The question always comes up in debates about teaching mathematics: how come the Japanese do so well at math, when they stress rote memorization, if memorization is the wrong way to go about teaching math? (It's usually said in a tone of smug satisfaction, as though there's no possible comeback other than to admit that a constructivist approach to mathematics must clearly be wrong because the Japanese aren't doing it.)
The answer: a little from column A, and a little from column B.
The Japanese do indeed expect kids to memorize a lot of facts, but that doesn't mean they teach by modeling procedures and then assigning students practice questions to follow those procedures. No, they present a problem which the students do not yet have the skills to solve, then the kids work in small groups to figure out the problem. At the end of the lesson, the teacher summarizes what was learned, and students are assigned a small number of questions to practise on at home.
In other words, they use EXACTLY the method we're being told to use - with the exception that they do not allow calculator use.
The single biggest difference between North America and Japan is the number of school days - Japanese students have far more. The next biggest difference is in average expectations. When American moms are asked what mark is acceptable in math, they generally say a B or a C. Japanese moms expect an A.
So - high expectations, a constructivist and problem-solving approach to mathematics, high support in the form of parental help and extra tutoring - that's nine-tenths of the items we're expected to include in our mathematics programs.
Oh, and I should point out that the rumours about this kind of math instruction ignoring basic computation skills are false. We do drill math facts; we just make sure to drill them AFTER students have achieved comprehension, rather than before or instead of.
For future reference: http://www.gphillymath.org/ExempPaper/TeacherPresent/Mastrull/SMastrull.pdf