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In this episode, we explore how math talks have transformed over time to maximize student learning. What started as a quiet, teacher-led process with random student responses has evolved into a dynamic and collaborative experience. By incorporating turn-and-talk strategies, student discourse, and whiteboards for modeling, classroom discussions have become more engaging and purposeful. We also discuss the impact of physical space—how moving students closer to the board fosters better participation and understanding. Tune in to hear how small shifts in structure and environment can lead to powerful math conversations!

Key Takeaways:

• Moving beyond hand-raising to structured student discourse.

• Encouraging peer discussions before sharing with the whole class.

• Purposefully choosing student responses to deepen understanding.

• Helping students visually represent their math reasoning.

• Positioning students near the board for more engaged discussions.

• How minor changes in structure can lead to deeper learning. 

Resources:

• How To Start The Year Off Right [Blog Post]
• Make Math Moments Online Workshop
• Assessment For Growth: A Blueprint Course For Standards Based Grading in Math Class
• Make Math Moments Problem Based Lessons & Units

Attention District Math Leaders:

Not sure what matters most when designing math improvement plans? Take this assessment and get a free customized report: https://makemathmoments.com/grow/ 

Ready to design your math improvement plan with guidance, support and using structure? Learn how to follow our 4 stage process. https://growyourmathprogram.com 

Looking to supplement your curriculum with problem based lessons and units? Make Math Moments Problem Based Lessons & Units

FULL TRANSCRIPT

Yvette Lehman

We’re going to dive in today to one of, think, my favorite topics and probably yours as well, which is math talks. I think math talks are near and dear to my heart because they were such a transformative practice in my classroom. It’s like one of the gateways to build my own fluency and support fluency with my students. So I think it’s an area that I’ve tried to continue to refine over the years because I know how impactful it is.

Kyle Pearce

Hmm. Hmm. I’m super excited to dive in because actually, I remember when math talks or at least the idea of a number talk was first introduced in my world. Now, again, doesn’t mean that people weren’t already doing this. But when it came into my sort of, you know, visual or into my my horizon here, my teaching horizon, I actually was very nervous to do it because I sort of was like, I don’t know how to do it and I’m not sure how to do it well and I didn’t have my own epiphany in how to do it, which means that really starting and starting slow is not a bad idea at all. And I think today we’re gonna dig into sort of some of the different phases that you might consider in slowly introducing math talks into your practice so that you can eventually evolve to a point where they become fluent and flexible and just a part of what you do in your classroom culture without having any of that maybe initial worry or anxiety that it might cause to some of our new educators to this process.

Jon Orr

Yvette, before we dive into that, unpack a little bit about how that impact that you said right at the beginning, know, like, I’m just, us a picture of like, what were you doing behind the scenes? What were you doing in the classroom to give, like, to make it so impactful for your own learning and your own fluency and the students that you had?

Yvette Lehman

think that before I started doing, know, we’re going to use number talks probably and math talks interchangeably throughout this, but I think what we’re really focusing on is more problem strings. I think we’ll be clear with the community that I think the greatest impact that I had or that impacted me as an educator was engaging in problem strings. And I think it’s because I had never really thought about operations beyond the procedure. And I hadn’t really thought about visual representations of operations and really

revealing the properties of the different operators and through my own engagement with problem strings, I built that understanding. So it’s like I, at the same time, built my conceptual understanding of the properties and the behaviors of the operators while increasing my own fluency so that I was more flexible and more strategic when I was operating with a variety of numbers.

We’re going to dive in today to one of, think, my favorite topics and probably yours as well, which is math talks. I think math talks are near and dear to my heart because they were such a transformative practice in my classroom. It’s like one of the gateways to build my own fluency and support fluency with my students. So I think it’s an area that I’ve tried to continue to refine over the years because I know how impactful it is.

