>Mathematics was never taught this way. The teaching of mathematics always began with concepts which then naturally led to constructions, algorithms, exercises, practice and problem solving. As Wayne pointed out, this statement isn't the result of years of studying how mathematics is taught and learned. It is a straw man that has been passed from one reformists to the next, like a baton.
Well, I think that's more or less correct, and my experience was that things were explained. How many in the class "got" the explanations, I'm not so sure. Many were dozing, I'm also sure.
So, the CC response to people dozing seems a bit like, well, we're going to force those slackers to "get it" by doing a whole bunch of problems with long drawn out (literally) "explanations" over and over. Its a bit ironic is it not?
The point of "getting it" (whether its explained to you, or you "figure it out" largely by yourself,) is simply to understand that what you are being asked to do makes sense, and is not some opaque mystery that you are just memorizing. Once one has got it, doing more problems the long drawn out way is (for some at least) a real turn off, one of those things that make people lose interest, or positively dread. And at that point it does really steal time away from the next step, which is to gain fluency. (Of course, the explanations should be revisited from time to time, to reinforce the learning.)
Another thing about the explanations, is that I think that's where students and teachers need to be extra sensitive to one another: the kids need to listen attentively to what's being shown or asked, and the teachers need to try to understand what sorts of obstacles may be present for this or that child and try alternative approaches if needed. So, in this crucial aspect, attempting to "can" and standardize conceptual understanding may create problems of its own.