Mike Steele, Pacing Discourse-Rich Lessons ROUNDING UP: SEASON 4 | EPISODE 13

As a classroom teacher, pacing lessons was often my Achilles' heel. If my students were sharing their thinking or working on a task, I sometimes struggled to decide when to move on to the next phase of a lesson.

Today we're talking with Mike Steele from Ball State University about several high-leverage practices that educators can use to plan and pace their lessons.

BIOGRAPHY

Mike Steele is a math education researcher focused on teacher knowledge and teacher learning. He is the past president of the Association of Mathematics Teacher Educators, editor in chief of the Mathematics Teacher Educator journal, and member of the NCTM board of directors.

RESOURCES

Journal Article

• "Pacing a Discourse-Rich Lesson: When to Move On"

Books

• 5 Practices for Orchestrating Productive Mathematics Discussions

• The 5 Practices in Practice [Elementary]

• The 5 Practices in Practice [Middle School]

• The 5 Practices in Practice [High School]

• Coaching the 5 Practices

TRANSCRIPT

Mike Wallus: Well, hi, Mike. Welcome to the podcast. I'm excited to talk with you about discourse-rich lessons and what it looks like to pace them.

Mike Steele: Well, I'm excited to talk with you too about this, Mike. This has been a real focus and interest, and I'm so excited that this article grabbed your attention.

Mike Wallus: I suppose the first question I should ask for the audience is: What do you mean when you're talking about a discourse-rich lesson? What does that term mean about the lesson and perhaps also about the role of the teacher?

Mike Steele: Yeah, I think that's a great question to start with. So when we're talking about a discourse-rich lesson, we're talking about one that has some mathematics that's worth talking about in it. So opportunities for thinking, reasoning, problem solving, in-progress thinking that leads to new mathematical understandings. And that kind of implicit in that discourse-rich lesson is student discourse-rich lesson. That we want not just teachers talking about sharing their own thinking about the mathematics, but opportunities for students to share their own thinking, to shape that thinking, to talk with each other, to see each other as intellectual resources in mathematics.

And so to have a lesson like that, you've got to have a number of things in place. You've got to have a mathematical task that's worth talking about. So something that's not just a calculation and we end up at an answer and that the discourse isn't just, "Let me relay to you as a student the steps I took to do this." Because a lot of times when students are just starting to experience discourse-rich lessons, that's kind of mode one that they engage in is, "Let me recite for you the things that I did." But really opportunities to go beyond that and get into the reasoning and the why of the mathematics. And hopefully to explore some approaches or perspectives or representations that they may not have defaulted to in their first run-through or their first experience digging into a mathematical task.

So the task has to have those opportunities and then we have to create learning environments that really foster those opportunities and students as the creators of mathematics and the teacher as the person who's shaping and guiding that discussion in a mathematically productive way.

Mike Wallus: One of the things that struck me is there is likely a problem of practice that you're trying to solve in publishing this article, and I wonder if we could pull the curtain back and have you talk a bit about what was the genesis of this article for you?

Mike Steele: Absolutely. So let me take us back about 20 or 25 years, and I'll take you back to some early work that went on around these sorts of rich tasks and discourse-rich lessons. So a lot of this legacy comes out of research or a project in the late nineties called the Quasar Project that helped identify: What is a rich task? What is a task, as the researchers described it, of high cognitive demand that has those opportunities for thinking and reasoning?

The next question that that line of research brought forward is, "OK, so we know what a task looks like that gives these opportunities. How does this change what teachers do in the classroom? How they plan for lessons, how they make those moment-to-moment decisions as they're engaged in the teaching of that lesson?" Because it's very different than actually when I started teaching middle school in the nineties, where my preparation was: I looked at the content I had for that day, I wrote three example problems I wanted to write on the board that I very carefully got all the steps right and put those up and explained them and answered some questions. "Alright, everybody understand that? OK, great, moving on." And then the students went and reproduced that. That's fine for some procedural things, but if I really wanted them to engage in thinking and reasoning, I had to start changing my whole practice.

