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Rounding Up

Rounding Up

著者： The Math Learning Center
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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 数学 科学
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  • Season 4 | Episode 18 – Dr. Jenny Bay-Williams, Productive Ways to Build Fluency with Basic Facts (Rerun)

    Season 4 | Episode 18 – Dr. Jenny Bay-Williams, Productive Ways to Build Fluency with Basic Facts (Rerun)
    2026/05/21
    Dr. Jenny Bay-Williams, Productive Ways to Build Fluency with Basic Facts ROUNDING UP: SEASON 4 | EPISODE 18 This summer we're replaying favorite listener episodes from the first four seasons of Rounding Up—like this one from Season 1. We'll return with all new episodes in early September. Ensuring students master their basic facts remains a shared goal among parents and educators. That said, many educators wonder what should replace the memorization drills that cause so much harm to their students' math identities. Today on the podcast, Jenny Bay-Williams talks about how to meet that goal and shares a set of productive practices that also support student reasoning and sensemaking. BIOGRAPHY Jennifer Bay-Williams is a professor of mathematics education at the University of Louisville. She has authored over 40 books and 100 journal articles and book chapters that focus on making mathematics meaningful to all students. She is an international leader in the field of mathematics education, frequently speaking at state, national, and international conferences and serving on national boards. RESOURCES "Eight Unproductive Practices in Developing Fact Fluency" article by Gina Kling and Jennifer M. Bay-Williams Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention book by Jennifer M. Bay-Williams and Gina Kling Math Fact Fluency companion website by Kentucky Center for Mathematics TRANSCRIPT Mike Wallus: Welcome to the podcast, Jenny. We are excited to have you. Jennifer Bay-Williams: Well, thank you for inviting me. I'm thrilled to be here and excited to be talking about basic facts. Mike: Awesome. Let's jump in. So, your recommendations start with an emphasis on reasoning. I wonder if we could start by just having you talk about the why behind your recommendation and a little bit about what an emphasis on reasoning looks like in an elementary classroom when you're thinking about basic facts. Jenny: All right, well, I'm going to start with a little bit of a snarky response: that the non-reasoning approach doesn't work. Mike and Jenny: (laugh) Jenny: OK. So, one reason to move to reasoning is that memorization doesn't work. Drill doesn't work for most people. But the reason to focus on reasoning with basic facts beyond that fact, is that the reasoning strategies grow to strategies that can be used beyond basic facts. So, if you take something like the making 10 idea—that 9 plus 6, you can move one over and you have 10 plus 5—is a beautiful strategy for a 99 plus 35. So, you teach the reasoning upfront from the beginning, and it sets students up for success later on. Mike: That absolutely makes sense. So, you talk about the difference between telling a strategy and explicit instruction. And I raise this because I suspect that some people might struggle to think about how those are different. Could you describe what explicit instruction looks like and maybe share an example with listeners? Jenny: Absolutely. First of all, I like to use the whole phrase: "explicit strategy instruction." So, what you're trying to do is have that strategy be explicit, noticeable, visible. So, for example, if you're going to do the making 10 strategy we just talked about, you might have two 10-frames. One of them is filled with nine counters, and one of them is filled with six counters. And students can see that moving one counter over is the same quantity. So, they're seeing this flexibility that you can move numbers around, and you end up with the same sum. So, you're just making that idea explicit and then helping them generalize. You change the problems up and then they come back and they're like, "Oh, hey, we can always move some over to make a ten"—or a twenty, or a thirty, or whatever you're working on. And so, I feel like, in using the counters, or they could be stacking Unifix cubes or things like that. That's the explicit instruction. It's concrete. And then, if you need to be even more explicit, you ask students in the end to summarize the pattern that they noticed across the three or four problems that they solved. "Oh, that you take the bigger number, and then you go ahead and complete a ten to make it easier to add." And then, that's how you're really bringing those ideas out into the community to talk about. For multiplication, I'm just going to contrast. Let's say we're doing [the] add a group strategy with multiplication. If you were going to do direct instruction, and you're doing 6 times 8, you might say, "All right, so when you see a six," then a direct instruction would be like, "Take that first number and just assume it's a five." So then, "Five eights is how much? Write that down." That's direct instruction. You're like, "Here, do this step. Here, do this step. Here, do this step." The explicit strategy instruction would have, for example—I like, for eights, boxes of crayons because they oftentimes come in eights. So, but they'd have five boxes of ...
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    26 分
  • Season 4 | Episode 17 – Jana Dean & Heather Byington, Supporting Multilingual Learners During Number Talks