Kyle Pearce

Hmm. Hmm. I’m super excited to dive in because actually, I remember when math talks or at least the idea of a number talk was first introduced in my world. Now, again, doesn’t mean that people weren’t already doing this. But when it came into my sort of, you know, visual or into my my horizon here, my teaching horizon, I actually was very nervous to do it because I sort of was like, I don’t know how to do it and I’m not sure how to do it well and I didn’t have my own epiphany in how to do it, which means that really starting and starting slow is not a bad idea at all. And I think today we’re gonna dig into sort of some of the different phases that you might consider in slowly introducing math talks into your practice so that you can eventually evolve to a point where they become fluent and flexible and just a part of what you do in your classroom culture without having any of that maybe initial worry or anxiety that it might cause to some of our new educators to this process.

Jon Orr

Yvette, before we dive into that, unpack a little bit about how that impact that you said right at the beginning, know, like, I’m just, us a picture of like, what were you doing behind the scenes? What were you doing in the classroom to give, like, to make it so impactful for your own learning and your own fluency and the students that you had?

Yvette Lehman

think that before I started doing, know, we’re going to use number talks probably and math talks interchangeably throughout this, but I think what we’re really focusing on is more problem strings. I think we’ll be clear with the community that I think the greatest impact that I had or that impacted me as an educator was engaging in problem strings. And I think it’s because I had never really thought about operations beyond the procedure. And I hadn’t really thought about visual representations of operations and really

Jon Orr

Did you feel like you did that more in preparation for the math talks or number talks or in the moment when you’re working with kids?

Yvette Lehman

I did it mostly in the moment, to be honest, at first. Like at first, it’s like I wasn’t doing a lot of planning ahead of time and I was super transparent with my students that I’m gonna learn alongside you. And sometimes, truthfully, I would do a problem string and it was a total flop. So then I would actually go to a colleague during the next break or my next prep and say, I just did this problem string.

you know, it fell apart. Can we work through it together? Figure out where I went wrong and then I’ll bring it back to my students tomorrow. And then I’d come back to them and say, hey, remember that problem string we did yesterday? I learned something new. Let’s try to explore it again. So I would definitely say my first year through where I was committed to routinely incorporating problem strings into my classroom, it was very messy.

Kyle Pearce

One thing that I think is really key right now to note is that there was sort of two paths you could have went down. And I think the more common path was not the path you went down, which is after that train wreck, you know, where you and I’ve been there, I know it. And I still you still have some of these train wrecks happen. It’s just I just expect them, you know, to happen every now and again, right? Where you think you had it, you think you understood it, you think that you had anticipated what students may say or do.

And then it completely doesn’t go that way. I’m actually thinking back to a recent live session that we all did. And Yvette and I were sort of, and this was with adults, by the way. And you and I were member division member and everybody went to the standard algorithm. We were like, there is nothing for us to actually work off of here. And you know, we really had to get creative. This happens all the time in number talks. And you could have, you could have went, you know what, this just isn’t for me.

like number talks don’t work or math talks don’t work because you didn’t have early success, but yet you did the logical thing to do, the real, the true learner’s thing to do, which is, okay, it’s talked about a lot. Maybe it’s more my inexperience than the actual structure or the actual protocol. And

I think for folks, when you’re thinking about doing this type of work, or maybe you’ve tried them before and maybe you’ve abandoned them before, keep in mind that there is learning to be done and you are not expected to become an expert overnight. So giving yourself that grace, I think is gonna be key.

Jon Orr

And it’s going to evolve. And I think that’s what we want to kind of highlight here is like we’ve all evolved, what we thought what was at the beginning and it’s evolved to where, you know, where things get added in, things get layered and things get changed, you know, and that evolution of say a math talk or a number talk changed over time based off our own learning, but also our own understanding of like what good practice looks like. So, Yvette, what did early…

Number talks, math talks look like for you. Problem strings.

Yvette Lehman

Yeah, so when, yeah, when this was first introduced to me or modeled for me, it looked very quiet. So imagine your students are all sitting around and the teacher puts a prompt up on the board. And then one thing that I was an early adopter of that I, you know, constantly promote is the use of silent gestures.

to support think time. And that was something I adopted really early on. I’m so grateful for it that that was introduced through the work of Sherry Parish where, you know, we were discouraging students from throwing their hands in the air or shouting out answers and giving them a quiet gesture so that they could tell us when they were ready. And I think providing that think time is so critical. So when you first walked into my classroom, you know, 10, 12 years ago and I was doing a number talk, it would have been very quiet.