So this bubbles up out of the original work of the 5 Practices for Orchestrating Productive Discussions [book] from Peg Smith and Mary Kay Stein. I had the opportunity actually to work with them both in the early two thousands at the University of Pittsburgh. And so as we were working on this five-practices framework that was supposed to help teachers think about, "What does a different conceptualization of planning and teaching look like that really gets us to this discourse-rich classroom environment where students are making sense of and grappling with mathematics and talking to each other in a meaningful way about it?" We worked with teachers around that and the five-practices [framework] is certainly helpful, but then as teachers were working with the five practices and they were anticipating student thinking, they were writing questions that assess and advance student thinking, some of the things that came up were, "OK, what are the moment-to-moment decisions and challenges related to that as we start planning and teaching in this way?"

And a number of common challenges came up. A lot of times when we were using a five-practice lesson, we were doing kind of a launch, explore, share, and discuss sort of format where we've got the teacher who's getting us started on a task, but we're not giving the farm away on that task. We're not saying too much and guiding their thinking. And then we let students have some time individually and in small groups to start messing around with the mathematics, working, talking. And then at some point we're going to call everybody together and we're going to share what the different ways of thinking were. We're going to try to draw that together. Peg Smith likes to talk about this as being more than a show-and-tell. So it's not just, "We stand up, we give our answer, we do that. Great." Next group, doing the same thing, and oftentimes they start to look alike. But there's some really meaningful thinking that goes on in that whole-class discussion.

So one of the really pragmatic concerns here is, "How do I know when to move?" So I've got students working individually, and maybe I gave them 3 minutes to get started. Was that enough? What can I see in the work they're doing? What questions am I going to hear to tell me, "OK, now it's a good moment to move to small groups." And then similarly, when you've got small groups working, they're cranking away on a task. There might be multiple subquestions in that task. What's my cue that we're ready to go on to that whole-class discussion?

We were in so many classrooms where teachers were really working hard to do this work, and this happens to me all the time. I have somehow miscalculated what students are going to be able to do—either how quickly they're going to be able to do it, or I expected them to draw on this piece of prior knowledge and it took us a while to get there, or they've flown through something that I didn't expect them to fly through. So I'm having to make some choice in a moment, saying, "This isn't exactly how I imagined it, so what do I do here?" And frequently with teachers that get caught in that dilemma, the first response is to take control back, [to] say, "OK, you're all struggling with this. Let's come back together and let me show you what you should have figured out here." And it's done with the best of intentions. We need to get some closure on the mathematical ideas. But then it takes us right away from what we were trying to do, which was have our students grapple with the mathematics.

And so we do this lovely polished job of putting that together and maybe students took the important things away from that, that they wanted to, maybe they didn't, but they didn't get all the way they were on their own. So that's really the problem of practice that this helps us to solve is, when we get in those positions of, "OK, I've got to make a call. I've got this much time left. I've got this sort of work that I see going on in the classroom. Am I ready? What can I do next?" That really keeps that ownership of the mathematics with our students but still gives me some ability to orchestrate, to shape that discussion in a way that's mathematically meaningful and that gets at the goals I had for the lesson.

Mike Wallus: Yeah, I appreciated that part of the article and even just hearing you describe that so much, Mike, because you gave words to I think what sat behind the dilemma that I found myself in so often, which was: I was either trying to gauge whether there was enough—and I think the challenge is we're going to get into, what "enough" actually might mean—but given enough time, whether I was confident that there was understanding, how much understanding was necessary. And what that translates into is a lack of clarity around "How do I use my time? How do I gauge when it's worth expending some of the time that I maybe hadn't thought about and when it's worth recognizing that perhaps I didn't need all of that and I'm ready to do something?"

So I think the next question probably should be: Let's talk about "enough." When you talk about knowing if you have enough, say a little bit more about what you mean and perhaps what a teacher might be looking and listening for.

