Podcast appearances and mentions of peter liljedahl

Are Problem Strings the same thing as Thin Slicing? In this episode Pam and Kim talk about the similarities between Problem Strings and Dr. Peter Liljedahl's Thin Slicing.Talking Points:Example Problem String:Calling on students strategically in a Problem StringStrategic seating arrangements for partner talkSimilarities between Problem Strings and Thin Slicing:Purposefully designed sequence of related problemsProblems given one at a timeIncreasing challengeCritical teacher planningOpen access for all studentsPurposeful variation to keep students challengedCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC 

I am joined by Dr. Peter Liljedahl, author of Building the Thinking Classroom. Dr. Peter Liljedahl is Professor of Mathematics Education in the Faculty of Education, and an associate member in the Department of Mathematics, at Simon Fraser University in Canada. He is a former high school mathematics teacher who has kept his research interest and activities close to the classroom. He is a member of the executive of the British Columbia Mathematics Teachers Association (BCAMT) and current president of the International Group for the Psychology of Mathematics Education. He consults regularly with teachers, schools, school districts, and ministries of education on issues of teaching and learning, thinking classrooms, assessment, and numeracy.

Engaging students in meaningful thinking and learning is essential for effective education. We explore the principles of creating a thinking classroom with Dr. Peter Liljeddahl, emphasizing the importance of collaboration, purposeful tasks, and a supportive learning environment.What we'll cover...- Discussion of non-thinking behaviors observed in traditional classrooms  - Introduction to the 14 key practices for building thinking classrooms  - Importance of random group formations for collaborative learning  - Strategies for implementing thinking tasks into classroom routines  - The role of teacher-student dynamics in fostering engagement  - Emphasis on valuing mistakes as learning opportunities  - How to incorporate playful and non-curricular tasks into learning  - Insights into Dr. Liljedahl's further resources and booksIf you enjoyed this conversation, be sure to subscribe for more insights on transforming education through innovative practices!About our guest...Dr. Peter Liljedahl is a Professor of Mathematics Education in the Faculty of Education and an associate member in the Department of Mathematics at Simon Fraser University in Vancouver, Canada. Dr. Liljedahl has authored or co-authored 9 books, 26 book chapters, 27 journal articles, and over 50 conference papers. His research interests are creativity, insight, and discovery in mathematics teaching and learning and teacher development. He consults regularly with schools, school districts, and ministries of education on issues of teaching and learning, assessment, and numeracy. Connect with Peter...Building Thinking Classrooms - the book!Got a story to share or question you want us to answer? Send us a message!About the podcastThe KindlED Podcast explores the science of nurturing children's potential and creating empowering learning environments.Powered by Prenda Microschools, each episode offers actionable insights to help you ignite your child's love of learning. We'll dive into evidence-based tools and techniques that kindle young learners' curiosity, motivation, and well-being. Got a burning question?We're all ears! If you have a question or topic you'd love our hosts to tackle, please send it to podcast@prenda.com. Let's dive into the conversation together!Important links:• Connect with us on social • Subscribe to The Sunday Spark• Get our free literacy curriculum Interested in starting a microschool?Prenda provides all the tools and support you need to start and run an amazing microschool. Create a free Prenda World account to start designing your future microschool today. More info at ➡️ Prenda.com or if you're ready to get going ➡️ Start My Microschool

It's Thumb Appreciation Day! So we begin with an amusing discussion about thumbs (are they fingers?). Then, since it is the week of the 2025 CPM Teacher Conference, we are taking a bit of a break from new content and giving you a reprise of our first conversation with Dr. Peter Liljedahl from 2022. After you listen to this part, you'll want to also go listen to Part 2 and Part 3 of the conversation. We'll be back with new content in March!Send Joel and Misty a message!The More Math for More People Podcast is produced by CPM Educational Program. Learn more at CPM.orgX: @cpmmathFacebook: CPMEducationalProgramEmail: cpmpodcast@cpm.org

Send us a textWe're back with Part 2 of our conversation with Christi Edwards, where she shares her final two strategies for ensuring students don't just succeed on class assignments but can apply their learning in future assessments and beyond. In this episode, Christi focuses on helping students regulate their own thinking and communicate their ideas effectively—two key skills that build confidence and deeper understanding.Key Topics Covered:How to teach students to self-regulate their thinking so they take ownership of their learning.The importance of in-the-moment reflection, not just after an assignment is complete.Why exit tickets and visual cues (like red, yellow and green cups) help students track their progress.How to encourage students to explain their thinking and engage in meaningful academic conversations.The power of questioning strategies to build deeper understanding and confidence.Resources Mentioned:Self-regulation tools (checklists, journals, anchor charts) to help students monitor their progress.Peter Liljedahl's “Building Thinking Classrooms” strategies for promoting student-driven discussions.Keisha King's episode on classroom discussions for tips on getting students to talk more.Quotable Moments:“Instead of asking students to show their work, ask them to show their thinking.” — Christi Edwards“Reflection shouldn't just happen at the end of an assignment—it needs to happen throughout the learning process.” — Ashley Shaw“A coach's job isn't to give teachers the answers—it's to help them become curious about their own teaching.” — Jason AdairDon't Miss:Ashley's realization: Why she needs to build reflection into her lessons earlier, not just at the end.Christi's exit ticket strategy that helps students assess their own understanding before they leave class.Jason's coaching takeaway: How instructional coaches can spark curiosity in teachers, just like teachers do for students.You can get feedback from Christi by sending us a message through social or email.   The Southern Regional Education Board is a nonprofit, nonpartisan organization that works with states and schools to improve education at every level, from early childhood through doctoral education and the workforce. Follow Us on Social: Facebook Instagram X

Guest: Alyssa Davis, Spectrum Elementary - 5th Grade In this episode, I sit down with Alyssa Davis to explore the power of active math learning strategies, including the transformative approach of Building Thinking Classrooms by Peter Liljedahl. We discuss practical ways to engage students, foster deep mathematical thinking, and create a classroom culture where every learner thrives. Even if you are not a math teacher, tune in for ideas for strategies that can be used in any lesson! Building Thinking Classrooms Online BTC Conferences and Events  

In this episode, Jamie and Fabian chat with Dr. Peter Liljedahl, the mind behind Building Thinking Classrooms. Peter shares how his journey into teaching wasn't a childhood dream but a path he stumbled into through coaching, carpentry, and a knack for helping others learn. They dive into how the Thinking Classroom approach works in not just math, but other subjects like social studies and language arts. Finally, Peter leaves us with a recommendation for a portable card game, perfect for life on the road, in our ever popular segment “Whatcha Been Playin'…?, Join @hofmannedu, @mrsjamiehalsey, and @findingmyaloha each week by subscribing to our podcast and rating and reviewing us on Apple Podcasts! Join our Discord on rebelteacheralliance.com or here. Find us on Instagram @rebelteacheralliance, on Twitter @rebelteacherpod, and on TikTok @rebelteacheralliance. Leave us a message here! Things mentioned on the show: - Building Thinking Classrooms - Dr. Liljedahl's book - Monopoly Deal - Monopoly but without the boring parts! - Vändtia - Classic Swedish Card Game --- Support this podcast: https://podcasters.spotify.com/pod/show/rebel-teacher-alliance/support

In this episode, Kyle, Maegan, and Dean welcome back Dr. Peter Liljedahl to discuss his ongoing work and insights in Building Thinking Classrooms. Together, they delve into a range of topics like the recent BTC conference, various strategies for using banners and partitioning student workspaces, and the evolving nature of the Thinking Classrooms practices. Tune in to also hear about the importance of student self-efficacy, identity in math, and the effects of math trauma. Peter highlights ongoing research, shares effective teacher practices, and offers valuable recommendations for further reading and professional development. This episode was recorded in early October, 2024.

Get ready to relive the timeless warmth of Peanuts as we celebrate Good Grief Day! We share personal stories and fond memories from iconic Peanuts TV specials, discussing the often hapless yet charming Charlie Brown and his interactions with friends like Lucy and Snoopy. Join us for part 2 of our conversation with Dr. Peter Liljedahl, who brings groundbreaking insights into Building Thinking Classrooms. Through the lens of his new book, explore innovative strategies like thin slicing tasks and their integration with CPM to foster student learning. To connect with Dr Liljedahl on X: @pgliljedahlSend Joel and Misty a message!The More Math for More People Podcast is produced by CPM Educational Program. Learn more at CPM.orgX: @cpmmathFacebook: CPMEducationalProgramEmail: cpmpodcast@cpm.org

First! Early Bird Deadline for the 2025 CPM Teacher Conference ends soon! Prices go up on November 15, 2024 - so don't miss out and have to pay more - sign up now!Ever wondered why anchovies are the perpetual outcasts of the pizza world? Join us as we celebrate National Pizza with the Works Except Anchovies Day with a lively discussion on pizza toppings. We boldly explore the sweet and spicy dance of pineapple and jalapeños, and ponder the sauce spectrum from classic marinara to zesty pesto. We'll tackle the eternal question of cheese quantity and share colorful pizza stories that are sure to leave you hungry for more. This episode, we welcome back Dr. Peter Liljedahl, sharing his global adventures in building thinking classroom and his insights into lesson closure and student learning retention. We discuss the power of effective note-making strategies, using  techniques like gallery walks and the teacher-scribe method to transform classroom dynamics. Learn about a groundbreaking four-quadrant template that's changing the game for student engagement. If you'd like to hear our first conversation with Peter Liljedahl - tune into Episode 2.17,Episode 2.18, and Episode 2.19.To connect with Peter Liljedahl on X: @pgliljedahlSend Joel and Misty a message!The More Math for More People Podcast is produced by CPM Educational Program. Learn more at CPM.orgX: @cpmmathFacebook: CPMEducationalProgramEmail: cpmpodcast@cpm.org

In this episode hosts Fabian, Jamie, and Scott share their recent classroom experiences, challenges, and successes. Scott discusses a field trip where his students engaged in wetlands restoration, fostering connections with nature and community involvement. Fabian introduces the concept of Vertical Non-Permanent Surfaces (VNPS) and how he's integrating thinking classrooms and student-led assessments into his teaching. Jamie shares her excitement about "Fat Bear Week," engaging her students in a fun and educational activity that combines wildlife awareness and classroom debate. This week, we want to hear what YOU've been playin…? Share on the Discord! Join @hofmannedu, @mrsjamiehalsey, and @findingmyaloha each week by subscribing to our podcast and rating and reviewing us on Apple Podcasts! Join our Discord on rebelteacheralliance.com or here. Find us on Instagram @rebelteacheralliance, on Twitter @rebelteacherpod, and on TikTok @rebelteacheralliance. Leave us a message here! Things mentioned on the show: - Vertical Non-Permanent Surfaces (VNPS) - A teaching strategy from Peter Liljedahl's Thinking Classroom practices  - Fat Bear Week --- Support this podcast: https://podcasters.spotify.com/pod/show/rebel-teacher-alliance/support

Classrooms with less monologue and more dialogue are key to increasing student thinking and student learning. Peter Liljedahl recommends teachers using a strategy that publicly, randomly groups students. The students visually seeing the groups form is an important element.  When having these random groups work at easy erase vertical boards, engagement and thinking increases. Students seeing each other's work and the teacher seeing and hearing student thinking around the room all add opportunities for increased engagement in problem solving. Mindshift: How to Get Kids Thinking Instead of Mimicking in Math Class Find Laura Wheeler's blog here and read her article here.  Subscribe to the Steve Barkley Ponders Out Loud podcast on iTunes or visit BarkleyPD.com to find new episodes!

