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.
Andre TOOM wrote: > > I absolutely agree. This is what I am trying to bring home all the time: > teenagers are normally interested in abstractions and can master them. > I quoted Vygotsky because I know his writings better, but I am sure > that Piaget had essentially the same opinion on this. Regretfully, > some teachers of mathematics don't know enough mathematics to offer > their students interesting problems. The students are frustrated and > educators misinterpret this frustration as lack of interest in > abstractions. Then these educators insist on using cumbersome and > fat-fetched `real-world' problems, the students are bored still more, > and all the situation gets into a vicious circle. > snip (quote from Powell's original message)
> Seimour Papers used such activities in his classes of Logo. > But his students were of elementary school age and I think > that this is important. For high school students this a ridiculous > infantilism. High school age is time for a powerful development > of abstract thinking and mastery of formalisms. > (This does not exclude athletics, games, picnics etc.) >