Does this concern me? Sure does! I have mentioned before and I'll say it again...I think the "idea" of Common Core could be a good one, but what I've seen so far is crap! The Pearson curriculum our district chose is a disaster and some of the CCSS standards are screwy. JMHO!
There is a
LOT of misinformation about the Common Core out there, which is leading a lot of people to conclude that it's, well, crap.
Plus, there are two aspects of the CC: the
standards, as written by university professors, and the
implementation of the standards, as written by companies focused on reducing costs and increasing profits. I've looked at the math standards pretty closely and find them to be outstanding. They emphasize understanding concepts over memorization methods. Math textbooks generally rely on memorization.
I agree with asking kids to explain their answers. If you can't explain it, how can your teacher be sure you understand it? Plus, explaining things well is a critical skill in the workplace. Scientists may come up with amazing new ideas, but if they can't explain them to other people (via papers, presentations, or informal discussions), their ideas will get nowhere. The same can be said for almost any field.
Obviously, there are limits. A fifth grader shouldn't be explaining how she knew that 4*12 is 48. But when kids are learning new concepts, they should absolutely have to explain how they got their answers.
I teach my kids. Sometimes my DD will consistently get the correct answer to something, but when I probe her for how she understands the ideas, I learn that she doesn't fully get them. This fact often comes to light when I want her to move to something more difficult --- I find that she only had a fuzzy understanding of the idea, which tripped her up when things got more complicated.