Mike Steele: Absolutely. And I think this is a hidden thread in that five-practices model because we say: "OK, we want that whole-class discussion to still be a site for learning where there are some new ideas that are coming together." So that then backs me up to thinking about the small-group work. I'm putting myself in that mode where I've got six groups working around the classroom. I'm circulating around; I'm asking questions. I of course don't see every single thing at any given moment that the small groups are doing. So I'm getting these little excerpts, these little 2- to 3-minute excerpts, when you stop into a group. So I think when we think about "enough," I want to think about, with that task that I'm doing, with what my mathematical goals are and knowing that we're going to have time on the backend of this whole-class discussion to pull some ideas together, to sharpen some things to clarify some of the mathematics.

Do I have enough mathematical grist for the mill here in what the small groups are doing to be able to then take that and make progress with students' thinking at the center—again, not taking over the thinking myself—to be able to do that work. So, for any given mathematical idea, as I've started thinking about this when I plan lessons using the five-practices model, I am really taking that apart. What's the mathematical nugget that I'm listening for here, that I'm looking for in students' work that tells me: "OK, we've gotten to a point where, if I were to call people together right now and get them thinking about it, that there's more to think about, but we're well on our way."

And also when I'm looking for that, knowing that I'm also not looking at those six groups all at exactly the same time. So, I want to look for those mile markers along the way that tell me we're getting close, but we're not all the way there. Because if I pick one that's, we're pretty much all the way there, that's the first group I come to and I'm going to circulate around to five more. They're going to have run out of interesting things to do, and they're off talking about, thinking about something else.

So, that really becomes the fine line: "What are those little mathematical ideas along the way that are far enough that get us towards our goals, but still we've got a little bit of the journey to go that we're going to go on together?"

Mike Wallus: This is so fascinating. The analogy that's coming together in my mind is almost like you're listening for the ingredients for a conversation that you want to have as a group. So it's not necessarily "Has everyone finished?" And that's your threshold. It's actually "Did I hear this idea starting to bubble up? Did I hear elements of this idea or this strategy start to bubble up? Is there an insight that's percolating in different groups?" And it's the combination of those things that the teacher is listening for, and that's kind of the gauge of enoughness. Is that an accurate analogy?

Mike Steele: It is, and I love that analogy because it reminds me of a favorite in our household as we're relaxing. We love to watch The Great British Baking Show. So, you're watching people take something from ingredients to a finished product. Now as you're watching that 20-minute segment, they're working on their technical challenge and they're all baking the same thing. I don't have to wait until the end of that, where they've presented their finished product, to have a good idea of what's going to happen. As I'm going through, as I'm watching 'em through that baking process, we're at the middle, my wife and I are talking, like, "Ooh, I've got concerns about that one. That one's looking good though." We get an idea of where it's going. So I think the ingredient analogy really lands with me. We don't have to wait. We're looking for those pieces to be able to pull that together, those ingredients. We're not waiting until there's a final product and saying—because then, what is there to say about it? "Oh, look, that looks great. Oh, that one, maybe not exactly what we'd intended." So, it's giving us those ingredients for that whole-class discussion.

Mike Wallus: The other thing that struck me as I was listening to you is: We're not teaching a task; we're teaching a set of ideas or relationships. The task is the vehicle. So, it's perfectly reasonable, it seems, to say, "We're going to pause at this point in the task, or at a place where students might not be entirely finished with the task. And we might have a conversation at that point because we have enough that we can have part of the conversation." And that doesn't mean that they don't go back to the task. But you're really helping me recognize that one of the places where I sometimes get stuck, or got stuck, when I was teaching, is task completion was part of my time marking. And I think really what you're challenging me and other educators to do is to say, "The task is just the vehicle. What's going on? What's percolating around that task as it's happening?" How does that strike you?

Mike Steele: Yeah, absolutely. And it was the same challenge with me and sometimes still is the same challenge with me. (laughs) Yeah, you give this task, and we think about that task as our unit of analysis as a teacher when we're planning. And so we want our students as we're using it to get to the end of it. It's a very natural thing to do.

