As a country we're falling behind NOT because of the school system, but the student quality and parental influence on importance of education. Being in the American school system from pre-school to medical school, I've noticed quite a few things.
I remember in elementary school, the learning pace was very slow because the teachers had to keep diverting attention to the black and latino (there were many, I grew up in a poor neighborhood) students who were really slow and couldn't adequately answer the teacher's questions. I remember this distinctly because I would win all the prizes for answering questions.
By the end of 3rd grade, I was able to complete all the math questions being taught to me in 7th grade. This was because my parents provided me with a lot of study material at home. Now my parents are not the crazy "study or die" kind, and they were poor so could not afford to send me to private school. They just encouraged me to learn, and they even bought me a Super Nintendo when I didn't want one.
This same slow pace of learning kept happening until I finally arrived at high school and could fill my schedule with AP courses. Taking 5 AP courses a year, FINALLY I felt like I was learning at a proper pace. It should have happened long ago. Now guess what the difference was? There was now not a single black student, and only a handful of latino students in the AP classes.
Fast forward to Medical school, there are only a few blacks and latinos in my class. When we compared our MCAT test scores, they scored WELL BELOW the white and asian students. This country is going to keep falling in science/math as the black and latino population grows. What scares me is that I can't even think of a solution to the problem, their IQ is inherently lower.