Teaching Philosophy
From helping fellow students in junior high, to being trained as a tutor in college, to becoming a TA coordinator while still an undergraduate, teaching others has been intertwined with my own learning. As a graduate student, I helped train incoming teaching assistants, co-authored their training manual and observed dozens of new TAs to assess their teaching and provide constructive feedback. By the time I reached UC Berkeley, I had already taught at three other institutions and in two different disciplines. The course I taught there seemed the perfect culmination of many years of teacher development. In that upper level course, I was able to rush through any tedious aspects of the subject, to focus on the most interesting principles and to present the key concepts geometrically and intuitively. The feedback I received at the end of the semester was quite positive, with one evaluation stating “This was the best course I’ve had here.”
My first semester teaching at the University of Montana was a rude awakening. In one of my courses, the first week of instruction brought vocal disapproval from some students and a near mass exodus from my section. As much as I would have liked somehow to blame the students, logically I had to be doing something wrong. To some extent, it was just a problem of finding the right level of difficulty but a deeper issue was the assumption that an “appropriate level” even existed for this particular course. The students came from a much broader variety of backgrounds than I had ever experienced in a single class, the university had mandated a policy of not enforcing pre-requisites and the students had widely differing goals in taking the course. While every class includes a range of learning styles, backgrounds and motivations, this course presented a true challenge for its instructor.
So, I adapted. I incorporated review into each chapter -- including basic algebra skills, I created group work that was suitable for several different skill levels and in the end I believe that I effectively taught my (remaining) students. However, the experience forced me to question my own course goals. While teaching had been so effective helping me to learn as a student, my own teaching was hampered by the perspectives I had held as a student. Apparently my primary course goal simply was to prepare the students for further math and science courses. I needed to reassess how I truly wanted my mathematics courses to fit into the ideals of higher education.
While each course is different and each group of students represents a different set of needs, some common goals throughout my current courses are developing communication and critical thinking skills, introducing mathematical thinking in new contexts and encouraging students to take responsibility for their own education.
To help develop critical thinking, I incorporate a certain amount of open-ended material. A useful model for me has been the “Homework with Elaboration” concept developed by Maria Andersen of Muskegon Community College. For these five point homework problems, a single point is awarded for an “elaboration” created by the student that develops the material in a direction beyond what was spelled out in the exercise. One point out of five seems to strike the right balance and by including steady stream of such assignments, the students quickly develop a sense of what is expected from them and an appreciation for the role of creativity in mathematics.
When possible, I let my students help choose the content or at least steer the emphasis of the course. In my “Contemporary Mathematics” course, I had the students rank a list of possible topics. Their responses were deeply divided. The topic ranked first by a small majority of student was chosen dead last or deemed unacceptable by nearly every other student. Consequently, I split the course into a “Financial” track and a separate “Games and Gambling” track. In order to appreciate the value of mathematical thinking, students need to see and to use it in a context that they deem valuable. For some students, this meant translating equations into monthly budgets. For others, this meant translating probabilities into correct poker strategy.
I spend a significant amount of class time on group work. Beyond adding variety to the course, it is a strong motivator for the students to keep current with the material. In addition, it gives me immediate feedback on student understanding and lets me provide some level of direct attention to nearly every student in the class. Ideally, an activity forces the group to articulate concepts that they are just on the verge of understanding. Proper excecution by the instructor keeps the students focussed on the entire group’s comprehension and engaged in dialogue rather than racing to finish.
For many schools, the reality of higher education is that students are balancing academics against a job or other significant responsibilities. Even in the “ideal” case of a student whose main focus is school, one course is balanced against another as well as against all the non-academic pursuits available. For me, an ideal grading scheme effectively lets the student choose the grade they want. It helps them prioritize the course within the context of their lives and helps them determine how much effort they are willing and able to commit. Some of the techniques I have used toward this end are: pass/fail tests that students have the option of retaking, self-selected homework assignments and optional course projects.
The higher goals of teaching mathematics are subtle. Rather than just learn a particular technique or definition, as educators we want our students to develop their critical thinking and problem solving skills, learn how to communicate precisely and effectively and appreciate the different intellectual culture that mathematicians represent. To some extent the course content is secondary – just a means to the end that the higher goals represent.
My primary focus as a teacher is to create an environment that facilitates the pursuit of these higher goals. By promoting cooperation and presenting multiple avenues for learning and assessment, by expanding the scope of the material included and challenging the students’ goals in taking and assumptions surrounding the course, I help students forge their own path to intellectual development.