And let me make this really concrete. If I'm doing a visual pattern task with third graders, we have, I think there's one of the elementary [5 Practices in Practice] book called "Tables & Chairs." So you've got these square tables that have four seats around them, and you're putting a string of tables together and asking kids to get at the generalization. "If you have any number of tables, how many people can you seat?"

And so I think early when I started giving those tasks, I was looking for, "OK, has everybody gotten to the rule? Have they gotten to that generalization? OK, now we can talk about it." And we can talk about the different ways people made sense of that geometrically and those connections, and that's what I want to get out of the whole-class discussion. But we don't even have to get there if groups have a sense of how that pattern is growing, even if they haven't gotten to the formal description of the rule. Because if they've gotten to that point, they've made some sense of the visual. They've made some of those connections. They've parsed that in different ways. That's plenty for me to have a good conversation, that we can come to that rule as a group and we can even come to it in different ways as a group. But it frees me up from being like, "OK, everybody got the rule? Everybody got the rule? Everybody got the rule?" Because that often resulted in, I'd have a couple of groups that maybe had been a little slower getting started and they're still getting there. And then I'm sitting there and I'm talking to them, I'm giving them these terribly leading questions. "Can we just get to the rule? Come on, let's go. You're almost there. We got it. We got it." And that then is, again, me taking over that thinking and not giving them the space for those ideas to breathe.

Mike Wallus: What else is jumping out for me is the ramifications for how thinking this way actually might shift the way that I would plan for teaching, but also how it might shift the way that I'm looking for evidence to assess students' progress during the task. So I wonder if you have situations or maybe some recommendations for: How might a person plan in ways that help them recognize the ways that the task can be a vehicle but also plan for the kind of evidence that they might be looking for along the way? Could you talk a little bit about that?

Mike Steele: Absolutely. So I'll give kind of a multi-layered description of this. When we're using a task that's got multiple solution paths that has these opportunities for diverse thinking, the five-practices framework tells us anticipating student thinking is a critical part of it. So, what are the different solution paths that students can take through it? So, if it's a visual pattern task, they may look at it this way with a visual. They may think about those tables like the tops and the bottoms and then the sides. They may think about the two ends of the tables having different numbers of chairs and the ones in between having a different number of chairs and parsing it that way. And we can develop those. It's actually, for me, quite a lot of fun to develop those fully formed solutions that students can do. And early on when I was enacting lessons like this, I would do that. I'd have those that I was looking for. I'd also think about questions I'd want to ask students who are struggling to get started or maybe were going down a path that may not be mathematically productive and the questions I might ask them to get them on a more mathematically productive path. And I'd go around and I'd look for those solutions, and I'd use that to think about my selecting, my sequencing, my connecting my whole-class discussion. So, great, check. That's layer one.

I think responding to the challenge of what's enough requires us to then take those solution paths apart—both the fully formed ones, maybe the incomplete thinking—and say, "OK, within that solution, what are the things that I want to see and hear that gives me some confidence that we're on this path, even if we're not at the end of this path, and that give me enough to think about?" So, if I think about, I'll go back again to this visual pattern task analogy. If I see groups that are talking about increases, so when we add a table, we're adding two chairs or they're making that distinction between those end tables and the center tables. And I've asked them a couple of questions like: OK, they've done that for 4, they've done that for 5. We may not have done that for 10 or 100 or a generalization, but that might be enough. So, I'm trying to take apart the mathematics and look for those little ideas within it. We've got this idea of a constant rate of change. We've got an idea that the number of tables and the number of chairs have a direct relationship here. So we're setting the stage for that functional thinking, even if, at a third grade level, we're not going to talk about that word. And those might be the important goals that I have for the lesson.

