Episodios

  • Season 4 | Episode 8 – Janet Walkoe & Margaret Walton, Exploring the Seeds of Algebraic Reasoning

    Season 4 | Episode 8 – Janet Walkoe & Margaret Walton, Exploring the Seeds of Algebraic Reasoning
    Dec 18 2025
    Janet Walkoe & Margaret Walton, Exploring the Seeds of Algebraic Reasoning ROUNDING UP: SEASON 4 | EPISODE 8 Algebraic reasoning is defined as the ability to use symbols, variables, and mathematical operations to represent and solve problems. This type of reasoning is crucial for a range of disciplines. In this episode, we're talking with Janet Walkoe and Margaret Walton about the seeds of algebraic reasoning found in our students' lived experiences and the ways we can draw on them to support student learning. BIOGRAPHIES Margaret Walton joined Towson University's Department of Mathematics in 2024. She teaches mathematics methods courses to undergraduate preservice teachers and courses about teacher professional development to education graduate students. Her research interests include teacher educator learning and professional development, teacher learning and professional development, and facilitator and teacher noticing. Janet Walkoe is an associate professor in the College of Education at the University of Maryland. Janet's research interests include teacher noticing and teacher responsiveness in the mathematics classroom. She is interested in how teachers attend to and make sense of student thinking and other student resources, including but not limited to student dispositions and students' ways of communicating mathematics. RESOURCES "Seeds of Algebraic Thinking: a Knowledge in Pieces Perspective on the Development of Algebraic Thinking" "Seeds of Algebraic Thinking: Towards a Research Agenda" NOTICE Lab "Leveraging Early Algebraic Experiences" TRANSCRIPT Mike Wallus: Hello, Janet and Margaret, thank you so much for joining us. I'm really excited to talk with you both about the seeds of algebraic thinking. Janet Walkoe: Thanks for having us. We're excited to be here. Margaret Walton: Yeah, thanks so much. Mike: So for listeners, without prayer knowledge, I'm wondering how you would describe the seeds of algebraic thinking. Janet: OK. For a little context, more than a decade ago, my good friend and colleague, [Mariana] Levin—she's at Western Michigan University—she and I used to talk about all of the algebraic thinking we saw our children doing when they were toddlers—this is maybe 10 or more years ago—in their play, and just watching them act in the world. And we started keeping a list of these things we saw. And it grew and grew, and finally we decided to write about this in our 2020 FLM article ["Seeds of Algebraic Thinking: Towards a Research Agenda" in For the Learning of Mathematics] that introduced the seeds of algebraic thinking idea. Since they were still toddlers, they weren't actually expressing full algebraic conceptions, but they were displaying bits of algebraic thinking that we called "seeds." And so this idea, these small conceptual resources, grows out of the knowledge and pieces perspective on learning that came out of Berkeley in the nineties, led by Andy diSessa. And generally that's the perspective that knowledge is made up of small cognitive bits rather than larger concepts. So if we're thinking of addition, rather than thinking of it as leveled, maybe at the first level there's knowing how to count and add two groups of numbers. And then maybe at another level we add two negative numbers, and then at another level we could add positives and negatives. So that might be a stage-based way of thinking about it. And instead, if we think about this in terms of little bits of resources that students bring, the idea of combining bunches of things—the idea of like entities or nonlike entities, opposites, positives and negatives, the idea of opposites canceling—all those kinds of things and other such resources to think about addition. It's that perspective that we're going with. And it's not like we master one level and move on to the next. It's more that these pieces are here, available to us. We come to a situation with these resources and call upon them and connect them as it comes up in the context. Mike: I think that feels really intuitive, particularly for anyone who's taught young children. That really brings me back to the days when I was teaching kindergartners and first graders. I want to ask you about something else. You all mentioned several things like this notion of "do, undo" or "closing in" or the idea of "in-betweenness" while we were preparing for this interview. And I'm wondering if you could describe what these things mean in some detail for our audience, and then maybe connect them back with this notion of the seeds of algebraic thinking. Margaret: Yeah, sure. So we would say that these are different seeds of algebraic thinking that kids might activate as they learn math and then also learn more formal algebra. So the first seed, the doing and undoing that you mentioned, is really completing some sort of action or process and then reversing it. So an example might be when a toddler stacks blocks or cups. I have lots of nieces and ...
