10 Teaching Philosophies for Undergraduate Mathematics Courses

Introduction

This semester I was gifted with the opportunity to teach Mathematical Reasoning at the University of Tennessee, affectionately known as “The Beautility of Mathematics” (the word “beautility” being a combination of beauty and utility). The course is aimed at art, psychology, architecture, and humanities students, among others, and instructors of the course hope students not only see mathematics they did not encounter in high school, but also develop an appreciation for how the subject matter can be applied directly to their disciplines of choice.

This semester has been very important for me in developing a teaching philosophy that is flexible enough to be applicable to different courses I may teach, because it is the first semester in which I have given any deliberate consideration to this matter. Next semester I will be working with my teaching mentor to write an initial teaching statement, which will become a part of any job applications I may send out later for postdoctoral positions in academia. To some extent, my reflections may act as a starting point for that more formal document that I will write and continue to revise later on.

In the meantime, I’ve begun to identify principles that are important for the way I teach. While I think it’s always important to consider a course structure — including how to design assignments and calculate grades — the unusual circumstances presented before us with COVID-19 have illuminated an even greater…