When one holds a set of beliefs sufficiently firmly to begin to risk the doctrinaire, it can be extremely salutary, if a tad uncomfortable, to be confronted with a person whom one cannot refrain from admiring, but whose beliefs include a number which are diametrically opposed to one's own. Thursday's Brown Bag provided that experience for me, and I think for a number of others present. By way of a videotape put out in 1966 by the MAA, we were all introduced to a gentleman about whom many of us had heard for a long time, to wit, R.L. Moore. Throughout the century (or thereabouts) that he was on the faculty at the University of Texas his style and methods were such that the absolutely standard phrase to be heard was not "I took topology from R.L. Moore", but "I took an R.L. Moore course." He launched the careers of an incredible number of very strong mathematicians, and many of them, and their students and their students' students, have gone on to teach "R.L. Moore courses", though I suspect generally at least somewhat modified ones.
So how did an R.L. Moore course work? Well, for a start, with no one but students at the board. Moore would give out problems with the understanding that students would neither look in a book nor confer with anyone, including each other. Students would then come to class and volunteer to put solutions on the board for the rest of the class to observe and criticize. To observe, that is, if they had a solution themselves. A student who was still working on a problem was encouraged to get up and leave the room so as not to lose the opportunity to think it through for himself. Moore was clear and explicit about the fact that one ought to be unhappy at seeing someone else's solution to a problem rather than coming up with one's own, although (and this I would love to have seen pursued a little further on the film) he also said that it was not invariably the case that getting up and leaving was the right thing to do.
So where does this run afoul of my firmly held notions? Certainly not over having students at the board -- students' intellectual autonomy is one of my dearest goals. Certainly not over having a course structured around problems -- I don't think it can be done that extremely in most subjects, but it's an enviable possibility. But forbidding students to work together, now there I have trouble. And having class be explicitly a competition to be the firstest with the mostest -- at that I balk, and will continue to do so.
We watched the whole film, which ate up all the official discussion time. A few of us sat around for a bit, though, talking it over. I mentioned my concern for the weaker students and expressed a conviction that Moore didn't mind acting as a filter to screen out some students. The conviction later began to fade as I thought about the delightful and delighted expression on Moore's face when the camera caught him chatting with random groups of students, clearly not just a chosen few. And it wound up completely squashed by a spontaneous note from a friend to whom I had mentioned the Brown Bag. She studied with Moore, and like every one of the many students of his that I have met over the years, speaks of him with a concentrated blend of awe and affection. She wrote, "I am puzzled by the misunderstanding of those who think he was an elitist or a man hostile to the less bright student, since I have never, before or since, encountered another person so totally engrossed the welfare of the students, all of them, from the best to the worst."
I'm hanging onto my convictions about how I will teach. But if I seem to be in danger of believing that it is the only way to teach, please, somebody sit me down in front of the R.L. Moore movie again! --