Episodios

  • Season 2 | Episode 18 - The Promise of Counting Collections - Guest: Danielle Robinson and Dr. Melissa Hedges

    Season 2 | Episode 18 - The Promise of Counting Collections - Guest: Danielle Robinson and Dr. Melissa Hedges
    May 23 2024
    Rounding Up Season 2 | Episode 18 – Counting Collections Guest: Danielle Robinson and Melissa Hedges Mike Wallus: Earlier this season, we released an episode focused on the complex and interconnected set of concepts that students engage with as they learn to count. In this follow-up episode, we're going to examine a powerful routine called “counting collections.” We'll be talking with Danielle Robinson and Dr. Melissa Hedges from the Milwaukee Public Schools about counting collections and the impact that this routine can have on student thinking. Mike: Well, welcome to the podcast, Danielle and Melissa. I can't tell you how excited I am to talk with y'all about the practice of counting collections. Danielle Robinson and Melissa Hedges: Thanks for having us. Yes, we're so excited to be here. Mike: I want to start this conversation by acknowledging that the two of you are actually part of a larger team of educators who really took this work on counting collections. You introduced it in the Milwaukee Public Schools. And, Melissa, I think I'll start with you. Can you take a moment to recognize the collaborators who have been a part of this work? Melissa: Absolutely. In addition to Danielle and myself, we are fortunate to work with three other colleagues: Lakesha King, Krista Beal, and Claire Madden. All three are early childhood coaches that actively support this work as well. Mike: So, Danielle, I wonder for some folks if we can help them see this practice more clearly. Can you spend time unpacking, what does counting collections look like in a classroom? If I walked in, what are some of the things that I might see? Danielle: Yeah, I think what's really amazing about counting collections is there might be some different ways that you might see counting collections happening in the classroom. When you walk into a classroom, you might see some students all over. Maybe they're sitting at tables, maybe they're on the carpet. And what they're doing is they're actually counting a baggie of objects. And really their job is to answer this question, this very simple but complicated question of, “How many?” And they get to decide how they want to count. Not only do they get to pick what they want to count, but they also get to pick their strategy of how they actually want to count that collection. They can use different tools. They might be using bowls or plates. They might be using 10-frames. They might be using number paths. You might see kiddos who are counting by ones. Danielle: You might see kids who are making different groupings. At times, you might also see kiddos [who] are in stations, and you might see a small group where a teacher is doing counting collections with a few kiddos. You might see them working with partners. And I think the beautiful piece of this and the unique part of counting collections within Milwaukee Public Schools is that we've been able to actually pair the counting trajectory from Doug Clements and Julie Sarama with counting collections where teachers are able to do an interview with their students, really see where they're at in their counting so that the kids are counting a just right collection for them—something that's not too easy, something that's not too hard, but something that is available for them to really push them in their understanding of counting. So, you're going to see kids counting different sizes. And we always tell the teachers it's a really beautiful moment when you're looking across the classroom and as a teacher, you can actually step back and know that every one of your kids are getting what they need in that moment. Because I think oftentimes, we really don't ever get to feel like that, where we feel like, “Wow, all my kids are getting what they need right now, and I know that I am providing the scaffolds that they need.” Mike: So, I want to ask you a few follow-ups, if I might, Danielle. Danielle: Yeah, of course. Mike: There's a bit of language that you used initially where I'm paraphrasing. And tell me where I get this wrong. You use the language “simple yet complicated,” I think. Am I hearing that right? Danielle: I did. I did, yeah. Mike: Tell me about that. Danielle: I think it's so interesting because a lot of times when we introduce this idea of counting collections with our teachers, they're like, “Wait a minute, so I'm supposed to give this baggie of a bunch of things to my students, and they just get to go decide how they want to count it?” And we're like, “Yeah, that is absolutely what we're asking you to do.” And they feel nervous because this idea of the kids, they're answering how many, but then there's all these beautiful pieces a part of it. Maybe kids are counting by ones, maybe they're deciding that they want to make groups, maybe they're working with a partner, maybe they're using tools. It's kind of opened up this really big, amazing idea of the simple question of how many. But there's just so many ...
