be fun. So in designing those games, we didn’t feel like it brought any advantage to make that a digital platform. But things that did bring advantages digitally, like the ability to project these beautiful images or to use short video in the classroom, that really was a value-add that enabled us to do something different in math class than we had done before, and to get kids talking in a different way than they ever had before. When I think about fluency, historically, if you say like, “OK, it’s time to practice our math facts,” you hear a lot of groans. And when I see a Building Fact Fluency classroom and I say, “OK, it’s BFF time!” There’s like a “YEAAAAHHH!” You know? And so that’s what we’re after.
Graham Fletcher (35:47):
It’s all about kids, really, for us. And I think at the heart of it, we made all the decisions with teachers and kids at the forefront of it.
Tracy Zager (35:55):
I know of high schoolers who are newcomers, who have experienced very little formal education, and speak in other languages, are using it as high schoolers, because it involves language and math and all the deep work in the properties and it’s accessible, but it’s also not at all condescending or patronizing. Like we designed it to be appropriate for older kids. So that’s just something that I think we’re both really proud of. One thing we thought a lot about, especially in the multiplication-division kit is how a classroom teacher could use it and a coordinating educator in EL, Title, special education, intervention could also use it because there’s so much in it, that students could get to be experts, if they got extra time in it, using something that’s related and would give them additional practice. So they could play a game a little bit earlier than the rest of the classes. And they could come in already knowing about that game, or they could do a related task. We have all these optional tasks that no classroom teacher would ever have time to teach it all. So the special educator could use it and have kids doing a Same and Different or a True/False, or some of the optional games. And then the work in both special education and general education could connect.
Dan Meyer (37:20):
I just wanna say that this is an area that for so many students, as you’ve said, Tracy, it presents a barrier for their inclusion in mathematics. It’s a very emotionally fraught area of mathematics. And we really appreciate the wisdom you brought here. And just the care you’ve brought to the product itself. Your knowledge of teaching, knowledge of math, and yeah, especially a love for students feels like it’s really infused throughout Building Fact Fluency. If our listeners want to know more outside of this podcast, outside of the product itself, where can they find your words, your voice? Where you folks at these days? Tell ’em, Graham would you?
Graham Fletcher (37:57):
You can find us at Stenhouse, Building Fact Fluency. And then Tracy and I, currently playing around, sharing ideas a lot on Twitter, under the hashtag #BuildingFactFluency. That’s kind of where we can all come together and share ideas. And then also on the Facebook community, where there’s lots of teachers sharing ideas.
Bethany Lockhart Johnson (38:19):
If you were to ask our listeners like, “Hey, if you wanna keep thinking about this, here’s something you could try or here’s something you could go do,” what could be a challenge that we could share that could help us continue this conversation?
Graham Fletcher (38:35):
Online you can actually download a full lesson string. And a lesson string is a series of activities and resources that are purposefully connected. You can pick one or two of those from the Stenhouse web site, Building Fact Fluency. You can try the game. You can try one of those strategy-based games. You can try an image talk and just see how it goes. And just share and reflect back, whether on Twitter or on Facebook. But it’s kind of there, if you wanna give it a whirl. And as Tracy was sharing, even if you’re a middle-school teacher or a high-school teacher, we really tried to think about those middle-school and high-school students keeping it grade level-agnostic. Just so every student has those opportunities for those mathematical conversations. So download a lesson string and give it a whirl, and we’d love to hear how it goes.
Dan Meyer (39:25):
Bethany and I will be working the same challenge with people in our life.
Bethany Lockhart Johnson (39:29):
Yes.
Dan Meyer (39:29):
Enjoying some fact fluency with people in our homes, perhaps. We’ll see. And we’ll be sharing the results in the Math Teacher Lounge Facebook group. Graham and Tracy, thanks so much for being here. It was such a treat to chat with you both.
Bethany Lockhart Johnson (39:42):
I love learning with you and just helping to shift this idea of fluency into something that can be accessible and powerful and positive.
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Meet the guests
Valerie Henry has been a math educator since 1986. She taught middle school math for 17 years and has worked as a lecturer at University of California Irvine since 2002. After doing her 2004 dissertation research on addition/subtraction fluency in first grade, Valerie created FactsWise, a daily mini-lesson approach that simultaneously develops fluency, number sense, and algebraic thinking. Additionally, she has provided curriculum and math professional development for K-12 teachers throughout her career, working with individual schools, districts, county offices of education, Illustrative Mathematics, the SBAC Digital Library, and the UCI Math Project.
Graham Fletcher has served in education as a classroom teacher, a math coach, and currently as a math specialist. He is continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary mathematics. He is the author of Building Fact Fluency and openly shares many of his resources at gfletchy.com. Follow him on Twitter.
Tracy Johnston Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of the Building Fact Fluency toolkits and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books by teachers, for teachers at Stenhouse Publishers. Follow her on Facebook.
About Math Teacher Lounge: The podcast
Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.
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