Sometimes I don't have the answers. But by actively doing research, I'm used to being in that position. I'm not afraid to say, ‘I have to think about that. Let's all think about it and figure it out together.'
Emily Dryden never takes for granted how difficult it is for students to learn new concepts. She's still learning herself.
Her research in spectral geometry examines mathematical questions involving the frequencies at which objects vibrate. What can the vibration frequencies tell us about an object? What can we say about the frequencies if we know the particular properties of an object? The focus of her work has broadened over the years, and she has discovered that it has applications in areas from medical imaging to telecommunications.
"I don't lose touch with the fact that learning new math is really hard," Dryden says. "When I go through my research process to explore and ask new questions, it forces me to practice certain habits. I think that makes me a better teacher in that I'm reminded to help my students to develop those same habits."
Although difficult and complex, mathematics isn't something to be feared, she says. For Dryden, the difficulty is part of the allure.
"I wanted something with continual intellectual struggle," says Dryden, who majored in French and mathematics as an undergraduate before choosing to pursue advanced study in math. "Sometimes I've questioned why, but I like to push myself and push my students. Making that choice says something about me and who I am."
Dryden takes that fearless approach to the classroom. A winner of the Bucknell Presidential Award for Teaching Excellence, she teaches her upper-level courses in a seminar format, rather than delivering lectures. Students do reading and problems in advance then bring their questions to class.
"Sometimes I don't have the answers," she says. "But by actively doing research, I'm used to being in that position. I'm not afraid to say, 'I have to think about that. Let's all think about it and figure it out together.'
"It's more work that way, but I think the skills the students learn are more transferrable. Most aren't going to graduate school for math, but many of them are going to work in a technical field where they have to learn new things. Being able to formulate and answer questions yourself is much more useful to them than me just teaching them a body of mathematics."
Posted Sept. 22, 2017