Rounding Up

著者： MLC - Mike Wallus
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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
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あらすじ・解説

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 3 | Episode 6 – Argumentation, Justification & Conjecture Guests: Drs. Jody Guarino and Chepina Rumsey

    Season 3 | Episode 6 – Argumentation, Justification & Conjecture Guests: Drs. Jody Guarino and Chepina Rumsey
    2024/11/21
    Rounding Up Season 3 | Episode 6 – Argumentation, Justification & Conjecture Guests: Jody Guarino and Chepina Rumsey Mike Wallus: Argumentation, justification, conjecture. All of these are practices we hope to cultivate, but they may not be practices we associate with kindergarten, first-, and second-graders. What would it look like to encourage these practices with our youngest learners? Today we'll talk about this question with Jody Guarino and Chepina Rumsey, authors of the book Nurturing Math Curiosity with Learners in Grades K–2. Welcome to the podcast, Chepina and Jody. Thank you so much for joining us today. Jody Guarino: Thank you for having us. Chepina Rumsey: Yeah, thank you. Mike: So, I'm wondering if we can start by talking about the genesis of your work, particularly for students in grades K–2. Jody: Sure. Chepina had written a paper about argumentation, and her paper was situated in a fourth-grade class. At the time, I read the article and was so inspired, and I wanted it to use it in an upcoming professional learning that I was going to be doing. And I got some pushback with people saying, “Well, how is this relevant to K–2 teachers?” And it really hit me that there was this belief that K–2 students couldn't engage in argumentation. Like, “OK, this paper's great for older kids, but we're not really sure about the young students.” And at the time, there wasn't a lot written on argumentation in primary grades. So, we thought, “Well, let's try some things and really think about, ‘What does it look like in primary grades?’ And let's find some people to learn with.” So, I approached some of my recent graduates from my teacher ed program who were working in primary classrooms and a principal that employed quite a few of them with this idea of, “Could we learn some things together? Could we come and work with your teachers and work with you and just kind of get a sense of what could students do in kindergarten to second grade?” So, we worked with three amazing teachers, Bethany, Rachael, and Christina—in their first years of teaching—and we worked with them monthly for two years. We wanted to learn, “What does it look like in K–2 classrooms?” And each time we met with them, we would learn more and get more and more excited. Little kids are brilliant, but also their teachers were brilliant, taking risks and trying things. I met with one of the teachers last week, and the original students that were part of the book that we've written now are actually in high school. So, it was just such a great learning opportunity for us. Mike: Well, I'll say this, there are many things that I appreciated about the book, about Nurturing Math Curiosity with Learners in Grades K–2, and I think one of the first things was the word “with” that was found in the title. So why “with” learners? What were y'all trying to communicate? Chepina: I'm so glad you asked that, Mike, because that was something really important to us when we were coming up with the title and the theme of the book, the message. So, we think it's really important to nurture curiosity with our students, meaning we can't expect to grow it in them if we're not also growing it in ourselves. So, we see that children are naturally curious and bring these ideas to the classroom. So, the word “with” was important because we want everyone in the classroom to grow more curious together. So, teachers nurturing their own math curiosity along with their students is important to us. One unique opportunity we tried to include in the book is for teachers who are reading it to have opportunities to think about the math and have spaces in the book where they can write their own responses and think deeply along with the vignettes to show them that this is something they can carry to their classroom. Mike: I love that. I wonder if we could talk a little bit about the meaning and the importance of argumentation? In the book, you describe four layers: noticing and wondering, conjecture, justification, and extending ideas. Could you share a brief explanation of those layers? Jody: Absolutely. So, as we started working with teachers, we'd noticed these themes or trends across, or within, all of the classrooms. So, we think about noticing and wondering as a space for students to make observations and ask curious questions. So, as teachers would do whatever activity or do games, they would always ask kids, “What are you noticing?” So, it really gave kids opportunities to just pause and observe things, which then led to questions as well. And when we think about students conjecturing, we think about when they make general statements about observations. So, an example of this could be a child who notices that 3 plus 7 is 10 and 7 plus 3 is 10. So, the child might think, “Oh wait, the order of the addends doesn't matter when adding. And maybe that would even work with other numbers.” So, forming a conjecture like ...
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    24 分
  • Season 3 | Episode 5 - Building Asset-Focused Professional Learning Communities - Guests: Summer Pettigrew and Megan Williams

