Rounding Up Por arte de portada

Rounding Up

De: MLC - Mike Wallus
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  • Resumen

  • Welcome to Rounding Up, the professional learning podcast brought to you by The Math Learning Center. Two things have always been true in education: Ongoing professional learning is essential, and teachers are extremely busy people. Rounding Up is a podcast designed to provide meaningful, bite-sized professional learning for busy educators and instructional leaders. I'm Mike Wallus, vice president for educator support at The Math Learning Center and host of the show. In each episode, we'll explore topics important to teachers, instructional leaders, and anyone interested in elementary mathematics education. Topics such as posing purposeful questions, effectively recording student thinking, cultivating students' math identity, and designing asset-based instruction from multilingual learners. Don't miss out! Subscribe now wherever you get your podcasts. Each episode will also be published on the Bridges Educator Site. We hope you'll give Rounding Up a try, and that the ideas we discuss have a positive impact on your teaching and your students' learning.
    2022 The Math Learning Center | www.mathlearningcenter.org
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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
Matemáticas Ciencia
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