I'm not a math teacher, and my children aren't school age yet, so I have no real experience with CC. Having said that, my sister-in-law is a high school math teacher currently teaching CC and she is not a fan.

I just read this synopsis:

http://math.berkeley.edu/~wu/CommonCoreVI.pdf

and it leads me to believe that CC is largely the answer to made-up problems. They want me to believe that understanding similar triangles is a prerequisite for understanding the slope of a line? I don't buy that. I don't believe that everyone comes to an understanding of the slope of a line in the same way. A geometrically minded person might envision triangles. An arithmetically minded person may be happy to understand it as a ratio. Someone with cycling experience may imagine hills of different grades. Let's consider a line with a slope of 0, or infinite slope. Where are their triangles now?

One of the things my sister-in-law is dealing with is asking high school students who are currently learning English to explain all their math steps. It seems that CC is injecting more english into math class, and in doing so, they are inhibiting these students in the single area where they used to be uninhibited.

Beyond that, I put myself in the place of these students who are asked to "show" and "explain" mathematical concepts, and I ponder what that implies. Does anyone know? Are they looking for paragraphs? Pictures? Movies? I tend to think in moving pictures. How often will teachers mark the explanations of gifted students as wrong because they don't understand them? How will this affect students on the autistic spectrum?

All in all, I'm not impressed. I am an engineer, and I make use of mathematical properties daily that I can't recall the names of. A concept by any other name works just the same, after all. I've commented before that I see mathematics as its own language, and offering a written explanation of a mathematical concept is asking for an unnecessary translation.

Personally, I don't see anything wrong with students demonstrating mastery by solving numerous varied problems on a theme. What goes on in their heads is their own business, and their ability to relate that to others is an issue wholly distinct from mathematical mastery.