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    17 m
  • Season 4 | Episode 7 - Tutita Casa, Anna Strauss, Jenna Waggoner & Mhret Wondmagegne, Developing Student Agency: The Strategy Showcase

    Season 4 | Episode 7 - Tutita Casa, Anna Strauss, Jenna Waggoner & Mhret Wondmagegne, Developing Student Agency: The Strategy Showcase
    Dec 4 2025
    Tutita Casa, Anna Strauss, Jenna Waggoner & Mhret Wondmagegne, Developing Student Agency: The Strategy Showcase ROUNDING UP: SEASON 4 | EPISODE 7 When students aren't sure how to approach a problem, many of them default to asking the teacher for help. This tendency is one of the central challenges of teaching: walking the fine line between offering support and inadvertently cultivating dependence. In this episode, we're talking with a team of educators about a practice called the strategy showcase, designed to foster collaboration and help students engage with their peers' ideas. BIOGRAPHIES Tutita Casa is an associate professor of elementary mathematics education at the Neag School of Education at the University of Connecticut. Mhret Wondmagegne, Anna Strauss, and Jenna Waggoner are all recent graduates of the University of Connecticut School of Education and early career elementary educators who recently completed their first years of teaching. RESOURCE National Council of Teachers of Mathematics TRANSCRIPT Mike Wallus: Well, we have a full show today and I want to welcome all of our guests. So Anna, Mhret, Jenna, Tutita, welcome to the podcast. I'm really excited to be talking with you all about the strategy showcase. Jenna Waggoner: Thank you. Tutita Casa: It's our pleasure. Anna Strauss: Thanks. Mhret Wondmagegne: Thank you. Mike: So for listeners who've not read your article, Anna, could you briefly describe a strategy showcase? So what is it and what could it look like in an elementary classroom? Anna: So the main idea of the strategy showcase is to have students' work displayed either on a bulletin board—I know Mhret and Jenna, some of them use posters or whiteboards. It's a place where students can display work that they've either started or that they've completed, and to become a resource for other students to use. It has different strategies that either students identified or you identified that serves as a place for students to go and reference if they need help on a problem or they're stuck, and it's just a good way to have student work up in the classroom and give students confidence to have their work be used as a resource for others. Mike: That was really helpful. I have a picture in my mind of what you're talking about, and I think for a lot of educators that's a really important starting point. Something that really stood out for me in what you said just now, but even in our preparation for the interview, is the idea that this strategy showcase grew out of a common problem of practice that you all and many teachers face. And I'm wondering if we can explore that a little bit. So Tutita, I'm wondering if you could talk about what Anna and Jenna and Mhret were seeing and maybe set the stage for the problem of practice that they were working on and the things that may have led into the design of the strategy showcase. Tutita: Yeah. I had the pleasure of teaching my coauthors when they were master's students, and a lot of what we talk about in our teacher prep program is how can we get our students to express their own reasoning? And that's been a problem of practice for decades now. The National Council of Teachers of Mathematics has led that work. And to me, [what] I see is that idea of letting go and really being curious about where students are coming from. So that reasoning is really theirs. So the question is what can teachers do? And I think at the core of that is really trying to find out what might be limiting students in that work. And so Anna, Jenna, and Mhret, one of the issues that they kept bringing back to our university classroom is just being bothered by the fact that their students across the elementary grades were just lacking the confidence, and they knew that their students were more than capable. Mike: Jenna, I wonder if you could talk a little bit about, what did that actually look like? I'm trying to imagine what that lack of confidence translated into. What you were seeing potentially or what you and Anna and Mhret were seeing in classrooms that led you to this work. Jenna: Yeah, I know definitely we were reflecting, we were all in upper elementary, but we were also across grade levels anywhere from fourth to fifth grade all the way to sixth and seventh. And across all of those places, when we would give students especially a word problem or something that didn't feel like it had one definite answer or one way to solve it or something that could be more open-ended, we a lot of times saw students either looking to teachers. "I'm not sure what to do. Can you help me?" Or just sitting there looking at the problem and not even approaching it or putting something on their paper, or trying to think, "What do I know?" A lot of times if they didn't feel like there was one concrete approach to start the problem, they would shut down and feel like they weren't doing what they were supposed to or they didn't know what the right way to solve it was. And then ...
