Thanks for the link. Very insightful. About halfway through, and the big point seems to be there is a common misunderstanding of the word understand. Existing, pre common core, textbooks have drifted away from teaching "understanding" of math to training in math techniques. If schools+parents+teachers+curriculum writers continue to misunderstand "understand", then the potential of common core would be lost.

I was blown away by his explanation of the distributive property proving that a negative times a negative equals a positive. I don't think that was taught in the seventies. Now I really want to make sure DS has that understanding (weekend mission, if sewing costumes leaves any time for it.)

i.e. you can't train thinking