Newsletter #34     Sundry Local Events

It's been an action-packed week and a half. There's no hope of doing it justice, but the odds will diminish yet further if I wait, so here goes.

First event was a Brown Bag featuring Neal and Ann Koblitz, newly returned from a trip to South Africa. They spent the majority of their time at the University of Western Cape, where Jan Persens (our all-too- brief guest in February) did a phenomenal job of connecting them up with people. Ann gave a couple of seminars in the history department, Neal worked with a bunch of math faculty, and together they went to four different middle schools that Jan lined up for them and did a Koblitz Special. This consists of a session from an hour and a half to two hours long in which they do mathematical activities ranging from number theory to graph theory to geometry. Net outcome is a lively experience giving the kids a broader and deeper idea of what mathematics can be and the Koblitzes an ever-broadening international perspective on the similarities and differences of kids around the world. Also, I should think, an international fan club that I can't imagine many mathematicians rivaling!

In the midst of this they also managed a side trip to Malawi, with one more middle school Koblitz Special there. On the whole, I think it served to increase their enthusiasm for Capetown, though class attention spans on a television-free island seemed to be good, and the general respect for teachers ran pleasantly high.

I think their highest kudos were for the students at the University of Western Cape. The university is not having an easy time of it--it is now officially integrated, but was formerly a "colored" institution (translation: for non-whites whose home language was English or Afrikaans) and no one has waved a magic wand to equalize opportunities. But the spirit and level of seriousness are impressive. The students, for instance, packed Ann's seminars, having clearly all done the preparatory reading, and then asked quite thoughtful questions. Gratifying, that!

Onward through the week and we get to another packed seminar, or rather colloquium. On Tuesday, Paul Zorn spoke to us of calculus at St. Olaf. He started off with a remark that has completely tied my tougue since, because it was so clearly correct: "I don't like to talk about calculus reform", said he, "because the calculus in question hasn't changed at all. What we are trying to do is teach it in a way that brings back some of the life that has been progressively squeezed out of it" (last bit paraphrased!) He traced the origin of his views to his graduate days here at UW, when he fell under the influence of the Curjel/Monk/ R.Warfield Business Calculus course. They did wonderful things with graphical reasoning (I can testify that they gave a whole new meaning to those little clear plastic rulers!) and he began his journey into the exploration of how much more there is to do than crank out an answer to a strait-jacketed series of canonical questions. So, for instance, he gets students playing around with the graph over the interval from -2pi to 2pi of y = x + a sin x for values of a getting larger and larger. Or y = x^2 + a sin x--same deal. By the same token, when it comes to convergence of series, he gets them grubbing around with numerical computations to see just how messing around with the terms of a series whose limit is known affects that limit. In general, what he does is take a no-holds-barred approach to getting students to engage with the mathematics itself instead of regarding the book and the class as a source of devices for the mechanical production of right answers.

Thursday we continued the calculus theme with a Brown Bag with Bill McCallum from the University of Arizona. UA has been part of the Harvard Calculus Consortium from the ground up, which gave us a slightly different perspective. This is a group which formed shortly after the clarion call of "Do Something!" rang through the mathematical community. It includes several universities, a couple of liberal arts colleges, at least one community college and one high school. Together they have generated, field-tested, revised and re-field-tested materials, culminating in the publication of a widely used calculus textbook. Someone asked Bill if technology played an essential role in all this, and his reply was that it is generally used, but not fundamental. The place where it played a fundamental role was in the launching of the whole process. It was when people realized that the standard calculus exam could be answered just as well by a computer as by a student that the dire need for change became clear. Again the heaviest emphasis is on getting the students to engage with the mathematics, though if his choice of examples is a correct indicator, the mechanism for encouraging this engagement is more the choice and use of context. One example which pointed up neatly a distinction he was making had to do with the length of days in Madrid. Once past the furor resulting from making the students find out for themselves whether Madrid is in the northern or southern hemisphere he asks a number of pertinant questions. And the student who has really Got It is the one who, in response to the question "So what does all that tell you about what's going on on April 13" replies not "the rate of change of the length of the day is 3.5 minutes per day" but "There are 3 and a half more minutes of sunlight than there were the day before!"

I'd buy that analysis of having Gotten It any day!