Mediated Learning Newsletter

Vol. 5, Issue 3: December 2005, page 2

Are Faculty Surrogates in the Learning Process?

Seth Braver
Co-winner of the Department of Mathematical Sciences Graduate Student Teaching Award

Articulate and soft-spoken, yet confident and out-going, it is easy to understand why students are attracted to Seth Braver, a co-winner of the Department of Mathematical Sciences Graduate Student Teaching Award in 2005. While discussing teaching, school, and mathematics, it is clear that Seth is concerned about more than surface-level learning. He is concerned that students think beyond textbooks and classes. Braver is an exemplar for teachers as he explains his goals for students and classes.

Bartleby and Seth Braver

After graduating from high school in Georgia, Seth moved to California, ostensibly to attend college at the University of California-Santa Cruz. After a year during which he rarely set foot in a classroom, he left school and worked a variety of minimum wage jobs, first in Atlanta and then in San Francisco, before returning to college,
enrolling at San Francisco State University as a psychology major.

“Psychology is a fascinating field, but the courses I took were so shapeless that I decided to switch majors. I still remember riding home in an overcrowded train with the SFSU catalog on my lap, hunting through it, with great enthusiasm and naiveté, for subjects with impressively rigorous-sounding names. I liked the celestial ring of astrophysics, but it would have taken too long to finish a degree in that subject, so I settled for pure mathematics. An idiotic way to choose a major, to be sure, but fortunately it led me to a very beautiful subject.”

Seth commented that one of the best lessons in his mathematics classes at San Francisco State did not concern mathematics per se. In a probability
course, his teacher often assigned famous problems far beyond the level of the students. He encouraged students to seek their solutions in the library, and report on what they had found.

For Seth, discovering the vast resources available at the library was immeasurably more important than anything he had learned in any of his classes up to that point. “It was then,” he said, “that I realized I could learn mathematics, or practically any other academic subject, on my own. In many of the courses I was taking, particularly in mathematics, the teachers read the textbook to us. Not literally, of course, but not too far from it either. I may not have known much mathematics at the time, but I certainly wasn’t illiterate, so I found this way of teaching rather bizarre. I went to the library and found better books than the ones assigned, and read those instead. When I had questions about what I read, I asked my teachers, or discussed them with a few fellow students. This felt much more natural. To this day, I don’t like taking classes in the usual sense; I’d rather set my own course of studies by taking independent studies and seminars in mathematics and auditing an occasional class outside of my department.”

After earning his bachelor’s degree, Seth returned to UC-Santa Cruz for graduate school. As the abstractions of graduate-level math were “being piled on top of each other,” he felt that he was losing track of the meaning of the mathematics that he studied, even though he could still succeed in his classes. As a corrective, he began to think more seriously about the history and philosophy of mathematics. “While I was at Santa Cruz, I had many discussions with Richard Mitchell, an excellent lecturer
in the mathematics department there. We both saw mathematics as a liberal art, and agreed that someone unable to appreciate William Faulkner’s novels probably lacks the aesthetic sense to distinguish beautiful mathematics from merely clever mathematics. Good mathematical taste, to Richard, invariably meant an inclination toward geometry and history, and I’m sure my dissertation, which is concerned with the early history of non-Euclidean geometry, has been at least partially influenced by his ideas.”

Seth says that he tries to put mathematics in a historical context when he teaches it. He admits that few of the classes he has taught as a teaching assistant lend themselves naturally to this approach, “In most of the courses here, for which I have been a TA, I only have time to answer a few homework problems when I meet the students. Teaching assistants have very shadowy roles in such a system.”

He mentioned that as a graduate student in Santa Cruz, he spent more time per week in the classroom, mainly teaching calculus to interested science students rather than “doing homework problems for students forced to take mathematics against their will,” as he described one of the classes that he has taught here. Concerning his teaching experience at Santa Cruz, Seth said, “It was there that I learned that I might actually have some talent for teaching.”

When asked what advice he would give to other teaching assistants, Seth confessed that his advice is a bit unorthodox:

• Don’t take the teaching role too seriously. In many respects, you are an unnecessary surrogate in the process. Students could learn almost anything you teach them by themselves, if they were truly interested. The best lessons you can offer are either those that will arouse your students’ interest or those that will expose them to areas in the intellectual landscape of which they may have been previously unaware. If they are interested and know where to look for resources, they will do so, and your role will be to guide them. At that point, you can do some real teaching. On the other hand, the classroom-textbook setup, with its ringing bells, attendance sheets, and final exams is very artificial. Don’t give it more credit than it deserves.
• At the same time, try to convey to your students that the University is a wonderful place for anyone with serious intellectual interests. Where else are you going to find so many scholars and students to exchange ideas with, or a library filled with all sorts of surprising treasures? These are the best parts of a formal education system, by far. If you can infect your students with a love of learning, then I think you will have succeeded as a teacher, whether or not they can evaluate triple integrals, conjugate Latin verbs, or what have you.

Seth Braver has interesting insights for all faculty. Perhaps recognizing the surrogacy role and learning how to help students identify good sources of material are equally as important as lectures.