Constructing a giant, inflatable geometric solid out of colored plastic tarp isn’t your typical geometry assignment.
But in Zachary Herrmann’s geometry class, it’s par for the course.
For the past five years, the math teacher has challenged his geometry students to create giant inflatables in a week-long, end of the year project. Working in groups of two to four, students are given a 100-by-40 foot piece of plastic tarp to transform into a multi-dimensional shape.
“I think it’s really important for students to engage in sustained, complex problem-solving,” Herrmann says, as he set up fans in the gym for students to display their projects Friday. “Some of the most sought-after jobs exercise skills like this.”
Herrmann first piloted the project in Sunnyvale, CA, where he taught for a year after graduate school at Stanford University, and he has repeated it for the past four years at ETHS. This year, however, he’s added some new dimensions. Students partnered with a class in Philadelphia working on a similar project, via Skype, and Herrmann gave them flip cameras to document their work.
“I’m really trying to push in all directions this year,” Hermann says. “There’s just so much technology that can enhance the classroom.”
Part of the funding for the materials comes from ETHS, while the rest comes from a five-year teaching grant Herrmann was awarded, called the Knowles Science Teaching Fellowship.
As students set up an array of tarps in red, yellow, blue and green, it soon became evident that not all were going to inflate. Some students were still frantically taping corners, while others crawled inside their shapes to feel for any holes. One girl used a ruler to push the top point of a giant, starfish-like object upright, while another crawled under the shape to keep it steady.
Watching his students struggle, Herrmann feels like the lesson is a success. Because it’s the challenges that result in real learning, he says. While a problem in a geometry textbook is “someone else’s problem,” as Herrmann explains, the problems that arise in designing something yourself “belong” to the students.
“They’ve got a real stake in being able to solve it,” he says. “I love that part.”
Figuring out the shape itself was a challenge for freshman Ben Bon’s group. Bon wanted to make something no one had done before, so he suggested a hexagonal frustum, a six-sided pyramid with a flat top.
“It took me like twenty minutes to explain,” he laughs.
Figuring out how to cut several dozen trapezoids to form the shape was the next part of the battle, while getting the tall yellow frustum to stand upright when they inflated was also a challenge. One after another, group members took turns pushing the narrow shape upright as it repeatedly threatened to fall over.
“Our lines were very close to being straight,” says group member Arri Dortch. “Meaning it didn’t look like a pyramid.”
Although the project is designed to build students’ problem-solving skills while drawing on their knowledge of geometry, the genesis of the idea came out of play. As a kid, Herrmann used to make inflatable shapes out of garbage bags in his living room.
“When I became a teacher, I thought, there’s a lot of geometry in this,” he says.
Students confirmed that there was something fun about this geometry lesson, too. As they gathered to talk about the projects at the end of class, one person yelled, “That was the best math lesson ever!”
Dortch concurs. Although she prefers algebra to geometry, she says this project was definitely fun, in part because she got to bond with her group along the way.
“I would do it again,” she says. “Maybe with a little shorter shape.”