By Dan Teague, posted September 28, 2015 —

I was at my desk on the first day of school when a student walked in and said, “I’m not in your class, but my father asked me to say hello.” After a short conversation (her father had been my student twenty-some years earlier), as she turned to go, she said, “Oh, he said to tell you that mathematical modeling changed his life.”

Her father did not say that I changed his life. There was nothing special about me; it was a course and the experiences it offered that were magical. We all know teachers with magnetic personalities who attract and build lifelong relationships with their students. Regrettably, with my limited interpersonal skills, I am not that teacher. I wish I were. But the good news is that I don’t have to be. It turns out that a course can also change lives.

I hear “Mathematical modeling changed my life” or something equivalent at class reunions and when alums visit, which they do pretty regularly. And every school can teach a course in mathematical modeling or have a modeling focus to its curriculum. Teaching mathematical modeling requires no superior knowledge, vivid personality, or dynamic instruction to be successful; just give students the chance to be creative and to work together on significant, challenging problems of interest to them. Students are extraordinarily good at what they like, and modeling gives them much to like in mathematics.

What is it about modeling that has such a powerful residual effect on students? I believe it comes from their seeing both mathematics and themselves as learners and users of mathematics in a new and intriguing light—a light that illuminates future possibilities that they had not before envisioned.

Sheila Tobias, in They’re Not Dumb, They’re Different (1990), and Elaine Seymour and Nancy M. Hewitt, in Talking about Leaving (1997), describe students who were very capable of success in STEM disciplines but who purposefully chose not to pursue STEM. My interpretation of their findings goes like this: In their courses in non-STEM disciplines, students would read a book or paper, and the conversation in class would focus on the students’ ideas and understandings. The key question would be, “What do you think about it?” In mathematics class, the focus is almost never on what students think but only on whether they remember what Descartes or Newton or some other mathematician thought. In non-STEM classes, the kids use their own minds; but in math class, they are always using someone else’s mind. In other classes, students create; in mathematics class, they only remember. So they leave STEM.

The notion that mathematics is done by “remembering how” can be very pernicious. It suggests that students can do only what they have been taught to do and that creative mathematical discovery is restricted to the genius few. Modeling changes this mindset. Modeling illustrates the power of students’ own mathematical inquiry and how their individual mathematical talents can be used collectively and creatively to investigate questions in every field of human endeavor. This awakening to new opportunities for using their mathematical talents in areas of live interest to them can be life changing.

I like to use Marianne Moore’s description of poetry—“imaginary gardens with real toads in them”—to highlight the duality of pure and applied mathematics. The abstract theory is the imaginary garden in which we see the beauty of mathematical structure. The real toads are the applications, the models, the uses of mathematics to understand the real world. Modeling gives students an opportunity to play with the real toads. And like the toads in the fairy tales that we read when when we were five, these toads have the power to change lives. 

DAN TEAGUE, teague@ncssm.edu, teaches at the North Carolina School of Science and Mathematics in Durham. He is interested in mathematical modeling and finding problems that connect concepts from different areas of mathematics.