What should the US do make math and science education here competitive with the best in the world?

Currently, our grade schoolers test a bit below the top countries kids, but not terribly. By middle school, we are beginning to fall further behind in math and science and American High Schoolers test near the bottom of the developer world in math and science.

Here’s an article from a group who thinks something akin to a school voucher system is the answer. Agree or not, do see the test score tables near the bottom of the article. They are informative.

Here’s a previous question on US education. The question is a bit different in focus, but offers some good thoughts. And the first answer in it contained a link to a wonderful blog written by a fellow who was a picked on nerd while in school and is looking back now as an adult, making his own recommendations about how to improve things.

Some think the influence of psychologist Jean Piaget and the constructivism http://en.wikipedia.org/wiki/Constructivism_(learning_theory) methods of teaching founded on his work have led to classes where kids are allowed to “invent” math on their own so as not to inhibit their creativity. Interestingly, that jibes pretty well with the nerd’s lament.

How would you make sure American kids stay in school to graduate, and come out with the skills they will need for success in the 21st century?