Wheelock Geometry Class Explores Gerrymandering
December 14, 2017
Wheelock's Math 245 Geometry class married the study of math and politics this semester, creating a website that explores the mathematical concepts behind the process of gerrymandering. The website defines gerrymandering as the dividing of a state, county, etc., into election districts so as to give one political party a majority in many districts while concentrating the voting strength of the other party into as few districts as possible.
The Geometry class, taught by Associate Professor of Mathematics Debra Borkovitz, is part of Wheelock's undergraduate degree program for prospective teachers. All students in the class are majoring in either Math for Teaching or Math/Science for Teaching. The Geometry class emphasizes the use of physical and computer models to create meaning, develop problem solving and communication skills, and to construct convincing mathematical arguments.
Borkovitz said her goals for the gerrymandering project were threefold:
- To teach the students the subtleties of geometry using a real-world situation
- To highlight an important issue tied directly to Wheelock's social justice mission
- To show students how to create a math lesson that really engages their future elementary school students
As part of the Gerrymandering project, the class was required to document its findings so that the data could be shared. Borkovitz said she was excited that the students chose to create a website, which most of them had never done before. "This was an authentic assignment to make something useful," Borkovitz said. "I though they could make a real contribution because there aren't a lot of places where all this information is gathered."
Borkovitz developed the idea for the Gerrymandering project after attending a summer workshop hosted by the Metric Geometry and Gerrymandering Group (MGGG), a Boston-based team of mathematicians launched by Moon Duchin of Tufts University to study applications of geometry and computing to U.S. redistricting. The workshop featured a special session designed to help educators find ways to incorporate voting, redistricting, and civil rights material into their curricula.
At Borkovitz's invitation, Duchin came to the Wheelock class as a guest lecturer to talk about MGGG's mission and also about the math that has shaped a Wisconsin gerrymandering case currently before the U.S. Supreme Court.
"Gerrymandering is a topic that isn't talked about very often," said Marissa Wray '20, a student in Math 245. "When we were doing this project, I thought it was interesting. But when Moon came in and talked about the Supreme Court case, I really felt like it was real-life."
Class member Nyssa Sconsoni '20 said many of her previous math class experiences were extremely structured, with students being taught a unit and then taking a test on the material. By contrast, she said the Gerrymandering project was a fun, interactive learning experience that allowed the class members to really explore the topic. "We got to make a website and learn in a really interactive way," she said. "We can take this experience into our own classrooms and not make everything so structured."
The Wheelock students' Gerrymandering website uses established mathematical equations to measure different types of compactness in voting districts in order to detect in what ways a district may be gerrymandered. It explains that a non-gerrymandered district would have high scores using the following measures:
- Harris (W/L): The shape created by the width and length of the district
- Polsby-Popper (4πA/p^2): The relationship between the district's area and its perimeter
- Reock (A/C): The district's area in relation to the area of the smallest circle that can be drawn containing the complete district
- Convex Hull (A/H): The district's area in relation to the area of its convex hull (a shape where any straight line that runs through the shape will only cross the perimeter twice)
The website includes real-life examples of voting districts across the United States, as well as graphics showing the various measurement systems and how they interact with each other. A particularly fun feature of the website is an interactive model that allows users to change a district's shape and watch how each change affects its compactness score, and thus, its potential effect on voting patterns.
"A lot of times students don't like math because they don't see how it applies in real life," said Wheelock student Lexie Smith '19. "Now, we can see and show our students how math is applied to their everyday life."
Classmate Emily Marchisio '19 agreed, adding that building a website was easier than she thought and would be a very user-friendly way to incorporate technology into any classroom. "It would be a good way to get kids to work together and do a project," she said.