Rounding Up Season 3 | Episode 2 – Responsive Curriculum Guest: Dr. Corey Drake Mike Wallus: When it comes to curriculum, educators are often told to implement with “fidelity.” But what does fidelity mean? And where does that leave educators who want to be responsive to students in their classrooms? Today we're talking with Dr. Corey Drake about principles for responsive curriculum use that invite educators to respond to the students in their classrooms while still implementing curriculum with integrity. Mike: One of the age-old questions that educators grapple with is how to implement a curriculum in ways that are responsive to the students in their classroom. It's a question I thought a lot about during my years as a classroom teacher, and it's one that I continue to discuss with my colleague at MLC, Dr. Corey Drake. As a former classroom teacher and a former teacher educator who only recently began working for an organization that publishes curriculum, Corey and I have been trying to carve out a set of recommendations that we hope will help teachers navigate this question. Today on the podcast, we'll talk about this question of responsive curriculum use and offer some recommendations to support teachers in the field. Mike: Welcome back to the podcast, Corey. I'm excited to have you with us again. Corey Drake: It's great to be with you again. Mike: So, I've been excited about this conversation for a while because this question of, “What does it mean to be responsive to students and use a curriculum?” is something that teachers have been grappling with for so long, and you and I often hear phrases like “implementation with fidelity” used when folks are trying to describe their expectations when a curriculum's adopted. Corey: Yeah, I mean, I think this is a question teachers grapple with. It's a question I've been grappling with for my whole career, from different points of view from when I was a classroom teacher and a teacher educator and now working at The Math Learning Center. But I think this is the fundamental tension: “How do you use a set of published curriculum materials while also being responsive to your students?” And I think ideas like implementation with fidelity didn't really account for the responsive-to-your-students piece. Fidelity has often been taken up as meaning following curriculum materials, page by page, word for word, task for task. We know that's not actually possible. You have to make decisions, you have to make adaptations as you move from a written page to an enacted curriculum. But still the idea of fidelity was to be as close as possible to the written page. Whereas ideas like implementation with integrity or responsive curriculum use are starting with what's written on the page, staying consistent with the key ideas of what's on the page, but doing it in a way that's responsive to the students who are sitting in front of you. And that's really kind of the art and science of curriculum use. Mike: Yeah, I think one of the things that I used to think was that it was really a binary choice between something like fidelity, where you were following things in what I would've described as a lockstep fashion. Or the alternative, which would be, “I'm going to make everything up.” And you've helped me think, first of all, about what might be some baseline expectations from a large-scale curriculum. What are we actually expecting from curriculum around design, around the audience that it's written for? I wonder if you could share with the audience some of the things that we've talked about when it comes to the assets and also the limitations of a large-scale curriculum. Corey: Yeah, absolutely. And I will say, when you and I were first teachers probably, and definitely when we were students, the conversation was very different. We had different curriculum materials available. There was a very common idea that good teachers were teachers who made up their own curriculum materials, who developed all of their own materials. But there weren't the kinds of materials out there that we have now. And now we have materials that do provide a lot of assets, can be rich tools for teachers, particularly if we release this expectation of fidelity and instead think about integrity. So, some of the assets that a high-quality curriculum can bring are the progression of ideas, the sequence of ideas and tasks that underlies almost any set of curriculum materials; that really looks at, “How does student thinking develop across the course of a school year?” And what kinds of tasks, in what order, can support that development of that thinking. Corey: That's a really important thing that individual teachers or even teams of teachers working on their own, that would be very hard for them to put together in that kind of coherent, sequential way. So, that's really important. A lot of curriculum materials also bring in many ideas that we've learned over the last decades about how children learn mathematics: the kinds of strategies children use, the different ways of thinking that children bring. And so, there's a lot that both teachers and students can learn from using curriculum materials. At the same time, any published set of large-scale curriculum materials are, by definition, designed for a generic group of students, a generic teacher in a generic classroom, in a generic community. That's what it means to be large scale. That's what it means to be published ahead of time. So, those materials are not written for any specific student or teacher or classroom or community. Corey: And so, that's the real limitation. It doesn't mean that the materials are bad. The materials are very good. But they can't be written for those specific children in that specific classroom and community. That's where this idea that responsive curriculum use and equitable instruction always have to happen in the interactions between materials, teachers, and students. Materials by themselves cannot be responsive. Teachers by themselves cannot responsibly develop the kinds of ideas in the ways that curriculum can, the ways they can when using curriculum as a tool. And, of course, students are a key part of that interaction. And so, it's really thinking about those interactions among teachers, students, and materials and thinking about, “What are the strengths the materials bring? What are the strengths the teacher brings?” The teacher brings their knowledge of the students. The teacher brings their knowledge of the context. And the students bring, of course, their engagement and their interaction with those materials. And so, it's thinking about the strengths they each bring to that interaction, and it's in those interactions that equitable and responsive curriculum use happens. Mike: One of the things that jumps out from what you said is this notion that we're not actually attempting to fix “bad curriculum.” We're taking the position that curriculum has a set of assets, but it also has a set of limitations, and that's true regardless of the curriculum materials that you're using. Corey: Absolutely. This is not at all about curriculum being bad or not doing what it's supposed to do. This assumes that you're using a high-quality curriculum that does the things we just talked about that has that progression of learning, those sequences of tasks that brings ideas about how children learn and how we learn and teach mathematics. And then, to use that well and responsibly, the teacher then needs to work in ways, make decisions to enact that responsibly. It's not about fixing the curriculum. It's about using the curriculum in the most productive and responsive ways possible. Mike: I think that's good context, and I also think it's a good segue to talk about the three recommendations that we want educators to consider when they're thinking about, “What does it mean to be responsive when you're using curriculum?” So, just to begin with, why don't we just lay them out? Could you unpack them, Corey? Corey: Yeah, absolutely. But I will say that this is work you and I have developed together and looking at the work of others in the field. And we've really come up with, I think, three key criteria for thinking about responsive curriculum use. One is that it maintains the goals of the curriculum. So again, recognizing that one of the strengths of curriculum is that it's built on this progression of ideas and that it moves in a sequential way from the beginning of the year to the end of the year. We want teachers to be aware of, to understand what the goals are of any particular session or unit or year, and to stay true to those goals, to stay aligned with those goals. But at the same time, doing that in ways that open up opportunities for voice and choice and sensemaking for the specific students who are in front of them in that classroom. And then the last is, we're really concerned with and interested in supporting equitable practice. And so, we think about responsive curriculum use as curriculum use that reflects the equity-based practices that were developed by Julia Aguirre and her colleagues. Mike: I think for me, one of the things that hit home was thinking about this idea that there's a mathematical goal and that goal is actually part of a larger trajectory that the curriculum's designed around. And when I've thought about differentiation in the past, what I was really thinking about was replacement that fundamentally altered the instructional goal. And I think the challenge in this work is to say, “Am I clear on the instructional goal? And do the things that I'm considering actually maintain that for kids or are they really replacing them or changing them in a way that will alter or impact the trajectory?” Corey: I think that's such a critical point. And it's not easy work. It's not always clear even in materials that have a stated learning goal or learning target for a session. There's still work to do for the teacher to say, “What is the mathematical goal? Not the activity, not the task, but what is the goal? What is the understanding I'm trying to support for my students as they engage in this activity?” And so, you're right. I think the first thing is, teachers have to be super clear about that because all the rest of the decisions flow from understanding, “What is the goal of this activity, what are the understandings that I am trying to develop and support with this session? And then I can make decisions that are enhancing and providing access to that goal, but not replacing it. I'm not changing the goal for any of my students. I'm not changing the goal for my whole group of students. Instead, I'm recognizing that students will need different ways into that mathematics. Students will need different kinds of supports along the way. But all of them are reaching toward or moving toward that mathematical goal.” Mike: Yeah. When I think about some of the options, like potentially, number choice; if I'm going to try to provide different options in terms of number choice, is that actually maintaining a connection to the mathematical goal, or have I done something that altered it? Another thing that occurs to me is the resources that we share with kids for representation, be it manipulatives or paper, pencil, even having them talk about it—any of those kinds of choices. To what extent do they support the mathematical goal, or do they veer away from it? Corey: Yeah, absolutely. And there are times when different numbers or different tools or different models will alter the mathematical goal because part of the mathematical goal is to learn about a particular tool or a particular representation. And there are other times when having a different set of numbers or a different set of tools or models will only enhance students' access to that mathematical goal because maybe the goal is understanding something like two-digit addition and developing strategies for two-digit addition. Well then, students could reach that goal in a lot of different ways. And some students will be working just with decade numbers, and some students will be working with decades and ones, and some students will need number pieces, and others will do it mentally. But if the goal is developing strategies, developing your understanding of two-digit addition, then all of those choices make sense, all of those choices stay aligned with the goal. Corey: But if the goal is to understand how base ten pieces work, then providing a different model or telling students they don't need to use that model would, of course, fundamentally alter the goal. So, this is why it's so critically important that we support teachers in understanding, making sense of the goal, figuring out how do they figure that out. How do you open a set of curriculum materials, look at a particular lesson, and understand what the mathematical goal of that lesson is? And it's not as simple as just looking for the statement of the learning goal and the learning target. But it's really about, “What are the understandings that I think will develop or are intended to develop through this session?” Mike: I feel like we should talk a little bit about context, because context is such a powerful tool, right? If you alter the context, it might help kids surface some prior knowledge that they have. What I'm thinking about is this task that exists in Bridges where we're having kids look at a pet store where there are arrays of different sorts and kinds of dog foods or dog toys or cat toys. And I remember an educator saying to me, “I wonder if I could shift the context.” And the question that I asked her is, “If you look at this image that we're using to launch the task, what are the particular parts of that image that are critical to maintain if you're going to replace it with something that's more connected to your students?” Corey: Connecting to your students, using context to help students access the mathematics, is so important and such an empowering thing for teachers and students. But you're asking exactly the right question. And of course, that all relates to, “What's the mathematical goal?” Again. Because if I know that, then I can look for the features of the context that's in the textbook and see the ways in which that context was designed to support students in reaching that mathematical goal. But I can also look at a different context that might be more relevant to my students, that might provide them better access to the mathematics. And I can look at that context through the lens of that mathematical goal and see, “Does this context also present the kinds of features that will help my students understand and make sense of the mathematical goal?” And if the answer is yes, and if that context is also then more relevant to my students or more connected to their lives, then great. That's a wonderful adaptation. That's a great example of responsive curriculum use. If now I'm in a context that's distracting or leading me away from the mathematical goal, that's where we run into adaptations that are less responsive and less productive. Mike: Well, and to finish the example, the conversation that this led to with this educator was she was talking about looking for bodegas in her neighborhood that her children were familiar with, and we end up talking quite a bit about the extent to which she could find images from the local bodega that had different kinds of arrays. She was really excited. She actually did end up finding an image, and she came back, and she shared that this really had an impact on her kids. They felt connected to it, and the mathematical goal was still preserved. Corey: I love that. I think that's a great example. And I think the other thing that comes up sometimes when we present these ideas, is maybe you want to find a different context that is more relevant to your students that they know more about. Sometimes you might look at a context that's presented in the textbook and say, “I really love the mathematical features here. I really see how knowing something about this context could help my students reach the mathematical goal, but I'm going to have to do some work ahead of time to help my students understand the context, to provide them some access to that, to provide them some entry points.” So, in your example, maybe we're going to go visit a pet store. Maybe we're going to look at images from different kinds of stores and notice how things are arranged on shelves, and in arrays, and in different combinations. So, I think there are always a couple of choices. One is to change the context. One is to do some work upfront to help your students access the context so that they can then use that context to access the mathematics. But I think in both cases, it's about understanding the goal of the lesson and then understanding how the features of the context relate to that goal. Mike: Let's shift and just talk about the second notion, this idea of opening up space for students' voice or for sensemaking when you're using curriculum. For me at least, I often try to project ideas for practice into a mental movie of myself in a classroom. And I wonder if we could work to help people imagine what this idea of opening space for voice or sensemaking might look like. Corey: I think a lot of times those opportunities for opening up voice and choice and sensemaking are not in the direct, action steps or the direct instructions to teachers within the lesson, but they're kind of in the in-between. So, “I know I need to introduce this idea to my students, but how am I going to do that? What is that going to look like? What is that going to sound like? What are students going to be experiencing?” And so, asking yourself that question as the lesson plays out is, I think, where you find those opportunities to open up that space for student voice and choice. It's often about looking at that and saying, “Am I going to tell students this idea? Or am I going to ask them? Are students going to develop their strategy and share it with me or turn it in on a piece of paper? Or are they going to turn and talk to a partner? Are they going to share those ideas with a small group, with a whole group? What are they going to listen for in each other's strategies? How am I going to ask them to make connections across those strategies? What kinds of tools am I going to make available to them? What kinds of choices are they going to have throughout that process?” Corey: And so, I think it's having that mental movie play through as you read through the lesson and thinking about those questions all the way through. “Where are my students going to have voice? How are they going to have choice? How are students going to be sensemaking?” And often thinking about, “Where can I step back, as the teacher, to open up that space for student voice or student choice?” Mike: You're making me think about a couple things. The first one that really jumped out was this idea that part of voice is not necessarily always having the conversation flow from teacher to student, but having a turn and talk, or having kids listen to and engage with the ideas that their partners are sharing is a part of that idea that we're creating space for kids to share their ideas, to share their voice, to build their own confidence around the mathematics. Corey: Absolutely. I think that, to me, is the biggest difference I see when I go into different classrooms. “Whose voice am I hearing most often? And who's thinking do I know about when I've spent 20 minutes in a classroom?” And there are some classrooms where I know a lot about what the teacher's thinking. I don't know a lot about what the students are thinking. And there are other classrooms where I can tell you something about the thinking of every one of the students in that room after 10 minutes in that classroom because they're constantly turning and talking and sharing their ideas. Student voice isn't always out loud either, right? Students might be sharing their ideas in writing, they might be sharing their ideas through gestures or through manipulating models, but the ideas are communicating their mathematical thinking. Really, student communication might be an even better way to talk about that because there are so many different ways in which students can express their ideas. Mike: Part of what jumped out is this notion of, “What do you notice? What do you wonder?” Every student can notice, every student can wonder. So, if you share a context before you dive right into telling kids what's going to happen, give them some space to actually notice and wonder about what's going on, generate questions, that really feels like something that's actionable for folks. Corey: I think you could start every activity you did with a, “What do you notice? What do you wonder?” Students always have ideas. Students are always bringing resources and experiences and ideas to any context, to any task, to any situation. And so, we can always begin by accessing those ideas and then figuring out as teachers how we might build on those ideas, where we might go from there. I think even more fundamentally is just this idea that all students are sensemakers. All students bring brilliance to the classroom. And so ,what we need to do is just give them the opportunities to use those ideas to share those ideas, and then we as teachers can build on those ideas. Mike: Before we close this conversation, I want to spend time talking about responsive curriculum use being a vehicle for opening up space for equity-based practice. Personally, this is something that you've helped me find words for. There were some ideas that I had an intuitive understanding of. But I think helping people name what we mean when we're talking about opening space for equity-based practice is something that we might be able to share with folks right now. Can you share how a teacher might take up this idea of creating space for equity-based practice as they're looking at lessons or even a series of lessons? Corey: Yeah, absolutely. And I think student voice and choice are maybe outcomes of equity-based practices. And so, in a similar way, I think teachers can begin by looking at a lesson or a series of lessons and thinking about those spaces and those decisions in between the action steps. And again, asking a series of questions. The equity-based practices aren't a series of steps or rules, but really like a lens or a series of questions that as a teacher, you might ask yourself as you prepare for a lesson. So, “Who is being positioned as mathematically capable? Who's being positioned as having mathematically important ideas? Are all of my students being positioned in that way? Are some of my students being marginalized? And if some of my students are being marginalized, then what can I do about that? How could I physically move students around so that they're not marginalized? How can I call attention to or highlight a certain student's ideas without saying that those ideas are the best or only ideas? But saying, ‘Look, this student, who we might not have recognized before as mathematically capable and brilliant, has a really cool idea right now.'” Corey: You and I have both seen video from classrooms where that's done brilliantly by these small moves that teachers can make to position students as mathematically brilliant, as having important or cool or worthwhile ideas, valuable ideas to contribute. So, I think it's those kinds of decisions that make such a difference. Those decisions to affirm learners' identities. Those aren't big changes in how you teach. Those are how you approach each of those interactions minute by minute in the classroom. How do you help students recognize that they are mathematicians, that they each bring valuable ideas to the classroom? And so, it's more about those in-between moments and those moments of interaction with students where these equity-based practices come to life. Mike: You said a couple things that I'm glad that you brought out, Corey. One of them is this notion of positioning. And the other one that I think is deeply connected is this idea of challenging places where kids might be marginalized. And I think one of the things that I've been grappling with lately is that there's a set of stories or ideas and labels that often follow kids. There are labels that we affix to kids within the school system. There are stories that exist around the communities that kids come from, their families. And then there are also the stories that kids make up about one another, the ideas that carry about, “Who's good at math? Who's not? Who has ideas to share? Who might I listen to, and who might I not?” And positioning, to me, has so much opportunity as a practice to help press back against those stories that might be marginalizing kids. Corey: I think that's such an important point. And I think, along with that is the recognition that this doesn't mean that you, as the individual teacher, created those stories or believed stories or did anything to perpetuate those stories—except if you didn't act to disrupt them. Because those stories come from all around us. We hear Pam Seda and Julia Aguirre and people like that saying, “They're the air we breathe. They're the smog we live in. Those stories are everywhere. They're in our society, they're in our schools, they're in the stories students tell and make up about each other.” And so, the key to challenging marginality is not to say, “Well, I didn't tell that story, I don't believe that story. But those stories exist, and they affect the children in my classroom, so what am I going to do to disrupt them? What am I going to do? Because I know the stories that are told about certain students, even if I'm not the one telling them, I know what those stories are. So how am I going to disrupt them to show that the student who the story or the labels about that student are, that they are not as capable, or they are behind or struggling or ‘low students.' What am I going to do to disrupt that and help everyone in our classroom community see the brilliance of that child, understand that that child has as much to contribute as anybody else in the math classroom?” And that's what it means to enact equity-based practices. Mike: You're making me think about an interview we did earlier this year with Peter Liljedahl, and he talked about this idea. He was talking about it in the context of grouping, but essentially what he was saying is that kids recognize the stories that are being told in a classroom about who's competent and who's not. And so, positioning, in my mind, is really thinking about—and I've heard Julia Aguirre say it this way—“Who needs to shine? Whose ideas can we bring to the center?” Because what I've come to really have a better understanding of, is that the way I feel about myself as a mathematician and the opportunities that exist within a classroom for me to make sense of math, those are really deeply intertwined. Corey: Yes, yes, absolutely. We are not focusing on marginality or identity just because it makes people feel good, or even just because it's the right thing to do. But actually in the math classroom, your identity and the expectations and the way you're positioned in that classroom fundamentally affect what you have opportunities to learn and the kinds of math you have access to. And so, we will do this because it's the right thing to do and because it supports math learning for all students. And understanding the role of identity and marginality and positioning in student learning is critically important. Mike: You're making me think about a classroom that we visited earlier this year, and it was a really dynamic math discussion. There was a young man, I'll call him David, and he was in a multilingual classroom. And I'm thinking back on what you said. At one point you said, “I can go into a classroom, and I can have a really clear idea of what the teacher understands, and perhaps less so with the kids.” In this case, I remember leaving thinking, “I really clearly understand that David has a deep conceptual understanding of the mathematics.” And the reason for that was, he generally volunteered to answer every single question. And it was interesting. It's not because the educator in the classroom was directing all of the questions to him, but I really got the sense that the kids, when the question was answered, were to almost turn their bodies because they knew he was going to say something. And it makes me think David is a kid who, over time, not necessarily through intention, but through the way that status works in classrooms, he was positioned as someone who really had some ideas to share, and the kids were listening. The challenge was, not many of them were talking. And so, the question is, “How do we change that? Not because anyone has any ill intent toward those other children, but because we want them to see themselves as mathematicians as well.” Corey: Yeah, absolutely. And that is part of what's tricky about this is that that's so important is that I think for many years we've talked about opening up the classroom for student talk and student discourse. And we do turn and talks, and we do think pair shares. And we've seen a lot of progress, I think, in seeing those kinds of things in math classrooms. And I think the next step to that is to do those with the kind of intentionality and awareness that you were just demonstrating there; which is to say, “Well, who's talking and how often are they talking? And what sense are people making of the fact that David is talking so much? What sense are they making? What stories are they telling about who David is as a mathematician? But also who they are as mathematicians. And what does it mean to them that even though there are lots of opportunity for students talk in that classroom, it's dominated by one or maybe two students. And so, we have opened it up for student discourse, but we have more work to do. We have more work to say, “Who's talking, and what sense are they making, and what does that look like over time? And how is mathematical authority distributed? How is participation distributed across the class? And, in particular, with intentionality toward disrupting some of those narratives that have become entrenched in classrooms and schools.” Mike: I think that's a great place for us to stop. I want to thank you again for joining us, Corey. It was lovely to have you back on the podcast. Corey: Thanks. It was great to be with you. Mike: 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. © 2024 The Math Learning Center | www.mathlearningcenter.org 

