When my children were in an elementary school in Fresno California they were put in the pull-out GATE (Gifted and Talented Education) program. There they did more open-ended exploration. To me that's a no-brainer. You do that with kids who have mastered the "canon" and are ready to build upon it. Nevertheless every one of those kids still sat in regular classes and did the timed drills etc with the rest. Had they not done so, and their skills fell behind, their GATE experience would have been a millstone around their educational necks.
Now I'm no rah-rah "my kids are better than yours" elitist on these matters and that's not why I bring this up. It is that I am enraged at the tendency for some to argue that because some program dealing with very talented students with a strong background is able to accomplish something with their demographic that somehow this means that it is an ideal way to teach average students. What is the basis for this argument? I fear it is as simple a logical error as causation reversal: Some seem to believe that open-ended instruction (etc) CAUSES students to be advanced. Uh, no. The observation of students having advanced abilities or backgrounds, in contrast, does open the door ("cause" is a bit of a strong word) to these possibilities with them. Causation reversal on this point is cargo cult deception.
If only fans of reform math were this concerned with rigorous controls and falsification exercises when considering their preferred education research.
I agree with that statement and add that some also seem to believe that traditional math worked only for a small group of students who happened to be advanced. I.e., the advanced nature of the student CAUSED traditional math to work. It failed for everyone else. The logic of this breaks down when one stops to define "advanced" and takes a close look at the other factors at work with traditional math. E.g., did the teachers teach it poorly or well? Of those for whom traditional math worked, what was the breakdown of IQ's and "advanced" nature of these students. For many if not most of the truly "advanced" students, the factual and procedural foundation for their success was predicated on their obtaining that foundation through the traditional teaching of math.
In the various online discussions of traditional vs reform math no one ever bothers to look at what is happening with the students who manage to make it through to HS calculus and major in a STEM field. For many of these students, they do a lot of practice and drills and memorization, either at home, or at a learning center, if they're not getting that through school. One has only to look at the Asian countries to see that Jukus and similar organizations are providing foundational skills to make these students excel at what appear to be inquiry-based assignments at school.