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    34 m
  • Season 4 | Episode 6 - Christy Pettis & Terry Wyberg, The Case for Choral Counting with Fractions

    Season 4 | Episode 6 - Christy Pettis & Terry Wyberg, The Case for Choral Counting with Fractions
    Nov 20 2025
    Christy Pettis & Terry Wyberg, The Case for Choral Counting with Fractions ROUNDING UP: SEASON 4 | EPISODE 6 How can educators help students recognize similarities in the way whole numbers and fractions behave? And are there ways educators can build on students' understanding of whole numbers to support their understanding of fractions? The answer from today's guests is an emphatic yes. Today we're talking with Terry Wyberg and Christy Pettis about the ways choral counting can support students' understanding of fractions. BIOGRAPHIES Terry Wyberg is a senior lecturer in the Department of Curriculum and Instruction at the University of Minnesota. His interests include teacher education and development, exploring how teachers' content knowledge is related to their teaching approaches. Christy Pettis is an assistant professor of teacher education at the University of Wisconsin-River Falls. RESOURCES Choral Counting & Counting Collections: Transforming the PreK-5 Math Classroom by Megan L. Franke, Elham Kazemi, and Angela Chan Turrou Teacher Education by Design Number Chart app by The Math Learning Center TRANSCRIPT Mike Wallus: Welcome to the podcast, Terry and Christy. I'm excited to talk with you both today. Christy Pettis: Thanks for having us. Terry Wyberg: Thank you. Mike: So, for listeners who don't have prior knowledge, I'm wondering if we could just offer them some background. I'm wondering if one of you could briefly describe the choral counting routine. So, how does it work? How would you describe the roles of the teacher and the students when they're engaging with this routine? Christy: Yeah, so I can describe it. The way that we usually would say is that it's a whole-class routine for, often done in kind of the middle grades. The teachers and the students are going to count aloud by a particular number. So maybe you're going to start at 5 and skip-count by 10s or start at 24 and skip-count by 100 or start at two-thirds and skip-count by two-thirds. So you're going to start at some number, and you're going to skip-count by some number. And the students are all saying those numbers aloud. And while the students are saying them, the teacher is writing those numbers on the board, creating essentially what looks like an array of numbers. And then at certain points along with that talk, the teacher will stop and ask students to look at the numbers and talk about things they're noticing. And they'll kind of unpack some of that. Often they'll make predictions about things. They'll come next, continue the count to see where those go. Mike: So you already pivoted to my next question, which was to ask if you could share an example of a choral count with the audience. And I'm happy to play the part of a student if you'd like me to. Christy: So I think it helps a little bit to hear what it would sound like. So let's start at 3 and skip-count by 3s. The way that I would usually tell my teachers to start this out is I like to call it the runway. So usually I would write the first three numbers. So I would write "3, 6, 9" on the board, and then I would say, "OK, so today we're going to start at 3 and we're going to skip-count by 3s. Give me a thumbs-up or give me the number 2 when you know the next two numbers in that count." So I'm just giving students a little time to kind of think about what those next two things are before we start the count together. And then when I see most people kind of have those next two numbers, then we're going to start at that 3 and we're going to skip-count together. Are you ready? Mike: I am. Christy: OK. So we're going to go 3… Mike & Christy: 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36. Christy: Keep going. Mike & Christy: 39, 42, 45, 48, 51. Christy: Let's stop there. So we would go for a while like that until we have an array of numbers on the board. In this case, I might've been recording them, like where there were five in each row. So it would be 3, 6, 9, 12, 15 would be the first row, and the second row would say 18, 21, 24, 27, 30, and so on. So we would go that far and then I would stop and I would say to the class, "OK, take a minute, let your brains take it in. Give me a number 1 when your brain notices one thing. Show me 2 if your brain notices two things, 3 if your brain notices three things." And just let students have a moment to just take it in and think about what they notice. And once we've seen them have some time, then I would say, "Turn and talk to your neighbor, and tell them some things that you notice." So they would do that. They would talk back and forth. And then I would usually warm-call someone from that and say something like, "Terry, why don't you tell me what you and Mike talked about?" So Terry, do you have something that you would notice? Terry: Yeah, I noticed that the last column goes up by 15, Christy: The last column goes up by 15. OK, so you're saying that you see this 15, 30, 45? Terry: Yes. Christy: In that last ...