This edWeb podcast is sponsored by The Modern Classrooms Project.The webinar recording can be accessed here.Building Thinking Classrooms in Mathematics by Peter Liljedahl has taken the mathematics education world by storm for its innovative pedagogical approach transforming classrooms into thinking classrooms.For an educator starting to build or already has the blended, self-paced, and mastery-based learning structures in place, the thought of integrating additional strategies can feel daunting and redundant. So why should an educator implement building thinking classrooms practices? If so, how are the practices best applied in a student-centered classroom?This edWeb podcast dives into the what, why, and how of implementing building thinking classrooms practices within the blended, self-paced, mastery-based learning structures of a blended, self-paced, and mastery-based learning.We explore:The 14 elements and 4 implementation toolkits of Building Thinking Classrooms in Mathematics by Peter LiljedahlThe rationale for instructional pedagogy that balances collaborative and independent learning to support deeper learningPractical integration of building thinking classrooms practices in a blended, self-paced, mastery-based learning structureWhen the practices can be implementedHow to scaffold implementation efficacy through the four toolkitsWhat a teacher can do to start tomorrowDiscover how to bring the best of two worlds together for the benefit of student learning. Leave with actionable steps to integrate building thinking classroom practices in your classroom! This edWeb podcast is of interest to teachers, school leaders, district leaders, and education technology leaders of all grade levels.The Modern Classrooms ProjectMeet every student's needs with classroom-tested techniques that help every student truly learn. Disclaimer: This post contains affiliate links. If you make a purchase, I may receive a commission at no extra cost to you.Learn more about viewing live edWeb presentations and on-demand recordings, earning CE certificates, and using accessibility features.

