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 ...