So that's the next phase of what I'm doing. In addition to those fully formed solutions, I'm figuring out: What are the little mathematical ideas in each that I would want to see or hear in my classroom that tell me, "OK, I have a good sense of where they are. I know where this bake's going to turn out 5 minutes from now on the show when they've taken it out of the oven." So, that's I think the next layer of that planning, of trying to figure out how to plan.

And then as we're in the moment in the classroom, being able to know what we're looking for and listening for. And the listening for me is really, really important. I think when I started doing this and I had a sense of, "What are the mathematical ideas I need to draw on?" I made the mistake of overly looking for those on paper. And if we think about how students make sense of writing things down, and sometimes despite our best efforts, the finality that comes with it: "If I've written it down, I have made it real." And if our thinking is still kind of this in-progress thinking, we may not be ready to write it down. So if I wait for it to be written on the page, I may have waited too long, or longer than I needed to, for everybody to get that idea. So again I want to make sure I listen for key words and phrases. And I might have a couple of questions teed up to help me hear those. And once I've heard those, I'm like, "OK, I am ready to go." And then for me—at least in my early fifties and not having the memory that I did when I was a 22-year-old, fresh-out-of-the-box classroom teacher—I need to have a way of keeping track of that and writing that down. So be it physical, be it digital, I want to say, "OK, I know what I'm listening for, what I'm looking for." And sometimes those may be interchangeable. If it's written on the page, great. If not, if I hear it, that's great too. And then if I've got a pretty good roster of that as I've moved through and say, "OK, I feel like all of my groups or most of my groups are at this point, there we go." I feel confident that when I pull us back together, it's not going to be me asking a question and then that terribly awkward sea of crickets out there. I'm like, "I know you were thinking about stuff; just give it to me. I know you've got this." But it gives me much more confidence that we're going to have that nice transition into a good whole-class discussion.

Mike Wallus: OK. There's a ton of powerful stuff that you just said. So I want to try to mark two things that really jump out for me. One is an observation that I think is important, and then one is a thought that I want to pick your brain around a little bit further.

I think the biggest piece that I heard you say, which as you were talking about, is this notion that I'm waiting for something to appear in written form. And it feels really freeing and it gives me a lot more space to say, "This is something I could hear or I could even see in the way that kids were manipulating materials. That that counts as evidence, and I don't have to literally see it written on a paper in order for me to count that that idea is in the room." I just want to name that for the audience because that feels tremendously important. Because from a practical standpoint, if we're waiting for it to be written, that takes more time. And it doesn't necessarily mean that suddenly it appeared and before when it was just in a child's mind or in the way that they were manipulating something, that it wasn't there. It was there. So I just want to mark that.

The other thing that you had me thinking about is, I know for myself, I've gone through and done some of the anticipation work in the five practices, but what struck me is when my colleagues and I would do that, we often would generate quite a few alternative strategies or ideas. But I feel like what we were looking at is the final outcome, like, "This counting by 1 strategy is what we might see. This decomposing numbers more flexibly is something we might see. This counting on strategy is something we might see." But what we didn't talk about that I think you're advocating for is: What are the moments within that that matter? It's almost like: What in the process of getting to this anticipated strategy is something that is useful or important that counts as one of those ingredients? So I want to run that past you and say, does that follow or am I missing something?

Mike Steele: It does. And I think those two things go together in a really important way because as you're talking about that pivotal moment in student thinking, as they're coming to this new understanding, as they're grappling with that mathematical idea, and thinking about, "What are the implications if we leverage that moment right there to then ask more questions to connect different ways of student thinking as compared to waiting till it's written down?" Because when it's written down, that exciting moment of the new discovery has passed. And so then when we want them to come revisit—"Tell us what you were thinking when you did that."—they're having to rewind and go back and reenact that.