Rounding Up Season 3 | Episode 1 – Grouping Practices That Promote Efficacy and Knowledge Transfer Guest: Dr. Peter Liljedahl Mike Wallus: We know from research that student collaboration can have a powerful impact on learning. That said, how we group students for collaboration matters—a lot. Today we're talking with Dr. Peter Liljedahl, author of “Building Thinking Classrooms in Mathematics,” about how educators can form productive, collaborative groups in their classrooms. Mike: Hello, Peter. Welcome to the podcast. Peter Liljedahl: Thanks for having me. Mike: So, to offer our listeners some background, you've written a book, called “Building Thinking Classrooms in Mathematics,” and I think it's fair to say that it's had a pretty profound impact on many educators. In the book, you address 14 different practices. And I'm wondering if you could weigh in on how you weigh the importance of the different practices that you addressed? Peter: Well, OK, so, first of all, 14 is a big number that publishers don't necessarily like. When we first started talking with Corwin about this, they were very open. But I know if you think about books, if there's going to be a number in the title, the number is usually three, five or seven. It's sometimes eight—but 14 is a ridiculous number. They can't all be that valuable. What's important about the fact that it's 14, is that 14 is the number of core practices that every teacher does. That's not to say that there aren't more or less for some teachers, but these are core routines that we all do. We all use tasks. We all create groups for collaboration. We all have the students work somewhere. We all answer questions. We do homework, we assign notes, we do formative, summative assessment. We do all of these things. We consolidate lessons. We launch lessons. Peter: These are sort of the building blocks of what makes our teaching. And through a lot of time in classrooms, I deduced this list of 14. Robert Kaplinsky, in one of his blog posts, actually said that he thinks that that list of 14 probably accounts for 95 percent of what happens in classrooms. And my research was specifically about, “How do we enact each of those 14 so that we can maximize student thinking? So, what kind of tasks get students to think, how can we create groups so that more thinking happens? How can we consolidate a lesson so we get more thinking? How can we do formative and summative assessments so the students are thinking more?” So, the book is about responding to those 14 core routines and the research around how to enact each of those to maximize thinking. Your question around which one is, “How do we put weight on each of these?” Peter: They're all important. But, of course, they're not all equally impactful. Building thinking classrooms is most often recognized visually as the thing where students are standing at whiteboards working. And, of course, that had a huge impact on student engagement and thinking in the classroom, getting them from sitting and working at desks to getting them working at whiteboards. But in my opinion, it's not the most impactful. It is hugely impactful, but the one that actually makes all of thinking classroom function is how we form collaborative groups, which is chapter two. And it seems like that is such an inconsequential thing. “We've been doing groups for forever, and we got this figured out. We know how to do this. But … do we really? Do we really have it figured out?” Because my research really showed that if we want to get students thinking, then the ways we've been doing it aren't working. Mike: I think that's a great segue. And I want to take a step back, Peter. Before we talk about grouping, I want to ask what might be an obvious question. But I wonder if we can talk about the “why” behind collaboration. How would you describe the value or the potential impact of collaboration on students' learning experiences? Peter: That's a great question. We've been doing collaborative work for decades. And by and large, we see that it is effective. We have data that shows that it's effective. And when I say “we,” I don't mean me or the people I work with. I mean “we, in education,” know that collaboration is important. But why? What is it about collaboration that makes it effective? There are a lot of different things. It could be as simple as it breaks the monotony of having to sit and listen. But let's get into some really powerful things that collaboration does. Number one, about 25 years ago, we all were talking about metacognition. We know that metacognition is so powerful and so effective, and if we get students thinking about their thinking, then their thinking actually improves. And metacognition has been shown time and time again to be impactful in learning. Some of the listeners might be old enough to remember the days where we were actually trying to teach students to be metacognitive, and the frustration that that created because it is virtually impossible. Peter: Being reflective about your thinking while you're thinking is incredibly hard to do because it requires you to be both present and reflective at the same time. We're pretty good at being present, and we're pretty good about reflecting on our experiences. But to do both simultaneously is incredibly hard to do. And to teach someone to do it is difficult. But I think we've also all had that experience where a student puts up their hand, and you start walking over to them, and just as you get there, they go, “Never mind.” Or they pick up their book, and they walk over to you, and just as they get to you, they just turn around and walk back. I used to tell my students that they're smarter when they're closer to me. But what's really going on there is, as they've got their hand up, or as they're walking across the room toward you as a teacher, they're starting to formulate their thoughts to ask a question. Peter: They're preparing to externalize their thinking. And that is an incredibly metacognitive process. One of the easiest forms of metacognition, and one of the easiest ways to access metacognition, is just to have students collaborate. Collaborating requires students to talk. It requires them to organize their thoughts. It requires them to prepare their thinking and to think about their thinking for the purposes of externalization. It is an incredibly accessible way of creating metacognition in your classroom, which we already know is effective. So, that's one reason I think collaboration is really, really vital. Peter: Another one comes from the work on register. So, register is the level of sophistication with which we speak about something. So, if I'm in a classroom, and I'm talking to kindergarten students, I set a register that is accessible to them. When I talk to my undergraduates, I use a different register. My master's students, my Ph.D. students, my colleagues, I'm using different registers. I can be talking about the same thing, but the level of sophistication with which I'm going to talk about those things varies depending on the audience. And as much as possible, we try to vary our register to suit the audience we have. But I think we've also all had that instructor who's completely incapable of varying their register, the one who just talks at you as if you're a third-year undergraduate when you're really a Great Eight student. And the ability to vary our register to a huge degree is going to define what makes us successful as a teacher. Can we meet our learners where they're at? Can we talk to them from the perspective that they're at? Now we can work at it, and very adept teachers are good at it. But even the best teachers are not as good at getting their register to be the same as students. Peter: So, this is another reason collaboration is so effective. It allows students to talk and be talked to at their register, which is the most accessible form of communication for them. And I think the third reason that collaboration is so important is the difference between what I talk in my book about the difference between absolute and tentative knowledge. So, I'm going to make two statements. You tell me which one is more inviting to add a comment to. So, statement number one is, “This is how to do it, or this is what I did.” That's statement number one. Statement number two is, “I think that one of the ways that we may want to try, I'm wondering if this might work.” Which one is more inviting for you to contribute to? Mike: Yes, statement number two, for many, many reasons, as I'm sitting here thinking about the impact of those two different language structures. Peter: So, as teachers, we tend to talk in absolutes. The absolute communication doesn't give us anything to hold onto. It's not engaging. It's not inviting. It doesn't bring us into the conversation. It's got no rough patches—it's just smooth. But when that other statement is full of hedging, it's tentative. It's got so many rough patches, so many things to contribute to, things I want to add to, maybe push back at or push further onto. And that's how students talk to each other. When you put them in collaborative groups, they talk in tentative discourse, whereas teachers, we tend to talk in absolutes. So, students are always talking to each other like that. When we put them in collaborative groups, they're like, “Well, maybe we should try this. I'm wondering if this'll work. Hey, have we thought about this? I wonder if?” And it's so inviting to contribute to. Mike: That's fascinating. I'm going to move a little bit and start to focus on grouping. So, in the book, you looked really closely at the way that we group students for collaborative problem-solving and how that impacts the way students engage in a collaborative effort. And I'm wondering if you could talk a little bit about the type of things that you were examining. Peter: OK. So, you don't have to spend a lot of time in classrooms before you see the two dominant paradigms for grouping. So, the first one we tend to see a lot at elementary school. So, that one is called “strategic grouping.” Strategic grouping is where the teacher has a goal, and then they're going to group their students to satisfy that goal. So, maybe my goal is to differentiate, so I'm going to make ability groups. Or maybe my goal is to increase productivity, so I'm going to make mixed-ability groups. Or maybe my goal is to just have peace and quiet, so I'm going to keep those certain students apart. Whatever my goal is, I'm going to create the groups to try to achieve that goal, recognizing that how students behave in the classroom has a lot to do with who they're partnered with. So that's strategic grouping. It is the dominant grouping paradigm we see in elementary school. Peter: By the time we get to high school, we tend to see more of teachers going, “Work with who you want.” This is called “self-selected groupings.” And this is when students are given the option to group themselves any way they want. And alert: They don't group themselves for academic reasons, they group themselves for social reasons. And I think every listener can relate to both of those forms of grouping. It turns out that both of those are highly ineffective at getting students to think. And ironically, for the exact same reason. We surveyed hundreds of students who were in these types of grouping settings: strategic grouping or self-selected groupings. We asked one question, “If you knew you were going to work in groups today, what is the likelihood you would offer an idea?” That was it. And 80 percent of students said that they were unlikely or highly unlikely to offer an idea, and that was the exact same, whether they were in strategic groupings or self-selected groupings. The data cut the same. Mike: That's amazing, Peter. Peter: Yeah, and it's for the same reason it turns out; that whether students were being grouped strategically or self-selected, they already knew what their role was that day. They knew what was expected of them. And for 80 percent of the students, their role is not to think. It's not to lead. Their role is to follow, right? And that's true whether they're grouping themselves socially, where they already know the social hierarchy of this group, or they're being grouped strategically. We interviewed hundreds of students. And after grade 3, every single student could tell us why they were in the group this teacher placed them in. They know. They know what you think of them. You're communicating very clearly what you think their abilities are through the way you group them, and then they live down to that expectation. So, that's what we were seeing in classrooms was that strategic grouping may be great at keeping the peace. And self-selected grouping may be fabulous for getting students to stop whining about collaboration. But neither of them was effective for getting students to think. In fact, they were quite the opposite. They were highly ineffective for getting students to think. Mike: So, I want to keep going with this. And I think one of the things that stood out for me as I was reading is, this notion that regardless of the rationale that a teacher might have for grouping, there's almost always a mismatch between what the teacher's goals are and what the student's goals are. I wonder if you could just unpack this and maybe explain this a bit more. Peter: So, when you do strategic grouping, do you really think the students are with the students that they want to be with? One of the things that we saw happening in elementary school was that strategic grouping is difficult. It takes a lot of effort to try to get the balance right. So, what we saw was teachers largely doing strategic grouping once a month. They would put students into a strategic group, and they would keep them in that group for the entire month. And the kids care a lot about who they're with, when you're going to be in a group for a month. And do you think they were happy with everybody that was in that group? If I'm going to be with a group of students for a month, I'd rather pick those students myself. So, they're not happy. You've created strategic groupings. And, by definition, a huge part of strategic grouping is keeping kids who want to be together away from each other. Peter: They're not happy with that. Self-selected groupings, the students are not grouping themselves for academic reasons. They're just grouping themselves for social reasons so that they can socialize, so they talk, so they can be off topic, and all of these things. And yes, they're not complaining about group work, but they're also not being productive. So, the students are happy. But do you think the teacher's happy? Do you think the teacher looks out across that room and goes, “Yeah, there were some good choices made there.” No, nobody's happy, right? If I'm grouping them strategically, that's not matching their goals. That's not matching their social goals. When they're grouping themselves in self-selected ways, that's matching their social goals but not matching my academic goals for them. So, there's always going to be this mismatch. The teacher, more often than not, has academic goals. The students, more often than not, have social goals. There are some overlaps, right? There are students who are like, “I'm not happy with this group. I know I'm not going to do well in this group. I'm not going to be productive.” And there are some teachers who are going, “I really need this student to come out of the shell, so I need to get them to socialize more.” But other than that, by and large, our goals as teachers are academic in nature. The goals as students are social in nature. Mike: I think one of the biggest takeaways from your work on grouping, for me at least, was the importance of using random groups. And I have to admit, when I read that there was a part of me thinking back to my days as a first-grade teacher that felt a little hesitant. As I read, I came to think about that differently. But I'm wondering if you can talk about why random groups matter, the kind of impact that they have on the collaborative experience and the learning experience for kids. Peter: Alright, so going back to the previous question. So, we have this mismatch. And we have also that 80 percent of students are not thinking; 80 percent of students are entering into that group, not prepared to offer an idea. So those are the two problems that we're trying to address here. So, random groups … random wasn't good enough. It had to be visibly random. The students had to see the randomness because when we first tried it, we said, “Here's your random groups.” They didn't believe we were being random. They just thought we were being strategic. So, it has to be visibly random, and it turns out it has to be frequent as well. About once every 45 to 75 minutes. See, when students are put into random groups, they don't know what their role is. So, we're solving this problem. They don't know what their role is. When we started doing visibly random groups frequently, within three weeks we were running that same survey. Peter: “If you know you're going to work in groups today, what is the likelihood you would offer an idea?” Remember the baseline data was that 80 percent of students said that they were unlikely or highly unlikely, and, all of a sudden, we have a hundred percent of students saying that they're likely or highly likely. That was one thing that it solved. It shifted this idea that students were now entering groups willing to offer an idea, and that's despite 50 percent of them saying, “It probably won't lead to a solution, but I'm going to offer an idea.” Now why is that? Because they don't know what their role is. So, right on the surface, what random groups does, is it shatters this idea of preconceived roles and then preconceived behaviors. So, now they enter the groups willing to offer an idea, willing to be a contributor, not thinking that their role is just to follow. But there's a time limit to this because within 45 to 75 minutes, they're going to start to fall into roles. Peter: In that first 45 minutes, the roles are constantly negotiated. They're dynamic. So, one student is being the leader, and the others are being the follower. And now, someone else is a leader, the others are following. Now everyone is following. They need some help from some external source. Now everyone is leading. We've got to resolve that. But there is all of this dynamicism and negotiation going on around the roles. But after 45 to 75 minutes, this sort of stabilizes and now you have sort of a leader and followers, and that's when we need to randomize again so that the roles are dynamic and that the students aren't falling into sort of predefined patterns of non-thinking behavior. Mike: I think this is fascinating because we've been doing some work internally at MLC around this idea of status or the way that … the stories that kids tell about one another or the labels that kids carry either from school systems or from the community that they come from, and how those things are subtle. They're unspoken, but they often play a role in classroom dynamics in who gets called on. What value kids place on a peer's idea if it is shared. What you're making me think is there's a direct line between this thing that we've been thinking about and what happens in small groups as well. Peter: Yeah, for sure. So, you mentioned status. I want to add to that identity and self-efficacy and so on and so forth. One of the interesting pieces of data that came out of the research into random groups was, we were interviewing students several weeks into this. And we were asking them questions around this, and the students were saying things like, “Oh, the teacher thinks we're all the same, otherwise they wouldn't do random groups. The teacher thinks we're all capable, otherwise they wouldn't do random groups.” So, what we're actually talking about here is that we're starting—just simply through random groups—to have a positive impact on student self-efficacy. One of the things that came out of this work, that I wrote about in a separate paper, was that we've known for a long time that student self-efficacy has a huge impact on student performance. But how do we increase, how do we improve student self-efficacy? Peter: There are a whole bunch of different ways. The work of Bandura on this is absolutely instrumental. But it comes down to a couple of things. From a classroom teacher perspective, the first thing, in order for a student to start on this journey from low self-efficacy to high self-efficacy, they have to encounter a teacher who believes in them. Except students don't listen to what we say. They listen to what we do. So, simply telling our students that we have confidence in them doesn't actually have much impact. It's how we show them that we have confidence in them. And it turns out that random groups actually have a huge impact on that. By doing the random groups, we're actually showing the kids that we believe in them and then they start to internalize this. So that's one thing. The work of Bandura about how we can start to shift student self-efficacy through mastery experiences, where they start to, for example, be successful at something. And that starts to have an impact that is amplified when students start to be successful in front of others, when they are the ones who are contributing in a small group. And that group is now successful. And that success is linked in some small or great part to your contributions; that self-efficacy is amplified because not only am I being successful, I'm being successful in a safe environment, but in front of others. Peter: Now, self-efficacy contributes to identity, and identity has an interesting relationship with status. And you mentioned status. So, self-efficacy is what I think of myself. Status is what others think of me. I can't control my status. I can't shift my status. Status is something that is bestowed on me by others. And, of course, it's affected by their interactions with me in collaborative spaces. So, how they get to see me operate is going to create a status for me, on me, by others. But the status gets to be really nicely evenly distributed in thinking classrooms when we're doing these random groups because everybody gets to be seen as capable. They all get to be someone who can be mathematical and someone who can contribute mathematically. Mike: I want to shift back for a moment to this idea of visibly random groups. This idea that for kids, they need to believe that it's not just a strategic grouping that I've called random for the sake of the moment. What are some of the ways that you've seen teachers visibly randomize their groups so that kids really could see the proof was right out there in front of them? Peter: So, we first started with just cards. So, we got 27 kids. We're going to use playing cards, we're going to have three aces, three 2S, three 3s, three 4s, and so on. We would just shuffle the deck, and the kids would come and take a card. And if you're a 4, you would go to the board that has a 4 on it. Or maybe that fourth 4 is there, so to speak. We learned a whole bunch of things. It has to be visible. And however way we do it, the randomization doesn't just tell them what group they're in, it tells them where to go. That's an efficiency thing. You don't want kids walking around the classroom looking for their partners and then spending 5 minutes deciding where they want to work. Take a card, you got a 7, you go to the 7 board. You got an ace, you go to the ace board. Peter: And that worked incredibly well. Some teachers already had Popsicle sticks in their classroom, so they started using those: Popsicle sticks with students' names. So, they would pull three Popsicle sticks and they would say, “OK, these students are together. These students are together.” At first, we didn't see any problems with that. That seemed to be pretty isomorphic … to using a playing card. Some teachers got frustrated with the cards because with a card, sometimes what happens is that they get ripped or torn or they don't come back. Or they come back, and they're sweaty or they're hot. And it's like, “OK, where were you keeping this card? I don't want to know. It's hot, it's dirty.” They got ink on it. The cards don't come back. The kids are swapping cards. And teachers were frustrated by this. So, they started using digital randomizers, things like Flippity and ClassDojo and Picker Wheel and Team Shake and Team Maker. Peter: There were tons of these digital randomizers, and they all work pretty much the same. But there was a bit of a concern that the students may not perceive the randomness as much in these methods. And you can amplify that by, for example, bringing in a fuzzy [die], a big one, and somebody gets to roll it. And if a 5 comes up, they get to come up and hit the randomized button five times. And now there's a greater perception of randomness that's happening. With Flippity, that turns out actually it'd be true. Turns out that the first randomization is not purely random, and the kids spot that pattern. And we thought, “OK, perfect. That's fine. As long as the students perceive it's random, that it is truly random, that the teacher isn't somehow hacking this so that they are able to impose their own bias into this space.” So, it's seemingly random, but not purely random. And everything was running fine until about six to eight months ago. I was spending a lot of time in classrooms. I think in the last 14 months I've been in 144 different classrooms, co-teaching or teaching. So, I was spending a lot of time in classrooms, and for efficiency's sake, a lot of these teachers were using digital randomizers. And then I noticed something. It had always been there, but I hadn't noticed it. This is the nature of research. It's also the nature of just being a fly on the wall, or someone who's observing a classroom or a teacher. There's so much to notice we can't notice it all. So, we notice the things that are obvious. The more time we spend in spaces, the more nuanced things we're able to notice. And about six to eight months ago, I noticed something that, like I said, has always been there, but I had never really noticed it. Peter: Teacher hits a randomized button, and all the students are standing there watching, waiting for the randomized groups to appear on the screen. And then somebody goes, “Ugh.” It's so small. Or somebody laughs. Or somebody's like, “Nooo.” And it's gone. It's in a moment, it's gone. Sometimes others snicker about it, but it's gone. It's a flash. And it's always been there, and you think it's not a big deal. Turns out it's a huge deal because this is a form of micro-bullying. This is what I call it, “micro-bullying.” Because when somebody goes, “Ugh,” everybody in the room knows who said it. And looking at the screen, they know who they said it about. And this student, themself, knows who said it, and they know that they're saying it about them. And what makes this so much worse than other overt forms of bullying is that they also are keenly aware that everybody in the room just witnessed and saw this happen, including the teacher. Peter: And it cuts deeply. And the only thing that makes bullying worse is when bullying happens in front of someone who's supposed to protect you, and they don't; not because we're evil, but because it's so short, it's so small, it's over in a flash. We don't really see the magnitude of this. But this has deep psychological effects and emotional effects on these students. Not just that they know that this person doesn't like them. But they know that everybody knows that they don't like them. And then what happens on the second day? The second day, whoever's got that student, that victimized student in their group, when the randomization happens, they also go, “Ugh,” because this has become acceptable now. This is normative. Within a week, this student might be completely ostracized. And it's just absolutely normal to sort of hate on this one student. Peter: It's just not worth it. It cuts too deeply. Now you can try to stop it. You can try to control it, but good luck, right? I've seen teachers try to say, “OK, that's it. You're not allowed to say anything when the randomization happens. You're not allowed to cheer, you're not allowed to grunt, you're not allowed to groan, you're not allowed to laugh. All you can do is go to your boards.” Then they hit the random, and immediately you hear someone go, “Ugh.” And they'll look at them, and the student will go, “What? That's how I breathe.” Or “I stubbed my toe where I thought of something funny.” It's virtually impossible to shut it down because it's such a minor thing. But seemingly minor. In about 50 percent of elementary classrooms that I'm in, where a teacher uses that digital randomizer, you don't hear it. But 50 percent you do. Almost 100 percent of high school classrooms I'm in you hear some sort of grunt or groan or complaint. Peter: It's not worth it. Just buy more cards. Go to the casino, get free cards. Go to the dollar store, get them cheap. It's just not worth it. Now, let's get back to the Popsicle stick one. It actually has the same effect. “I'm going to pull three names. I'm going to read out which three names there are, and I'm going to drop them there.” And somebody goes, “Ugh.” But why does this not happen with cards? It doesn't happen with cards because when you take that card, you don't know what group you're in. You don't know who else is in your group. All you know is where to go. You take that card, you don't know who else is in your group. There's no grunting, groaning, laughing, snickering. And then when you do get to the group, there might be someone there that you don't like working with. So, the student might go, “Ugh.” But now there's no audience to amplify this effect. And because there's no audience, more often than not, they don't bother going, “Ugh.” Go back to the cards, people. The digital randomizers are fast and efficient, but they're emotionally really traumatizing. Mike: I think that's a really subtle but important piece for people who are thinking about doing this for the first time. And I appreciate the way that you described the psychological impact on students and the way that using the cards engineers less of the audience than the randomizer [do]. Peter: Yeah, for sure. Mike: Well, let's shift a little bit and just talk about your recommendations for group size, particularly students in kindergarten through second grade as opposed to students in third grade through fifth grade. Can you talk about your recommendations and what are the things that led you to them? Peter: First of all, what led to it? It was just so clear, so obvious. The result was that groups of three were optimal. And that turned out to be true every setting, every grade. There are some caveats to that, and I'll talk about that in a minute. But groups of three were obvious. We saw this in the data almost immediately. Every time we had groups of three, we heard three voices. Every time we heard groups of four, we heard three voices. When we had groups of five, we heard two voices on task, two voices off task, and one voice was silent. Groups of three were just that sort of perfect, perfect group size. It took a long time to understand why. And the reason why comes from something called “complexity theory.” Complexity theory tells us that in order for a group to be productive, it has to have a balance between diversity and redundancy. Peter: So, redundancy is the things that are the same. We need redundancy. We need things like common language, common notation, common vocabulary, common knowledge. We need to have things in common in order for the collaboration to even start. But if all we have is redundancy, then the group is no better than the individual. We also have to have diversity. Diversity is what every individual brings to the group that's different. And the thing that happens is, when the group sizes get larger, the diversity goes up, but redundancy goes down. And that's bad. And when the group sizes get smaller, the redundancy goes up, but the diversity goes down. And that's bad. Groups of three seem to have this perfect balance of redundancy and diversity. It was just the perfect group size. And if you reflect on groups that you've done in your settings, whatever that setting was, you'll probably start to recognize that groups of three were always more effective than groups of four. Peter: But we learned some other things. We learned that in K–2, for example, groups of three were still optimal, but we had to start with groups of two. Why? Because very young children don't know how to collaborate yet. They come to school in kindergarten, they're still working in what we call “parallel,” which means that they'll happily stand side by side at a whiteboard with their own marker and work on their own things side by side. They're working in parallel. Eventually, we move them to a state that we call “polite turn-taking.” Polite turn-taking is we can have two students working at a whiteboard sharing one marker, but they're still working independently. So, “It's now your turn and you're working on your thing, and now it's my turn, I'm working on my thing.” Eventually, we get them to a state of collaboration. And collaboration is defined as “when what one student says or does affects what the other student says or does.” Peter: And now we have collaboration happening. Very young kids don't come to school naturally able to collaborate. I've been in kindergarten classrooms in October where half the groups are polite turn-taking, and half the groups are collaborating. It is possible to accelerate them toward that state. But I've also been in grade 2 classrooms in March where the students are still working in parallel or turn-taking. We need to work actively at improving the collaboration that's actually happening. Once collaboration starts to happen in those settings, we nurtured for a while and then we move to groups of three. So, I can have kindergartens by the end of the year working in groups of three, but I can't assume that grade 2s can do it at the beginning of the year. It has a lot to do with the explicit efforts that have been made to foster collaboration in the classroom. And having students sit side by side and pair desks does not foster collaboration. It fosters parallel play. Peter: So, we always say that “K–2, start with groups of two, see where their level of collaboration is, nurture that work on it, move toward groups of three.” The other setting that we had to start in groups of two were alternate ed settings. Not because the kids can't collaborate, but because they don't trust yet. They don't trust in the process in the educational setting. We have to nurture that. Once they start to trust in working in groups of two, we can move to groups of three. But the data was clear on this. So, if you have a classroom, and let's say you're teaching grade 6, and you don't have a perfect multiple of three, what do you do? You make some groups of two. So, rather than groups of four, make some groups of two. Keep those groups of two close to each other so that they may start to collaborate together. Peter: And that was one of the ironies of the research: If I make a group of four, it's a Dumpster fire. If I make two groups of two and put them close to each other, and they start to talk to each other, it works great. You start with groups of two. So, having some extra groups of two is handy if you're teaching in high school or any grade, to be honest. But let's say you have 27 students on your roster, but only 24 are there. There's going to be this temptation to make eight groups of three. Don't do it. Make nine groups, have a couple of groups of two. Because the minute you get up and running, someone's going to walk in late. And then when they walk in late, it's so much easier to plug them into a group of two than to have them waiting for another person to come along so that they can pair them or to make a group of four. Mike: Yeah, that makes sense. Before we close, Peter, I want to talk about two big ideas that I really wish I would've understood more clearly when I was still in the classroom. What I'm thinking about are the notion of crossing social boundaries and then also the concept of knowledge mobility. And I'm wondering if you could talk about each of them in turn and talk about how they relate to one another. Peter: Certainly. So, when we make our groups, when we make groups, groups are very discreet. I think this comes from that sort of strategic grouping, or even self-selected groupings where the groups are really separate from each other. There are very well-defined boundaries around this group, and everything that happens, happens inside that group, and nothing happens between groups. In fact, as teachers, we often encourage that, and we're like, “No, do your own work in your group. Don't be talking to the other groups.” Because the whole purpose of doing strategic groups is to keep certain kids away from each other, and that creates a very non-permeable boundary between the groups. But what if we can make these boundaries more porous, and so that knowledge actually starts to flow between the groups. This is what's called “knowledge mobility,” the idea that we don't actually want the knowledge to be fixed only inside of a group. Peter: The smartest person in the room is the room. We got to get that knowledge moving around the room. It's not groups, it's groups among groups. So, how can we get what one group is achieving and learning to move to another group that's maybe struggling? And this is called “knowledge mobility.” The easiest way to increase this is we have the students working at vertical whiteboards. Working at vertical whiteboards creates a space where passive knowledge mobility is really easy to do. It's really easy to look over your shoulder and see what another group is doing and go, “Oh, let's try that. They made a table of values. Let's make a table of values. Or they've done a graph, or they drew a picture” or whatever. “We'll steal an idea.” And that idea helps us move forward. And that passive can also lead to more active, where it's like, “I wonder what they're doing over there?” Peter: And then you go and talk to them, and the teacher can encourage this. And both of these things really help with mobilizing knowledge, and that's what we want. We don't want the only source of knowledge to be the teacher. Knowledge is everywhere. Let's get that moving around the room within groups, between groups, between students. And that's not to say that the students are copying. We're not encouraging copying. And if you set the environment up right, they don't copy. They're not going to copy. They'll steal an idea, “Oh, let's organize our stuff into a table of values,” and then it's back to their own board and working on that. And the other way that we help make these boundaries more porous is by breaking down the social barriers that exist within a classroom. All classrooms have social barriers. They could be gender, race. They could be status-based. Peter: There are so many things that make up the boundaries that exist within classrooms. There are these social structures that exist in schools. And one of the things that random groups does is it breaks down these social barriers because we're putting students together that wouldn't normally be together. And our data really reveals just how much that happens; that after three weeks, the students are coming in, they're socializing with different students, students that hadn't been part of their social structure before. They're sitting together outside of class. I see this at the university where students are coming in, they almost don't know each other at all. Or they're coming in small groups that are in the same class. They know each other from other courses, and within three, four weeks, I'm walking through the hallways at the university and I'm seeing them sitting together, working together, even having lunch together in structures that didn't exist on day one. There are so many social structures, social barriers in classrooms. And if we can just erode those barriers, those group structures are going to become more and more porous, and we're creating more community, and we're reducing the risk that exists within those classrooms. Mike: I think the other piece that jumps out for me is when I go back to this notion of one random grouping, a random grouping that shifts every 45 to 75 minutes. This idea of breaking those social boundaries—but also, really this idea that knowledge mobility is accelerated jumps out of those two practices. I can really see that in the structure and how that would encourage that kind of change. Peter: Yeah. And it encourages both passively and actively. Passive in the sense that students can look over the shoulder, active that they can talk to another group. But also passively from the teacher perspective, that random groups does a lot of that heavy lifting. But I can also encourage it actively when a group asks a question. Rather than answering their question, looking around the room going, “You should go talk to the sevens over there.” Or “We're done. What do we do next?” “Go talk to the fours. They know what's next.” That, sort of, “I as a teacher can be passive and let the random groups do a lot of the heavy lifting. But I can also be active and push knowledge around the room. By the way, I respond to students' questions.” Mike: Well, and I think what also strikes me is you're really distributing the authority mathematically to the kids as well. Peter: Yeah, so we're displacing status, we're increasing identity. We're doing all sorts of different things that are de-powering the classroom, decentralizing the classroom. Mike: Well, before we go, Peter, I'm wondering if there are any steps that you'd recommend to an educator who's listening. They want to start to dabble, or they want to take up some of the ideas that we've talked about. Where would you invite people to make a start? Peter: So, first of all, one of the things we found in our research was small change is no change. When you make small changes, the classroom as a system will resist that. So, go big. In building thinking classrooms, random groups is not a practice that gets enacted on its own. It's enacted with two other practices: thinking tasks, which is chapter one of my book, random groups, which is chapter two. And then, getting the students working at vertical whiteboards. These are transformational changes to the classroom. What we're doing in doing that is we're changing the environment in which we're asking students to behave differently. Asking students to behave differently in exactly the same environment that they behaved a certain way for five years already is almost impossible to do. If you want them to behave differently, if you want them to start to think, you're going to have to create an environment that is more conducive to thinking. Peter: So, that's part of it. The other thing is, don't do things by half measures. Don't start doing, “Well, we're going to do random groups on Mondays, but we're going to do strategic groups the rest of the days,” or something like this. Because what that communicates to students is that the randomness is something that you don't really value. Go big. We're doing random groups. We're always doing random groups. Have the courage. Yes, there's going to be some combinations that you're going to go, “Uh-oh.” And some of those are going to be really uh-oh combinations. But you're also going to have way more situations where you go and then it turns out to be amazing. So, have that courage. Go with the random groups and do it persistently and consistently. Because there is going to be resistance. The students are going to resist this thing because at least when you're being strategic, you're being thoughtful about it. Peter: But this feels like too much chance. And they start to attribute, they start to map their emotions around being placed in strategic groups, which were often for a month, into this setting. And what we need to do is, we need to show that this is not that by being consistent, doing it randomly, doing it frequently, so they start to realize that this is different. This is not the kind of grouping structures that have happened in the past. And do it. Do it consistently, persistently. Do it for at least 10 days before you start to really see and really reap those benefits. Mike: I think that's a really great place to stop. Thank you so much for joining us on the podcast, Peter. It really has been a pleasure chatting with you. Peter: Thanks so much. It's been a great conversation. Mike: 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. © 2024 The Math Learning Center | www.mathlearningcenter.org

