Mathematics Department update

Gywn Coogan discusses designing a math curriculum that encourages students to collaborate.

May 1, 2020

Gwyn Coogan '83 first experienced the Academy as a two-year boarding student and was drawn back nearly 20 years later to teach. Prior to her faculty appointment in 2002, she earned a bachelor’s degree at Smith College and a doctorate in mathematics from the University of Colorado. A former director of the Exeter Mathematics Institute, Coogan is dedicated to sharing the school’s pedagogy with others and improving math instruction for all students.

Talk to Coogan about Exeter’s Math Department and you’ll find “excellence” and “relevance” are the common denominators — and that is by effort and design. The chair of the department never stops considering new ways to grow and enhance the program for a changing student body. “The students who are coming to our school are coming with a slightly different background than they used to 30 years ago,” Coogan says. “If the curriculum that most kids are learning before they get to our school has changed, we want to change to reflect that, to move them from wherever they are to wherever they think they should go. You have to move kids closer to the edge of mathematics.”

Instead of standard textbooks, Coogan and her team use problem sets, first written by Exeter math faculty nearly 30 years ago specifically for Exonians to build problem-solving skills that emphasize not the answer, but the winding path to get there. And every summer, faculty gather to reevaluate and update each of these 3,700 math problems. “We want problems that are engaging enough that at times you need to talk to your friends about them and get ideas,” Coogan says. “But we also want kids to be able to formulate their own questions.”

You have to move kids closer to the edge of mathematics.”
Gwyn Coogan

Exeter’s problem sets are available free online for other educators to use, and the inquiry-based pedagogy behind them is also taught by PEA faculty at annual Exeter Mathematics Institutes held at schools across the country. “We’re proud of the fact that people look to our materials and borrow our materials and try to replicate what we do in our classrooms,” Coogan says. “We want to be leaders in our discipline.”

Instructor Gwyn Coogan works with a student

Department quick takes

Students pursue their passions

Many students enroll in a math class every term, every year they are at Exeter, and Coogan ensures that there are classes to challenge and inspire them. “We have about 40 kids every year who need classes beyond Calculus,” Coogan says. “We try to offer a topics course each term, proposed and developed by individual teachers, for those students who seek to push themselves beyond the standard curriculum. ... It involves a lot of creative effort on the parts of the teachers, who mostly have PhDs, to create these courses. One of the appeals of teaching at our school is the ability to create a course and to have students who can learn it.”

Custom curriculum

“We do write our own materials, and this involves constant effort on our part to keep it updated and relevant and alive and correct,” Coogan says. Calculations become conversations, and math emerges as an essential tool to analyze and understand the world with problems that provide insights into some of the toughest social issues of the day, including citizenship, gentrification, food deserts and wealth gaps in America. “In our problems we also use names that don’t have a gender affiliated with them, so there are problems that involve Pat and Kim. If we can allow students to see themselves in the problems, it’s going to just catch them in a way that they might not be caught.” Coogan is looking to include non-gender names that are used around the world. “If all sorts of people are allowed to be the scientist that figures out the next prime number, then that’s going to bring some people up that might not have thought of themselves as math people. It’s a small thing, but I think it can have a positive impact.”

Engaged faculty

Mathematics faculty attend two major conferences each year to stay current with developments in their field and also to share Exeter’s math curriculum with others. “Talking about teaching a modern algebra course through inquiry-based learning is something that appeals to college-level teachers and also high school teachers,” Coogan says. In an effort to further diversify the Math Department, four new doctorate-level mathematicians recently joined the faculty. “We’re bringing so much depth into our department,” Coogan says. “It’s really helpful to get teachers from a variety of backgrounds. A diverse department makes our courses richer and more meaningful to more people.”

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