Quote by ideasrule
All Chinese students who intend to study the sciences (as opposed to the humanities) are required to know these off the top of their heads.

My wife was an elementary school teacher in Taiwan. Chinese students who intended to study in the sciences are expected to *know* formula off the top of their heads. They aren't expected to *memorize* the formula. I'm willing to bet that if you ask most Chinese science students how to derive the formula, they can.
Math involves a negligible amount of memorization, considering the variety of dates, events, names, and implications that a history or philosophy student has to remember. I really don't think students are having trouble because they can't memorize a few formulas; they're having trouble because they can't understand them.

The way that math is taught in East Asia requires a negligible amount of memorization. Students in the US have problems with math because they are taught memorization and not understanding.
all the problems are difficult and take a lot of thinking to solve. There's also a huge, almost unbearable amount of homework because the competition for admission to university is intense. When I was in grade 6, I did about an hour of math homework every evening, plus half an hour of math at lunchtime. And how many hours does the typical American sixthgrader do?

Exactly. And if you have lots of trouble, then you go to a "bushiban." Being more "intuitive" doesn't mean "easier." What really annoys me about American math is that people see (correctly) that East Asian students work very hard at math, and so assuming that you can get the US system to work by just spending more effort on a system that don't work.
Also there is a huge investment in good math teachers.