From book bans to chronic absenteeism to phone distractions, it's a hard time to be a teacher. But amidst all the challenges, there's something surprising happening among math teachers. Some of them say they're more excited to go to work than ever before. Why? Because of a new approach to teaching math called “thinking classrooms” that has students up out of their seats and engaged in problem-solving. In this episode, MindShift listeners will hear a thinking classroom in action and reflections from the teacher and her students. Listeners also will learn about this model from the researcher who developed it, Peter Liljedahl.

Guest Lorenzo Rodriguez has been a math educator for the past eight years, joyfully honing his craft and developing a pedagogy that works to convince students that a mathematician can be anybody, with any background, who thinks in any language. He has served as the Math Department Chair and Activities Director, worked within our cross-curricular Cybersecurity pathway, and hosted “math labs,” collaborative days spent engaging in dialogue about how best to support mathematical thinking in our diverse classrooms. Summary This is part 2 of an episode I aired with Dr. Peter Liljedahl last week. Peter created the program “Building Thinking Classrooms in Mathematics” that Lorenzo uses. Our conversation here delves into the challenges and rewards of transforming math education. Lorenzo shares his journey from traditional teaching methods to a more student-centered approach. He emphasizes the importance of building buy-in among colleagues and sparking student curiosity to foster a love of math. The conversation highlights the power of project-based learning and real-world connections in making math relevant and engaging for students. Lorenzo's implementation of the Thinking Classrooms model showcases how collaborative problem-solving can transform the classroom dynamic. The episode also addresses the need to rethink assessment to better measure student understanding and growth. The episode concludes with a hopeful outlook on the future of math education, emphasizing the potential to create more equitable and engaging learning experiences for all students. Social Media Social Media: X (twitter) - @getoffyourath About Jeff Jeff Ikler is the Director of Quetico Leadership and Career Coaching. “Quetico” (KWEH-teh-co). He works with leaders in all aspects of life to identify and overcome obstacles in their desired future. He came to the field of coaching after a 35-year career in educational publishing. Prior to his career in educational publishing, Jeff taught high school U.S. history and government. Jeff has hosted the “Getting Unstuck—Cultivating Curiosity” podcast for 5 years. The guests and topics he explores are designed to help listeners think differently about the familiar and welcome the new as something to consider. He is also the co-host of the Cultivating Resilience – A Whole Community Approach to Alleviating Trauma in Schools, which promotes mental health and overall wellness. Jeff co-authored Shifting: How School Leaders Can Create a Culture of Change. Shifting integrates leadership development and change mechanics in a three-part change framework to help guide school leaders and their teams toward productive change.  

Guest Dr. Peter Liljedahl is a Professor of Mathematics Education in the Faculty of Education at Simon Fraser University and author of the best-selling book, Building Thinking Classrooms in Mathematics (Grades K-12): 14 Teaching Practices for Enhancing Learning. Peter is a former high school mathematics teacher whose work emphasizes collaborative learning for a more effective mathematics education.  Most recently, he received the Læringsprisen [Learning Award] for Changing the way we think about Education in Denmark (2022). Summary The podcast episode explores Professor Liljedahl's journey in understanding how teaching practices affect student learning in math classrooms. He shares his observations of a teacher struggling to implement problem-solving, leading to student frustration and disengagement. This prompted him to research the psychology of mathematics education and develop the "thinking mathematics classroom" approach, emphasizing practices such as using vertical whiteboards, random grouping of no more than three students, and note-making. The discussion delves into the benefits of these methods, such as increased student engagement, collaboration, and the ability for teachers to provide timely support. Dr. Liljedahl also addresses the challenges of balancing direct instruction and messy learning, as well as the origins and difficulties of the algebra curriculum. The episode concludes with a discussion on the future of education, emphasizing the importance of teachers and the need for more training in neuroscience and child psychology. Bonus tracks I've also included two bonus tracts with Peter and Danelle on my website blog post for this episode. One speaks specifically about student note-making, another of Peter's practices. The second tract speaks to Algebra's challenge to student success. Social Media Website- https://www.buildingthinkingclassrooms.com/ Twitter-  @pgliljedahl Instagram - @buildingthinikingclassrooms Facebook - https://www.facebook.com/BTCthinks About Jeff Jeff Ikler is the Director of Quetico Leadership and Career Coaching. “Quetico” (KWEH-teh-co). He works with leaders in all aspects of life to identify and overcome obstacles in their desired future. He came to the field of coaching after a 35-year career in educational publishing. Prior to his career in educational publishing, Jeff taught high school U.S. history and government. Jeff has hosted the “Getting Unstuck—Cultivating Curiosity” podcast for 5 years. The guests and topics he explores are designed to help listeners think differently about the familiar and welcome the new as something to consider. He is also the co-host of the Cultivating Resilience – A Whole Community Approach to Alleviating Trauma in Schools, which promotes mental health and overall wellness. Jeff co-authored Shifting: How School Leaders Can Create a Culture of Change. Shifting integrates leadership development and change mechanics in a three-part change framework to help guide school leaders and their teams toward productive change.

Enter to win a free set of Wipebook Flipcharts for your Thinking Classroom: ⁠www.wipebook.com/TTT⁠ Join Kyle and Dean as they engage in a lively conversation with Peter Liljedahl and Maegan Giroux about the newest addition to the world of Building Thinking Classrooms: Mathematics Tasks for the Thinking Classroom, Grades K-5. This book is specially crafted for K-5 educators and goes beyond being just a collection of tasks. It encapsulates years of research and classroom experience from the Thinking Classrooms approach, providing a comprehensive guide that combines effective pedagogy with engaging tasks to ignite student thinking. From the official release of the book to in-depth discussions about curricular and non-curricular tasks, perseverance levels, and the intricacies of crafting tasks that spark curiosity and encourage deep thinking, this episode is packed with insights. You'll hear firsthand how the book came to life, the philosophy that underpins it, and how it's set to make a difference in classrooms around the world. Tune in to hear more about this newly available resource and even more ideas on how to build your Thinking Classroom.

In this episode of Room to Grow, our hosts discuss ways to support student sense-making in teaching and learning mathematics. Building out on the ideas shared in Episode 3 of Room to Grow, Curtis and Joanie dive more deeply into what it means for students to “make sense of mathematics.” They discuss what it looks and sounds like when students are making sense, as opposed to just repeating back learned ideas, and consider which classroom structures and teacher moves might best support students' sense-making. They acknowledge that sense-making is not more or less important than learning mathematical skills and fluency, but that it is a part of deep learning and of a student's ability to generalize their understanding.  As Peter Liljedahl says in Building Thinking Classrooms, “The goal of building thinking classrooms is not to find engaging tasks for students to think about. The goal of thinking classrooms is to build engaged students that are willing to think about any task.” We encourage you to explore the resources below, referenced in this episode:The Standards for Mathematical Practice, now referenced in most states' math standards and originally published by the Council of Chief State School Officers and the Governor's Association;Jo Boaler's Math-ish book and website;Peter Liljedahl's book and website Building Thinking Classrooms, and Robert Kaplinsky's blog post about why you should read it. Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

Seamus welcomes Rachel Rahmlow from Teacher to Millionaire to discuss her mission to ensure educators make the best of their money and become financially secure in their careers.  Rachel also shares insights into her life, her practice, professional development, and where she goes for inspiration.  Also mentioned in this episode are Instagram accounts; @eastnash.teacher, @funny_math_teacher, @TeacherFinancialPlanner, @TheMathGuru, and @pgliljedahl.

Enter to win a free set of Wipebook Flipcharts for your Thinking Classroom: ⁠www.wipebook.com/TTT⁠ In this episode, Kyle has a conversation with Judy Larson (@JudytaLarsen), Associate Professor at University of Fraser Valley and longtime Building Thinking Classrooms teacher. Deeply entrenched in math education and an unwavering advocate for innovative teaching, Judy shares her captivating journey alongside Peter Liljedahl. From the initial shock of abandoning traditional teaching to adopting Thinking Classroom practices, Judy recollects her transformative experiences both as a learner and an educator. We explore the roots of Building Thinking Classrooms, including practices like visibly random groups, vertical non-permanent surfaces, and the pivotal role of meaningful notes in shaping students' and teachers' approaches to learning. We also touch on the impact of social media in fostering a vibrant community of educators dedicated to revolutionizing math education. Tune in as we venture into discussions about decolonization, the dynamics of group work, and the perpetual evolution of Thinking Classrooms.

