You may have read about how badly American 15 year olds did on the the new international math test and what that says about how we teach math. For example, in combined math literacy, the US came in 24th out of the 29 industrialized countries in the OECD, scoring 483 on a scale where the OECD average was 500 and the standard deviation was 100. (Hong Kong was first at 550, followed by Finland, South Korea, Netherlands, Japan and Canada. Last was Tunisia (359), preceded by Indonesia and Mexico (385).
In reality, the U.S. score doesnt say much of anything about how we, or anybody else, teaches math. What we mostly see is the usual dog bites man story: the ability of the students matters more than their schooling. U.S. whites scored 512 on math literacy, which would have ranked them 13th out of 29 OECD countries, between Denmark and France, right in the middle of the pack of European countries. The US score was dragged down by Hispanics (4430.69 standard deviations below the white score) and African-Americans (4170.95 standard deviations lower).
Oddly, Asian-Americans scored only 506, a little below whites, even though Northeast Asian countries averaged 527 or higher, but perhaps the explanation is that students in Southeast Asia did much worse (Thailand 417, Indonesia 360), and Asian-Americans are no longer so much restricted to Northeast Asians.
The strong showing by Canada compared to the U.S. may reflect the benefits of a more selective immigration system, compared to the U.S. system, which selects less than 10% of legal immigrants on wealth-creating talent. Most legal immigrants to America get in on being related to a previous immigrant, while illegal immigrants get in on ability to walk across the desert at night. Canada, in contrast, has relatively few illegal immigrants.
One tribute to the quality of American schools does emerge from studying the data: Hispanic-Americans did fare much better than students in Mexico (443 vs. 385); 385 is a genuinely bad score considering what a small elite of students in Mexico stay in school through age 15 to be tested. So, if your schools are as horrible as Mexican schools evidently are, you can hurt your students, but at the American-European level of quality of schooling, you run into diminishing marginal returns. Progress is possiblewe apparently have improved schooling a little since the decadent 70s, but the dramatic differences in scores typically come from changing students (or showing them how to cheat on the tests), not teachers.