If we have the ability to capture those neurons firing at full throttle in that moment of a new mathematical insight and then use that to build on as a teacher and to really get where we want to go with the lesson, I feel like we're doing the right thing by kids by trying to seize that moment, to leverage it. We always have time to write down what we think we learned later on at the end of the lesson. It's a great task for homework. And that's another thing I love about leaving some things unfinished with a task is, that's just a delightful homework assignment. And the kids love it because they don't feel like I've asked them to do anything new. (laughs) Just write down what you understood about this, and now we're codifying it kind of at a different place in the process.

Mike Wallus: Well, OK, and that makes me think about something else. Because you've helped me recognize that I don't have to wait for a final solution in writing that's fleshed out in order to start a whole-group conversation. But I think what you're saying is, it changes the tone and maybe also the purpose and the impact of that conversation on students. Because if I have a task that I'm midway through and suddenly there's a conversation that helps create some understanding, some aha moments, if my task is unfinished and I had an aha, I probably really want to go back to that and see if I can apply that aha. And that's kind of cool to imagine like a classroom where you have a bunch of kids dying to go back and see if they can figure out how they can put that to use. Now you wouldn't always have to do that, but that strikes me as different than a consolidation conversation where it's kind of like, "Well, everything's finished. What have we learned?" Those are valuable. But I'm just really, I think in love with the possibility that a conversation that doesn't always wait until final solutions creates for learning.

Mike Steele: And when I've seen this done effectively, there are these moments that happen. Mike, they're exactly what you're describing, is that there's an insight that comes up in the whole-class conversation, and you will see people going back to their paper or their tablet that they were doing their original work on and start writing. And we know oftentimes with kids, I remember so many times in my classroom where we're having this discussion, this important point comes up, and everybody's kind of frozen. And I'm like, "No, you should write that down. That's the important thing. Write that down." And when you see it happen organically, it's because something really catalyzed in insight that was important enough that they went back to that work and said, "Oh, I want to capture this."

Mike Wallus: So, I'm wondering if there are habits of mind, habits in planning, or habits in practice that we could distill down. So, how would you unpack the things that a person might do if they're listening and they're like, "I want to do this today," or "I want to do this at my next planning."? Could you talk a little bit about what are the baby steps, so to speak, for a person?

Mike Steele: Yeah, and I think the first one is really about getting into the mathematics and going deep with the mathematics in the task that you're hoping to teach. As somebody who is trained as a secondary math teacher, and early in my career, I was like, "Oh, I know what the math is. I don't need to spend the time on the math." I can't tell you how wrong I was about that. So anticipating those ways of thinking, thinking about where those challenges are, that sort of thing, is absolutely critically important to doing that work. And giving the time and space for that to happen. I mean, it was almost without fail. Every time I shorted myself on the time to think about the mathematics and just popped open my instructional resource and said, "Here we go. Class starts in 5 minutes. Let's get going on this," I'd bump into things that I was like, "Oh, I wish I had thought about that mathematical idea first." Or there'd be a question that would come up that I'd be totally unprepared to answer and I could have been prepared to answer. Now, we're not going to anticipate every way of thinking that students have or every question that they'll have, but I always find that if I've thought through it, I'm probably in a better position to give a meaningful answer to it or ask a good question back in response. And it also frees up my cognitive load to actually spend some time on those questions that I didn't expect rather than trying to make sense of everything as if it's the first time I'm seeing it.

And then along with that, doing this as a group, we used to sit in our PLC sessions and start to solve tasks together and share our thinking about, "OK, what are the mathematical ideas that we're really trying to take apart here?" And there were always insights that didn't occur to me that would occur to somebody else that added to my own thinking. And now in an increasingly digitally connected age, we don't necessarily have to be in the same room with people to do that. We can do that at a distance and still be very effective.

