I love it when different portions of my life gently collide. This morning I read an article on professional development for elementary school teachers, in preparation for an ECML meeting tomorrow. I finished it in some haste to get to a Brown Bag, working madly on shifting gears en route--and I needn't have shifted at all. Both were about using case studies to help people develop the art of teaching, and the similarities far outweighed the differences. The article dealt with the case studies presented in the Developing Mathematical Ideas seminars which are the backbone of our elementary teacher NSF project (that's the ECML). The central observation was that case studies provide excellent fodder for discussion, but if the conversation is genuine and open, then the leader must constantly make decisions about the extent to which to lead--not to mention how to do so. Too much leading is akin to a sit-down-and-shut-up lecture on how to do inquiry style teaching, but too little can produce, or at least permit, total chaos. I was still digesting the analysis of this balance when Bill McCallum, having shown us a delightful set of case studies that his FIPSE-funded project is producing to help teach new TA's how to teach, began describing the down side of using them. "I thought the case study was about one thing", he said, "but the class all thought it was about something quite else." Yes, indeed, we are talking about the same world!
His calculus education lecture furthered that connectedness, though not so specifically to one of our projects. It was about teaching calculus to students who have the latest in calculators--the jobbies that can do derivatives and integrals and all sort of other stuff. But Bill was carefully and firmly NOT addressing the issue of whether these calculators are a Good Thing or a Bad Thing. His contention is that the calculators are here to stay, and our job is to find ways in which we can make good use of them. In particular, he suggests that they can be used to give us a window on how students are thinking (windows of that nature are a major item on the search list in the current K-12 education thrust.) He had a number of examples, but the ones that stuck in my mind were a set where students had used their calculators to graph a function. One of the graphs was easily recognizable as an order-of-operation glitch, but the other, with a little probing, showed that the student had superimposed some quite correct thinking on the calculator mush he had produced, and a lot could be sorted out by that.
The other type of use that Bill suggested was exemplified by a worksheet on which were a bunch of functions rigged so that blind button punching (which, as Bill points out, is not an invention of the calculator generation, but merely an updated version of blind pencil-pushing) would yield a derivative of 1 or 0. The question for the student to answer became "How could you have predicted that?"
Last week's Calculus Education speaker and Brown Bag guest, Michael Freeman from the University of Kentucky, sounded another of my favorite themes. He was describing what sounds like a really nice version of a Treisman-type program they have had going on there for a number of years. He chortled gleefully over the fact that a uniform recruiting message indicating an opportunity to learn a lot by working very hard regularly produces classes heavily dominated by women, members of minorities and rural students, with the result that those are the students whose course averages, determined by uniform examinations, top all the lists. Clearly the materials used in the workshops are important, as is the training received by the two or three graduate students a year who travel to the center Treisman operates in Texas. But the message Mike gave repeatedly, in varying contexts and wordings, was that from what he could see, the one totally indispensable item in the whole system is the sense of community the students develop, and the strength of the bond and support that that gives.
I like that message.