I have no idea if its cultural or genetic, but the difference is there in the classroom. Its pretty clear that various programs run by the state aren't making much of a difference. If you need to change the culture of kids to make them better at math, then we should do that. Although I have no idea how to quantify what that culture is and how to apply that change across a school.
edit: also, note, you've said a lot of stuff about categories. But categories can blend into each other and cause ambiguity at the margins. But that doesn't remove the validity of there being categories. When I look at the kids who come in to competitive math programs, and these are kids who are more than a standard deviations above the mean in performance, I see a lot of uniformity. One can try to construct various explanations for this, but you can't tell me that there were NO kids from underrepresented ethnicities that had two professional parents and good exposure to mathematics early. We have plenty of racial diversity in the early math programs. And in the Bay Area there are plenty of professionals sending their kids to these programs from all ethnicities. And still, ten years later its the Chinese and Taiwanese American kids that are in the Olympiad team. And even at a lower level, say SAT math, we see the performance skewed by race in the same way. I am ethnically Indian. And Indians are as interested in math as Chinese. We all send our kids to math tutoring. We are mostly engineers in the Bay Area. And even so, at the very top of the distribution, there are some Indian kids ... but far more Chinese American and Taiwanese kids. These are just facts. I don't take it as a slam against my ethnicity that we don't do as well in math as the Chinese. There's more to life than math after all.
edit: also, note, you've said a lot of stuff about categories. But categories can blend into each other and cause ambiguity at the margins. But that doesn't remove the validity of there being categories. When I look at the kids who come in to competitive math programs, and these are kids who are more than a standard deviations above the mean in performance, I see a lot of uniformity. One can try to construct various explanations for this, but you can't tell me that there were NO kids from underrepresented ethnicities that had two professional parents and good exposure to mathematics early. We have plenty of racial diversity in the early math programs. And in the Bay Area there are plenty of professionals sending their kids to these programs from all ethnicities. And still, ten years later its the Chinese and Taiwanese American kids that are in the Olympiad team. And even at a lower level, say SAT math, we see the performance skewed by race in the same way. I am ethnically Indian. And Indians are as interested in math as Chinese. We all send our kids to math tutoring. We are mostly engineers in the Bay Area. And even so, at the very top of the distribution, there are some Indian kids ... but far more Chinese American and Taiwanese kids. These are just facts. I don't take it as a slam against my ethnicity that we don't do as well in math as the Chinese. There's more to life than math after all.