I am responding to B. Becker, who said, on Fri. 7/7:
>It is instead the native >ability of the teacher to accomplish that intuitively knowable (but >impossible to replicate in the form of different new or old fangled >educational teaching methods) ability to TEACH his or her students. ... >So, I believe that no matter the educational method, the educational endeavor >fails unless you have both gifted teachers and youngsters raised and >acculturated in a society in such a way to be responsible enough to take the >gift their teachers have to offer.
As one engaged in the endeavor to help those who WILL BE TEACHERS in k-9 classrooms learn how to be effective teachers of mathematics, I cannot buy into this "native ability" and "gifted" stuff--I simply refuse to be so pessimistic and narrow.
If Becker's view were widely believed, would we let him be the evaluator of each prospective teacher's "native ability" according to his idea of what type of "gift" was prerequisite to success in the classroom? This is at complete variance with all the discussion about the fact that there are many ways to be a successful teacher (successful meaning that the teacher provides/supports an environment conducive to students learning and doing mathematics in a meaningful way).
My job is provide prospective teachers with experiences that will help them get moving along a path to finding ways to structure their work with their students so that meaningful mathematics learning will occur. I don't get to select the ones that I think are gifted and work only with them; I doubt that we'd pick the same ones as gifted even if we were allowed to do so. The likelihood that we would not agree on criteria underlies this discussion of appropriate teaching methods, yes?
I'll leave it for k-12 teachers to speak to the necessity and methods for helping learners who were not "raised and acculturated in a society in such a way to be responsible enough to take the gift their teachers have to offer." I see that "Katherine G. Harris" <email@example.com> has made an excellent start on that thread.
Marsha Landau firstname.lastname@example.org Associate Professor, Mathematics Education National-Louis University 2840 Sheridan Rd Evanston, IL 60201