Classwork and homework in a seminar class

Before the (spring 2010) term started, I talked with some alumni about their experiences in the undergraduate seminar classes at M.I.T., and they suggested that I add more structure to my class (Seminar in Number Theory) than just student talks. In particular, some of the alumni felt that they only managed to establish a solid grasp of the subjects of their own talks, and that some kind of exercises after each talk might help solidify things. I think the format I chose has some room for improvement, but the students did seem to be on top of all of the material, at least for the first half of the term.

Basic format

The class lasted 50 minutes, and the first 30 minutes was devoted to student lectures. During the lecture, the student would find appropriate times to write down two exercises on the subject of the talk, and during the last 20 minutes, there would be discussion and working on those problems in groups. The instructor (me) and the lecturer(s) would assist the groups working on the problems. The students then had to write up their solutions as homework (to be turned in weekly), and I would grade it for both style and mathematical correctness.

I chose to do group work, because I was used to it from my calculus TA experience, and I thought it would make students more willing to seek each other out if they had questions in the future. I was hoping that by getting the speakers to assist, the speakers could see in a direct way what parts of their talks went over the heads of the audience. One of the reasons for asking for homework writeups was that I wanted to see the students’ mathematical writing before they wrote the first drafts of their projects, but I didn’t want to impose a large workload on them.

After spring break, I stopped collecting homework, and I stopped having the speakers rehearse their talks with me. This was partly because I wanted them to concentrate on their final projects, and partly because I didn’t think I had much more to teach them that wouldn’t come from practice. The latter reason may have been a poor judgment.

Results

I didn’t have much trouble getting the students to discuss problems and work in groups, but I never managed to get the speakers to assist in a meaningful way. I think they felt awkward approaching a group of their peers and offering help. Mostly, they would sit and work on the problems with neighbors. I discussed this briefly with Susan Ruff, and she suggested that some pre-talk coaching might help with this, e.g., when helping the student prepare for the first presentation. I would be interested to hear more about how this could be done.

The homework was rather bothersome to grade, but my stylistic feedback seemed to clear up some of the most obviously bad habits. I tried to make sure the questions were reasonable by discussing them with the speakers ahead of time, but I forgot to do so on a couple occasions, and those speakers invariably made the problems harder than I would have liked. Grace Lyo recently suggested that the speakers do some of the homework grading, so they can pick up stylistic cues from their classmates, and possibly get more indirect feedback about how well they communicated certain concepts in the lectures. Also (ideally) they would pick problems that were easier to grade. This sounds like a very interesting idea, but I haven’t thought much about details of implementation.

After spring break, when I stopped the rehearsals and homework, the speakers stopped offering questions for classwork during their lectures, and the end of each class tended to turn to general mathematical discussion. My impression was that the students became somewhat less engaged with the material. I think some of this can be put down to general fatigue as the term progressed, or a result of the subject matter moving from the primary textbooks that they were reading and into various papers, but perhaps the lack of work made them less focused. In retrospect, I think I should have just scaled the homework down to one problem instead of eliminating it entirely.

Discussion

First of all, I would be interested to hear ideas for fleshing out Susan Ruff’s proposal about coaching students to aid in group work. This seems like it could potentially help them if they become TAs in the future. I’ve never led any teacher training, so all of my experience is on the receiving end (and several years in the past).

Second, any ideas about getting speakers to grade some of the students’ homework would be appreciated. I imagine some discussion with students about grading rubrics may have to take place for each homework. There is also the complication that I collected the homework once a week (because the students said that frequent deadlines would threaten their sanity), so there were questions from three talks on each homework. This suggests the solution of dividing the homeworks into 3 roughly equal piles (say A,B,C), having speaker A (resp. B,C) grade the problem introduced in lecture A (resp. B,C), and having the instructor do the remaining 2/3 of the grading after collecting the partially graded papers from the speakers. Alternatively, one could coordinate some kind of scheduled exchange in which the speakers do all of the grading.

Finally, I would be interested to hear any other ideas about refining the format of this class, or potential pitfalls that I may have missed due to dumb luck.

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MAA Mathematical Communication (mathcomm.org) is a developing collection of resources for engaging students in writing and speaking about mathematics. The site originated in the MIT Department of Mathematics and was expanded through support from an NSF grant.