Newsletter #80     Polya, Colin Adams et al

I am once again up against the choice between doing a set of spiffy events the injustice of describing them all very swiftly and doing them the still greater injustice of leaving them entirely unmentioned. Frustrating, but given that I leave in nine hours for Bordeaux to immerse myself in Didactique for a bit, the handwriting is firmly on the wall -- in French, yet even! So here goes.

I shall begin, slightly arbitrarily, with the April 5 Brown Bag. That was the one at which a bunch of us watched a videotape of George Polya enticing a charmingly 1960's style class into creatively guessing their way through a problem chosen for the occasion (i.e., not part of the curriculum of a course) and then creatively reasoning about their guesses. He asked them "If you divide space up with five planes, how many pieces will space be divided into?" -- leaving it to them to discover the need to require general position, which they did. Not having bumped into that particular problem, I watched with a refreshingly open mind, but now I would like to look at the tape again and watch his choices of responses to students and the timing of his questions and when he was leading and when he really was letting them loose. How did he take a completely unfamiliar bunch of students and induce them to work their way up to the point where a young lady on the back row successfully spotted a pretty sophisticated pattern in a table of values and predicted the correct result? The one choice that needed no prior knowledge to spot was his response to her prediction. He made positive noises (as he had on a number of occasions) and had her explain her reasoning, but he neither gave an absolute validation nor offered a sketch of a proof. Instead he left it open, with the class sufficiently engaged so that it's hard to imagine that groups of them didn't charge out and pile into completing the problem on their own. Impressive!

Next up the pike was the Pacific Northwest MAA meeting at Seattle Pacific University on Saturday the 7th. Lead-off speaker for that was Colin Adams of Williams College, speaking in the guise of Mel Slugbate, of Slugbate and Mossbutter Real Estate Brokers ["Need to escape from the humdrum everyday boredom of Euclidean geometry? Time for a vacation from the same old straight lines, that tiresome parallel postulate and the usual formulas for area and perimeter of a circle? Then you are ready for Hyperbolic Condos, situated in lovely hyperbolic space. It's not just one of the most beautiful spots one can conjure up, it's an investment of Gaussian proportions."] For combination of solid content and inspired hamming he has no equal!

Later in the day's program came a panel of graduate students, including our own Dan Fox, giving information and comfort to a large and very interested collection of undergraduates from all over the area. There were other good things, too, but I missed them.

Monday we cashed in on Colin Adams' presence in the area to have two PFF events. The first was a lunchtime gathering of a bunch of graduate students, at which Colin spoke and answered questions about life as a faculty member at a liberal arts college. And very nicely he did it, too. It's always pleasant to listen to someone who is completely sure that he is exactly where he wants to be, doing exactly what he wants to do! In the evening we had a bigger shebang, centered around yet another talk by Colin ("Why Knot?" -- he's a knot theorist!) and a bang-up Faculty Club buffet dinner. The underlying objective was community expansion and building, which made it very pleasing that we were able to entice in faculty members from Seattle U., Central Seattle Community College, Shoreline Community College and Seattle Pacific University. A good and lively time was had by all.

As Colin whooshed out of town, in whooshed the AERA (American Education Research Association.) Hundreds of talks and sessions and thousands of people. I only got to a couple of sessions (one that was worth it for the title alone: "How we know what we know about how we know what we know" -- on brain neurology!), but it did afford me the opportunity to hang out with several of my favorite people, including not one, not two, but three former PFF speakers. One was Gail Burrill, whose visit in May of '98 produced not only several talks but some good connections around the Seattle educational community (see Another was David Clarke, who visited a couple of times and gave talks that left everyone clamoring for more (see,, and And yet another was Susan Pirie (, who introduced us to a theory of learning that still regularly crops up in conversations. In fact, for a cool conclusion, one of her students produced a talk and paper comparing and contrasting analysis of a particular student's work using Susan's theory and that of Alan Schoenfeld, who will be our next PFF speaker (May 17 and 18 -- not to be missed!) Talk about connections!

I had better hold it at that. Any one of the above paragraphs could be expanded by a factor of at least three, but pausing to do so might be a tad unwise. I have it on good authority that suitcases for a two week trip are supposed to contain something more than books, notes and a laptop computer! --

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