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    37 m
  • Season 4 | Episode 5 - Ramsey Merritt, Improving Students' Turn & Talk Experience

    Season 4 | Episode 5 - Ramsey Merritt, Improving Students' Turn & Talk Experience
    Nov 6 2025
    Ramsey Merritt, Improving Students' Turn & Talk Experience ROUNDING UP: SEASON 4 | EPISODE 5 Most educators know what a turn and talk is—but are your students excited to do them? In this episode, we put turn and talks under a microscope. We'll talk with Ramsey Merritt from the Harvard Graduate School of Education about ways to revamp and better scaffold turn and talks to ensure your students are having productive mathematical discussions. BIOGRAPHY Ramsey Merritt is a lecturer in education at Brandeis University and the director of leadership development for Reading (MA) Public Schools. He has taught and coached at every level of the U.S. school system in both public and independent schools from New York to California. Ramsey also runs an instructional leadership consulting firm, Instructional Success Partners, LLC. Prior to his career in education, he worked in a variety of roles at the New York Times. He is currently completing his doctorate in education leadership at Harvard Graduate School of Education. Ramsey's book, Diving Deeper with Upper Elementary Math, will be released in spring 2026. TRANSCRIPT Mike Wallus: Welcome to the podcast, Ramsey. So great to have you on. Ramsey Merritt: It is my pleasure. Thank you so much for having me. Mike: So turn and talk's been around for a while now, and I guess I'd call it ubiquitous at this point. When I visit classrooms, I see turn and talks happen often with quite mixed results. And I wanted to start with this question: At the broadest level, what's the promise of a turn and talk? When strategically done well, what's it good for? Ramsey: I think at the broadest level, we want students talking about their thinking and we also want them listening to other students' thinking and ideally being open to reflect, ask questions, and maybe even change their minds on their own thinking or add a new strategy to their thinking. That's at the broadest level. I think if we were to zoom in a little bit, I think turn and talks are great for idea generation. When you are entering a new concept or a new lesson or a new unit, I think they're great for comparing strategies. They're obviously great for building listening skills with the caveat that you put structures in place for them, which I'm sure we'll talk about later. And building critical-thinking and questioning skills as well. I think I've also seen turn and talks broadly categorized into engagement, and it's interesting when I read that because to me I think about engagement as the teacher's responsibility and what the teacher needs to do no matter what the pedagogical tool is. So no matter whether it's a turn and talk or something else, engagement is what the teacher needs to craft and create a moment. And I think a lot of what we'll probably talk about today is about crafting moments for the turn and talk. In other words, how to engage students in a turn and talk, but not that a turn and talk is automatically engagement. Mike: I love that, and I think the language that you've used around crafting is really important. And it gets to the heart of what I was excited about in this conversation because a turn and talk is a tool, but there is an art and a craft to designing its implementation that really can make or break the tool itself. Ramsey: Yeah. If we look back a little bit as to where turn and talk came from, I sort of tried to dig into the papers on this. And what I found was that it seems as if turn and talks may have been a sort of spinoff of the think-pair-share, which has been around a little bit longer. And what's interesting in looking into this is, I think that turn and talks were originally positioned as a sort of cousin of think-pair-share that can be more spontaneous and more in the moment. And I think what has happened is we've lost the "think" part. So we've run with it, and we've said, "This is great," but we forgot that students still need time to think before they turn and talk. And so what I see a lot is, it gets to be somewhat too spontaneous, and certain students are not prepared to just jump into conversations. And we have to take a step back and sort of think about that. Mike: That really leads into my next question quite well because I have to confess that when I've attended presentations, there are points in time when I've been asked to turn and talk when I can tell you I had not a lot of interest nor a lot of clarity about what I should do. And then there were other points where I couldn't wait to start that conversation. And I think this is the craft and it's also the place where we should probably think about, "What are the pitfalls that can derail or have a turn and talk kind of lose the value that's possible?" How would you talk about that? Ramsey: Yeah, it is funny that we as adults have that reaction when people say, "Turn and talk." The three big ones that I see the most, and I should sort of say here, I've probably been in 75 to 100 buildings and triple or quadruple ...
