At 16:42 -0400 7/23/97, David L. Hanson wrote: > ... The idea that the extremely math capable >student needs to learn something about math from the least math >capable student is pure utopian poppycock.
Your response (apparently in response to a post I made) brings to mind the old adage, "Don't confuse me with the facts; my mind is made up." I was not quoting theory, but relaying things I have experienced. This most assuredly is not "utopian" or "poppycock". Perhaps if you had any real rejoinder to my statement, you could have saved us the embarassment of your name-calling non-argument.
Further, you are apparently misrepresenting my statement, which follows: "I have seen many cases where that proverbial 150-IQ student gains important insights from supposedly less able students." (a) Note that I did not say "needs to"; I do not claim to know all truth. However, I have seen the power of different kinds of learners interacting. The common misconception I was attempting to address is that the "able" students don't get anything from this exchange. They very often do. (b) Note the key word *supposedly* in "supposedly less able". The usual meaning of "able" or "capable" usually is "does well at tests of mathematics" which is quite circular. The important question is whether the tests measure anything important. I have seen many students with low test scores who had significant insights about mathematics. I have seen students with high test scores who seemed to primarily excel at applying formulas and had little real mathematical ability. (Please note that I am emphatically *not* asserting that all students who score high on standardized math tests are not "able".)
In any case, the important question seems to be how we can help all students reach their potential, and I question how labels of this kind ("able", "capable" etc.) further our goal.