Recently, on this blog, we discussed the performance of US 8th graders on the NAEP, and how that compared with exams taken by students in various countries. As usual, Singapore came out right at the top. The vast majority of Singaporean students were deemed proficient; a far lower percentage of American students were.
Of course, the US has a long tradition of incorporating what works in other countries here. So it comes as no surprise that a number of districts have adopted "Singapore Math" curricula. Some have achieved test gains after doing so, though educational studies are almost impossible to control (i.e., are the gains from the curriculum, or the fact that the teachers went through additional training, and were excited about it? Etc.) You can read a handful of articles about the roll-outs here.
I don't have any personal experience with Singapore math. I haven't observed a class learning it. But reading over these articles, I have to say that the curriculum seems to be doing a number of things right.
First, kids learn fewer topics each year, but learn them more in depth. American kids might see 30 math concepts a year, and then re-cover 25 of them the next year. Singapore math does not repeat concepts. You learn a concept, then move on or build on it.
There are pros and cons to this. One of the reasons American schools review so many concepts is that kids move around, and there is no national curriculum (or even state curriculum sometimes). Singapore kids might move from school to school, but they'll be covering the same stuff even if they do. Kids who move into Singapore math districts in the US wind up with some big gaps.
But on the other hand, covering and then recovering concepts leads to burn-out and shallow knowledge. American students have covered various basic arithmetic concepts many times by the time they officially get to algebra. But they may not actually understand what's going on. I had a conversation with a grade school child recently in which he asked how old my baby was. Six months, I told him. So how long until he's a year old? the child asked. I turned it around and asked the kid how many months were in a year. Once we established that there were twelve, I repeated the original question. The child was somewhat confused. I have no doubt that if I'd given him a worksheet saying "12-6 = ?" he would know what to do. But a multi-step word problem requires deeper understanding of what subtraction is and why you use it. American schools tend to skimp on these.
Singapore math also encourages students to do problems in their heads, to talk them out, and to draw visual representations of the problem (as an intermediate step to doing that visual work in your head). There is some stress on speed in order to keep kids interested. I developed all kinds of short cuts and visual ways of figuring out problems when I did math contests in school, and those skills certainly helped me master various concepts. Singapore math seems to incorporate these strategies into the curriculum for kids who aren't on the Math Counts team. That's certainly a good thing.
I am not sure how this winds up working for highly gifted children. To accommodate them in a Singapore Math curriculum, one would have to rely on acceleration. If a kid has mastered the year's 10 concepts, bump her to the next year. But, on the other hand, even in the absence of acceleration, Singapore math seems to bring so many kids up to the advanced level on international comparisons that perhaps even many gifted kids are reasonably challenged. After all, Singaporean 4th graders start learning algebra (though they don't call it that -- it's presented as simply figuring out numbers you don't know in a problem).