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    28 m
  • Season 4 | Episode 4 - Pam Harris, Exploring the Power & Purpose of Number Strings

    Season 4 | Episode 4 - Pam Harris, Exploring the Power & Purpose of Number Strings
    Oct 23 2025
    Pam Harris, Exploring the Power & Purpose of Number Strings ROUNDING UP: SEASON 4 | EPISODE 4 I've struggled when I have a new strategy I want my students to consider and despite my best efforts, it just doesn't surface organically. While I didn't want to just tell my students what to do, I wasn't sure how to move forward. Then I discovered number strings. Today, we're talking with Pam Harris about the ways number strings enable teachers to introduce new strategies while maintaining opportunities for students to discover important relationships. BIOGRAPHY Pam Harris, founder and CEO of Math is Figure-out-able™, is a mom, a former high school math teacher, a university lecturer, an author, and a mathematics teacher educator. Pam believes real math is thinking mathematically, not just mimicking what a teacher does. Pam helps leaders and teachers to make the shift that supports students to learn real math. RESOURCES Young Mathematicians at Work by Catherine Fosnot and Maarten Dolk Procedural fluency in mathematics: Reasoning and decision-making, not rote application of procedures position by the National Council of Teachers of Mathematics Bridges number string example from Grade 5, Unit 3, Module 1, Session 1 (BES login required) Developing Mathematical Reasoning: Avoiding the Trap of Algorithms by Pamela Weber Harris and Cameron Harris Math is Figure-out-able!™ Problem Strings TRANSCRIPT Mike Wallus: Welcome to the podcast, Pam. I'm really excited to talk with you today. Pam Harris: Thanks, Mike. I'm super glad to be on. Thanks for having me. Mike: Absolutely. So before we jump in, I want to offer a quick note to listeners. The routine we're going to talk about today goes by several different names in the field. Some folks, including Pam, refer to this routine as "problem strings," and other folks, including some folks at The Math Learning Center, refer to them as "number strings." For the sake of consistency, we'll use the term "strings" during our conversation today. And Pam, with that said, I'm wondering if for listeners, without prior knowledge, could you briefly describe strings? How are they designed? How are they intended to work? Pam: Yeah, if I could tell you just a little of my history. When I was a secondary math teacher and I dove into research, I got really curious: How can we do the mental actions that I was seeing my son and other people use that weren't the remote memorizing and mimicking I'd gotten used to? I ran into the work of Cathy Fosnot and Maarten Dolk, and [their book] Young Mathematicians at Work, and they had pulled from the Netherlands strings. They called them "strings." And they were a series of problems that were in a certain order. The order mattered, the relationship between the problems mattered, and maybe the most important part that I saw was I saw students thinking about the problems and using what they learned and saw and heard from their classmates in one problem, starting to let that impact their work on the next problem. And then they would see that thinking made visible and the conversation between it and then it would impact how they thought about the next problem. And as I saw those students literally learn before my eyes, I was like, "This is unbelievable!" And honestly, at the very beginning, I didn't really even parse out what was different between maybe one of Fosnot's rich tasks versus her strings versus just a conversation with students. I was just so enthralled with the learning because what I was seeing were the kind of mental actions that I was intrigued with. I was seeing them not only happen live but grow live, develop, like they were getting stronger and more sophisticated because of the series of the order the problems were in, because of that sequence of problems. That was unbelievable. And I was so excited about that that I began to dive in and get more clear on: What is a string of problems? The reason I call them "problem strings" is I'm K–12. So I will have data strings and geometry strings and—pick one—trig strings, like strings with functions in algebra. But for the purposes of this podcast, there's strings of problems with numbers in them. Mike: So I have a question, but I think I just want to make an observation first. The way you described that moment where students are taking advantage of the things that they made sense of in one problem and then the next part of the string offers them the opportunity to use that and to see a set of relationships. I vividly remember the first time I watched someone facilitate a string and feeling that same way, of this routine really offers kids an opportunity to take what they've made sense of and immediately apply it. And I think that is something that I cannot say about all the routines that I've seen, but it was really so clear. I just really resonate with that experience of, what will this do for children? Pam: Yeah, and if I can offer an additional word in there, it ...
