Teaching Philosophy

I feel that teaching mathematics is an opportunity given to a select few to help others learn better ways to solve problems, understand new concepts, and incorporate mathematics into their daily lives. We are not only charged with teaching students mathematics but also the skills necessary for deductive reasoning. Students should leave our classes with skills that will serve them no matter what their eventual profession.

To meet these goals, I feel that students need to see that mathematics is prevalent in many areas of their lives. We must make mathematics accessible by using real world examples and hands-on exercises. We must encourage students to apply themselves, and we must support their efforts with our time and understanding. We must be willing to try new methods of instruction and to use technology when appropriate.

I have tried to accomplish this in many ways. I employ CAS as an exploratory tool to help students discover concepts and to give them the ability to use programs such as Maple and Mathematica to make their own discoveries. My research relied on my ability to use technology to make conjectures and then use my knowledge to prove the results. I feel that my students should be able to do the same thing given a little guidance. I also use small group projects as a way to help students grasp difficult concepts. I find that this serves two functions: it gets students to think about the concept in question and it helps them learn how to work with others. Many students will later find that these skills are useful in many other situations.

In the past I have used writing projects to help students internalize concepts. The assignments ranged from summarizing a theorem to researching an historical development such as that of the derivative. I now find that I am beginning to use writing assignments more frequently in my courses. In fact, I would like to develop/implement a foundations course that focuses on helping students learn how to identify and summarize the key ideas of a proof. Ideally, the students would present their thoughts to the class. My interest in such a course comes from directing Independent Study at The College of Wooster and noticing the difficulty many students have with understanding proofs. This is one area that I think Project NExT has helped me develop into a better teacher.

In attending The Ohio State University, I have seen a school with a strong focus on research. While advancement of the field of mathematics is a noble pursuit, I have found that, for me, teaching far surpasses the joys to be found in research. I enjoy discovering new connections and insights, but I would much rather help students gain the necessary skills to make their own discoveries. Seeing a student make the connection that allows them to understand a small piece of mathematics is what I feel teaching is all about. I cannot imagine a more rewarding experience.

© 2005 Dr. Jon Breitenbucher
Last modified: November 24, 2005 at 12:03:08 AM.