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    28 m
  • Season 2 | Episode 17 – Making Sense of Spatial Reasoning - Guest: Dr. Robyn Pinilla

    Season 2 | Episode 17 – Making Sense of Spatial Reasoning - Guest: Dr. Robyn Pinilla
    May 9 2024
    Rounding Up Season 2 | Episode 17 – Spatial Reasoning Guest: Dr. Robyn Pinilla Mike Wallus: Spatial reasoning can be a nebulous concept, and it's often hard for many educators to define. In this episode, we're talking about spatial reasoning with Dr. Robyn Pinilla from the University of Texas, El Paso. We'll examine the connections between spatial reasoning and other mathematical concepts and explore different ways that educators can cultivate this type of reasoning with their students. Mike: Welcome to the podcast, Robyn. I'm really excited to be talking with you about spatial reasoning. Robyn Pinilla: And I am excited to be here. Mike: Well, let me start with a basic question. So, when we're talking about spatial reasoning, is that just another way of saying that we're going to be talking about ideas that are associated with geometry? Or are we talking about something bigger? Robyn: It's funny that you say it in that way, Mike, because geometry is definitely the closest mathematical content that we see in curricula, but it is something much bigger. So, I started with the misconception and then I used my own experiences to support that idea that this was just geometry because it was my favorite math course in high school because I could see the concepts modeled and I could make things more tangible. Drawing helped me to visualize some of those concepts that I was learning instead of just using a formula that I didn't necessarily understand. So, at that time, direct instruction really ruled, and I'm unsure what the conceptual understandings of my teachers even were because what I recall is doing numbers 3 through 47 odds in the back of the book and just plugging through these formulas. But spatial reasoning allows us to develop our concepts in a way that lead to deeper conceptual understanding. I liked geometry, and it gave me this vehicle for mathematizing the world. But geometry is really only one strand of spatial reasoning. Mike: So, you're already kind of poking around the question that I was going to ask next, which is the elevator description of, “What do we mean when we talk about spatial reasoning and why does it matter? Why is it a big deal for students?” Robyn: So, spatial reasoning is a notoriously hard to define construct that deals with how things move in space. It's individually how they move in space, in relation to one another. A lot of my ideas come from a network analysis that [Cathy] Bruce and colleagues did back in 2017 that looked at the historical framing of what spatial reasoning is and how we talk about it in different fields. Because psychologists look at spatial reasoning. Mathematics educators look at spatial reasoning. There [are] also connections into philosophy, the arts. But when we start moving toward mathematics more specifically, it does deal with how things move in space individually and in relation to one another. So, with geometry, whether the objects are sliding and transforming or we're composing and decomposing to create new shapes, those are the skills in two-dimensional geometry that we do often see in curricula. But the underlying skills are also critical to everyday life, and they can be taught as well. Robyn: And when we're thinking about the everyday constructs that are being built through our interactions with the world, I like to think about the GPS on our car. So, spatial reasoning has a lot of spatial temporal processes that are going on. It's not just thinking about the ways that things move in relation to one another or the connections to mathematics, but also the way that we move through this world, the way that we navigate through it. So, I'll give a little example. Spatial temporal processes have to do with us running errands, perhaps. How long does it take you to get from work to the store to home? And how many things can you purchase in the store knowing how full your fridge currently is? What pots and pans are you going to use to cook the food that you purchase, and what volume of that food are you and your family going to consume? So, all those daily tasks involve conceptions of how much space things take. And we could call it capacity, which situates nicely within the measurement domain of mathematics education. But it's also spatial reasoning, and it extends further than that. Mike: That is helpful. I think you opened up my understanding of what we're actually talking about, and I think the piece that was really interesting is how in that example of “I'm going to the grocery store, how long will it take? How full is my fridge? What are the different tools that I'll use to prepare? What capacity do they have?” I think that really helped me broaden out my own thinking about what spatial reasoning actually is. I wonder if we could shift a bit and you could help unpack for educators who are listening, a few examples of tasks that kids might encounter that could support the development of spatial reasoning. Robyn: Sure. My research ...