When you shift your teaching practices from “I do, we do, you” to a problem based approach that engages students to think first you will often be led to question how you give feedback to students. In this episode we speak with Diane Hamilton, an elementary classroom teacher from Toronto Ontario. Diane has been implementing the 14 strategies from Peter Liljedahl's book Building Thinking Classrooms and is here to dig into how to give effective feedback to her students instead of grades. Stick around and you'll: Discover innovative self-assessment techniques that empower students to take charge of their learning in mathematics, turning passive learners into active participants.Learn how to develop and communicate effective success criteria, a crucial step in providing feedback that genuinely enhances student understanding and performance.Gain insights into structuring self-assessment and growth-focused activities into your weekly routine, ensuring consistent student progress and deeper comprehension of mathematical concepts.This is another Math Mentoring Moment episode where we chat with a teacher like you who is working through some problems of practice and together we brainstorm ways to overcome them. You'll Learn: Practical self-assessment methods to facilitate student involvement and ownership in their mathematics learning;How can I develop success criteria and share them with students so I can give effective feedback; How can I structure self assessment and growth in mathematics into my weekly routine; Resources: Assessment For Growth: A Blueprint Course For Standards Based Grading in Math ClassMake Math Moments Problem Based Lessons & UnitsDistrict Math Leaders: How are you ensuring that you support those educators who need a nudge to spark a focus on growing their pedagogical-content knowledge? What about opportunities for those who are eager and willing to elevate their practice, but do not have the support? Book a call with our District Improvement Program Team to learn how we can not only help you craft, refine and implement your district math learning goals, but also provide all of the professional learning supports your educators need to grow at the speed of their learning. Book a short conversation with our team now. Get a Customized Math Improvement Plan For Your District.Are you district leader for mathematics? Take the 12 minute assessment and you'll get a free, customized improvement plan to shape and grow the 6 parts of any strong mathematics program.Take the assessment

Thin sliced problems were coined by Peter Liljedahl in his book Building Thinking Classrooms in Mathematics.What are thin sliced problems & how can you use them to meet all the needs of your students? Be sure to listen as we go through the 9 simple steps to using thin sliced word problems in your math classroom.  In this episode we will chat about: thin sliced problems naturally differentiateusing thin sliced problems in your math classroommaking sure every student is learningLinks: 

If the instructional door you chose to open isn't working, find a different door! We can hold high expectations for our students AND meet them where they are at the same time! Tune in as our second married teaching couple, Ken and Kendra Versoi, drop amazing and tangible strategies for effective facilitation (hint, hint it starts with Relationships). @SuzannahEvans2@saeed_shaneNecessary Conditions, Geoff KrallBuilding Thinking Classrooms, Peter Liljedahl

This episode has a portion where Tim & Melisa screenshared the tool mentioned, you can watch the video recording here. Join hosts Dean and Kyle as they chat with Tim Brzezinski (@TimBrzezinski) and Melisa McCain (@mccainm), advocates for Building Thinking Classrooms and improving assessment practices. Their conversation is focused on a grading tool, crafted by Tim, Melisa, and their colleagues. This tool, deeply rooted in the principles of Building Thinking Classrooms, provides teachers a tool to actualize the assessment practices laid out by Peter Liljedahl around student assessment. Discover how this innovative rubric, available at http://tinyurl.com/BTCrubric, was designed not just to evaluate, but to enhance students' understanding and learning experiences. The episode delves into the tool's development, design, and its transformative impact on both teaching and learning. This discussion is not just theoretical; it's a practical guide for educators looking to adopt a more effective and empathetic approach to assessment. Tune in to learn how you can implement this game-changing tool in your classroom and foster deeper understanding in your students.

Welcome to Part 2 of my interview with Peter Liljedahl. If you missed Part 1 go listen to Episode 93, all about breaking down the 2 ways to consolidate. In this episode, Peter and I talk about concepts that will likely come up in your consolidating. This episode is jam packed with goodness! In this episode we will chat about: thick understandingmoving from simple understanding to sophisticated understandingbuilding a thinking classroomAbout our guest Peter Liljedahl:

In this episode, Dr. Seipp discussed a refreshing new mindset in math instruction based on Peter Liljedahl's book, Building Thinking Classrooms in Mathematics. A group of teachers and students from Eisenhower Middle School talk about their experience with this framework, specifically thin-slicing lessons, as well as successes with its overall implementation.

Are you building a thinking classroom? I know many teachers are thinking about sense making and helping their students think about math. Peter Liljedahl talks all about this in his book "Building Thinking Classrooms". You won't want to miss my chat with Peter!In this episode we will chat about: consolidationbeing a curatorlearn with your studentsAbout our guest Peter Liljedahl:

For the final episode of 2023, I begin my new weekly episodes about building the The Thinking Classroom. The "Thinking Classroom" model has been coined by mathematician Dr. Peter Liljedahl and his work of creating math learning spaces that encourage students to think more with their math tasks. In this episode (161), I talk about the inspiration I got from the Chey and Pav podcast and how I am building it into my curriculum. In this first episode I give a quick breakdown of the Thinking Classroom Model. What materials I will be using for student work and recording. How I am using the Eduprotocols model with it, especially with Hexagonal Thinking. Show Notes Post-it Dry Erase Sheets White Board Wall Paper Rocketbook Beacons Wipeboard Start Building a Thinking Classroom EduProtocols Cult of Pedagogy Hexagonal Thinking Hexagon Graphic Organizer --- Send in a voice message: https://podcasters.spotify.com/pod/show/pixelclassroom/message Support this podcast: https://podcasters.spotify.com/pod/show/pixelclassroom/support

