There's a couple of schools of thought with standardized testing between the US and other countries and compulsory public education:

1. Some people believe we're losing our global competitiveness to other countries, such as S. Korea and other Asian countries in particular. S. Korea, Singapore, and other Asian countries traditionally score high on standardized math exams.

2. Others, such as Diane Ravitch who initially supported CC and Bush jr, have reversed course and believe it's a bunch of poppycock. They say that the US in particular has never scored high on those standardized tests. Moreover, Ravitch says that standardized test score argument is weak when we consider the overall creativity and originality of US patents, technologies, or companies such as Google and Facebook.

Here's Ravitch's blog on it - http://dianeravitch.net/2013/12/03/my-view-of-the-pisa-scores/

3. Some say Finland and northern European (sans UK who seem to be caught up in national testing and standards) take a more hands-off approach to reading and other standardized tests and this ultimately breeds more successful students. Denmark, on the other hand, has been widely touted as the happiest people on earth for a number of years.

4. Some in China, such as Zhao Bowen, are now trying to locate and isolate high intelligence to spawn superbabies. Read this article - http://dianeravitch.net/2013/12/03/my-view-of-the-pisa-scores/

In order to breed a Leonard da Vinci, though, you need to have the mind of a scientist AND the mind of the artist. In the US, we tend to forget that second part and that's to the country's detriment, imo. You need that divergent thinking that comes with music, the arts, creating, the humanities, etc.

IMO, we need to take a much more individualized, personal approach to education - more like unschooling. This isn't going to happen though. But the harsh reality is that we need friendly, kind car mechanics who are technical whizzes but don't test well on standardized tests as much as we do people who score off-the-chart on those standardized tests. And I was really cursing public education for ditching auto shop when I needed a car mechanic!