And then the last thing I'll talk about here in terms of getting started is: We are so good as teachers at sharing an interesting task that we found or that we used with our students with our colleagues. "Here's this thing I use in my class. It was great. You're a couple days behind me in the pacing. Maybe you can use this next Tuesday." What we I think are less good at is bringing back the outcomes of that and talking about that. "Here's what students did." I loved it when we had opportunities to gather a group of teachers in the PLC with student work from a task they did and talk about it and see: What did students make sense of? What were the questions that I asked that were helpful, or that maybe weren't helpful, in teaching that lesson. Because we'll share the task, but my goodness, the questions that we came up with to ask students in the moment, those are just as portable from one classroom to another. And we should be thinking about, just like we think about digital archives to share those tasks and those lesson plans—like sharing those questions, sharing that student work—those are the other legs of that stool that are important for really helping us do this work in a meaningful and collaborative way. Because if we don't talk about the outcomes of what students learned, the task could be great, it could be interesting, but so what? What's the important mathematical insights that kids took away from it?

Mike Wallus: Yeah, I'm kind of in love with this notion that in addition to sharing tasks, sharing questions that really generated an impact in the classroom space or sharing moments of insight that led to something that jumped out. It's fascinating to think about taking those ideas and building them into a regular PLC process. It just has so much potential.

Before we close the conversation, I wanted to ask you a question that I ask almost every guest: If someone wanted to learn more about the ideas that you've shared today, what are some of the resources you'd recommend?

Mike Steele: Well, I've talked quite a bit about the work of the 5 Practices for Orchestrating Productive Discussions and that series of books that have been written over the past 15 years on that—the resources that are available online for that, I think, would be a great place to start. I've only scratched the surface at taking you through those five practices—which are actually six practices, because early on we realized that attention to the task we select and the goals for that task is the important "practice zero." In fact, it was a teacher that pointed that out to Peg Smith. And that's the lovely thing. So the reason I've stayed in touch with and helped to develop this work over the years is because when we see teachers taking it up, not only is it meaningful, but the feedback we get from teachers then shapes the next things that we do with it. So there's the original 5 practices book that kind of presents the model, shows some examples of tasks and how you go through the model.

But then in 2019 and 2020, we published a series called The 5 Practices in Practice that, there's a book for each grade band—elementary, middle, and high school. But those were the ones that really aggregated the challenges that we heard from teachers over 10 years of doing this work and started to address those challenges. How do you overcome those things? We also, for each of those books, there's brand-new original video that we took in urban classrooms that illustrated teachers working really effectively with the five practices. I was able to be in the room when we filmed all of the high school classrooms in Milwaukee, Wisconsin, and it was just amazing to see that work.

And then the last piece that I'll suggest to that, which is a book that came out relatively recently in that series. There is a Coaching the 5 Practices book. So if you are a coach, instructional leader who's looking to support a team and a PLC in doing exactly this sort of work that we've been talking about, the Coaching the 5 Practices book is an incredible resource for thinking about how you can structure that work.

Mike Wallus: OK. I have to also ask you, can you give a shout out to the article that you recently wrote and published as well, the title and where people could find it?

Mike Steele: Absolutely. Yes. The article is called "Pacing a Discourse-Rich Lesson: When to Move On," and I authored it alongside an elementary and middle school teacher who provided a reflection on it. It comes from the classroom of a high school teacher, Michael Moore, in Milwaukee, who we filmed for the [5 Practices in Practice] high school book. So I drew from his classroom. And then Kara Benson in Zionsville Community Schools right here in Zionsville, Indiana. And Kelly Agnew who teaches in Muncie Community Schools, which is where Ball State [University] is located. Each provided a reflection from an elementary and middle school standpoint about the ideas in the article. It was published in NCTM'S practitioner journal, Mathematics Teacher: Learning and Teaching PK-12, in the Volume 118, Issue 11, from November of 2025.

Mike Wallus: That's fantastic. And for listeners, just so you know, we're going to put a link to all of the resources that Mike shared.

I think this is probably a good place to stop, Mike. I suspect we could talk for much longer. I just want to thank you, though, for taking the time to join the podcast. It has been an absolute pleasure chatting with you.

Mike Steele: The pleasure has been all mine. As you can tell, I love talking about these ideas, and I was so glad to have the opportunity to share a little bit of this with the audience.

Mike Wallus: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability.

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