Newsletter #46     The Freudenthal Institute

Theres nothing quite like setting out to look for a pot of gold and finding instead a gold mine. Its called the Freudenthal Institute. I went in wearing one hat and hoping for a few ideas, and wound up switching hats so often that I may never again be able to comb my hair, and with so many ideas that I very much doubt that I will ever get every one of them sorted out.

A little background is perhaps in order. The past couple of years have revived in me a long dormant love affair with the Netherlands and the Dutch people and language (by a process involving Hildegard von Bingen and the Camino de Santiago, but thats another story.) I therefore decided that my summer itinerary would include a stay with some Dutch friends. Then there floated into my mind the vague memory of an institute where a bunch of Dutch academics do Interesting Things with regard to K-12 education. Given my memory that the Dutch school system has a lot in common with ours, and my observation that their results on the TIMSS testing were quite stellar, I decided (with my CCML hat firmly in place) that I needed to explore a bit. Further floating memory came up with a Freudenthal/Wisconsin connection by way of the Math in Context curriculum to which we introduced our participants last year, so when Gail Burrill visited in the spring, I asked her advice. With her enthusiastic endorsement of the plan, not to mention her introductions to a couple of people at the institute, I decided to extend my visit (these are GOOD friends I was staying with!) and explore properly. Gail's introductions netted me an appointment on September 1, and my preparation for the appointment netted me a webpage ( which was my first inkling that things were going to be more exciting than I had thought.

My actual visit began with Martin van Reeuwijk (one of Gail's introducees) giving me a compact history of the institute. Thumbnail sketch: it began in the early 70's when Hans Freudenthal, a mathematician of considerable renown, became perturbed over the growing adoption of New Math ideas--not because he didn't approve of the mathematics involved, but because he felt it was elitist, and that school math should be Math for All, not just for potential mathematicians. He began experimenting with what he called Realistisch Wiskunde (Realistic Mathematics). Others joined him, with ideas about how to experiment, and how to design assessment, and the whole bundle of associated issues. It got so successful that people in other disciplines complained, causing a temporary reversal (educational politics seem to be a universal ailment), but is now extremely solidly established, and busy generating ideas for a downward extension of the changes in education which they have largely launched at the upper levels. They generate ideas and try them out, and the publishers of textbooks (there are four major publishers) pick up as many as they like, which seems to be a fair number. Meanwhile, in the late eighties, Tom Romberg, who was involved in the development of the NCTM Standards, looked around to find someone to help him demonstrate that this was not all just a pie-in-the-sky set of notions. Observing the Realistisch Wiskunde in action, he decided it was just what he needed. The result was that the Institute set up a sequence of lessons which were then taught by all of the teachers at a Madison high school in which (here we go!) Gail Burrill was a lead teacher. Connection established--the first of a number in the U.S., in fact.

Interesting, and just what I wanted to know--I picked up a batch of texts and modules and commentaries into which I plan to delve. But then things began expanding. First I mentioned my plans to spend the couple of weeks between then and my next visit to the Institute working with Guy Brousseau on the teaching and learning of Probability. Martin's ears pricked up, because in the Netherlands, as here, people are recognizing that Probability should be taught well down into the K-12 system, and discovering the hazards involved in the attempt. So I went off to Bordeaux armed with some of their Probability modules and a mandate to keep them posted on what develops from that. I also picked up a couple more references to pursue on my return and an invitation (on which I had to be reassured later) to use their photocopier as much as I liked.

That day came to a spectacular conclusion: Jan de Lange, director of the Institute and Gail's other introducee, whisked me off to the shore, where he and his wife (another Freudenthal Instituter) took me to dinner at a fantastic seaside restaurant and filled me in on more of the Institute activities past and present.

After my Bordeaux interlude, I returned to chase down a batch of references in the Nieuwe Wiskrant (the Institutes quarterly journal)--that's when the photocopier got some pretty heavy action. One that I looked up expecting it to be about probability turned out to be an interesting debate on certainty and uncertainty in mathematics, which brought out another hat. As English editor of Nicolas Balacheff's website on proof ( I am supposed to be on the lookout for pertinent material, and certainty and proof seem pretty closely related to me!

I also intentionally donned another hat and begged a further introduction from Martin, because I am about to teach a course on plane and spherical geometry, and one of the institute members (Jan van de Brink) has been specializing in the teaching of the latter. Net result was a couple of interesting conversations and a bunch of neat materials, some in English and some in Dutch, one of which I already translated because it is so obviously of interest to my upcoming class. I was also introduced to a prayer rug with operating instructions: a built-in compass and a booklet listing cities in (backward) alphabetical order with instructions on how to turn the rug to face Mecca. Jan and his colleagues chose Kibla (the direction of Mecca) as a subject for a series of lessons not just because it is a good application, but because so many students in Dutch schools are now Islamic, and they wanted to make a cultural reference point. (Islam, by the way, appears to work on a Mercator projection.)

Enough hats, yes? No! In the course of perusing the Nieuwe Wiskrant, I discovered that there is a thriving organization of Women in Mathematics. Actually, it has become Women in the Exact Sciences, but that will do. It was founded by a bunch of women who found themselves feeling uncomfortably isolated because all of the mathematicians around them were men, and feeling worried because so many girls were dropping out of mathematics or avoiding the more challenging tracks in mathematics, and thereby cutting themselves off from many professional opportunities--a remarkably familiar sounding batch of concerns. They have a web page (but be warned: it's just in Dutch!), some publications including a book, and even an office. Unfortunately, the office was closed, so I had to resort to introducing myself in writing, but I pulled that hat firmly down over my eyebrows and introduced myself as chairman of the education committee of the American Women of Mathematics, which ought to generate at least some interest and, with luck, a connection between the two organizations. At the very least it should generate enough information for my next column in the AWM newsletter, thereby putting me in the stunningly unfamiliar position of knowing a full issue in advance what I am going to write about!

Any doubts about my having struck gold?

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