> Whenever I think I understand Toom, like a chameleon he changes. > Suddenly he is quoting Vygotsky, Piaget, and (I believe he meant) > Seymour Papert. I wonder what they would think of the tone and content > of "Mathematically Correct" which Andre so ardently endorses? If I were > you, Professor Toom I wouldn't let those at "Mathematically Correct" > know that you espouse such radically constructivist ideas--The ideas of > the three people you have mentioned would certainly be anathema to those > who want to discredit, debunk, and stop the reforms embodied in the > Standards.
Howard is desperately trying to define my position in terms of present-day politics. However, I use more important reference-points. I am not on the side of `Mathematically Correct' or `radical constructivism'. I am on the side of Euclid. My position happens to have much in common with members of the `Mathematically Correct' just because all of us care about mathematics, not because of some conspiracy between us. I don't understand what does Howard mean by `radically constructivist ideas' and why does he mention them in this context.
Some member of this list claimed that I fight the battle between Russian and Americans. Wrong. I fight the battle between enlightenment and obscurantism. Last year I taught a course of History of Mathematics. We studied Euclid's Elements and I used this pretext to teach my students some beautiful classical geometry about which they had no idea. The students were delighted and one asked: is there a book where all these wonderful theorems are collected? I answered: yes, it was published more than 2000 years ago. I was proud as if it were me who wrote Elements. I remember that Eratosthenes was nicknamed `Beta'. Who was Alpha? Perhaps, Euclid? Besides them I am only a small Epsilon, but I am greater than zero and proud of it!
Now about NCTM "standards". From time to time another mistake is found. The last time it was Jack Roach who found a mistake in the `ice-cream' problem. But what is most important for me is not just presence of these mistakes, it is rather absence in the "standards" of almost everything that makes me proud that I am a mathematician. Look through chapters `Mathematics as reasoning' - you will find NOT ONE classical example. Can you imagine a History of Art which ignores Parthenon and starts straight from Andy Warhol's Campbell Soup? Or World History which starts from last year's yard sale? The NCTM "standards" are of this kind. They are barbarous, provincial and anti-cultural. They ignore world civilization.
Andre Toom Department of Mathematics email@example.com University of the Incarnate Word Tel. 210-646-0500 (h) 4301 Broadway 210-829-3170 (o) San Antonio, Texas 78209-6318 Fax 210-829-3153