Newsletter #35     TIMMS, CCML and Didactique

After a hiatus that gives a whole new meaning to the word "asynchronous", here comes a newsletter. It being the first of the year, I need to start with an apology and an explanation. The former goes to people on the allmath list who are also on my newsletter address list--I think you will get two copies of this one. But only this one, I promise! The latter goes to the newcomers to allmath (and a welcome to you all!) This is part of a series of newsletters about goings on in and around the UW math department on and around issues of teaching and learning. Their timing is unpredictable (intervals so far have ranged from under four days to over four months) and their content likewise, but the general premise is that A) many interesting events do indeed occur on that front and B) many people are interested in said events but C) in a large department it is hard to find out about them. On the other hand, it is not the case that everybody is interested in them, so to avoid becoming departmental junk mail, I only send the first of the year to the allmath address. If you would like to receive the rest, hit the reply button (the reply-to- individual one!) and tell me and I will be happy to add you to the list. The previous 34, by the way, are on the Web at

Onward to news. The most obvious recent event was Thursday's Brown Bag on TIMSS (=Third International Math and Science Study.) Or rather on one small corner of one piece of TIMMS. The study included 41 countries, but focused most heavily on Japan, Gemany and the US, in which there was a heavy videotaping component. Educational researchers from several countries studied miles of tapes and volumes of transcripts and arrived at a number of conclusions, all of them subjects of lively discussion throughout the educational community. They also produced some videotapes for general viewing. These are not the ones they studied (strict anonymity was guaranteed to the teachers being studied) but rather tapes of volunteers, selected to match the generalizations the researchers were able to reach. On Thursday we watched two eighth grade geometry classes, the first in the US and the second in Japan (yes--there were subtitles!) The Japanese one was a blast--after a brief reminder of the content of the previous day's class on areas of triangles the teacher set up a quite challenging problem couched in terms of plots of land ("This one belongs to Eda. Eda, is it OK if we move the boundary over to here?") Students were given three minutes to work on their own, then another three with the option of discussing it. They then presented their solutions, and the teacher summed them up and pushed the challenge onward. The American class, on the other hand...well, what is there to say about a class whose total intellectual content was the definitions of complementary, supplementary and vertical angles? It was pretty depressing. So the first obvious question for discussion was "Is it really that bad?" For a start, certainly not always. One of the most shocked and appalled among us was the experienced seventh grade teacher here on sabbatical for a Masters degree. She works closely with the other math teachers in her building, and none of them would be caught dead teaching that lesson. And those of us throwing ourselves into the effort to bring about the kind of teaching whose current buzz word is Standards-based very much hope that it doesn't represent the future--it exemplifies quite neatly a fair number of the practices we are trying to change. The discussion, which profitted from a particularly nice blend of discussors from within the department and from other parts of campus, ranged through the issues of what needed changing, what could possibly cause it to change, what factors resist that change, and related topics. Oddly enough, we did not come up with a solution.

Ranging back further in time, we get to two issues from the summer, both of which will be appearing in much more detail attached to my home page, as soon as I revive the html and attachment skills which were so painstakingly taught me last spring. One is a report on the summer workshop of Creating a Community of Mathematics Learners (aka the NSF Project). We did a week on Probability, had a wonderful time and have, to our delight, been getting rave reviews from the participants.

The other requires a bit more explanation, but I'll go ahead with it, since the explanation also answers one of the FAQ's that keeps coming at me, to wit: "What is it that you do when you go tootling off to France in the summer?" The short answer is that I have been working with Didactique, which is a research program in mathematics education. In particular, ever since my sabbatical in 1991-92, I have been working with some others translating and editting some of the basic works of Guy Brousseau, who founded the field. Since hitherto essentially nothing has appeared in English, this filled a genuine hole, and was eagerly awaited by a bunch of people in math education with enough connections to know about Didactique, but not enough French to dig into it. The book was published last summer by Kluwer. After a mercifully brief didactical identity crisis, I progressed to working on another paper of Brousseau's on my favorite of his concepts, the didactical contract (the implicit contract between teacher and students which exists in some form in every classroom.) The article was well known, but had never been formally published and was a magnificent mixture of wonderful ideas and patches where the prose and/or the ideas became incomprehensible. Net result of two really exciting September weeks of working with Brousseau and his wife (a retired school teacher--really good at editting and nicely fierce about run-on sentences) was a pair of papers under joint authorship to be jointly published in English and French. The heart and soul are, of course, the original paper.

It is the current, roughly penultimate, English version of those which is now attached to my Homepage, under the title "The case of Gael".

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