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    24 m
  • Season 2 | Episode 16 – Strengthening Tasks Through Student Talk - Guest: Drs. Amber Candela and Melissa Boston

    Season 2 | Episode 16 – Strengthening Tasks Through Student Talk - Guest: Drs. Amber Candela and Melissa Boston
    Apr 18 2024
    Rounding Up Season 2 | Episode 16 – Strengthening Tasks Through Student Talk Guests: Dr. Amber Candela and Dr. Melissa Boston Mike Wallus: One of the goals I had in mind when we first began recording Rounding Up was to bring to life the best practices that we aspire to in math education and to offer entry points so that educators would feel comfortable trying them out in their classrooms. Today, we're talking with Drs. Amber Candela and Melissa Boston about powerful but practical strategies for supporting student talk in the elementary math classroom. Welcome to the podcast, Amber and Melissa. We're really excited to be talking with you today. Amber Candela: Thank you for having us. Melissa Boston: Yes, thank you. Mike: So we've done previous episodes on the importance of offering kids rich tasks, but one of the things that you two would likely argue is that rich tasks are necessary, but they're not necessarily sufficient, and that talk is actually what makes the learning experience really blossom. Is that a fair representation of where you all are at? Melissa: Yes. I think that sums it up very well. In our work, which we've built on great ideas from Smith and Stein, about tasks, and the importance of cognitively challenging tasks and work on the importance of talk in the classroom. Historically, it was often referred to as “talk moves.” We've taken up the term “discourse actions” to think about how do the actions a teacher takes around asking questions and positioning students in the classroom—and particularly these talk moves or discourse actions that we've named “linking” and “press”—how those support student learning while students are engaging with a challenging task. Mike: So I wonder if we could take each of the practices separately and talk through them and then talk a little bit about how they work in tandem. And Melissa, I'm wondering if you could start unpacking this whole practice of linking. How would you describe linking and the purpose it plays for someone who, the term is new for them? Melissa: I think as mathematics teachers, when we hear linking, we immediately think about the mathematics and linking representations or linking strategies. But we’re using it very specifically here as a discourse action to refer to how a teacher links student talk in the classroom and the explicit moves a teacher makes to link students' ideas. Sometimes a linking move is signaled by the teacher using a student's name, so referring to a strategy or an idea that a student might've offered. Sometimes linking might happen if a teacher revoices a student's idea and puts it back out there for the class to consider. The idea is in the way that we're using linking, that it's links within the learning community, so links between people in the classroom and the ideas offered by those people, of course. But the important thing here that we're looking for is how the links between people are established in the verbal, the explicit talk moves or discourse actions that the teacher's making. Mike: What might that sound like? Melissa: So that might sound like, “Oh, I noticed that Amber used a table. Amber, tell us how you used a table.” And then after Amber would explain her table, I might say, “Mike, can you tell me what this line of Amber's table means?” or “How is her table different from the table you created?” Mike: You're making me think about those two aspects, Melissa, this idea that there's mathematical value for the class, but there's also this connectivity that happens when you're doing linking. And I wonder how you think about the value that that has in a classroom. Melissa: We definitely have talked about that in our work as well. I’m thinking about how a teacher can elevate a student's status in mathematics by using their name or using their idea, just marking or identifying something that the student said is mathematically important that's worthy of the class considering further. Creating these opportunities for student-to-student talk by asking students to compare their strategies or if they have something to add on to what another student said. Sometimes just asking them to repeat what another student said so that there's a different accountability for listening to your peers. If you can count on the teacher to revoice everything, you could tune out what your peers are saying, but if you might be asked to restate what one of your classmates had just said, now there's a bit more of an investment in really listening and understanding and making sense. Mike: Yeah, I really appreciate this idea that there's a way in which that conversation can elevate a student's ideas, but also to raise a student's status by naming their idea and positioning it as important. Melissa: I have a good example from a high school classroom where a student [...] was able to solve the contextual problem about systems of equations, so two equations, and it was ...