    Season 4 | Episode 17 – Jana Dean & Heather Byington, Supporting Multilingual Learners During Number Talks
    2026/05/07
    Jana Dean & Heather Byington, Supporting Multilingual Learners During Number Talks ROUNDING UP: SEASON 4 | EPISODE 17 What might it be like to engage in a number talk as a multilingual learner? How would you communicate your ideas, and what scaffolds might support your participation? Today, we're talking with Jana Dean and Heather Byington about ways educators can support multilingual learners' engagement and participation during number talks. BIOGRAPHIES Heather Byington has taught all grade levels over the span of her 27-year career as a bilingual public educator. She currently teaches middle school mathematics and English language support classes in Lacey, Washington. She is also a student at Washington State University pursuing a PhD in Mathematics Education. Jana Dean currently serves as CEO of the Mathematics Education Collaborative and supports a fantastic team of middle school math teachers in North Thurston Public Schools. Her research focuses on the intersection of content learning and language learning. RESOURCES Judit Moschkovich research Math Between Us blog "Number Talks: A Whole Class Routine for Learning Language for Learning Mathematics" article Mathematics Education Collaborative website jdean@mec-math.org Jana Dean email TRANSCRIPT Mike Wallus: Welcome to the podcast, Jana and Heather. I am so excited to be talking with you both today. Jana Dean: Good morning. Yeah, thanks for having us. Heather Byington: Thanks so much for having us. Mike: Absolutely. Jana, before we begin talking about the ways that teachers can support multilingual learners during number talks, I wonder if you can offer a working definition that would help educators visualize what a number talk actually looks like. Jana: Yeah, I'd be happy to do that. A number talk in terms of how we worked with the routine in this project consisted of the teacher providing some sort of visual prompt, starting either with a visual pattern of dots or a computation problem. And then the students get wait time, time to think about how they might solve that problem. And then as they share their strategies, the teacher records and asks them questions about their reasoning for why they approached the problem in the way that they approached it. The teacher creates what I like to think of as a visual mediator of student ideas. So the students' ideas become visible as they share them. So children who are listening can listen to the dialog or conversation between the person sharing and the teacher, but the ideas actually become visible as they're being shared. And the teacher always verifies with the student whether or not they've been understood. And the goal is not for the student to be right, but for the teacher and student to understand each other. Mike: That's really helpful. Heather, is there anything else you'd add to that? Heather: In terms of the way that we worked with it with multilingual learners and increasing their opportunities for engagement in the routine, we always gave them an option of talking to a partner and rehearsing their answer before they volunteered to share with the whole group. We prioritized calling on multilingual learners if they volunteered. And we also did a final reflection at the end. So those were some enhancements that we added onto the routine. Mike: I think that's really helpful and I'm excited to talk a little bit more about the details of those, Heather. One of the things that really struck me as we were preparing for this conversation was reading about the ways that some of the multilingual learners you worked with, how they described their experience during number talks. And it helped me to see the experience from their perspective and rethink some of the ways that I'd facilitated number talks in the past. And I'm wondering if you could share a bit about some of the feelings students told you that they were experiencing. Jana: Yeah. One of the things we suspected before we started was that as a language learner myself, talking about ideas that you're just forming in a language you're in the process of learning can be really intimidating. It's very challenging. So they were nervous. And when I interviewed fourth graders about their experience in number talks, even facilitated with language acquisition in mind, they talked about how much courage it took them to share their ideas. They also talked about and could very keenly remember moments when they had made a contribution that their teacher made use of or a time when they made a contribution that another student made use of later. So there was a lot of pride they felt in having shared their ideas once they found ways to do that. They also talked about how much easier it was to share our ideas than it was to share my idea. And so if, for instance, we had given them the opportunity—and like Heather said, we almost always gave them the opportunity to talk with a partner—they would often share using the pronoun ...
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    34 分
  • Season 4 | Episode 16 – Kristin Frang, Understanding the Roots of Fluency with Addition & Subtraction