I would have had a prompt on the board. Students would have been quietly waiting with a thumb up to show me that they were ready. And then I would have asked somebody, you know, okay, can you share an answer? All right, can somebody explain your strategy? And it was a lot of teacher, student, teacher, student. And I was the one doing the modeling and one or two or three students maybe were sharing their thinking.

Kyle Pearce

Hmm. And yeah, and I would say, I would say for a very long time, think time was not something I felt comfortable giving to students, right? Because it becomes silent, the classroom becomes very silent, and you’re almost like, who, who’s move next? You know, like, what do I say? What do I do? So as educators, as the ones who are leading the lesson, oftentimes, we tend to lead a little bit too quickly. So being intentional,

so that in your mind you prepare, okay, it is going to be quiet and we’re going to allow all students to have time and maybe even more time than you might think they need, right? And I would argue probably need to prepare for that because they do need more time than you might anticipate. That’s gonna be a huge move and we’ll give all students an opportunity to feel kind of welcomed into that conversation. Now, I’m wondering though, because here’s something that I

thought early in the process. And I’m curious how you perceive this, is because of those silent gestures, I also sort of thought that it had to be very like one-to-one conversation. And what I mean by that is that I would then ask a student to share a response. One student shares a response, and then the next student might share a response. But it’s very back and forth between teacher and student. Is that?

the way or can we incorporate some of some more mathematical discourse into this conversation here?

Yvette Lehman

think the reason that that structure stopped working for me and I saw I learned from other effective teachers and adjusting that approach is it’s twofold. One, it’s like my favorite, one of my favorite quotes from Lucy West, it’s teacher student, teacher student sleepy time for everybody else. Like it really allows disengagement for the students who are not sharing. The other problem is you don’t know what they’re going to say. So you’re blindly pulling a student’s strategy.

without having any idea of how you want to sequence the solutions. Right, and that became very problematic because sometimes I found myself, I wasn’t ready to go there at that point in the lesson and the other students weren’t either, but I happened to choose somebody who’s thinking was outside of the goal for that particular string, and then we spent 20 minutes unpacking it.

Kyle Pearce

The hope and pray method.

Jon Orr

And I think, you what, like this, you bring up a huge point because I think when teachers even today think about, you know, stepping back from the I do, we do, you do type model, they think about that. They think about that moment where they’re like, okay, well, I’m gonna get students to share their strategy and it’s gonna be a one-to-one and I’m just gonna like, what do you think? And I don’t know what they’re gonna say. They’re gonna say something back to me and I gotta be able to handle that. Like, do I have to be able to tell them they’re wrong? Or how do I handle like,

This is off topic, you know what mean? How do I navigate that? And I think teachers think about that when they think about student interaction and discourse in the classroom. And that’s why they shy away from it. It’s because it’s like, we have no idea where this is gonna go, even though you know where you want it to go, right? And it’s the selecting, the sequencing, the ability to give students to turn and talk time.

that allows you to be flexible in that moment and then pluck the right, like you’re crafting a story that you, like you want to be able to craft a story in these types of environments. And it’s like that turn and talk time. And for me, for the turn and talk time happened very quickly because of that, because it’s like, well, I don’t know what that, I don’t want to be able to position like that student’s gonna say something and it’s like,

I got to be able to like let them down easy or you know, like, or the or it’s crickets, right? It’s in that that was for me for a while is like, well, who’s gonna be the one, you know, and then it’s like, do I choose? And then or do I like, or like in order, like draw, draw popsicle sticks? Or for me was like the turn and talk happens so quickly, mostly because of the you know, the think pair share idea of like, if they tell each other first, then it’s so much easier to pull the information

from the class because they got it verified from the person next door and now they’re willing to share. for me it was like two-fold itself. Like you said Yvette, it was like I can get more engagement by a turn and talk quickly, but also I can listen to see who I should pull from when I wanna craft that learning goal.

Kyle Pearce

Right. Now, just to confirm, too, I think what John’s saying is it happened quickly like it in your process, in the progression, not that you want it to happen quickly in the classroom, that it’s going to be fast or only give them so much time. So don’t want anyone to misunderstand that. And I think if we go back to, we’ll call it those failed early number talks or math talks or problem strings, whatever you want to call them.