Rounding Up Season 2 | Episode 8 – It's a Story, Not a Checklist! Guest: Dr. John Staley Mike Wallus: There's something magical about getting lost in a great story. Whether you're reading a book, watching a movie, or listening to a friend, stories impart meaning, and they capture our imagination. Dr. John Staley thinks a lot about stories. On this episode of Rounding Up, we'll talk with John about the ways that he thinks that the concept of story can impact our approach to the content we teach and the practices we engage in to support our students.  Well, John, welcome to the podcast. We're really excited to talk with you today. John Staley: I'm glad to be here. Thank you for the invitation, and thank you for having me. Mike: So when we spoke earlier this year, you were sharing a story with me that I think really sets up the whole interview. And it was the story of how you and your kids had engaged with the themes and the ideas that lived in the Harry Potter universe. And I'm wondering if you could just start by sharing that story again, this time with the audience. John: OK. When I was preparing to present for a set of students over at Towson University and talking to them about the importance of teaching and it being a story. So the story of Harry Potter really began for me with our family—my wife, Karen, and our three children—back in '97 when the first book came out. Our son Jonathan was nine at that time and being a reader and us being a reading family, we came together. He would read some, myself and my wife would read some, and our daughter Alexis was five, our daughter Mariah was three. So we began reading Harry Potter. And so that really began our journey into Harry Potter. Then when the movies came out, of course we went to see the movies and watch some of those on TV, and then sometimes we listened to the audio books. And then as our children grew, because Harry Potter took, what, 10 years to develop the actual book series itself, he's 19 now, finally reading the final book. By then our three-year-old has picked them up and she's begun reading them and we're reading. So we're through the cycle of reading with them.  But what they actually did with Harry Potter, when you think about it, is really branch it out from just books to more than books. And that right there had me thinking. I was going in to talk to teachers about the importance of the story in the mathematics classroom and what you do there. So that's how Harry Potter came into the math world for me, [chuckles] I guess you can say. Mike: There's a ton about this that I think is going to become clear as we talk a little bit more.  One of the things that really struck me was how this experience shaped your thinking about the ways that educators can understand their role when it comes to math content and also instructional practice and then creating equitable systems and structures. I'm wondering if we can start with the way that you think this experience can inform an educator's understanding for content. So in this case, the concepts and ideas in mathematics. Can you talk about that, John? John: Yeah, let's really talk about the idea of what happens in a math classroom being a story. The teaching and learning of mathematics is a story that, what we want to do is connect lesson to lesson and chapter to chapter and year to year.  So when you think about students' stories, and let's start pre-K. When students start coming in pre-K and learning pre-K math, and they're engaging in the work they do in math with counting and cardinality initially, and as they grow across the years, especially in elementary, and they're getting the foundation, it's still about a story. And so how do we help the topics that we're taught, the grade level content become a story? And so that's the connection to Harry Potter for me, and that's what helped me elevate and think about Harry Potter because when you think about what Harry Potter and the whole series did, they've got the written books. So that's one mode of learning for people for engaging in Harry Potter.  Then they went from written books to audiobooks, and then they went from audiobooks to movies. And so some of them start to overlap, right? So you got written books, you got audiobooks, you got movies—three modes of input for a learner or for an audience or for me, the individual interested in Harry Potter, that could be interested in it. And then they went to additional podcasts, Harry Potter and the Sacred Text and things like that. And then they went to this one big place called Universal Studios where they have Harry Potter World. That's immersive. That I can step in; I can put on the robes; I can put the wand in my hand. I can ride on, I can taste, so my senses can really come to play because I'm interactive and engaged in this story. When you take that into the math classroom, how do we help that story come to life for our students? Let's talk one grade. So it feels like the content that I'm learning in a grade, especially around number, around algebraic thinking, around geometry, and around measurement and data. Those topics are connected within the grade, how they connect across the grade and how it grows. So the parallel to Harry Potter's story—there's, what, seven books there? And so you have seven books, and they start off with this little young guy called Harry, and he's age 11. By the time the story ends, he's seven years later, 18 years old. So just think about what he has learned across the years and how what they did there at Hogwarts and the educators and all that kind of stuff has some consistency to it. Common courses across grade levels, thinking, in my mind, common sets of core ideas in math: number, algebra, thinking, geometry, measurement of data. They grow across each year. We just keep adding on.  So think about number. You're thinking with base ten. You then think about how fractions show up as numbers, and you're thinking about operations with whole numbers, base ten, and fractions. You think about decimals and then in some cases going into, depending if you're K–8 or K–5, you might even think about how this plays into integers. But you think about how that's all connected going across and the idea of, “What's the story that I need to tell you so that you understand how math is a story that's connected?” It's not these individual little pieces that don't connect to each other, but they connect somehow in some manner and build off of each other. Mike: So there are a couple of things I want to pick up on here that are interesting. When you first started talking about this, one of the things that jumped out for me is this idea that there's a story, but we're not necessarily constrained to a particular medium. The story was first articulated via book, but there are all of these ways that you can engage with the story. And you talked about the immersive experience that led to a level of engagement. John: Mm-hmm. Mike: And I think that is helping me make sense of this analogy—that there's not necessarily one mode of building students' understanding. We actually need to think about multiple modes. Am I picking up on that right? John: That's exactly right. So what do I put in my tool kit as an educator that allows me to help tap into my students' strengths, to help them understand the content that they need to understand that I'm presenting that day, that week, that month, that I'm helping build their learning around? And in the sense of thinking about the different ways Harry Potter can come at you—with movies, with audio, with video—I think about that from the math perspective. What do I need to have in my tool kit when it comes to my instructional practices, the types of routines I establish in the classroom?  Just think about the idea of the mathematical tools you might use. How do the tools that you use play themselves out across the years? So students working with the different manipulatives that they might be using, the different mathematical tools, a tool that they use in first grade, where does that tool go in second grade, third grade, fourth grade, as they continue to work with whole numbers, especially with doing operations, with whatever the tool might be? Then what do you use with fractions? What tools do you use with decimals? We need to think about what we bring into the classroom to help our students understand the story of the mathematics that they're learning and see it as a story. Is my student in a more concrete stage? Do they need to touch it, feel it, move it around? Are they okay visually? They need to see it now, they're at that stage. They're more representational so they can work with it in a different manner or they're more abstract. Hmm. Oh, OK. And so how do we help put all of that into the setting? And how are we prepared as classroom teachers to have the instructional practices to meet a diverse set of students that are sitting in our classrooms? Mike: You know, the other thing you're making me think about, John, is this idea of concepts and content as a story. And what I'm struck by is how different that is than the way I was taught to think about what I was doing in my classroom, where it felt more like a checklist or a list of things that I was tracking. And oftentimes those things felt disconnected even within the span of a year.  But I have to admit, I didn't find myself thinking a lot about what was happening to grade levels beyond mine or really thinking about how what I was doing around building kindergartners' understanding of the structure of number or ten-ness. John: Mm-hmm. Mike: How that was going to play out in, say, fifth grade or high school or what have you. You're really causing me to think how different it is to think about this work we're doing as story rather than a discrete set of things that are kind of within a grade level. John: When you say that, it also gets me thinking of how we quite often see our content as being this mile-wide set of content that we have to teach for a grade level. And what I would offer in the space is that when you think about the big ideas of what you really need to teach this year, let's just work with number. Number base ten, or, if you're in the upper elementary, number base ten and fractions. If you think about the big ideas that you want students to walk away with that year, those big ideas continue to cycle around, and those are the ones that you're going to spend a chunk of your time on. Those are the ones you're going to keep bringing back. Those are the ones you're going to keep exposing students to in multiple ways to have them make sense of what they're doing. And the key part of all of that is the understanding, the importance of the vertical nature as to what is it I want all of my students sitting in my classroom to know and be able to do, have confidence in, have their sense of agency. Like, “Man, I can show you. I can do it, I can do it.” What do we want them to walk away with that year? So that idea of the vertical nature of it, and understanding your learning progressions, and understanding how number grows for students across the years is important. Why do I build student understanding with a number line early? So that when we get the fractions, they can see fractions as numbers. So later on when we get the decimals, they can see decimals as numbers, and I can work with it. So the vertical nature of where the math is going, the learning progression that sits behind it, helps us tell the story so that students, when they begin and you are thinking about their prior knowledge, activate that prior knowledge and build it, but build it as part of the story.  The story piece also helps us think about how we elevate and value our students in the classroom themselves. So that idea of seeing our students as little beings, little people, really, versus just us teaching content. When you think about the story of Harry Potter, I believe he survived across his time at Hogwarts because of relationships. Our students make it through the math journey from year to year to year to year because of relationships. And where they have strong relationships from year to year to year to year, their journey is a whole lot better. Mike: Let's make a small shift in our conversation and talk a little bit about this idea of instructional practice. John: OK.  Mike: I'm wondering how this lived experience with your family around the Harry Potter universe, how you think that would inform the way that an educator would think about their own practice? John: I think about it in this way. As I think about myself being in the classroom—and I taught middle school, then high school—I'm always thinking about what's in my tool kit. I think about the tools that I use and the various manipulatives, the various visual representations that I need to have at my fingertips. So part of what my question would be, and I think about it, is what are those instructional strategies that I will be using and how do I fine-tune those? What are my practices I'm using in my routines to help it feel like, “OK, I'm entering into a story”?  Harry Potter, when you look at those books, across the books, they had some instructional routines happening, some things that happen every single year. You knew there was going to be a quidditch match. You knew they were going to have some kind of holiday type of gathering or party or something like that. You knew there was going to be some kind of competition that happened within each book that really, that competition required them to apply the knowledge and skills from their various courses that they learned. They had a set of core courses that they took, and so it wasn't like in each individual course that they really got to apply. They did in some cases, they would try it out, they'd mess up and somebody's nose would get big, ears would get big, you know, change a different color. But really, when they went into some of those competitions, that's when the collection of what they were learning from their different courses, that's when the collection of the content. So how do we think about providing space for students to show what they know in new settings, new types of problems? Especially in elementary, maybe it's science application type problems, maybe they're doing something with their social studies and they're learning a little bit about that. As an educator, I'm also thinking about, “Where am I when it comes to my procedural, the conceptual development, and the ability to think through and apply the applications?” And so I say that part because I have to think about students coming in, and how do I really build this? How do I strike this balance of conceptual and procedural? When do I go conceptual? When do I go procedural? How do I value both of them? How do I elevate that? And how do I come to understand it myself? Because quite often the default becomes procedural when my confidence as a teacher is not real deep with building it conceptually. I'm not comfortable, maybe, or I don't have the set of questions that go around the lesson and everything. So I've got to really think through how I go about building that out. Mike: That is interesting, John, because I think you put your finger on something. I know there have been points in time during my career when I was teaching even young children where we'd get to a particular idea or concept, and my perception was, “Something's going on here and the kids aren't getting it.” But what you're causing me to think is often in those moments, the thing that had changed is that I didn't have a depth of understanding of what I was trying to do. Not to say that I didn't understand the concept myself or the mathematics, but I didn't have the right questions to draw out the big ideas, or I didn't have a sense of, “How might students initially think about this and how might their thinking progress over time?” So you're making me think about this idea that if I'm having that moment where I'm feeling frustrated, kids aren't understanding, it might be a point in time where I need to think to myself, “OK, where am I in this? How much of this is me wanting to think back and say, what are the big ideas that I'm trying to accomplish? What are the questions that I might need to ask?” And those might be things that I can discover through reflection or trying to make more sense of the mathematics or the concept. But it also might be an opportunity for me to say, “What do my colleagues know? Are there ways that my colleagues are thinking about this that I can draw on rather than feeling like I'm on an island by myself?” John: You just said the key point there. I would encourage you to get connected to someone somehow. As you go through this journey together, there are other teachers out there that are walking through what they're walking through, teaching the grade level content. And that's when you are able to talk deeply about math. Mike: The other thing you're making me think about is that you're suggesting that educators just step back from whether kids are succeeding or partially succeeding or struggling with a task and really step back and saying, like, “OK, what's the larger set of mathematics that we're trying to build here? What are the big ideas?” And then analyzing what's happening through that lens rather than trying to think about, “How do I get kids to success on this particular thing?” Does that make sense? Tell me more about what you're thinking. John: So when I think about that one little thing, I have to step back and ask myself the question, “How and where does that one thing fit in the whole story of the unit?" The whole story of the grade level. And when I say the grade level, I'm thinking about those big ideas that sit into the big content domains, the big idea number. How does this one thing fit into that content domain? Mike: That was lovely. And it really does help me have a clearer picture of the way in which concepts and ideas mirror the structures of stories in that, like, there are threads and connections that I can draw on from my previous experience to understand what's happening now. You're starting to go there.  So let's just talk about where you see parallels to equitable systems and structures in the experience that you had with Harry Potter when you were in that world with your family. John: First, let's think about this idea of grouping structures. And so when you think about the idea of groups and the way groups are used within the classroom, and you think about the equitable nature of homogeneous, heterogeneous, random groupings, truly really thinking about that collectively. And I say collectively in this sense, when you think about the parallel to the Harry Potter story, they had a grouping structure in place. They had a random sorting. Now who knows how random it was sometimes, right? But they had a random sorting the minute the students stepped into the school. And they got put into one of the four houses. But even though they had that random sorting then, and they had the houses structured, those groups, those students still had opportunities as they did a variety of things—other than the quidditch tournaments and some other tournaments—they had the opportunity where as a collection of students coming from the various houses, if they didn't come together, they might not have survived that challenge, that competition, whatever it was. So the idea of grouping and grouping structures and how we as educators need to think about, “What is it really doing for our students when we put them in fixed groups? And how is that not of a benefit to our students? And how can we really go about using the more random grouping?”  One of the books that I'm reading is Building Thinking Classrooms [in Mathematics: Grades K–12: 14 Teaching Practices for Enhancing Learning]. And so I'm reading Peter [Liljedahl]'s book and I'm thinking through it in the chapter when he talks about grouping. I think I read that chapter and highlighted and tapped every single page in it multiple times because it really made me think about what's really happening for our students when we think about grouping. So one structure and one part to think about is, “What's happening when we think we're doing our grouping that's not really getting students engaged in the lesson, keeping them engaged, and benefiting them from learning?” Another part, and I don't know if this is a part of equitable systems and structures or just when I think about equity work: One of the courses that they had to take at Hogwarts was about the history of wizarding. I bring that up in this space because they learned about the history of what went on with wizards and what went on with people. And to me, in my mindset, that's setting up and showing the importance of us sharing the history and bringing the history of our students—their culture, their backgrounds, in some cases their lived experiences—into the classroom. So that's us connecting with our students' culture and being culturally responsive and bringing that into the classroom. So as far as an equitable structure, the question I would ask you to think about is, “Do my students see themselves in my mathematics classroom?”  And I say it that way versus “in the mathematics,” because some people will look at the problems in the math book and say, “Oh, I don't see them there. I don't see, oh, their names, their culture, their type of foods.” Some of those things aren't in the written work in front of you. But what I would offer is the ability for me as the educator to use visuals in my classroom, the ability for me to connect with the families in my classroom and learn some of their stories, learn some of their backgrounds—not necessarily learn their stories, but learn about them and bring that in to the space—that's for me to do. I don't need a textbook series that will do that for me. And as a matter of fact, I'm not sure if a textbook series can do that for you, for all the students that you have in your classroom or for the variety of students that you have in your classroom, when we think about their backgrounds, their culture, where they might come from. So thinking about that idea of cultural responsiveness, and really, if you think about the parallel in the Harry Potter series, the history of wizarding and the interaction, when you think about the interaction piece between wizards and what they call Muggles, right? That's the interactions between our students, learning about other students, learning about other cultures, learning about diverse voices. That's teaching students how to engage with and understand others and learn about others and come to value that others have voice also. Mike: I was just thinking, John, if I were to critique Hogwarts, I do wonder about the houses. Because in my head, there is a single story that the reader comes to think about anyone who is in Harry's house versus, say, like Slytherin house. John: Yes. Mike: And it flattens anyone who's in Slytherin house into bad guys, right? John: Mm-hmm. Mike: And so it makes me think there's that element of grouping where as an educator, I might tell a single story about a particular group, especially if that group is fixed and it doesn't change. But there's also, like, what does that do internally to the student who's in that group? What does that signal to them about their own identity? Does that make sense? John: That does make sense. And so when you think about the idea of grouping there at Hogwarts, and you think about these four fixed groups, because they were living in these houses, and once you got in that house, I don't think anybody moved houses. Think about the impact on students. If you put them in a group and they stay in that group and they never change groups, you will have students who realize that the way you did your groups and the way you named your groups and the way they see others in other groups getting more, doing different, and things like that. That's a nice caution to say the labels we put on our groups. Our kids come to internalize them and they come to, in some cases, live up to the level of expectations that we set for “just that group.” So if you're using fixed groups or thinking about fixed groups, really I'd offer that you really get into some of the research around groups and think, “What does it do for students?” And not only what does it do for students in your grade, but how does that play out for students across grades? If that student was in the group that you identified as the “low group” in grade 2, [exhales] what group did they show up in grade 3? How did that play with their mindset? Because you might not have said those words in front of students, but our students pick up on being in a fixed group and watching and seeing what their peers can do and what their peers can't do, what their group members can do and what their group can't do. As our students grow from grades 2 to 3, 4, 5, that really has an impact. There's somewhere between grade 3 and 5 where students' confidence starts to really shake. And I wonder how much of it is because of the grouping and types of grouping that is being used in the classroom that has me in a group of, “Oh, I am a strong doer [of mathematics]” or, “Oh, I'm not a good doer of mathematics.” And that, how much of that just starts to resonate with students, and they start to pick that up and carry that with them, an unexpected consequence because we thought we were doing a good thing when we put 'em in this group. Because I can pull them together, small group them, this and that. I can target what I need to do with them in that moment. Yeah, target what you need to do in that moment, but mix them up in groups. Mike: Just to go back and touch on the point that you started with. Building Thinking Classrooms has a lot to say about that particular topic among others, and it's definitely a book that, for my money, has really caused me to think about a lot of the practices that I used to engage in because I believed that they were the right thing to do. It's a powerful read. For anyone who hasn't read that yet, I would absolutely recommend it. John: And one last structure that I think we can speak to. I've already spoken to supports for students, but the idea of a coherent curriculum is I think an equitable structure that systems put in place that we need to put in place that you need to have in place for your students. And when I say a coherent curriculum, I'm thinking not just your one grade, but how does that grow across the grades? It's something for me, the teacher, to say, “I need to do it my way, this way…”. But it's more to say, “Here's the role I play in their pre-K to 12 journey.” Here's the chapter I'm going to read to them this year to help them get their deep understanding of whichever chapter it was, whichever book it happened to be of.  In the case of the parallel of Harry Potter, here's the chapter I'm doing. I'm the third grade chapter, I'm the fourth grade chapter, I'm the fifth grade chapter. And the idea of that coherent curriculum allows the handoff to the next and the entry from the prior to be smoother. Many of the curriculums, when you look at them, a K–5 curriculum series will have those coherent pieces designed in it—similar types of tools, similar types of manipulatives, similar types of question prompts, similar types of routines—and that helps students build their confidence as they grow from year to year. And so to that point, it's about this idea of really thinking about how a coherent curriculum helps support equity because you know your students are getting the benefit of a teacher who is building from their prior knowledge because they've paid attention to what came before in this curriculum series and preparing them for where they're going. And that's quite often what the power of a coherent curriculum will do.  The parallel in the Harry Potter series, they had about five to seven core courses they had to take. I think about the development of those courses. Boom. If I think about those courses as a strand of becoming a wizard, [laughs] how did I grow from year to year to year to year in those strands that I was moving across? Mike: Okay, I have two thoughts. One, I fully expect that when this podcast comes out, there's going to be a large bump in whoever is tracking the sale of the Harry Potter series on Amazon or wherever it is.  John: [laughs] Mike: But the other question I wanted to ask you is what are some books outside of the Harry Potter universe that you feel like you'd recommend to an educator who's wanting to think about their practice in terms of content or instructional practices or the ways that they build equitable structure? John: When I think about the works around equitable structure, I think about The Impact of Identity and K–8 Mathematics: Rethinking Equity-Based Practices by Julia Aguirre, Karen Mayfield-Ingram, and Danny Martin as being one to help step back and think about how am I thinking about what I do and how it shows up in the classroom with my students.  Another book that I just finished reading: Humanizing Disability in Mathematics Education[: Forging New Paths]. And my reason for reading it was I continue to think about what else can we do to help our students who are identified, who receive special education services? Why do we see so many of our students who sit in an inclusive environment—they're in the classroom on a regular basis; they don't have an IEP that has a math disability listed or anything along those lines—but they significantly underperform or they don't perform as well as their peers that don't receive special education services. So that's a book that got me just thinking and reading in that space.  Another book that I'm reading now, or rereading, and I'll probably reread this one at least once a year, is Motivated[: Designing Mathematics Classrooms Where Students Want to Join In] by Ilana [Seidel] Horn. And the reason for this one is the book itself, when you read it, is written with middle schools' case stories. Part of what this book is tackling is what happens to students as they transition into middle school. And the reason why I mentioned this, especially if you're elementary, is somewhere between third grade and fifth grade, that process of students' self-confidence decreasing their beliefs in themselves as doers of math starts to fall apart. They start to take the chips in the armor. And so this book, Motivated itself, really does not speak to this idea of intrinsic motivation. “Oh, my students are motivated.” It speaks to this idea of by the time the students get to a certain age, that upper fifth grade, sixth grade timeframe, what shifts is their K, 1, 2, 3, “I'm doing everything to please my teacher.” By [grades] 4 or 5, I'm realizing, “I need to be able to show up for my peers. I need to be able to look like I can do for my peers.” And so if I can't, I'm backing out. I'm not sharing, I'm not volunteering, I'm not “engaging.”  So that's why I bring it into this elementary space because it talks about five pieces of a motivational framework that you can really push in on, and not that you push in on all five at one time. [chuckles] But you pick one, like meaningfulness, and you push in on that one, and you really go at, “How do I make the mathematics more meaningful for my students, and what does it look like? How do I create that safe space for them?” That's what you got to think about. Mike: Thanks. That's a great place to stop. John Staley, thank you so much for joining us. It's really been a pleasure. John: Thank you for having me. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling individuals to discover and develop their mathematical confidence and ability. ©2023 The Math Learning Center - www.mathlearningcenter.org

-Building thinking classrooms- around the notion that students spend time in classrooms not thinking. Many structures are not designed for thinking, and instead for conformity and compliance. 15 years of research before the book, and the research continues. -One of the least conducive places to have students do thinking is at their seat writing in their notebook, but one of the most conducive spaces for students to do thinking is standing in random groups of three, at a whiteboard or something vertical and erasable. It is about getting them up and thinking.  -Task in relation to the student. If we want our students to think we have to give them something to think about. To be a thinking task it needs a particular relationship to the student. -The whiteboard is a better space for that thinking to manifest. Everyone has to be able to access the task. -Whiteboard- Everyone is oriented with the work the same way, they can see other students' progress, I can access their learning more readily, I as the teacher can intervene right now. Standing is just so much better than sitting. When students are sitting they feel anonymous. The further from the student, the more anonymity. When they feel anonymous they are more disengaged. -More engagement from a question if written on a whiteboard, as opposed to printed on paper.  -You have five minutes. They are with you on your feet and talking to each other. Research shows beyond five minutes, the more passive students become and the transition to being an active learner is harder. - In a thinking classroom you say the minimum possible to start question number one. Then we can give them another question and another. We can never unsay what we say at the beginning. The moment we tell them how to do it, we have sucked the thinking out of the task. Need to bring order to their thoughts. -Mimicking: Template for exactly how to do this problem. Mimicking is not the same as thinking or learning. It is mastering or memorizing routines that they truly need to make meaning. Students take the process and plug it into the template teachers present. Mimicking always runs out. How do we break these habits? How do we help students and ourselves break these habits? We have to break the habit ourselves and then support them and give them success. -Students don't listen to what we say, they listen to what we do. When teachers are too perfect, students try to be too perfect.  - I can't hear what you are saying, your actions are too loud.  -Divergent vs. convergent thinking - Gallery walk. The teacher is the guide and we are taking a tour. We are going to look at little portions of the boards. Present the tentative learning with students. Others talk about the board work, we invite them to think about it and draw conjectures about what it is, and then that creates a thinking discussion about this and engages in a variety of different boards this way. Are they thinking? - We are the educators, we are creating the experience. We are very deliberate about what that experience is.  -Random groups - creates a space where students can actually learn from each other. Random groups is the engine to make all of this work. -How can I help teachers' notice things? -Try to pull from teachers something that is absolutely positive about what they already do. What is the best lesson you ever taught? How do we amplify their successes instead of the urgency of the immediate? Connect with Peter: Buildingthinkingclassrooms.com Facebook: Groups→ Search “Building Thinking Classrooms” and find your group 50+

In Episode 131, Chey and Pav reflect on how they've been implementing "Thinking Classrooms" in their respective learning spaces. The "Thinking Classroom" model has been coined by mathematician Dr. Peter Liljedahl and his work of creating math learning spaces that encourage students to think more with their math tasks. This problems based approach has several best practices attached to it (outlined by this edutopia post by Peter, himself) and Chey and Pav talk about a few of the first chapters and how they've implemented these strategies. Pav teaches Math and Science, and Chey teaches Language and History - so it has been interesting to see how the two of them use the Thinking Classroom model in different ways to support learning. Learn more about Building Thinking Classrooms from his book found here, and his website. Chey and Pav are always open and willing to engage in meaningful chatter about educational topics. Check out all their content at cheyandpav.com. The Chey and Pav Show! A rich discussion with several a-ha! moments throughout. Tune into this great chat, and as always, be a part of it by tagging @CheyandPav #CheyandPav on X! Tell us what you think, interact, and give us your feedback and reflections. Check out all the podcast episodes, recent and upcoming presentations, the Chey and Pav Blog, and all the other amazing things they are up to at CheyandPav.com! If you're looking for dynamic presenters for professional development, or a seminar or keynote address for a conference, please reach out to us at info@cheyandpav.com. Chey and Pav Educational Services, Inc.

