The United States participates in TIMSS studies, in which math and science achievement of American students are compared against those of students in about 40 other nations.
I teach 8th grade, so I know what 8th grade results are. We're above average in both math and science. Not much, but definitely better than average.
In 2003, the US math score was 504, to an average of 466.
In 2003 the US science score was 527 to an average of 473.
That being said, the lack of a comprehensive US policy on education causes huge differences in achievement. Some southeastern states are almost third-world, and the upper midwest has states which rank with Japan and Hong Kong.
In some places, I'd have my kids in private school, too. But in most places, it's a waste of money, if you want them to have a good education.
There's another factor involved; in secondary schools, almost all nations have weeded out the low performers, who are either in technical training for a trade, or dropped out. We keep them in an academic track, which drives down the average scores.
What is remarkable are the math scores. Unlike most countries, we don't introduce algebra to most middle school students. And yet our middle school students still outperform most students from other nations in math. Not bad.