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Speaking the Language of Math


Loving math and persuasively sharing that love are two different things, which is why students in Math 235 present research projects to their classmates and take a 25-minute oral exam one-on-one with their professor.

Math 235 Differential Equations is a “speaking-intensive course” that builds on the Mathematics Department’s longtime commitment to developing student writing and speaking skills. A second speaking-intensive math course will debut next semester — Math 361 Number Theory with Applications, taught by Associate Professor of Mathematics Courtney Gibbons. At Hamilton, courses across the disciplines emphasize oral and written communication.

Intended math major Claire Lavalley ’22 signed up for Differential Equations without noticing its emphasis on speaking, and initially she was daunted to learn she would face an oral test. “It’s different than a French oral exam or a poetry presentation or something. It made me realize that I was not only going to have to understand the material myself but how to communicate it to others, which is a totally different skill than I’m used to in math courses,” she says.

Associate Professor of Mathematics Andrew Dykstra was instrumental in making Differential Equations speaking-intensive. “Math is as much a language as a science,” he says. In his syllabus, Dykstra tells students that writing and speaking are at the heart of higher-level math. “The oral communication skills you develop in this course will serve you well in your career, even if your career ends up having nothing to do with math,” he assures them.

When Dykstra first decided to use oral exams, he turned to Hamilton’s Quantitative & Symbolic Reasoning and Oral Communication centers to develop practice tests. He doesn’t require students to take the practice test, but almost all of them do, working with peer tutors. Lavalley took the practice exam, which proved to be time well spent.

For the first part of the actual test, students get two questions in advance and pick one to answer. Lavalley was excited to talk about her topic with Dykstra. “And then for part two, I was definitely nervous. I didn’t know what he was going to ask about,” she recalls. “But it was a good test of on-the-spot thinking and oral-communications skills, because not only did I have to think, but I had to talk through my thinking process as I was figuring it out. It was hard, but it went well.”

A former exam tutor for Dykstra, Levi Lorenzo ’19 is now a math doctoral student at the University of Colorado Boulder, and he remains a champion of the speaking-intensive approach.  “When you go into industry or the real world, being able to communicate more advanced ideas on a level that's more basic and understandable to people who don't necessarily have that background is really, really valuable,” he says.

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