Wednesday, February 22, 2017

How I run my advanced seminar

The topic of how to run seminars came up tonight on twitter:

I chimed in with some 140 character summaries of how I do things, and given some of the responses figured it would be worthwhile to lay things out in more detail here.

Last year I introduced a new 3rd year elective logic module at Durham. Over the course of 22 weeks I wanted to cover both basic model and proof theory of modal logic (essentially, the first half of Hughes & Cresswell's book) and Gödel's Incompleteness Theorem(s), and I was given the option of either one 1-hour lecture a week plus a 1-hour tutorial every other week, or a 2-hour seminar every week. You do the math; the seminar nets me more face-time, so that's what I went for.

One of the most important lessons I learned about learning logic I learned in my very first logic class. I was a senior in high school, enrolled at my local two-year university as a special student, and I was taking intro logic along with 8 other people. By the end of the semester, 6 of the other 7 had come to me for tutoring, because I was the only one who had any idea what was going on. And this is when I learned that the single best way to learn logic is to teach it to someone else. It's easy enough to read a textbook, read a proof, listen to someone go through a proof on a board and at each step go "yeah, okay, I buy that. Seems reasonable to me." It's a totally different story to be forced to understand the content well enough to be able to explain and justify it to someone else.

With this knowledge in hand, I went into the seminar with a plan, one that I figured would either work brilliantly or go completely pear-shaped: I would do the first seminar or two, to get everything going, but after that, we were going to treat this as a proper seminar, which means active student participation, which in my specific case meant: Every student was to be responsible for two of the seminars over the course of the year. And by "be responsible", they'd take the assign material and learn it well enough to be able to present it to the rest of the class, handling any questions. My primary role in the course was to (a) be available while they prepared for their presentations, in case they had any questions or needed clarification in advance; (b) to answer any questions that arose during the course of the presentation that the presenter couldn't answer; and (c) to add information or supplementary material that wasn't present in the textbook so I couldn't expect the presenter to know anyway. A secondary role was to be the back-up, so that if something went terribly wrong, I could step in and finish off the seminar.

When I explained the plan to the students, I specifically said that I didn't want to assign seminars, that I'd much rather take volunteers on a rolling basis; this way, people could pick weeks that worked for them in terms of content and their other workloads. And you know what? Only once or twice did I have to suggest to someone "Hey, you haven't yet done a seminar on this topic---" (since there were two broad topics, and each student had to do two seminars) "---why don't you do next week?" The first year I also had a number of auditors, and I, of course, didn't require that they do the presentations---but even some of them volunteered (some more than once!) The presentations are not assessed, and they do not contribute in any way to the student's final mark.

And it worked great. This was clear both from the capability of which they handled their responsibilities, giving clear and well-thought-out presentations, but also from the informal feedback I got---one student said that there is a lot more pressure to really understand the material if you are to present it, and thus he felt he learned it a lot better, and that of course gives them a better foundation for receiving the content they aren't presenting on.

Last year, the course was primarily technical in nature, so the extent of the content to be presented each week was pretty well circumscribed: We'd set a number of pages we hoped to get through---always a number that if we didn't get through them all, there was space in the schedule to let them roll over to the next week. This year, the course is half Gödel and half philosophy of math, but with the same seminar-presentation principle, I expect each student to do one technical presentation and one philosophical. We had our first of the philosophical ones last week, and I'll admit, I wasn't sure how it would go: On the one hand, it's relatively straightforward to take two hours worth of technical material, learn it, present it, and answer clarification or explanatory questions along the way. It's a completely different thing to, on the other hand, summarize and explain philosophical concepts and stimulate a good discussion. I was bowled over by how well it went. Because each of them has already been the person in the spotlight at least once in the course already, everyone knows everyone else and everyone is happy to talk to everyone else, so it meant that when discussion did get going, they were talking to each other (or to the presenter) and not to me, which is the thing I find most difficult about running a good discussion; as soon as I say something, they all turn and focus on me and try to answer to me, rather than to just talk.

So, 1.5 years into using this technique in my advanced seminar, and I have found it an utterly resounding success, and everything I have heard from my students has been positive. If you've got the right number of people do do it (I've 15-18 students; occasionally two will present jointly, either one doing the first hour and the other doing the second hour, or both doing it in tandem---and this reminds me of a important point which is that given that it's two hours, and logic is hard, we ALWAYS take a short break half-way through), I highly recommend this approach.

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