Are we pushing kids too far too early in math? That's the issue raised in a recent Washington Post article. Looking at some school in northern Virginia, there is a rush to have kids in Algebra I by the end of middle school. There are obvious benefits to this, but there are also some serious concerns raised. Foremost among them is the frenetic pace required to get to algebra.
As I've studied math curricula around the world and looked at the recent NCTM and government-funded studies, I wonder if rushing all this math through so quickly is really such a good idea. In places like Singapore, Japan, and China, it seems that the emphasis is more on depth of understanding than it is on just reaching specific target topics. As I traveled through some great Indian schools, I was struck at the depth of the kids' mathematical understanding. The seemed to have achieved "automaticity" and could actually play around with numbers more so I've seen in the US.
All of my observations are highly impressionistic, but they also reflect what others have said and researched. As the "math crisis" grows in the public perception, I think the issue of breadth and depth is going to define how we want to move ahead. I suspect that standardized-testing types will push for more breadth while the more progressive types will push for the increased depth. As an outsider to the whole math issue, my voice isn't quite authoritative, but my sympathies do lie with the progressives on this one.