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Wednesday, September 30, 2015

Math-Modeling PD Takes Teachers Beyond the Common Core

Liana Heitin, assistant editor for Education Week summarizes, "A National Science Foundation-funded pilot introduces elementary teachers to advanced problem-solving."

Sera Lee, a 5th grade teacher at Freedom Hill Elementary School in Fairfax, Va., works on a problem during a small-group session at a math-modeling training at George Mason University. Experts say that introducing modeling to younger students can improve their critical-thinking and application skills in math.
Photo: Education Week

Many math teachers around the country have adjusted their expectations for students as a result of the Common Core State Standards. But a pilot professional-development program is going above and beyond the new benchmarks by teaching small groups of elementary teachers in three states to teach a math skill that's typically been reserved for high school and college students.

The three-year project, known as "Immersion" and funded by a $1.3 million grant from the National Science Foundation, is focused on mathematical modeling.

Young children start using physical models in mathematics as soon as they can count. But mathematical modeling is something different and more complex: It's the process of taking an open-ended, multifaceted situation, often from life or the workplace, and using math to solve it.

"Sometimes making a mathematical argument helps you make decisions that seem too big or messy to understand," explains Rachel Levy, an associate professor of mathematics at Harvey Mudd College in Claremont, Calif., who is leading the Immersion project.

The idea is to get young students seeing how mathematics can be applied to everyday life—in essence, an extension of the common standards' push for critical thinking and application.

Here's an example: A group of students wants to buy pizza for a class party. The teacher asks them to consider the different ways they might select a pizza place (cost, taste, proximity to school, etc.), and to come up with a mathematical argument to justify which pizza place is the best. The students then create a method, or model, that other classes could use for deciding on a pizza place as well.

Unlike much of what students learn in math class, these big, messy problems tend to have multiple entry points and no single right answer.

"Traditionally, students are sort of told and shown everything they're supposed to learn—solve this kind of problem this way, and so on," said Martin Simon, a mathematics education professor at New York University, who is not involved with the NSF project. "But mathematical modeling is a very different kind of process. ... It's engaging students in the process of thinking about a situation and trying to find ways to mathematize that situation."

Because mathematical modeling requires higher-level thinking, decisionmaking, and synthesis of various skills, it's not generally taught to younger pupils. In fact, according to Simon, it hasn't historically been part of K-12 teaching at all...

Padmanabhan Seshaiyer and Jennifer Suh, both mathematics professors at George Mason, opened the session by asking the teachers to brainstorm the kinds of problems they've had to solve in their own lives recently. On poster paper, the teachers wrote queries such as:

Is it worth driving farther to get cheaper gas?

Should I fix up my house before I sell it? What rooms should I do?

We're driving to Atlanta with a 2-year-old and a beagle—when is the best time to leave?

The exercise served to get the teachers thinking about how often they encounter problems that might benefit from mathematical modeling. The participants then tried a problem together. They looked at a larger room in the building that had been split into two smaller classrooms, with a temporary wall and door connecting them. They worked on figuring out how the new configuration of the room would affect the amount of time it takes people to exit in the event of an emergency.

As they worked, Seshaiyer asked the teachers to identify their "assumptions and constraints," words typically used in engineering classes, referring to the factors they believe to be true and those that limit their solutions. For example, an assumption might be that the doors to the hallway could not be moved. The number of doors and their positions would be constraints.

One teacher suggested testing the problem with a prototype—putting marbles into a box designed like the room and tilting it to see how they exit with and without the extra wall.
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Source: Education Week