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    16 m
  • Season 2 | Episode 15 – Making Sense of Story Problems - Guest: Drs. Aina Appova and Julia Hagge

    Season 2 | Episode 15 – Making Sense of Story Problems - Guest: Drs. Aina Appova and Julia Hagge
    Apr 4 2024
    Rounding Up Season 2 | Episode 15 – Making Sense of Story Problems Resources: Schema-Mediated Vocabulary in Math Word Problems Guest: Drs. Aina Appova and Julia Hagge Mike Wallus: Story problems are an important tool that educators use to bring mathematics to life for their students. That said, navigating the meaning and language found in story problems is a challenge for many students. Today we're talking with Drs. Aina Appova and Julia Hagge from [The] Ohio State University about strategies to help students engage with and make sense of story problems. Mike: A note to our listeners. This podcast was recorded outside of our normal recording studio, so you may notice some sound quality differences from our regular podcast. Mike: Welcome to the podcast, Aina and Julia. We're excited to be talking to both of you. Aina Appova: Thank you so much for having us. We are very excited as well. Julia Hagge: Yes, thank you. We're looking forward to talking with you today. Mike: So, this is a conversation that I've been looking forward to for quite a while, partly because the nature of your collaboration is a little bit unique in ways that I think we'll get into. But I think it's fair to describe your work as multidisciplinary, given your fields of study. Aina: Yes, I would say so. It's kind of a wonderful opportunity to work with a colleague who is in literacy research and helping teachers teach mathematics through reading story problems. Mike: Well, I wonder if you can start by telling us the story of how you all came to work together. And describe the work you're doing around helping students make sense of word problems. Aina: I think the work started with me working with fifth-grade teachers, for two years now, and the conversations have been around story problems. There's a lot of issues from teaching story problems that teachers are noticing. And so, this was a very interesting experience. One of the professional development sessions that we had, teachers were saying, “Can we talk about story problems? It's very difficult.” And so, we just looked at a story problem. And the story problem, it was actually a coordinate plane story problem. It included a balance beam, and you're supposed to read the story problem and locate where this balance beam would be. And I had no idea what the balance beam would be. So, when I read the story, I thought, “Oh, it must be from the remodeling that I did in my kitchen, and I had to put in a beam, which was structural.” Aina: So, I'm assuming it's balancing the load. And even that didn't help me. I kept rereading the problem and thinking, “I'm not sure this is on the ceiling, but the teachers told me it's gymnastics.” And so even telling me that it was gymnastics didn't really help me because I couldn't think, in the moment, while I was already in a different context of having the beam, a load-bearing beam. It was very interesting that—and I know I'm an ELL, so English is not my first language—in thinking about a context that you're familiar with by reading a word or this term, “balance beam.” And even if people tell you, “Oh, it's related to gymnastics”—and I've never done gymnastics; I never had gymnastics in my class or in my school where I was. It didn't help. And that's where we started talking about underlying keywords that didn't really help either because it was a coordinate plane problem. So, I had to reach out to Julia and say, “I think there's something going on here that is related to reading comprehension. Can you help me?” And that's how this all started. ( chuckles ) Julia: Well, so Aina came to me regarding her experience. In fact, she sent me the math problem. She says, “Look at this.” And we talked about that. And then she shared frustration of the educators that she had been working with that despite teaching strategies that are promoted as part of instructional practice, like identifying mathematical keywords and then also reading strategies have been emphasized, like summarizing or asking questions while you're reading story problems. So, her teachers had been using strategies, mathematical and also reading, and their students were still struggling to make sense of and solve mathematical problems. Aina’s experience with this word problem really opened up this thought about the words that are in mathematical story problems. And we came to realize that when we think about making sense of story problems, there are a lot of words that require schema. And schema is the background knowledge that we bring to the text that we interact with. Julia: For example, I taught for years in Florida. And we would have students that had never experienced snow. So, as an educator, I would need to do read alouds and provide that schema for my students so that they had some understanding of snow. So, when we think about math story problems, all words matter—not just the mathematical terms, but also the words that ...
