Teaching Philosophy

Donald Estep

My ideas about teaching are all oriented around the belief that learning is essentially an individual process. In other words, the degree to which we can learn something depends primarily on our own innate ability and the amount of work we put into learning, e.g., through reading, thinking, and working problems. I believe that there is actually little possibility of transferring the understanding in one mind directly into another mind. This is perhaps more radical than seems at first, because in my experience, many university faculty believe that lecturing is primarily a process for transferring the knowledge and understanding in their heads into the minds of the students and, consequently, view lecturing as the beginning and the end of educating students. This is not to say lecturing is unimportant. It is just that there is more to lecturing than just being a method for getting notes down into the students’ notebooks.

In my view, the role of the teacher in the learning process parallels the role of a coach in the training of an athlete. First of all, of course, the teacher has the responsibility for choosing the topics to study and how the material should be approached. The best instructor can do no better than the material with which he or she works; an observation that is readily apparent in appraising the typical calculus courses taught around the country. Unfortunately, the choices are often limited in this regard because of the available instructional material and, at least in large state universities, by the inertia that builds up in course syllabi. I feel that a general revolution in the way mathematics texts are written is sorely needed. Second, the instructor should provide the students with the “big picture” to help them get past the blindness that often results from struggling to master details and also provide students with alternate ways to think about the material. An instructor should try to monitor the students’ understanding and lay down alternate paths at places that cause difficulty. Third, the instructor must provide support, incentive, and discipline for the students’ efforts to learn. Learning is difficult and requires discipline, and most students need supplements to their own self-discipline. Grades are commonly used as both incentive and a form of discipline. But, an instructor should try to go beyond this by establishing a relationship with students that enforces their desire to do well. This is perhaps the closest analog between the role of the instructor and the role of a coach. It is important for an instructor to establish a relationship with the students in which they know that the instructor cares very much about how well they learn and perform and, in turn, in which the students care whether or not they disappoint the instructor’s expectations for their performance. Now, it is not possible in the typical single instructor-multiple student class to establish such a close personal relationship with each student on a one-to-one basis. But, it is possible to form one-sided relationships from the students to the instructor, e.g., by giving the students a glimpse of the instructor’s life as a student and as a mathematician and their own struggles with understanding mathematics.

On the topic of the need for discipline, I can narrow my belief about learning further in the case of mathematics in the sense that I believe the success in learning mathematics is determined primarily by the number of good problems one succeeds in doing. Thus the construction of good assignments and exams and a fair grading policy that gives students feedback so they can improve their performance is a critical part of good teaching.