Jon Orr

Yeah, so it was like, exactly. No, exactly.

Kyle Pearce

I’m going to argue that that is one of the critical points in which things can go south, right? By not knowing. So when you vet, when you started and you went, OK, I’m going to pick a random student and this student takes you to, you know, some very, you know, tangent sort of approach that may may be great. You know, it might be awesome, but it’s like, but you haven’t heard it before. So you’re processing it under, you know, on stage as you’re doing this in front of all the kids. But then

You’re also not ready to bring the rest of the students there, because you’re picturing all of the students that are going to go, what the heck’s going on here? I just lost everyone. And that’s the beginning of the derailment of the train, right? So giving that turn in talk time, as John had mentioned, looking at the, and really what it is, it’s almost like a mini five practices experience. So I also wanted to mention this for those who are thinking right now and they’re going, let’s say you’re a leader, let’s say you’re working in a PLC group and you’re going for

If five practices is something that you’ve been wanting to dig into, or maybe you’re in a book talk, or you’re exploring, doing it and applying it at the number talk or math talk level is a great place to start because ultimately what you’re doing is you’re doing the five practices but like in a very condensed sort of format, which is great for trying to better understand the process and to get you more confident to lead a full problem-based lesson that’s going to follow the five practices.

Yvette Lehman

And I think just to clarify what you’re saying, Kyle, is that when we give students a chance to turn and talk, we position ourselves to monitor. So then we are walking around the room and that’s why I like even a think pair square. So it’s like, I need to give enough talk time. Again, it’s gonna increase engagement, it’s gonna increase student confidence once they’ve had confirmation from their peers, you’re gonna have more participation.

But that gives me time to monitor the thinking in the classroom and then strategically select and sequence who’s going to share their strategy today. Because as you mentioned, I know the learning goal. I know what the outcome of that particular number talk, what I want it to be. And so I can then strategically select strategies that are going to help us get closer to that goal.

Kyle Pearce

I love it. And really what you’re doing is you’re essentially you’re setting yourselves up so that you know where you want to go. But then you also know if maybe students didn’t hit the mark, it gives you an opportunity to give them another prompt, for example. Imagine, and we’ve all been there before, you give students an idea to think on. And if they’re just thinking on their own and they all misinterpreted because maybe I wasn’t clear. And when you hear them having this conversation,

you get a sense as to whether, are we like on the right path or do we need a little bit more, you know, redirection? Do we need a little bit more information? Do I need to reword something? So I think that’s really critical. So turning and talking. So math talks in my mind, I’m picturing is not a quiet experience. It’s not supposed to be quiet. Everyone’s sitting, looking straight and a one-on-one sort of engagement opportunity. This is an opportunity for all students to share. Okay, now here’s the other one.

math talks, number talks, problem strings. I hear it all the time. Many educators and teachers have this idea that when you’re doing any type of number talk routine, that everything has to happen mentally. It has to happen upstairs. There’s no writing. There’s no modeling. It’s all about getting efficient with math facts. And sometimes that might be true, right? At sometimes.

What else can really open the door here to really getting the most out of this experience that you’re going to be doing in the classroom?

Yvette Lehman

another strategy that I’ve seen implemented in really effective classrooms. And I agree, when I first started this work, I thought it had to be like pencils down all the time. Where I really saw a great impact though, was when early in the development of the strategy or model. So let’s say you’re gonna engage in problem strings. And I’m thinking of mini lessons, Cathy Fosnows work, where oftentimes you have multiple days of a similar strategy or model. In the first few days,

It can’t just be this teacher using the model as a tool for thinking. So that’s what I used to do, right? I would have the students share their strategy and then I would model it. But then I was the only one interacting with the model as a tool. And so I think it’s really important and I hate to make definitive statements, but I’m gonna actually say this. I think it’s important for students to interact with the model themselves.

during the process. so having a whiteboard or giving them whiteboard markers so they can write on a desk or something so that they can actually leverage the model early on and see the strategy in action I think is really critical. And then at some point to your point, Kyle, like does that mean every single time you do a number talk they need to have a whiteboard? No, like there will be a point where of course the goal is for them to be able to visualize this in their head. That’s the goal is that they have this as a tool for thinking that they can visualize and they don’t need to rely on the visual representation on paper or whiteboard.