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    44 m
  • Season 4 | Episode 3 - Kim Montague—I Have, You Need: The Utility Player of Instructional Routines

    Season 4 | Episode 3 - Kim Montague—I Have, You Need: The Utility Player of Instructional Routines
    Oct 9 2025
    Kim Montague, I Have, You Need: The Utility Player of Instructional Routines ROUNDING UP: SEASON 4 | EPISODE 3 In sports, a utility player is someone who can play multiple positions competently, providing flexibility and adaptability. From my perspective, the routine I have, you need may just be the utility player of classroom routines. Today we're talking with Kim Montague about I have, you need and the ways it can be used to support everything from fact fluency to an understanding of algebraic properties. BIOGRAPHY Kim Montague is a podcast cohost and content lead at Math is Figure-out-able™. She has also been a teacher for grades 3–5, an instructional coach, a workshop presenter, and a curriculum developer. Kim loves visiting classrooms and believes that when you know your content and know your kids, real learning occurs. RESOURCES Math is Figure-out-able!™ Podcast Math is FigureOutAble!™ Guide (Download) Journey Coaching TRANSCRIPT Mike Wallus: Welcome to the podcast, Kim. I am really excited to talk with you today. So let me do a little bit of grounding. For listeners without prior knowledge, I'm wondering if you could briefly describe the I have, you need routine. How does it work, and how would you describe the roles that the teacher and the student play? Kim Montague: Thanks for having me, Mike. I'm excited to be here. I think it's an important routine. So for those people who have never heard of I have, you need, it is a super simple routine that came from a desire that I had for students to become more fluent with partners of ten, hundred, thousand. And so it simply works as a call-and-response. Often I start with a context, and I might say, "Hey, we're going to pretend that we have 10 of something, and if I have 7 of them, how many would you need so that together we have those 10?" And so it's often prosed as a missing addend. With older students, obviously, I'm going to have some higher numbers, but it's very call-and-response. It's playful. It's game-like. I'll lob out a question, wait for students to respond. I'm choosing the numbers, so it's a teacher-driven purposeful number sequence, and then students figure out the missing number. I often will introduce a private signal so that kids have enough wait time to think about their answer and then I'll signal everyone to give their response. Mike: OK, so there's a lot to unpack there. I cannot wait to do it. One of the questions I've been asking folks about routines this season is just, at the broadest level, regardless of the numbers that the educator selects, how would you describe what you think I have, you need is good for? What's the routine good for? How can an educator think about its purpose or its value? You mentioned fluency. Maybe say a little bit more about that and if there's anything else that you think it's particularly good for. Kim: So I think one of the things that is really fantastic about I have, you need is that it's really simple. It's a simple-to-introduce, simple-to-facilitate routine, and it's great for so many different grade levels and so many different areas of content. And I think that's true for lots of routines. Teachers don't have time to reintroduce something brand new every single day. So when you find a routine that you can exchange pieces of content, that's really helpful. It's short, and it can be done anywhere. And like I said, it builds fluency, which is a hot topic and something that's important. So I can build fluency with partners of ten, partners of a hundred, partners of thousand, partners of one. I can build complementary numbers for angle measure and fractions. Lots of different areas depending on the grade that you're teaching and what you're trying to focus on. Mike: So one of the things that jumped out for me is the extent to which this can reveal structure. When we're talking about fluency, in some ways that's code for the idea that a lot of our combinations we're having kids think about—the structure of ten or a hundred or a thousand or, in the case of fractions, one whole and its equivalence. Does that make sense? Kim: Yeah, absolutely. So we have a really cool place value system. And I think that we give a lot of opportunities, maybe to place label, but we don't give a lot of opportunities to experience the structure of number. And so there are some very nice structures within partners of ten that then repeat themselves, in a way, within partners of a hundred and partners of a thousand and partners of one, like I mentioned. And if kids really deeply understand the way numbers form and the way they are fitting together, we can make use of those ideas and those experiences within other things like addition, subtraction. So this routine is not simply about, "Can you name a partner number?," but it's laying foundation in a fun experience that kids then are gaining fluency that is going to be applied to other work that they're doing. Mike: I love that, and I think it's a great...