    Season 3 | Episode 5 - Building Asset-Focused Professional Learning Communities - Guests: Summer Pettigrew and Megan Williams
    2024/11/07
    Rounding Up Season 3 | Episode 05 - Building Asset-Focused Professional Learning Communities Guests: Summer Pettigrew and Megan Williams Mike Wallus: Professional learning communities have been around for a long time and in many different iterations. But what does it look like to schedule and structure professional learning communities that actually help educators understand and respond to their students’ thinking in meaningful ways? Today we're talking with Summer Pettigrew and Megan Williams from the Charleston Public Schools about building asset-focused professional learning communities. Hello, Summer and Megan. Welcome to the podcast. I am excited to be talking with you all today about PLCs. Megan Williams: Hi! Summer Pettigrew: Thanks for having us. We're excited to be here. Mike: I'd like to start this conversation in a very practical place, scheduling. So, Megan, I wonder if you could talk just a bit about when and how you schedule PLCs at your building. Megan: Sure. I think it's a great place to start, too, because I think without the structure of PLCs in place, you can't really have fabulous PLC meetings. And so, we used to do our PLC meetings once a week during teacher planning periods, and the teachers were having to give up their planning period during the day to come to the PLC meeting. And so, we created a master schedule that gives an hour for PLC each morning. So, we meet with one grade level a day, and then the teachers still have their regular planning period throughout the day. So, we were able to do that by building a time for clubs in the schedule. So, first thing in the morning, depending on your day, so if it's Monday and that's third grade, then the related arts teachers—and that for us is art, music, P.E., guidance, our special areas—they go to the third-grade teachers’ classrooms. The teachers are released to go to PLC, and then the students choose a club. And so, those range from basketball to gardening to fashion to STEMs. We've had Spanish club before. So, they participate with the related arts teacher in their chosen club, and then the teachers go to their PLC meeting. And then once that hour is up, then the teachers come back to class. The related arts teachers are released to go get ready for their day. So, everybody still has their planning period, per se, throughout the day. Mike: I think that feels really important, and I just want to linger a little bit longer on it. One of the things that stands out is that you're preserving the planning time on a regular basis. They have that, and they have PLC time in addition to it. Summer: Uh-hm. Megan: Correct. And that I think is key because planning time in the middle of the day is critical for making copies, calling parents, calling your doctor to schedule an appointment, using the restroom … those kind of things that people have to do throughout the day. And so, when you have PLC during their planning time, one or the other is not occurring. Either a teacher is not taking care of those things that need to be taken care of on the planning period. Or they're not engaged in the PLC because they're worried about something else that they've got to do. So, building that time in, it's just like a game-changer. Mike: Summer, as a person who’s playing the role of an instructional coach, what impact do you think this way of scheduling has had on educators who are participating in the PLCs that you're facilitating? Summer: Well, it's huge. I have experienced going to A PLC on our planning and just not being a hundred percent engaged. And so, I think having the opportunity to provide the time and the space for that during the school day allows the teachers to be more present. And I think that the rate at which we're growing as a staff is expedited because we're able to drill into what we need to drill into without worrying about all the other things that need to happen. So, I think that the scheduling piece has been one of the biggest reasons we've been so successful with our PLCs. Mike: Yeah, I can totally relate to that experience of feeling like I want to be here, present in this moment, and I have 15 things that I need to do to get ready for the next chunk of my day. So, taking away that “if, then,” and instead having an “and” when it comes to PLCs, really just feels like a game-changer. Megan: And we were worried at first about the instructional time that was going to be lost from the classroom doing the PLC like this. We really were, because we needed to make sure instructional time was maximized and we weren't losing any time. And so, this really was about an hour a week where the teachers aren't directly instructing the kids. But it has not been anything negative at all. Our scores have gone up, our teachers have grown. They love the kids, love going to their clubs. I mean, even the attendance on the grade-level club day is so much better because they love coming in. And they start the day really getting ...
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    18 分
  • Season 3 | Episode 4 - Making Sense of Unitizing: The Theme That Runs Through Elementary Mathematics - Guest: Beth Hulbert

