Guess who <email@example.com> writes: > If you learn to play the guitar or any >other musical instrument, you are first taught how to place your hands >and how to move them. You will practice scales on the piano, not >knowing why at the time, but that practice lays a firm foundation even >though the understanding is missing initially.
It's been a long time, but I'm pretty sure that they wanted me to understand key signatures and circle-of-fifths from the beginning, before I had much "firm foundation" of playing skill. (Not to mention that music teaching also has its radical critics, for some of the same reasons as math teaching -- it turns off more people than it turns on.)
I think, too, that the original context of this thread has been lost among the big ideas. We are talking about a population of kids who have already failed at learning arithmetic. So we *know for sure* that more of the same is *not* going to do *these* kids any good. Maybe giving them some actual mathematics won't work either, for many of them, but maybe it will, and it certainly can't do any worse than yet another year of remedial arithmetic.