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    32 m
  • Season 2 | Episode 14 – Mathematizing and Modeling The World Around Us - Guest: Erin Turner, Ph.D.

    Season 2 | Episode 14 – Mathematizing and Modeling The World Around Us - Guest: Erin Turner, Ph.D.
    Mar 21 2024
    Rounding Up Season 2 | Episode 14 – Three Resources to Support Multilingual Learners Guest: Dr. Erin Turner Mike Wallus: Many resources for supporting multilingual learners are included with curriculum materials. What's too often missing though is clear guidance for how to use them. In this episode, we're going to talk with Dr. Erin Turner about three resources that are often recommended for supporting multilingual learners. We'll unpack the purpose for each resource and offer a vision for how to put them to good use with your students. Mike: Well, welcome to the podcast, Erin. We are excited to be chatting with you today. Erin Turner: Thank you so much for inviting me. Mike: So, for our listeners, the starting point for this episode was a conversation that you and I had not too long ago, and we were talking about the difference between having a set of resources which might come with a curriculum and having a sense of how to use them. And in this case, we were talking about resources designed to support multilingual learners. So, today we're going to talk through three resources that are often recommended for supporting multilingual learners, and we're going to really dig in and try to unpack the purpose and offer a vision for how to put them to use with students. What do you think? Are you ready to get started, Erin? Erin: I am. Mike: Well, one of the resources that often shows up in curriculum are what are often referred to as sentence frames or sentence stems. So, let's start by talking about what these resources are and what purpose they might serve for multilingual learners. Erin: Great. So, a sentence stem, or sometimes it's called a sentence starter, this is a phrase that gives students a starting place for an explanation. So, often it includes three or four words that are the beginning part of a sentence, and it's followed by a blank that students can complete with their own ideas. And a sentence frame is really similar. A sentence frame just typically is a complete sentence that includes one or more blanks that again, students can fill in with their ideas. And in both cases, these resources are most effective for all students who are working on explaining their ideas, when they're flexible and open-ended. So, you always want to ensure that a sentence stem or a sentence frame has multiple possible ways that students could insert their own ideas, their own phrasing, their own solutions to complete the sentence. The goal is always for the sentence frame to be generative and to support students' production and use of language—and never to be constraining. Erin: So, students shouldn't feel like there's one word or one answer or one correct or even intended way to complete the frame. It should always feel more open-ended and flexible and generative. For multilingual learners, one of the goals of sentence stems is that the tool puts into place for students some of the grammatical and linguistic structures that can get them started in their talk so that students don't have to worry so much about, “What do I say first?” or “What grammatical structures should I use?” And they can focus more on the content of the idea that they want to communicate. So, the sentence starter is just getting the child talking. It gives them the first three words that they can use to start explaining their idea, and then they can finish using their own insights, their own strategies, their own retellings of a solution, for example. Mike: Can you share an example of a sentence frame or a sentence stem to help people understand them if this is new to folks? Erin: Absolutely. So, let's say that we're doing number talks with young children, and in this particular number talk, children are adding two-digit numbers. And so, they're describing the different strategies that they might use to do either a mental math addition of two-digit numbers, or perhaps they've done a strategy on paper. You might think about the potential strategies that students would want to explain and think about sentence frames that would mirror or support the language that children might use. So, a frame that includes blanks might be something like, “I broke apart (blank) into (blank) and (blank).” If you think students are using 10s and 1s strategies, where they're decomposing numbers into 10s and 1s. Or if you think students might be working with open number lines and making jumps, you might offer a frame like, “I started at (blank), then I (blank),” which is a really flexible frame and could allow children to describe ways that they counted on on a number line or made jumps of a particular increment or something else. The idea again is for the sentence frame to be as flexible as possible. You can even have more flexible frames that imply a sequence of steps but don't necessarily frame a specific strategy. So, something like, “First I (blank), then I (blank)” or “I got my answer by (blank).” Those can be ...