    Season 4 | Episode 16 – Kristin Frang, Understanding the Roots of Fluency with Addition & Subtraction
    2026/04/23
    Kristin Frang, Understanding the Roots of Fluency with Addition & Subtraction ROUNDING UP: SEASON 4 | EPISODE 16 Research suggests that supporting students' fluency with addition and subtraction hinges on understanding how children's mathematical thinking develops. So what are the concepts and ideas that play a part in fluency with combinations to 10, 20, and beyond? Today, we'll explore this question with Kristin Frang, director of instructional programs at Integrow Numeracy Solutions. BIOGRAPHY Kristin Frang is the director of instructional programs for Integrow Numeracy Solutions. She designs resources and services that support states, districts, schools, and individuals in transforming numeracy education. RESOURCES "Understanding Units Coordination" Season 4, Episode 11 of the Rounding Up podcast Integrow Numeracy Solutions website blog email address On Track to Numeracy book by Lucinda "Petey" MacCarty, Kurt Kinsey, David Ellemor-Collins, and Robert J. Wright TRANSCRIPT Mike Wallus: Welcome to the podcast, Kristin. It is so great to be talking with you today. Kristin Frang: It's great to be here. I feel so honored to be on this podcast. Mike: Before we dive into a conversation about addition and subtraction, I'd like to do a bit of grounding. So you're currently the director of instructional programs for Integrow Numeracy Solutions. I wonder if briefly you could tell the listeners: What is Integrow Numeracy Solutions, and what's its mission? Kristin: Yeah. Integrow Numeracy Solutions' mission is to transform numeracy education by connecting research with practice and empowering educators to advance student mathematical thinking and success. But I really want to bring that mission to life through a story, just a quick story, if I can. Prior to my role with Integrow, I was a K–12 mathematics consultant. And one of the things that I did was, when the Common Core [State Standards] were released, I worked with teachers to transition to the then-new standards. We studied many documents together, including progression documents that were included in the standards, and teachers were honestly fascinated by this idea of a progression and that they were embedded into the standard. But I remember an instance where we had been studying these progressions and a teacher came up and said to me, "I know where my students are at; I can see them in these progressions. But how do I get them to the next stage?" And I didn't have an answer (laughs) at that point. I was a former middle school and high school teacher. I was working with elementary teachers. I was studying, just like them, these progression documents, and I could only categorize the reasoning that was in front of us. And so that next step to say, "Oh, this is what I would do and bring into action in the classroom," I didn't have an answer for. And so that's really where I was introduced to Integrow—formerly [the] US Math Recovery Council, but now Integrow Numeracy Solutions. And at the heart of our mission to empower educators is to bring research to the classroom in accessible and practical ways that advance student reasoning. We do this in professional learning, we do it in supplemental resources, and we also hire and train educators to deliver high-dosage tutoring for students to accelerate their learning. Mike: I want to just linger on something you said, which was—and I really appreciate both the truth of the statement you made and also the vulnerability, which is to say—I think for many teachers, there's this experience of, "I can see my students in these progressions, but I'm not sure what to do when it comes to making moves to shift where they're at or help them move." And I think that's a profound truth for so many teachers. And I think it's really important that folks like you, who are doing this work, acknowledge that that's a place you were in once as well because that's so true for so many of us. Kristin: Yeah. There's always a new thing where we're watching students, we're thinking about the next steps. And so often it boils down to categorizing the things that students are doing now, but not often figuring out: What are the true actions that we take with real children who are in front of us to get them to progress in their own reasoning? We can tell them the next step, but my belief system that is aligned with Integrow Numeracy Solutions is that the most powerful thing is to help students have those experiences and create that understanding themselves. And to do that, it's more complex than just knowing what the next benchmark is for them. Mike: I think that's a helpful introduction. And I also find it to be a good segue for all the questions that I wanted to explore today. So let me start here: It feels important to acknowledge that supporting students' addition and subtraction fluency actually hinges on understanding how children's mathematical thinking develops. So I wonder if you can talk about some of...
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    34 分
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