Carol Schumacher

What is the Definition of Definition? and Other Mathematical Cultural Conundrums

Abstract:

Helping our students think like mathematicians should be at the center of every class we teach. The particular topic will affect which parts of thinking mathematically we might address, but the goal of every math class should be to turn out students who can bring mathematical reasoning to bear in the context of the material taught in the course. In order to help our students think like mathematicians, we teachers must think deeply about what is going on in our students' heads. But this also takes an unusual amount of self-reflection. We need to understand how we think about things. Unfortunately, thinking mathematically is often something that comes naturally to people who eventually go on to get Ph.D.'s in mathematics. Thus we have no idea how we learned to think this way, and we are often not even aware of how much is really going on in our own heads when we attack a mathematical question. I can attest to the fact that this was certainly true of me. As I have become more self-aware, I believe my teaching has improved tremendously. In addition to trying to illustrate some of the insights acquired over many years, the talk will be filled with illustrative examples of activities that can be used in different courses to help students engage the mathematical ideas of the course as mathematicians do every day.

Biography:

Carol Schumacher is Professor of Mathematics at Kenyon College in Gambier, OH. She received a BA in Mathematics from Hendrix College in 1982 and a Ph.D. in Mathematics from The University of Texas at Austin in 1989. She joined the Kenyon faculty in the fall of 1988. Carol loves teaching and is the winner of Kenyon's Trustee Teaching Award. She is very interested in inquiry-based learning (IBL) and is the author of two texts written to support an inquiry-based approach: Chapter Zero-Fundamental Notions of Abstract Mathematics, 2E and Closer and Closer-Introducing Real Analysis. Carol just completed her third term as chair of the mathematics department at Kenyon and is one of a team of MAA members working on the 2015 CUPM Curriculum Guide to Majors in the Mathematical Sciences.