Newsletter #39     Calculus and Clinic

Rapid typing time--I'm two Brown Bags in arrears! I'll be a little sketchy on both.

Actually, I think the first of them is inherently sketchy. That was the Brown Bag at which we tackled the issue of calculus yet again. We did so in the hope of being of some use to the department's ad hoc committee to review first year calculus, which kindly supplied us with a set of questions. In the end, I'm not sure if we made progress toward an answer to any of them, and I know for sure we handed the committee at least twice as many questions as they handed us, so I'm not so sure it was a winning proposition for them. But our intentions were honorable.

I think I need to enter a caveat. In my efforts to write up this Brown Bag my attempt to maintain editorial impartiality, or at least fairness, completely blew a gasket. The only way I could get the writing back on the rails was to abandon the attempt altogether. So the prose is loaded and I may well slip in a few things that I wish I had said but didn't. Fair warning!

The first portion of the conversation centered around the issue of reducing class sizes. At least one among us is firmly convinced that such a reduction is non-beneficial, on the basis that students will expect mollycoddling from anyone they can see without binoculars. Standards should be maintained by giving a pretty tough test before the drop date and telling anyone whose score is below a certain point that they should get out while the getting is good. This would obviously clear out some deadwood, but bonfires aren't allowed on campus. Presumably the ones dropping out of 126 could find spots vacated by the ones dropping out of 125, who in turn...but there is an obvious problem ultimately. Though on the other hand it certainly is true that someone who categorically and unambiguously does not belong in a course does not benefit one whit from a "There, there, dear, it will all be all right." As I said, we produced more questions than we answered.

David Prince brought up a metaphor for the math department's role in life which provides a nice clear image, though not a comforting one: the departments of natural sciences and engineering can be regarded as a sort of intake pipe, and the high schools can be regarded as an output pipe, and we function as the connecting pipe. The location of the intake pipe hasn't moved. On the other hand, the widely held perception is that the output pipe is coming in steadily lower (a sentiment whose parallel I regularly hear from our middle school teachers in CCML, I might add.) This means that we as the intermediate pipe keep having to get both longer and steeper--not a pleasant state of affairs.

And here I will throw in a thought which is neither original nor something I managed to bring up in the Brown Bag, but it is distinctly relevant. High schools all around the state are trying very hard to produce what we want by way of students. They have lots of problems, some equivalent to ours, some not. But one of their problems, it seems to me, is that we have not done a good job of telling them what it is we do want. Doing so is an enormous job, and you don't catch me leaping up and saying "Let me! Let me!!", but what you do catch me doing fairly frequently is wincing when conversing with high school teachers. There are some distinct smudges on my conscience.

Back to the Brown Bag: David Prince made another highly pertinant contribution, this one along the lines of what one needs to do about the students who are floundering in our courses. In his own section he decided to run some problem workshops which were optional for his students. An impressive number of students from the middle third of his class became regular attenders of the sessions, and he felt that their problem-solving skills really benefitted. Only snag was that the sessions wound up taking two or three hours a day, five days a week, and even the indefatigable Dave had to admit that this is not something he could make a regular habit of.

I haven't done the discussion justice. I've only put down a few bits and pieces, and we had a full hour of thoughtful comments from a lot of interested people. It just doesn't seem to encapsulate.

Loyce Adams' Brown Bag two weeks later, on the other hand, encapsulates beautifully. She was talking about Clinic, which is a regular but splendidly varied seminar in Applied Math. Every doctoral student must take it at least twice. The faculty keep their ears to the ground for interesting problems that turn up from industry or from other departments on campus (well, maybe it's ears to the telephone) and then turn the students loose on them. For instance, a crystalographer became perturbed over the unpredictability of whether one particular crystal would grow into "this kind of shape" or "that kind of shape" (you hadda been there). The situation turned out to be completely amenable to modelling, and even generalizable--producing both a batch more crystals and a joint paper with one of the graduate students. Another project required much swearing to secrecy because it involved a device whose inventor wanted to patent and sell it. The students carried out the computations desired, and then pointed out a radically simpler method for producing the device.

This quarter was to have been Clinicless, but things took an unexpected bounce over Christmas break, and Loyce is up to her eyeballs once again. This time it is of a quite different format: Loyce got a call from Aaron Feik, North Shore's District Mathematics Specialist, whom she had met at an early CCML event. It seems that North Shore is in the throes of a choice between two rather different elementary school curricula. Ultimately the choice is in the hands of the teachers, but Feik was interested in having the curricula looked at from the point of view of someone who doesn't simply produce mathematics, but actually uses it, so as to provide the teachers with one useful chunk of information. Loyce, feeling highly uncertain what the response might be, put the option out for graduate students to sign up for Clinic in the form of observation and analysis of the curricula--and twelve students immediately signed on. A great bunch, and by the time she spoke to us they had already done a huge amount of preparation. The major worry point at the time of the Brown Bag was whether teachers would be willing to invite them into their classrooms. I can now report (there are some virtues to being dilatory) that after Loyce went with a batch of them to an after school meeting at which teachers were comparing notes on their experiences the students wound up with essentially unanimous invitations. A large, and earned, accolade. I have the privilege of accompanying them for some of the observations, so I should produce a follow-up report...sometime.

I shall finish on a high, keen note with a quotation I just picked up at our current series of CCML workshops on Communicating with Parents and the Rest of the World Outside of School (not the official title!) It was produced for the K-12 context but seems to me applicable in a phenomenal range of contexts:

"I'm not worried. It's not my problem--the hole's in your end of the boat."

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