A Lesson in Calculus from the Late, Great Dr. Molly Gustin

A TAC-New England Junior Mathematics class recently class discovered a fun way to look at a problem from another angle — literally.

In the second semester of the Junior Mathematics Tutorial, students learn the basics of calculus, following a Cartesian treatment of algebra. This week, juniors were studying trigonometric functions and their inverses. Tutor Dr. Josef Froula explained the inverse trigonometric function by appealing to an example he learned from the late TAC tutor Dr. Molly Gustin: “Graph the function, and then lie down behind the blackboard. The function you see is the inverse of the original function.”

“It struck me that, with the innovation of dry-erase markers, we could sketch these functions on the window and see what she was asking us to imagine,” said Dr. Froula. A student drew the function on the window, and the entire section went outside to test Dr. Gustin’s theory. Students and tutor alike lay on the grass outside to see the inverse function for themselves, laughing as they came to appreciate the brilliance of the idea.

“Dr. Molly Gustin always insisted on appealing to the imagination in the study of calculus,” Dr. Froula reflected. “She was not only a brilliant mathematician and music theorist, but an outstanding teacher whose enthusiasm was contagious. I owe my love of mathematics in large part to her.”