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    38 m
  • Season 2 | Episode 13 – Rough Draft Math - Guest: Dr. Amanda Jansen

    Season 2 | Episode 13 – Rough Draft Math - Guest: Dr. Amanda Jansen
    Mar 7 2024
    Rounding Up Season 2 | Episode 13 – Rough Draft Math Guest: Dr. Amanda Jansen Mike Wallus: What would happen if teachers consistently invited students to think of their ideas in math class as a rough draft? What impact might this have on students' participation, their learning experience, and their math identity? Those are the questions we'll explore today with Dr. Mandy Jansen, the author of “Rough Draft Math,” on this episode of Rounding Up. Mike: Well, welcome to the podcast, Mandy. We are excited to be talking with you. Mandy Jansen: Thanks, Mike. I'm happy to be here. Mike: So, I'd like to start by asking you where the ideas involved in “Rough Draft Math” originated. What drove you and your collaborators to explore these ideas in the first place? Mandy: So, I work in the state of Delaware. And there's an organization called the Delaware Math Coalition, and I was working in a teacher study group where we were all puzzling together—secondary math teachers—thinking about how we could create more productive classroom discussions. And so, by productive, one of the ways we thought about that was creating classrooms where students felt safe to take intellectual risks, to share their thinking when they weren't sure, just to elicit more student participation in the discussions. One way we went about that was, we were reading chapters from a book called “Exploring Talk in School” that was dedicated to the work of Doug Barnes. And one of the ideas in that book was, we could think about fostering classroom talk in a way that was more exploratory. Exploratory talk, where you learn through interaction. Students often experience classroom discussions as an opportunity to perform. "I want to show you what I know.” And that can kind of feel more like a final draft. And the teachers thought, “Well, we want students to share their thinking in ways that they're more open to continue to grow their thinking.” So, in contrast to final draft talk, maybe we want to call this rough draft talk because the idea of exploratory talk felt like, maybe kind of vague, maybe hard for students to understand. And so, the term “rough draft talk” emerged from the teachers trying to think of a way to frame this for students. Mike: You're making me think about the different ways that people perceive a rough draft. So, for example, I can imagine that someone might think about a rough draft as something that needs to be corrected. But based on what you just said, I don't think that's how you and your collaborators thought about it, nor do I think that probably is the way that you framed it for kids. So how did you invite kids to think about a rough draft as you were introducing this idea? Mandy: Yeah, so we thought that the term “rough draft” would be useful for students if they have ever thought about rough drafts in maybe language arts. And so, we thought, “Oh, let's introduce this to kids by asking, ‘Well, what do you know about rough drafts already? Let's think about what a rough draft is.’” And then we could ask them, “Why do you think this might be useful for math?” So, students will brainstorm, “Oh yeah, rough draft, that's like my first version” or “That's something I get the chance to correct and fix.” But also, sometimes kids would say, “Oh, rough drafts … like the bad version. It's the one that needs to be fixed.” And we wanted students to think about rough drafts more like, just your initial thinking, your first ideas; thinking that we think of as in progress that can be adjusted and improved. And we want to share that idea with students because sometimes people have the perception that math is, like, you're either right or you're wrong, as opposed to something that there's gradients of different levels of understanding associated with mathematical thinking. And we want math to be more than correct answers, but about what makes sense to you and why this makes sense. So, we wanted to shift that thinking from rough drafts being the bad version that you have to fix to be more like it's OK just to share your in-progress ideas, your initial thinking. And then you're going to have a chance to keep improving those ideas. Mike: I'm really curious, when you shared that with kids, how did they react? Maybe at first, and then over time? Mandy: So, one thing that teachers have shared that's helpful is that during a class discussion where you might put out an idea for students to think about, and it's kind of silent, you get crickets. If teachers would say, “Well, remember it's OK to just share your rough drafts.” It's kind of like letting the pressure out. And they don't feel like, “Oh wait, I can't share unless I totally know I'm correct. Oh, I can just share my rough drafts?” And then the ideas sort of start popping out onto the floor like popcorn, and it really kind of opens up and frees people up. “I can just share whatever's on my mind.” So that's one ...
