It seems to me a huge mistake to suppose by explaining national differences in math achievements we will understand any better variation in math scores by class or so called race within the US.
Does anyone know anything about the mathematical preparedness of, say, elementary school teachers in impoverished areas? It could be that they are themselves so woefully ignorant and hateful of math that they do nothing more than implicitly demonstrate a single algorithm (say partial sum multiplication instead of lattice multiplication) in a few examples and then give countless like problems to their students as busy work. Students gain no conceptual understanding of what it is they are doing or why they are doing it one way rather than another (in fact they may never be taught that there is no one best way). Learning by rote may fail to inspire. Teachers are only interested in state test scores, so they may just pile up practice problems before exams while students are left with no interest and no understanding the day after the examination.
And there may be no one at home to pick up the slack of the unprepared school teachers.
Perhaps Mr. Casey will inform me that part of the problem is not the teachers.
Warm regards, Jan
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