Learning together

I like teaching classes that I haven't taught before. In seven and a half years of teaching at USC, I have taught about ten different courses. This is somewhat unusual in an environment where many faculty prefer to teach a relatively small stable set of courses over time.

I confess I do this mostly because I like the excitement of mastering new material, and gain a lot of value from learning while teaching. But, it struck me today, I also do this in part because it is precisely when I'm teaching material that I'm not deeply familiar with, that I feel closest to students, most sympathetic to how they perceive the material, most understanding about what they may find challenging. And it's a pleasure to feel  thus connected to the student's doubts and uncertainties, because then we're on the same team, learning together.

There is a risk, of course, that I am caught short when explaining some concept that I don't completely grasp myself. At such moments, if I can set aside my ego, and approach the situation with humility instead of trying to hide my ignorance, I find that the honest act of showing students how I deal with what I don't understand (say, by trying to re-derive some mathematical expression from first principles, or by saying out loud what I'm myself confused by, so that potentially a student can help me figure out some simple fact I'm ignoring) is itself of value to them. I've had students tell me after class that they found it helpful to watch me model how to overcome my own uncertainties.

My research group and I often meet to read a technical paper or parts of a book together. The way we organize these sessions, which can last anywhere from two to four hours, none of us, including I, have read the material before. We take turns reading a few paras each, stopping periodically to make sure we all fully understand what we have read (descriptions of algorithms, equations, proofs of theorems, the experimental setup, etc.). We are often puzzled, of course, but because there are usually ten or more of us in the room, one of us is likely to figure out the answer quickly. These sessions are always a pleasurable and rewarding experience, and help my students and me bond with each other, enhancing our sense of shared identity as a group.

One of my Ph.D. students once remarked after such a session, "I wish our classes were more like this!" and it struck a chord in me. It occurred to me that such a reading-based class could indeed offer a refreshing experience of non-authoritarian, communal learning.

In Spring 2006, I taught such a class at the graduate level, with about fifteen students. Because I was starting to move my own research interests more significantly in this direction, I told the students from the very start, we would together learn about different optimization techniques and their application to communication networks. We had a three-hour class in the evening once each week. I specifically asked for and got a small classroom where we could all sit around a table. For the first hour or so I would present a lecture covering requisite background material (such as KKT conditions for solving constrained optimization problems in closed form, linear programming, convex optimization and Lagrange duality), and then we would read a paper which used that theory in the context of a communication or network algorithm/protocol  (e.g., optimal popularity-based replication in P2P networks,  primal-dual techniques for network utility maximization). Beyond this, the students worked on research projects either alone or in pairs where they took the tools we learned and applied them to a networking problem of their own choice.  Looking back over all the courses I've taught to date, this was easily the most enjoyable experience I've had as a teacher (the 5/5 course evaluations I got that semester indicate that the students had found the experience valuable too).

There were many reasons why this class went so well, including the small class size, the balanced mix of theory and applications, a highly motivated set of students, the diverse and interesting material, and the outstanding teaching assistant I had that semester, but I am certain that one of the biggest factors was the fact that we were, in a very real sense, learning together. I have warm memories of us all huddled closely around the table in this small room each week, reading and discussing papers late into the spring evening.