I will try to address a few of the various interesting comments.
The comments take very different positions on the importance of mathematics in a modern economy. A couple of things are pretty clear: most employees do not need a lot of math, but math is becoming more valuable for a larger fraction of the tasks in more advanced economies. For example, it is difficult to use regression analysis in ways that illuminates without understanding some of the basic mathematical concepts that lie behind regressions. The statistical theory of estimation need not be mastered, but someone limited to only cookbook knowledge of regressions can make serious mistakes.
The fear of math among many Americans is common, and this fear prevents them from reading simple figures, analyzing say the relation between housing prices and interest rates, understanding probabilities in medical and other areas, etc. Still, many jobs are designed such that only very basic math, even only arithmetic, is required.
The advantage of the American "build up" learning system is that people can more readily change their minds about what interests them as they try out different programs. It also implies that there are second and third chances as students can decide their interests are different than what they had believed, and workers can shift to entirely new lines of work. That flexibility is less common in the learning structures of many other countries.
Obviously, memorization is important to learning, and it is said, for example, that first year medical school is mainly about memorizing various pieces of information about the human body. Perhaps too I exaggerated the importance of rote learning in the Japanese and other educational systems. But Japanese businessmen and scientists frequently complain about an excessive emphasis on rote learning. My experience with Japanese students in the U.S. is that especially at the beginning they have difficulty in thinking on their own, and rely too much on what their teachers told them.
I believe schools systems should establish minimum standards for graduation that are meaningful, but not very difficult. Then individual high schools can top that up to an extent determined by their student bodies.
As I argued in previous posts, inequality in American earnings has grown greatly during past 25 years, in large measure because of increasing demands in a modern economy for workers who have considerable knowledge. Graduates of elite universities have benefited the most from the greater emphasis on knowledge, but all groups that invest in knowledge and information do better in modern knowledge-based economies. I believe America has adopted better than most other rich countries to these changes, in part because of the flexibility in its learning system, and in part because of its emphasis on lifelong learning.