One of the most frustrating aspects of working on the improvement of math education is dealing with an educational establishment that makes decisions based on fads and opinions rather than empirical facts.
Now, let us accept that there are different approaches to teaching mathematics, with a major divide between the “reform, discovery approaches” and the more “traditional, direct instruction” approaches. Reform/discovery approaches became the rage among the educational community in the 1990s and I believe it is a major, but not sole, reason that math performance has lagged.
As a scientist, it would seem to me that the next step is clear: test a variety of curriculum approaches in the classroom, insuring the class demographics are similar, and find out what works best. In short, do a carefully controlled experiment with proper statistics and find the truth in an empirical way. But what frustrates me is that such experimentation is virtually never done by the educational bureaucracy. They seem to go from fad to fad and student progress suffers. Reform math, Integrated Math, Teach for America, Whole Language, and many more.