    Season 3 | Episode 4 - Making Sense of Unitizing: The Theme That Runs Through Elementary Mathematics - Guest: Beth Hulbert
    2024/10/24
    Rounding Up Season 3 | Episode 4 – Making Sense of Unitizing: The Theme That Runs Through Elementary Mathematics Guest: Beth Hulbert Mike Wallus: During their elementary years, students grapple with many topics that involve relationships between different units. This concept, called “unitizing,” serves as a foundation for much of the mathematics that students encounter during their elementary years. Today, we're talking with Beth Hulbert from the Ongoing Assessment Project (OGAP) about the ways educators can encourage unitizing in their classrooms. Welcome to the podcast, Beth. We are really excited to talk with you today. Beth Hulbert: Thanks. I'm really excited to be here. Mike: I'm wondering if we can start with a fairly basic question: Can you explain OGAP and the mission of the organization? Beth: Sure. So, OGAP stands for the Ongoing Assessment Project, and it started with a grant from the National Science Foundation to develop tools and resources for teachers to use in their classroom during math that were formative in nature. And we began with fractions. And the primary goal was to read, distill, and make the research accessible to classroom teachers, and at the same time develop tools and strategies that we could share with teachers that they could use to enhance whatever math program materials they were using. Essentially, we started by developing materials, but it turned into professional development because we realized teachers didn't have a lot of opportunity to think deeply about the content at the level they teach. The more we dug into that content, the more it became clear to us that content was complicated. It was complicated to understand, it was complicated to teach, and it was complicated to learn. So, we started with fractions, and we expanded to do work in multiplicative reasoning and then additive reasoning and proportional reasoning. And those cover the vast majority of the critical content in K–8. And our professional development is really focused on helping teachers understand how to use formative assessment effectively in their classroom. But also, our other goals are to give teachers a deep understanding of the content and an understanding of the math ed research, and then some support and strategies for using whatever program materials they want to use. And we say all the time that we're a program blind—we don't have any skin in the game about what program people are using. We are more interested in making people really effective users of their math program. Mike: I want to ask a quick follow-up to that. When you think about the lived experience that educators have when they go through OGAP’s training, what are the features that you think have an impact on teachers when they go back into their classrooms? Beth: Well, we have learning progressions in each of those four content strands. And learning progressions are maps of how students acquire the concepts related to, say, multiplicative reasoning or additive reasoning. And we use those to sort, analyze, and decide how we're going to respond to evidence in student work. They're really maps for equity and access, and they help teachers understand that there are multiple right ways to do some mathematics, but they're not all equal in efficiency and sophistication. Another piece they take away of significant value is we have an item bank full of hundreds of short tasks that are meant to add value to, say, a lesson you taught in your math program. So, you teach a lesson, and you decide what is the primary goal of this lesson. And we all know no matter what the program is you're using that every lesson has multiple goals, and they're all in varying degrees of importance. So partly, picking an item in our item bank is about helping yourself think about what was the most critical piece of that lesson that I want to know about that's critical for my students to understand for success tomorrow. Mike: So, one big idea that runs through your work with teachers is this concept called “unitizing.” And it struck me that whether we're talking about addition, subtraction, multiplication, fractions, that this idea just keeps coming back and keeps coming up. I'm wondering if you could offer a brief definition of unitizing for folks who may not have heard that term before. Beth: Sure. It became really clear as we read the research and thought about where the struggles kids have, that unitizing is at the core of a lot of struggles that students have. So, unitizing is the ability to call something 1, say, but know it's worth maybe 1 or 100 or a 1,000, or even one-tenth. So, think about your numbers in a place value system. In our base 10 system, 1 of 1 is in the tenths place. It's not worth 1 anymore, it's worth 1 of 10. And so that idea that the 1 isn't the value of its face value, but it's the value of its place in that system. So, base 10 is one of the first big ways that kids have to understand unitizing. Another ...
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    30 分

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