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    31 m
  • Season 4 | Episode 2 - Dr. Sue Looney - Same but Different: Encouraging Students to Think Flexibly

    Season 4 | Episode 2 - Dr. Sue Looney - Same but Different: Encouraging Students to Think Flexibly
    Sep 18 2025
    Sue Looney, Same but Different: Encouraging Students to Think Flexibly ROUNDING UP: SEASON 4 | EPISODE 2 Sometimes students struggle in math because they fail to make connections. For too many students, every concept feels like its own entity without any connection to the larger network of mathematical ideas. On the podcast today, we're talking with Dr. Sue Looney about the powerful same and different routine. We explore the ways that teachers can use this routine to help students identify connections and foster flexible reasoning. BIOGRAPHY Sue Looney holds a doctorate in curriculum and instruction with a specialty in mathematics from Boston University. Sue is particularly interested in our most vulnerable and underrepresented populations and supporting the teachers that, day in and day out, serve these students with compassion, enthusiasm, and kindness. RESOURCES Same but Different Math Looney Math TRANSCRIPT Mike Wallus: Students sometimes struggle in math because they fail to make connections. For too many students, every concept feels like its own entity without any connection to the larger network of mathematical ideas. Today we're talking with Sue Looney about a powerful routine called same but different and the ways teachers can use it to help students identify connections and foster flexible reasoning. Well, hi, Sue. Welcome to the podcast. I'm so excited to be talking with you today. Sue Looney: Hi Mike. Thank you so much. I am thrilled too. I've been really looking forward to this. Mike: Well, for listeners who don't have prior knowledge, I'm wondering if we could start by having you offer a description of the same but different routine. Sue: Absolutely. So the same but different routine is a classroom routine that takes two images or numbers or words and puts them next to each other and asks students to describe how they are the same but different. It's based in a language learning routine but applied to the math classroom. Mike: I think that's a great segue because what I wanted to ask is: At the broadest level—regardless of the numbers or the content or the image or images that educators select—how would you explain what [the] same but different [routine] is good for? Maybe put another way: How should a teacher think about its purpose or its value? Sue: Great question. I think a good analogy is to imagine you're in your ELA— your English language arts—classroom and you were asked to compare and contrast two characters in a novel. So the foundations of the routine really sit there. And what it's good for is to help our brains think categorically and relationally. So, in mathematics in particular, there's a lot of overlap between concepts and we're trying to develop this relational understanding of concepts so that they sort of build and grow on one another. And when we ask ourselves that question—"How are these two things the same but different?"—it helps us put things into categories and understand that sometimes there's overlap, so there's gray space. So it helps us move from black and white thinking into this understanding of grayscale thinking. And if I just zoom out a little bit, if I could, Mike—when we zoom out into that grayscale area, we're developing flexibility of thought, which is so important in all aspects of our lives. We need to be nimble on our feet, we need to be ready for what's coming. And it might not be black or white, it might actually be a little bit of both. So that's the power of the routine and its roots come in exploring executive functioning and language acquisition. And so we just layer that on top of mathematics and it's pure gold. Mike: When we were preparing for this podcast, you shared several really lovely examples of how an educator might use same but different to draw out ideas that involve things like place value, geometry, equivalent fractions, and that's just a few. So I'm wondering if you might share a few examples from different grade levels with our listeners, perhaps at some different grade levels. Sue: Sure. So starting out, we can start with place value. It really sort of pops when we look in that topic area. So when we think about place value, we have a base ten number system, and our numbers are based on this idea that 10 of one makes one group of the next. And so, using same but different, we can help young learners make sense of that system. So, for example, we could look at an image that shows a 10-stick. So maybe that's made out of Unifix cubes. There's one 10-stick a—stick of 10—with three extras next to it and next to that are 13 separate cubes. And then we ask, "How are they the same but different?" And so helping children develop that idea that while I have 1 ten in that collection, I also have 10 ones. Mike: That is so amazing because I will say as a former kindergarten and first grade teacher, that notion of something being a unit of 1 composed of smaller units is such a big deal. And we can talk about ...