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    22 m
  • Season 2 | Episode 12 – Counting - Guest: Dr. Kim Hartweg

    Season 2 | Episode 12 – Counting - Guest: Dr. Kim Hartweg
    Feb 22 2024
    Rounding Up Season 2 | Episode 12 – Counting Guest: Dr. Kim Hartweg Mike Wallus: Counting is a process that involves a complex and interconnected set of concepts and skills. This means that for most children, the path to counting proficiency is not a linear process. Today we're talking with Dr. Kim Hartweg from Western Illinois University about the big ideas and skills that are a part of counting, and the ways educators can support their students on this important part of their math journey. Mike: Well, hey, Kim, welcome to the podcast. We're excited to be talking with you about counting. Kim Hartweg: Ah, thanks for having me. I'm excited, too. Mike: So, I'm fascinated by all of the things that we're learning about how young kids count, or at least the way that they attend to quantities. Kim: Yeah, it's exciting what all is taking place, with the research and everything going on with early childhood education, especially in regards to number and number sense. And I think back to an article I read about a 6-month-old baby who's in a crib and there's three pictures in this crib. One of them has two dots on it, another one has one dot, and then a third one has three dots. And a drum sounds, and it goes boom, boom, boom. And the 6-month-old baby turns their head and eyes and they look at the picture with three dots on it. And I just think that's exciting that even at that age they're recognizing that three dots [go] with three drum beats. So, it's just exciting. Mike: So, you're actually taking us to a place that I was hoping we could go to, which is, there are some ideas and some concepts that we associate with counting. And I'm wondering if we could start the podcast by naming and unpacking a few of the really important ones. Kim: OK, sure. I think of the fundamental counting principles, three different areas. And for me, the first one is that counting sequence, or just learning the language and that we count 1, 2, 3, 4, 5. However, in the English language, it's much more difficult [than] in other languages when we get beyond 10 because we have numbers like 11, 12, 13 that we never hear again. Like, you hear 21, 31, 41, but you don't hear 11. Again, it's the only time it's ever mentioned. So, I think it's harder for students to get that counting sequence for those who speak English. Mike: I appreciate you saying that because I remember reading at one point that in certain Asian languages, the number 11, the translation is essentially 10 and 1, as opposed to for English speakers where it really is 11, which doesn't really follow the cadence of the number sequence that kids are learning: 1, 2, 3, 4, and so on. Kim: Exactly. Yes. Mike: It picks up again at 21, but this interim space where the teen numbers show up and we're first talking about a 10 and however many more, it's not a great thing about the English language that suddenly we decided to call those things that don't have that same cadence. Kim: Yeah, after you get past 20, yes. And if you think of kids when they hear the number 16, a lot of times they'll say, “A 1 and a 6 or a 6 and a 1?” Because they hear 16, so you hear the 6 first. But like you said, in other languages, it's 10 six, 10 seven, 10 eight. So, it kind of fits more naturally with the way we talk and the language. Mike: So, there's the language of the counting sequence. Let's talk about a couple of the other things. Kim: OK. One-to-one correspondence is a key idea, and I think of this when I was first starting to teach undergraduate students about early math education. I had kids at the same age, so at a restaurant or wherever we happened to be, I'd get out the sugar packets and I would have them count. And at first when they're maybe 2 years old or so, and they're just learning the language, they may count those sugar packets as 1, 2, 3. There may be two packets. There may be five packets. But everything is 1, 2, 3, whether there's again, five packets or two packets. So, once they get that idea that each time they say a number word that it counts for an actual object and they can match them up, that's that idea of one-to-one correspondence to where they say a number and they either point or move the object so you can tell they're matching those up. Mike: OK, let's talk about cardinality because this is one that I think when I first started teaching kindergarten, I took for granted how big of a leap this one is. Kim: Yeah, that's interesting. So, once they can count out and you have five sugar packets and they count 1, 2, 3, 4, 5, and you ask how many are there, they should be able to say five. That's cardinality of number. If they have to count again, 1, 2, 3, 4, 5, then they don't have cardinality of number, where whatever number they count last is how many is in that set. Mike: Which is kind of amazing actually. We're asking kids to decide that “I've figured out this idea that when I say a number name, I'm talking about an ...
