Teaching philosophy -- Mike Daven

The prevailing thought that strikes me when first I meet a new class is that, during this term, this group and I will be learning something new together. From the first class day, I make a point that I am a student myself, though I have been at it for a bit longer. I emphasize that the class should feel free to approach me about any and all questions they may have. Most importantly, I try to impress upon them the fact that they are largely in control of the class. I see my role in the class as more "tour guide" than "lecturer-grader".

We who have ever stood before a math class have seen in the eyes of our students that peculiar twin phenomena of "math anxiety" and the scared or indifferent student. We might recall having once experienced that same fear during our own academic career. I do not believe this fear is unfounded, but can in many cases be traced back to the indifference of some of our fellow teachers. If a student finds the material difficult and the teacher unapproachable, then that student soon decides that there is little hope of picking up the material.

The fault here lies mainly with the teacher, of course, but it is the student who suffers. I try to always remember this as I teach. I go strictly by first name in my classes, I have many and flexible office hours, and I always treat each of my students with the respect that I wish them to have for me, which respect I hope to earn. In reforming the curriculum, I believe that much emphasis should be placed on reforming ourselves as teachers. An ineffective teacher cannot present even the most basic material in a meaningful way. If we really want our students to understand, we must first reach out and try to understand them.

But I said that the learning done in a classroom should be done together, as a class. I make an effort to have the students work with one another, with pop quizzes worked in groups and by students working problems together during office hours. In so doing, each student has an opportunity to see how their peers visualize the material, and by trying to explain to each other, they often reach a better understanding of the mathematics themselves. Not coincidentally, this affords me a glimpse at how well I have gotten through to the class, and often I gain a new perspective on a problem.

There will always be that question many of us dread, "My major is ...When will I ever use this?" When confronted by a student with such an attitude, I try to instill in them a sense of the bigger picture, of what they are likely to experience all through their studies. I realize that most of the undergraduates who pass through my classroom will never need to take a derivative or factor a quadratic. However, by studying mathematics, they may develop specific skills and techniques, and more importantly, the students will gain an analytical perspective that may be applied far beyond the classroom. For this purpose, mathematics is invaluable.

Hopefully, the students bring ideas from class home with them. The internet provides a way to provide additional support outside the classroom. I keep a set of practice quizzes, current quizzes, my syllabus, and an update page available, through which the students may fill out the framework provided in class. Every term, I find new ways in which the internet helps extend the classroom. I also hope to integrate other media as teaching aids, such as Maple or Mathematica, if the resources are available.