<< 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.>>
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******************** On the contrary, trans-national comparisons can be educational.
For example - in Japan, burakumin (a caste-like group, so designated historically apparently because they did "dirty" jobs like butcher animals) are a "discriminated minority." They look Japanese, they speak Japanese, but, on average, they do worse in school, on IQ tests, are more likely to be delinquent, etc. The same kind of gaps that we are always wringing our hands about in the U.S. - and they do a bit of hand-wringing in Japan, as well. Educational to hear people do that, over a "difference" that you, yourself, can't perceive, and which, when explained to you, seems nonsensical (unlike the entirely natural and rational distinctions made in the US...).
If this "achievement gap" exists in other places and times, in somewhat different forms, but always involved in an opposition like inferior/superior, civilized/primitive, clean/unclean (whether the basis for distinction is color, or language, or religion, or whatever) - then explanations like bad genes, bad teachers, bad home life, linguistic peculiarities - don't wash. The only constant is the opposition itself, not the genes, teachers, languages and home lives, which vary from place to place.
In the US, the public conversation focuses mainly on the difference between - "Them", the supposedly unusual case - and everybody else. But actually, it's not the case that the poor&black have these low scores, and everybody else's scores are randomly distributed. There tends to be a gradient. Average SAT scores here in the Washington mill town where I live are likely to be lower than in Medina (a rich neighborhood in Bellevue, "funky cold Medina"). Whatever explanations you construct to explain the difference between the poor&black and everybody else presumably have to be extended to explain the entire gradient of differences.
Are SAT scores here worse than in Medina but better than in Seattle's White Center district (i.e. ghetto) because our teachers are "woefully ignorant" in comparison with Medina's, but somewhat less "ignorant" than those who work in White Center? If so, how come the quality of teaching seems to follow class, race, and power gradients? Why do you think that might be and how would you propose to change it?
And do you think that if, miraculously, all the teachers from Medina transfered here, and all the teachers here were bused to Medina, that our SAT scores would also exchange places? (And did YOU go to a school where the majority of the teachers were inspiring? Hey, where was that?)
Les