In this episode, join Kyle, Dean, and Maegan as they share the latest insights gleaned from Peter Liljedahl on the new ideas taking hold in Thinking Classrooms. They take a deep dive into the art of crafting a Thinking Classroom lesson, dissecting the distinct phases of launch, body, and close. Explore how the nature of your task, be it divergent or convergent, shapes the optimal approach to concluding your lesson. Discover three new methods for wrapping up sessions: delve into the power of notice and name consolidation, embrace the collaborative notes strategy, and spice up your check for understanding with the mild-medium-spicy approach. Tune in for practical tips on seamlessly incorporating these freshly-developed closing techniques into your own Thinking Classroom. Elevate your teaching game with this enriching episode! To see images of each of these closing methods, visit: https://thinkthankthunk.kylewebb.ca/ep-10/ At the end, Dean mentions Tim Brzesinski's (⁠@TimBrzezinski⁠) BTC rubric which you can find here: ⁠http://tinyurl.com/BTCrubric

In this episode, Jenn and I interview Peter Liljedahl, the author of Building Thinking Classrooms in Mathematics: 14 Teaching Practices for Enhancing Learning. As former math teachers, Jenn and I had a great time talking with Peter about concrete and actionable ways teachers can improve math instruction. The practices are simple, high impact, and are easy and cheap to implement. Given what we know now, not implementing these 14 practices borders on educational malpractice. As always, send your comments, questions, and show ideas to mike@schoolleadershipshow.com.  Consider rating the podcast in iTunes and leaving a comment.  And please pass the show along to your colleagues.  Additionally, if you have other NON-education books with implications for school leaders, send those suggestions our way, too. And finally, If you or someone you know would like to sponsor the show, send Mike an email at mike@schoolleadershipshow.com.

With decades of experience in education, Dr. Peter Liljedahl realized that classrooms and workspaces have long been failing to engage those within them. He began a push to shift the paradigm of learning by challenging every classroom norm he could find - and it worked. Dr. Liljedahl was able to increase student thinking and engagement, and his revolutionary ideas are now able to be applied to work around the world.Dr. Peter Liljedahl is an author, researcher, and Professor of Faculty Education at Simon Fraser University in Vancouver, Canada. He has authored or co-authored 38 journal articles, over 50 conference papers, and 12 books including Building Thinking Classrooms. Working within education for decades, Peter consults regularly with schools, school districts, and ministries of education on issues of teaching and learning, assessment, and numeracy. In this episode, Dart and Peter discuss:- Peter's redesign of the classroom and how it can be applied to work- How to create an environment that cultivates thinking- Transforming norms to achieve better results- The importance of collaboration in work and learning- The best ways to evaluate employee performance- Deconstructing ideas into actionable points- What creates “Aha!” moments- The structure of a good task- And other topics…Dr. Peter Liljedahl is an author, researcher, and Professor of Faculty Education at Simon Fraser University in Vancouver, Canada. He has authored or co-authored over 38 book chapters, 38 journal articles, over 50 conference papers, and 12 books including Building Thinking Classrooms. Working within education for decades, Peter consults regularly with schools, school districts, and ministries of education on issues of teaching and learning, assessment, and numeracy. Peter is the current president of the Canadian Mathematics Education Study Group (CMESG) and the International Group for the Psychology of Mathematics Education (PME). He also serves on various editorial boards and is a senior editor of IJSME. Dr. Liljedahl recently received the Cmolik Prize for the enhancement of public education in BC as well as the Margaret Sinclair Memorial Award for innovation and excellence in mathematics education.Resourced mentioned:Building Thinking Classrooms in Mathematics, Grades K-12, by Peter Liljedahl: https://www.amazon.com/Building-Thinking-Classrooms-Mathematics-Grades/dp/1544374836Weapons of the Weak, by James Scott: https://www.amazon.com/Weapons-Weak-Everyday-Peasant-Resistance/dp/0300036418 A Pattern Language, by Christopher Alexander: https://www.amazon.com/Pattern-Language-Buildings-Construction-Environmental/dp/0195019199Connect with Peter:https://buildingthinkingclassrooms.com/Facebook Groups: Thinking Classrooms

Today we speak with Robert Barth, a high school math teacher from the South side of Chicago. Robert shares his experience with teaching with the original flipped classroom model and how he's morphed it over the years to incorporate Peter Liljedahl's work on Building Thinking Classrooms and the Make Math Moments “Real” Flipped Classroom approach incorporating teaching through task. Listen in as Robert wonders how to engage students who give push back when working in groups and sharing their thinking. You'll hear about teacher moves you can make to motivate students who seem to be unwilling to engage and how to balance your class time between “group thinking” and “individual thinking”. This is another Math Mentoring Moment episode where we chat with a teacher like you who is working through some problems of practice and together we brainstorm ways to overcome them. You'll Learn: Why the “double-flipped” classroom model might be helpful for those who have struggled to implement problem based lessons in the past;Why taking the time to be explicit with students as to why we do what we do in math class; The teacher moves we can leverage to motivate students who seem unwilling to engage;Why too much “group-think” time can may limit the necessary “individual-think” time that students need to individually reflect; and,How we can incorporate routines to intentionally promote the development of relational trust in our mathematics communities.Resources: Quiet - Susan Cain [Book]Episode 204: How To Craft Mentoring Moments - Jim StrachanMake Math Moments Problem Based Lessons & UnitsDistrict Math Leaders: How are you ensuring that you support those educators who need a nudge to spark a focus on growing their pedagogical-content knowledge? What about opportunities for those who are eager and willing to elevate their practice, but do not have the support? Book a call with our District Improvement Program Team to learn how we can not only help you craft, refine and implement your district math learning goals, but also provide all of the professional learning supports your educators need to grow at the speed of their learning. Book a short conversation with our team now.  Please help new listeners find the show. Leave a rating or review on your platform. Get a Customized Math Improvement Plan For Your District.Are you district leader for mathematics? Take the 12 minute assessment and you'll get a free, customized improvement plan to shape and grow the 6 parts of any strong mathematics program.Take the assessment

In this episode we bring back on the podcast for the third time the godfather of the Thinking Classroom Peter Liljedahl. We spoke with Peter way back on episode 21 of the podcast about how he built the components of the thinking classroom, episode 98 on group work and how to choose tasks, and in this episode Peter breaks down the three components of closing your lessons so students walk away feeling confident and connected to the learning that took place. You'll Learn: Why it is so uplifting when an entire group is speaking about the same idea;How to see improvement with your students when Building A Thinking Classroom;Why Building Thinking Classrooms is still a problem to be solved;Why the “closing out of the lesson” is one of the most important elements of a Thinking Classrooms Lesson;Why we need to improve student experiences in math class;Why you need to close out the lesson by tying a bow on it;Why worked examples can carry a lot of benefit in how we construct them, but also how we review or reference them; What is the difference between closing out a lesson and consolidating a lesson?Resources: Building Thinking ClassroomsMake Math Moments Problem Based Units & TasksDistrict Math Leaders: How are you ensuring that you support those educators who need a nudge to spark a focus on growing their pedagogical-content knowledge? What about opportunities for those who are eager and willing to elevate their practice, but do not have the support? Book a call with our District Improvement Program Team to learn how we can not only help you craft, refine and implement your district math learning goals, but also provide all of the professional learning supports your educators need to grow at the speed of their learning. Book a short conversation with our team now. Please help new listeners find the show. Leave a rating or review on your platform. Get a Customized Math Improvement Plan For Your District.Are you district leader for mathematics? Take the 12 minute assessment and you'll get a free, customized improvement plan to shape and grow the 6 parts of any strong mathematics program.Take the assessment

Join Kyle and Maegan as they dive into Chapter 15 from Building Thinking Classrooms by Peter Liljedahl. They address the big question surrounding how teacher can realistically implement all of the Thinking Classroom practices without overwhelming themselves and their students. They get into the four toolkits laid out in the book and share some tips and ideas on how to best implement each toolkit. Additionally, they briefly address the challenges presented when we see students being really successful in groups, but struggling on individual assessments and discuss the alternate pseudosequence provided for teachers who are already comfortable teaching in a Thinking Classroom. Image of the 4 Toolkits: https://bit.ly/BTC-framework Image of the 2 Toolkits for already experienced Thinking Classroom teachers: https://bit.ly/reBTC-framework This episode is the final in the series where we go through each chapter of Building Thinking Classrooms by Peter Liljedahl.

Join Kyle and Maegan as they dive into Chapter 14 from Building Thinking Classrooms by Peter Liljedahl. They discuss the big question most teachers have about Thinking Classrooms: how do we grade our students? By utilizing the navigation instruments as grading tools, they share how teachers can shift from a points-gathering paradigm towards a data-gathering paradigm and better reflect the achievement of learners in a Thinking Classroom. A large portion of this episode discusses questions addressed in the FAQ and builds on Maegan and Kyle's classroom experience. The Myth of Objectivity in Mathematics Assessment by Lew Romagnano (PDF) Image of the 3 different parachute packers: https://bit.ly/BTCparachutepackers Image of a navigation instrument used to determine a grade: https://bit.ly/BTCnavgrade This episode is the fifteenth in the series where we go through each chapter of Building Thinking Classrooms by Peter Liljedahl.

Join Kyle and Maegan as they dive into Chapter 13 from Building Thinking Classrooms by Peter Liljedahl. They discuss how all assessment should be formative assessment, and some of it will end up being summative. We dive into how to use the navigation instruments suggested in the book and explore how they can better support students in better understanding where they are in their learning journey. In the second half of the episode, you'll hear them dive into the FAQ's and share some of their experiences implementing these in the classroom. Tune in to hear how these simple navigation instruments can become a game-changer in your Thinking Classroom for you and your students. Image of a navigation instrument for Repeating Patterns: https://bit.ly/RPnavinstrument Maegan's Marching Band example: https://bit.ly/MGmarchingband This episode is the fourteenth in the series where we go through each chapter of Building Thinking Classrooms by Peter Liljedahl.

Join Kyle and Maegan as they dive into Chapter 12 from Building Thinking Classrooms by Peter Liljedahl. They discuss the idea of evaluating what we value in our Thinking Classroom. If we value perserverence, risk-taking, and collaboration we need to evaluate these in order to develop these competencies in our students. Listen in for a simple, but effective, way of remixing traditional rubrics into something that connects better with how our students learn. This chapter is essential for fostering effective thinkers in our classrooms. An example of one of these rubrics. This episode is the thirteenth in the series where we go through each chapter of Building Thinking Classrooms by Peter Liljedahl.

Peter Liljedahl is literally changing the math classroom.  His book "Building Thinking Classrooms" has taken the educational world by storm with a simple message: instead of teaching students to memorize, we have to teach them to think.  Sounds trite, but if you ... think about it, traditional classrooms are not designed that way!Today, Peter explains to Vanessa how a "thinking classroom" swaps out tables for vertical whiteboards to reduce barriers for student interaction in problem-solving, and how small randomized groups foster collaboration that lifts the whole class.  He also shares what his time as an Olympic athlete (yep!) taught him about the difference between focusing on the rewarding work of process vs the perilous trap of focusing on outcomes.About Peter: (Website, Twitter)Dr. Peter Liljedahl is a Professor of Mathematics Education in the Faculty of Education and an associate member in the Department of Mathematics at Simon Fraser University in Vancouver, Canada.  He consults regularly with schools, school districts, and ministries of education on issues of teaching and learning, assessment, and numeracy.Connect with us:Vanessa Vakharia: @themathguru (Insta, Twitter, TikTok)Math Therapy: @maththerapy (Twitter)

How we teach and what we teach are both really important. In this episode Pam and Kim wrap up their discussion on Peter Liljedahl's book Building Thinking Classrooms and how it meshes with the Math Is Figure-Out-Able movement.Talking Points:When we suggest to defront the classsroomDon't let language hamper the math for students during a Rich TaskConsolidation versus Math CongressUse hints and extensions to keep students at the edge of the Zone of Proximal development and that requires knowing the math deeplyTeachers need to know both the "how" and the "what" of the math for students to be successfulSee Ep 128 for more about students can do more than they can say and say more than they can representCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics education

We think Dr. Peter Liljedahl has some great ideas about how to keep students thinking and reasoning in math class. In this episode Pam and Kim continue to discuss some of his ideas and how they align with the Math is Figure-Out-Able mindset. Talking Points: Which questions to answer Get in, get outApproach groups with your own questionUsing neutral responsesCheck out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC

We love it when students are thinking and reasoning, and it's important to know how best to build and experience sophisticated strategies. In this episode Pam and Kim continue discussing Dr. Peter Liljedahl's work and finetune where it's appropriate to use vertical nonpermanent surfaces, and what other kind of tasks we should be doing whole class with students.Talking Points:Randomized Groups at Vertical Non Permanent Surfaces in random groups are great for Rich Tasks that follow your curriculum Problem Strings are best used whole class to build specific strategies, models, and big ideasSee Episode 157 for Pam and Kim's introductory comments about Dr. Liljedahl's work. Check out Pam's social media (I changed this to "Pam's" since it doesn't include mine)Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC

We want our students to be confident problem solvers who can think and reason through complex problems. In this episode, Pam and Kim highlight some of Dr. Peter Liljedahl's work on Building Thinking Classrooms to use student's natural inclinations to help them work better and more collaboratively. Talking Points:It's about thinking, not mimickingThinking Tasks not mimicking tasksVertical Non Permanent SurfacesVisibly random groupsIt takes time for kids to accept working in random groupsPulse of the room: Are student's opting out? What math are groups using?The "how " is important, but so is the "what"Check out our social mediaTwitter: @PWHarrisInstagram: Pam Harris_mathFacebook: Pam Harris, author, mathematics educationLinkedin: Pam Harris Consulting LLC

How can we build thinking classrooms to create memorable math moments? In this special episode we share our opening session of the 2022 Make Math Moments Virtual Summit.Join Kyle, Jon, and Peter Liljedahl as they unpack how elements of a Thinking Classroom are entwined in the Make Math Moments 3-Part Framework. You'll Learn: How to structure your lessons so they are engaging and encourage student thinking;What classroom structures can you put together to make every moment in your classroom matter;What are key questions you can ask students to gain the most insight into their thinking. Resources: Make Math Moments Virtual SummitTake the Make Math Moments Math Program Assessment Tool [Classroom Teacher & Leader Versions]Join the Academy - Free for 30 DaysDistrict Leader Resources:Take the Make Math Moments Math Program Assessment Tool The Make Math Moments District Planning Workbook [First 3 pages] Learn About Our District Improvement ProgramAre you a district mathematics leader interested in crafting a mathematics professional learning plan that will transform your district mathematics program forever? Book a time to chat with us!Other Useful Resources and Supports: Make Math Moments Framework [Blog Article]Make Math Moments Problem-Based Lessons & Units Get a Customized Math Improvement Plan For Your District.Are you district leader for mathematics? Take the 12 minute assessment and you'll get a free, customized improvement plan to shape and grow the 6 parts of any strong mathematics program.Take the assessment

In too many classrooms, our students aren't really thinking. What they're doing instead is more like mimicking, and my guest Peter Liljedahl is determined to change that. In this episode, we'll learn about his Thinking Classroom approach to instruction, where students are up on their feet, actively and collaboratively problem-solving, in a format that has taken the math world (and beyond) by storm.  Thanks to Listenwise and Wipebook for sponsoring this episode.