Kyle Pearce

And to clarify as well. Yeah, and to clarify to like you’re not necessarily saying you’re not in I’m I know what you’re what you’re talking about. You’re talking about like individual like handheld personal whiteboards like you’re not saying like, you know, like incorporate vertical non permanent surfaces into this experience. We’re not saying you can’t do that. But at the same time, like you’re talking about giving students something they can write with. I’m guessing that the whiteboard to by having it sort of like personal

might be helpful that they can show you, right? I also like to get in the habit. If students are drawing on a whiteboard or using paper, pen and paper or pencil and paper, it doesn’t really matter what they’re writing on. I always like them to describe what they’ve drawn to me as the educator versus just like picking it up and showing me because it forces them to kind of communicate what they’ve done and think about what they’ve done a little bit as well. So like these are little things that of course I never did early on.

But as you progress, you can incorporate so many different of the eight effective teaching practices into this one protocol. And again, I want people picturing this. If I could run an effective math talk or a number talk problem string, whatever it is you want to call it, if I can do that well, I can then start extending this idea to the rest of my teaching experiences in the classroom as well.

Jon Orr

Yeah, it’s like it’s like the baby step, you know, the gateway to like, you know, I think that’s that’s how I remember starting is thinking about, I’m going to do warm ups because I was a very traditional teacher for a long time. We’re to do warm ups. then the warm ups evolved. The warm ups evolved from this to this to this the way we’re talking about, know, and using the tools we’re talking about using the models we’ve been talking about like like this. This is something we’ve talked about many times here on the podcast is that a lot of times when you you you’re working with a coach or

you’re, say, attending a conference or listening to a podcast. And they’re describing a classroom that does not sound like or look like your classroom. And a lot of times we think we have to jump from where we are to that classroom. And like, sometimes you get that impression that when you’re working with a coach, the coach is like expecting you to make a leap from here to here. But know the fact that when we describe this, this

this procedure, you know, this routine, we’re describing that it evolved over the course of many years and trial and error and experience of stepping forward and trying this routine and adjusting and learning and what works and what doesn’t work with the group you have in front of you. And, and at no time should you always, you know, think that you have to jump from where you are now to this magic, magic place that you’re all of sudden doing this.

the way that you’re hearing about it or seeing it in live action, it’s a progression that you yourself have to take, which though you won’t get to take unless you do step forward in tiny bit, right? And take that kind of like, let me try this to start, but knowing that you’re going to evolve is really important to kind of like let that sink in and go, it’s a process and not a final destination where I just have to do it this way. And that’s the only way.

That’s not the way to think about this, because even today, we are still going, this is going to evolve. It’s going to change. It’s going to continually grow. And we’re always going to, say, get better at, say, the protocols that we’re trying with our students. So don’t think that these routines are, this is what it looks like, or this is what it looks like. It’s a progression.

Kyle Pearce

I love it. as I think about everything we’ve considered here, and we’ve sort of, I would say, inched up through different phases of how we might run this protocol. But in my mind, everyone listening could have a very different picture of what it looks like in the classroom. And I’ll be honest and say, I used to just do, when I first started, I would do my problem strings.

where students were in the classroom, the way the classroom was set up. And it was only when I saw Yvette actually do a move that I kind of fell in love with it. And I thought, must be because she teaches elementary. And Yvette, would gather students around to try to get them close, almost like a tight-knit community. And it might mean taking their chairs. in elementary, might mean sitting at the carpet or

doing something like that. And I was in high school thinking, you know, that’s not going to work here. But the first time I worked with a remedial math class, grade 12, at a school. And this was a school with a bunch of students who traditionally were not fans of school in general or math class. And I got them to gather around. And just how different the experience was, I sort of fell in love. So that

tell me and tell everyone here about other considerations that go beyond like what you’re saying and doing and more about like the actual classroom environment.

