Newsletter #17     John Conway

The newsdrought is over--largely broken by one John Conway. Just attending his Milliman lectures was already food for considerable pedagogic thought, given his stellar combination of flair and casual mastery of technique. Player L and Player R, however invisible, made a great contribution to Tuesday's development of a number system based on their choices in the games Conway supplied them with (fortunately we didn't have to figure out the rules for the one played with two boxes of chalk and an eraser.) Less obvious, but more continuous, was the contribution made by his ability to make the blackboard say what he wanted it to say (though his complaints when his row of circles didn't turn out quite identical in size were a little painful to one who is triumphant when her circles turn up as ellipses rather than polygons.)

There was more, though--an undiluted dose of Conway on teaching/learning, thanks to a Brown Bag. It was, like any Conway performance, a good show with a lot of interesting content. He talked mostly about a course he has done several times at Princeton entitled "Geometry and the Imagination." It leads the delightfully untrammeled existence of a course which is not a prerequisite for any other. Its instructors can therefore take a no-holds-barred approach to firing up the students' interest in, engagement with and ownership of geometry. It is (or at any rate was) team taught by three (3) professors who clearly, despite the odd squabble, had a marvelous time working together. In fact, that was one of Conway's key discoveries and messages: doing that course converted him to a complete addiction to co-teaching, preferably by sharing a course, but given the hit that that makes on a departmental budget, more probably pairing up with someone doing the same course at a nearby hour. Some of the profit comes from picking up each other's ideas, some from spotting things you don't agree with, and lots from generally batting things around.

As far as specific tactics go, some were highly geometry-specific (for the one involving Fred Holt's chin and an imaginary flashlight you hadda been there), but others apply more widely. In particular, the team was much concerned to get students really discussing things with each other. So they would get the students into groups of three or four, write several questions on the board and stroll out. After a few minutes one of them would stick his head in the room and if there wasn't enough noise he would "shout a bit" at them. After a quarter of an hour or so there would be plenty of noise, and the difficulty would be getting it to stop so that there could be a general class discussion. Conway's solution to this is to sneak into the room, then do a vigorous arm-waving leap several feet into the air, accompanied by an indescribable howling yelp. Definitely an attention-getter, but I was already deciding not to imitate that one before he mentioned having split his pants doing it!

The next element of that procedure is to get the students to be willing to go public with their conclusions or discussions. For that, he finds it very helpful to keep a supply of funny hats and put one on the head of one student per group. That student is then the designated reporter. His feeling is that students are far less shy talking about ideas they can attribute to someone else. The tactic is a close relative of Carl Swenson's use of a card deck ("this time the diamonds have to collect the worksheets and the hearts are the reporters...") but I would love to see the funny hats--especially as produced by Conway!

His final philosophical point, stemming directly from his feeling that his students had gained tremendous insight and confidence from thrashing out ideas before being handed too much information, was that he feels strongly that course design needs to include less "coverage" and more room for students' intellectual grappling-time. That's an idea that deserves some thought--but careful thought, clearly, because at its extreme lies an amorphous cloud of undirected tid-bits. A non-supportable extreme position, but no more so than the reading-out- loud-from-a-yellowed-set-of-notes position that lies at the opposite extreme. Somewhere between lie one or more happy mediums. (media?)

And on top of all that, he left us with some really applied information: how to look at a pair of bicycle tracks and tell which was made by the front tire and which direction the bicycle was going. You don't get that out of your average Brown Bag!

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