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    19 m
  • Season 2 | Episode 11 – Translanguaging - Guest: Tatyana Kleyn, Ed.D.

    Season 2 | Episode 11 – Translanguaging - Guest: Tatyana Kleyn, Ed.D.
    Feb 8 2024
    Rounding Up Season 2 | Episode 11 – Translanguaging Guest: Tatyana Kleyn Mike Wallus: Over the past two years, we've done several episodes on supporting multilingual learners in math classrooms. Today we're going back to this topic to talk about “translanguaging,” an asset-focused approach that invites students to bring their full language repertoire into the classroom. We'll talk with Tatyana Kleyn about what translanguaging looks like and how all teachers can integrate this practice into their classrooms. Mike: Well, welcome to the podcast, Tatyana. We're excited to be talking with you today. Tatyana Kleyn: Thank you. This is very exciting. Mike: So, your background with the topic of multilingual learners and translanguaging, it's not only academic. It's also personal. I'm wondering if you might share a bit of your own background as a starting point for this conversation. Tatyana: Yes, absolutely. I think for many of us in education, we don't randomly end up teaching in the areas that we're teaching in or doing the work that we're doing. So, I always like to share my story so people know why I'm doing this work and where I'm coming from. So, my personal story, I work a lot at the intersection of language migration and education, and those are all three aspects that have been critical in bringing me here. So, I was actually born in what was the Soviet Union many, many years ago, and my family immigrated to the United States as political refugees, and I was just 5½ years old. So, I actually never went to school in the Soviet Union. Russian was my home language, and I quickly started speaking English, but my literacy was not quick at all, and it was quite painful because I never learned to read in my home language. I never had that foundation. Tatyana: So, when I was learning to read in English, it wasn't meaning making, it was just making sounds. It was kind of painful. I once heard somebody say, “For some people, reading is like this escape and this pure joy, and for other people it's like cleaning the toilet. You get in and you get out.” And I was like, “That's me. I'm the toilet cleaner.” ( laughs ) So, that was how reading was for me. I always left my home language at the door when I came into school, and I wanted it that way because I, as a young child, got this strong message that English was the language that mattered in this country. So, for example, instead of going by Tatyana, I went by Tanya. So, I always kind of kept this secret that I spoke this other language. I had this other culture, and it wasn't until sixth grade where my sixth-grade teacher, Ms. Chang, invited my mom to speak about our immigration history. Tatyana: And I don't know why, but I thought that was so embarrassing. I think in middle school, it's not really cool to have your parents around. So, I was like, “Oh my God, this is going to be horrible.” But then I realized my peers were really interested—and in a good way—and I was like, “Wait, this is a good thing?” So, I started thinking, “OK, we should be proud of who we are and let just people be who they are.” And when you let people be who they are, they thrive in math, in science, in social studies, instead of trying so hard to be someone they're not, and then focusing on that instead of everything else that they should be focusing on as students. Mike: So, there's a lot there. And I think I want to dig into what you talked about over the course of the interview. I want to zero in a little bit on translanguaging though, because for me, at least until quite recently, this idea of translanguaging was really a new concept, a new idea for me, and I'm going to guess that that's the case for a lot of the people who are listening to this as well. So, just to begin, would you talk briefly about what translanguaging is and your sense of the impact that it can have on learners? Tatyana: Sure. Well, I'm so glad to be talking about translanguaging in this space specifically, because often when we talk about translanguaging, it's in bilingual education or English as a second language or is a new language, and it's important in those settings, right? But it's important in all settings. So, I think you're not the only one, especially if we're talking about math educators or general elementary educators, it's like, “Oh, translanguaging, I haven't heard of that,” right? So, it is not something brand new, but it is a concept that Ofelia García and some of her colleagues really brought forth to the field in the early 2000s … around 2009. And what it does is instead of saying English should be the center of everything, and everyone who doesn't just speak English is peripheral. It's saying, “Instead of putting English at the center, let's put our students' home language practices at the center. And what would that look like?” So, that wouldn't mean everything has to be in English. It wouldn't mean the teacher's language practices are ...
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