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    28 m
  • Season 4 | Episode 1 - Dr. Christopher Danielson, Which One Doesn't Belong Routine

    Season 4 | Episode 1 - Dr. Christopher Danielson, Which One Doesn't Belong Routine
    Sep 4 2025
    Christopher Danielson, Which One Doesn't Belong? Routine: Fostering Flexible Reasoning ROUNDING UP: SEASON 4 | EPISODE 1 The idea of comparing items and looking for similarities and differences has been explored by many math educators. Christopher Danielson has taken this idea to new heights. Inspired by the Sesame Street song "One of These Things (Is Not Like the Others)," Christopher wrote the book Which One Doesn't Belong? In this episode, we'll ask Christopher about the routine of the same name and the features that make it such a powerful learning experience for students. BIOGRAPHY Christopher Danielson started teaching in 1994 in the Saint Paul (MN) Public Schools. He earned his PhD in mathematics education from Michigan State University in 2005 and taught at the college level for 10 years after that. Christopher is the author of Which One Doesn't Belong?, How Many?, and How Did You Count? Christopher also founded Math On-A-Stick, a large-scale family math playspace at the Minnesota State Fair. RESOURCES What Is "Which One Doesn't Belong?" Talking Math With Your Kids by Christopher Danielson Math On-A-Stick 5 Practices for Orchestrating Productive Mathematics Discussion by Margaret (Peg) Smith & Mary Kay Stein How Many?: A Counting Book by Christopher Danielson How Did You Count? A Picture Book by Christopher Danielson TRANSCRIPT Mike Wallus: The idea of comparing items and looking for similarities and differences has been explored by many math educators. That said, Christopher Danielson has taken this idea to new heights. Inspired by Sesame Street's [song] "One of These Things (Is Not Like the Others)," Christopher wrote the book Which One Doesn't Belong? In this episode, we'll ask Christopher about the Which one doesn't belong? routine and the features that make it such a powerful learning experience for students. Well, welcome to the podcast, Christopher. I'm excited to be talking with you today. Christopher Danielson: Thank you for the invitation. Delightful to be invited. Mike: I would love to chat a little bit about the routine Which one doesn't belong? So, I'll ask a question that I often will ask folks, which is: If I'm a listener, and I don't have prior knowledge of that routine, how would you describe it for someone? Christopher: Yeah. Sesame Street, back in the day, had a routine called Which one doesn't belong? There was a little song that went along with it. And for me, the iconic Sesame Street image is [this:] Grover is on the stairs up to the brownstone on the Sesame Street set, and there are four circles drawn in a 2-by-2 grid in chalk on the wall. And there are a few of the adults and a couple of the puppets sitting around, and they're asking Grover and singing the song, "Which One of Them Doesn't Belong?" There are four circles. Three of them are large and one is small—or maybe it's the other way around, I don't remember. So, there's one right answer, and Grover is thinking really hard—"think real hard" is part of the song. They're singing to him. He's under kind of a lot of pressure to come up with which one doesn't belong and fortunately, Grover succeeds. Grover's a hero. But what we're wanting kids to attend to there is size. There are three things that are the same size. All of them are the same shape, three that are the same size, one that has a different size. They're wanting to attend to size. Lovely. This one doesn't belong because it is a different size, just like my underwear doesn't belong in my socks drawer because it has a different function. I mean, it's not—for me there is, we could talk a little bit about this in a moment. The belonging is in that mathematical and everyday sense of objects and whether they belong. So, that's the Sesame Street version. Through a long chain of math educators, I came across a sort of tradition that had been flying along under the radar of rethinking that, with the idea being that instead of there being one property to attend to, we're going to have a rich set of shapes that have rich and interesting relationships with each other. And so Which one doesn't belong? depends on which property you're attending to. So, the first page of the book that I published, called Which One Doesn't Belong?, has four shapes on it. One is an equilateral triangle standing on a vertex. One is a square standing on a vertex. One is a rhombus, a nonsquare rhombus standing on its vertex, and it's not colored in. All the other shapes are colored in. And then there is the same nonsquare thrombus colored in, resting on a side. So, all sort of simple shapes that offer simple introductory properties, but different people are going to notice different things. Some kids will hone in on that. The one in the lower left doesn't belong because it's not colored in. Other kids will say, "Well, I'm counting the number of sides or the number of corners. And so, the triangle doesn't belong because all the others have four and it has three." Others will...
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