Common Core math teaches how things work, it's just different, so people think it's wrong. But when you actually pay attention and learn it, it helps explain things better at a more fundamental level.
However, parents didn't learn this way, so it's bad.
It can, and it should. However, that doesn't mean that the books are doing it successfully, and the teachers understand the underlying principles.
Too many years ago, I was pleasantly shocked at looking at what was being covered in elementary education by tutoring a friend. They were teaching discrete mathematics, different numbering systems ... forcing the teachers to learn how think in a different system. It was inspired (and harder then I would have expected). However, the book author's did not seem to realize what they were doing or why. They were meeting the requirements without understanding why they were requirements. It unfortunately seemed far too appropriate for what would be happening in many grade schools.
There is a widespread misconception, especially amongst its critics, that Common Core prescribes how to teach. It generally just sets goals.
There are dozens of Common Core compliant math curriculums that teach in all sorts of ways, some are more "how" some are more "drill". The more trendy curriculums make a false promise of a painless "How" that ends up with kids neither learning How it Works, or How to get the right answer.
However, parents didn't learn this way, so it's bad.