Yvette Lehman

Yeah, and I think this speaks to also why we need to keep our math talks short. Like this isn’t something that students should be up at the board doing for 30, 40 minutes. It’s like it’s intended to be a 15, 20 minute routine and then we can pick up tomorrow. So in our classroom, we were in a middle school classroom, we actually had a carpet, which probably was very uncomfortable for our 13, 14 year olds at first when we were like, you’re gonna come and sit at the carpet. But it’s like, you could come and sit at the carpet, you could stand around the circle, you could bring your chair.

all my only requirement was that there was no desk between you and I. And the reason for that is like, as soon as you have physical barrier between yourself and the speaker, there’s that opportunity for anonymity and to disengage. And so it’s like for these 15 minutes, you’re gonna come and you’re gonna be apart and you’re gonna be actively engaged and then we’re gonna send you back and you’re gonna do the next part of the lesson. But it was really important to me that we really came together and that’s why I also kept it brief.

You know, it didn’t drag on for 30, 40 minutes. I was really mindful that this is, you’re gonna come, you’re gonna be really engaged for the next 15 minutes. You’re gonna be a part of your community. You’re gonna show me your thinking. You’re gonna share with your peers and then we’re gonna go back and we’re gonna move on to the next part of the lesson. So that’s just another consideration. You know, bring them up, bring them close. Standing for 10, 15 minutes is not a burden. It may feel like it. And if that’s obviously not accessible for the students, of course we can accommodate and have flexible seating, but just another consideration.

John, you mentioned about this idea of like that we’re constantly evolving and progressing and like I’m already ready to evolve. And like just this year I learned something new that I didn’t know before that I absolutely need to take back to the classroom, which is this idea of I’ve always loved problem strings. I mentioned like many lessons resource from Kathy Fosno has been a huge influence on my content knowledge and my teaching practice. But now I’ve recognized that for me, I struggled with the transfer.

It’s like I would teach a strategy and leverage a model, but then I wasn’t always seeing students apply it when they were problem solving. And that was a barrier for me. And then, you know, engaging in the work of Jennifer Bay Williams and Johnson Giovanni this year, I identified a piece that I was missing, which is the opportunity for them to look at a variety of problems or sentences and determine when that strategy makes sense and when it does not.

And that was not something I had ever done. So, you know, if I teach doubling and having, did I then put up six or eight problems and say, okay, of these problems, which one would you double and have and why? And so to me, that’s a huge missing piece in my practice that I’m going to bring back when I, you know, am back to the classroom.

Jon Orr

Love it. Love it. The elements of fluency of being able to select and sequence and decide, I think we often miss out on when we are helping our students develop real fluency strategies. So I’m glad you brought that up. Today we talked about number talks and structure, also map talks or problem strings or number strings. Those types of mini structures that we can be using in our classrooms. When we think about the six components of our

classroom tree. We’re always trying to strengthen those six up. And specifically when I think about routines here, we’re thinking about the limbs of the tree, which are like our teacher moves, our routines, our structures on how to strengthen this. we know that in order to be able to effectively utilize those limbs, those routines, like the way that we’re talking here, a necessary precursor.

is really to make sure that our roots of our tree are strong. Like how well do we understand the models, the strategies that we want our students to be engaged in so that when we are in those number talks, we can move flexibly. know what to look for. You know, we’ve we’ve done the mathematics ourselves without calculators. We’ve done the mathematics with the models, with the strategies, and we have to take that time and that time, you know, that time takes it does take experience and and and repetition on our own part.

to able to be flexible in the moment to effectively run those. So when we think about our tree, if we’re going to be performing the limbs well, and it doesn’t even matter what limb, today we talked specifically about these routines, but any sort of routine you’re doing in your classroom, any sort of structure, any sort of lesson technique, you are better at that technique if you’re strengthening the roots. So if you had to choose which one would you want to do, you want to do both, but focus on the roots as well, make that a priority.

because you can strengthen the roots, can strengthen all the other parts of your tree at the same time. If you don’t know all the parts of the tree, can head on over to makemathmoments.com forward slash report, makemathmoments.com forward slash report. You can fill out a quick survey, learn about the six parts of the tree, and actually we’ll pinpoint which one you maybe should focus on next.

Jon Orr

Thanks everyone. Take care.

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