Newsletter #96     2nd International Congress on the Teaching of Mathematics (at the undergraduate level.) [AWM]

This one comes in two pieces, proportioned like a horse and rabbit stew (one horse, one rabbit.) The major part is an AWM Newsletter column describing a conference which, thanks to departmental support, I was able to attend in early July. What follows it is the result of coming back inspired by the congress and plunging straight into a Medieval Music workshop. Part of the homework was to write a poem. In fact, we then had to set them to music, but if you're very nice I promise not to sing it to you.

One of the accomplishments of which I am most proud is the creation of a regularly meeting quasi-organization entitled WaToToM. It enables Washington's Teachers of Teachers of Mathematics to converse, collaborate and occasionally even conspire, with considerable pleasure and profit.

Apply to that a scaling factor of ten to some non-trivial power and you will arrive at a recent accomplishment of Deborah Hughes-Hallett and some colleagues in which I had the great good fortune to participate. This was the 2nd International Congress on the Teaching of Mathematics (at the undergraduate level.) It took place from July 1 to 6 on the island of Crete, with English as the official language. Like its 1998 predecessor on the island of Samos, it was a smashing success -- so much so, in fact, that an attempt to describe it in a few paragraphs is a clear demonstration of classical hubris. I'll do it anyway, of course, but do bear in mind that this is the perspective of one of several hundred participants, coming from one of over fifty countries. The backbone of the program was the series of ten invited lectures, one to three of which began each day. They make a good, representative point at which to begin my description, not only because the speakers came from eight different countries but because they covered a large number of issues and enriched all discussions by providing a wide spread of points of view. The opening lecture focused on the beauty and grandeur of mathematics. Professor Terzioglu, of Sabanca University in Istanbul, Turkey, pointed out that although we live always in a world of changing views and opinion tug-of-wars, "yet below this surface is another world, the world of the infinite, where progress is always in a steady forward direction. In this world there can be no notion of "the shortness of the human life span" or even "time"; definitely no notion of material gains, for each idea is a drop that will expand within the never-ending flow that endures beyond centuries and millenniums. This may be why we mathematicians are perhaps among those people who can sense the true meaning of the word "infinite" in the most acute way.

Mathematics is a precious human achievement. It transcends boundaries of all kinds -geographical, historical, national, philosophical or linguistic. Mathematics is accumulative and ageless.... The proof attributed to Euclides is still valid today." [All the quotations are from the CD-ROM of the Proceedings of the Congress]

Later on, Professor Bourguignon, research director of the CNRS in France, elaborated on the nature of mathematics: "one of key features to hope and generate a different attitude towards Mathematics among new generations of students, is to make it perceptible to them that there are questions which presently do not have answers. Progress on them can be of different types: either they can be considered as non interesting (a highly subjective judgment of course), and as such not worthy of further investigation, or impossible to answer (realizing that some important statements in Mathematics can be proved to be non provable was one of the major achievements in XXth century Mathematics due to Kurt Gdel), or just beyond reach of present methods and concepts.

Giving some idea that there are challenges around us, and making them perceptible, and at the same time meaningful, is a challenge in itself. Today, to my knowledge, not much thought has been put towards this goal, and this lack of investment becomes a handicap in our societies where the relation of students to schools has changed a lot because of the huge amount of information on a variety of subjects they have access to outside the school system. If we are to have a chance of convincing a large portion of the school population that Mathematics is a living science, the minimum we must achieve is to prove it has a future. We cannot take this for granted, and we have to design tools to do that." After a series of extremely cogent remarks (intended as seeds for debate) on the state of the teaching of mathematics, Bourguignon concluded with a challenge: "A political figure of the first half of last century in France, Edouard HERRIOT, is remembered for having said "La culture, c'est ce qui reste quand on a tout oubli" [Culture is what is left when everything has been forgotten]. I have the feeling that mathematicians have too often forgotten that building a mathematical culture is a responsibility that has been entrusted with them. It is indeed much broader than just training the new generation of people who are going to replace us as specialists. I am afraid that, at this moment, we, as a community, have not put enough thinking to our broad responsibilities." Other speakers chose to address more specific aspects of mathematics education, from the importance and value of visualization to the application of the Dutch Realistic Mathematics Education in a differential equations course in Korea. The last speaker was Alan Schoenfield who, true to form, sent us all out charged up. This he did by starting with a thumbnail sketch of the contents of his paper on Making Mathematics Work for all Children: Issues of Standards, Testing and Equity (summarized in this column in the Jan/Feb 2002 issue) and tying it in with various of the week's previous talks to show how universally and internationally mathematics is key to issues of social equity. He then described a new project with which he is involved. If all goes well, the project will provide a bunch of potentially marginalized middle school kids with a major mathematical boost, provide their teachers with a useful learning experience, provide the teaching community at large with a valuable model, and provide researchers with significant information. If all goes well, he said -- and what does that mean? What does it entail? How do you arrange it? How do you even recognize it for sure? "Tune in again in another four years," he said, "and I might be able to tell you something!"

The talks, as I said, were the backbone of the Congress. At the first supporting level were three panel discussions. Since these tended to occur right after a rather heavy lunch, I can't give you many details, but the topics were indeed interesting: "On the Role of the History of Mathematics in Mathematics Education," "Mathematics is for All," and "Teaching undergraduate mathematics, based on the corresponding ICMI study."

The next level of support occurred on the lower level of the conference center, where the rooms had titles like Athena, Artemis and Minos, rather than the upper level with the powerhouses: Zeus and Secretariat. These were the Parallel Sessions, two sets of twenty-minute sessions per day, eleven at a time. They spanned the width of the conference themes: Educational Research, Technology, Innovative Teaching Methods, Curricular Innovations, Preparation of Teachers, Mathematics and Other Disciplines, and Distance Learning. Predictably enough, some provoked a "Wow!" and some an "Eh???" Even the latter often spurred interesting conversations, though, as did the poster sessions (especially, for me, some nifty Australian mathematical fiber art.) And with those interesting conversations we get to the heart of the whole experience - and here is one spot where I know my perspective is a shared one. There is nothing equivalent to spending a week with a collection of people who have come from all over the world because of a shared interest in the issues about which one feels most passionately. Nothing stirs up ideas as much as bouncing them around with folks who are coming at them from such a variety of angles. Nothing solidifies convictions like finding them shared.

Beyond that is something I treasure so much that I shall risk banality by trying to express it: the sense of being part of a huge, global community. I made some new acquaintances and friendships and deepened some old friendships, with people from Israel and Italy and South Africa and France and the United States. To some of them I have, I hope, something to offer, and from all of them I have a lot to learn. And more to the point, any of us knows that if some need comes up, any of the rest of us stands ready to try to meet it. What more can a Congress create?


"Just give me words to deal with and I'm fine

And take away those square roots, y's and 4's.

I love to read and write, but I decline

To change my views: math'matics is for bores."

Minds from ages past, and now, and yet to come combine

The infinite was Euclid's, and was Fermat's, and is mine.

"Pourquoi les maths?" the French schoolchildren whine,

"Wiskunde? N!", the young Dutch scholar roars,

"No math for us", deaf students shout in sign,

And close their minds to beauty as it soars.

Minds from ages past, and now, and yet to come combine

The infinite was Euclid's, and was Fermat's, and is mine.

To love and teach math'matics is to pine

To lift those eyes (and spirits) from the floors,

To shape those hearts and minds so they incline

To hear and take in through their very pores:

Math'matics is no mystery, produced behind closed doors,

The infinite was Euclid's, and was Fermat's, and is yours.

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