Good districts are giving teachers extra training and having teachers work collaboratively to develop these skills. It’s true that many people who go into elementary education are better and more comfortable at teaching reading/writing than at math/science.
Good teachers are not adamant about ways to solve a math problem when a kid comes up with a novel solution. Common Core makes clear that there are multiple ways of solving single problems–whether by using the standard algorithm, graphically, or some other way. So, teachers with that training should be open to “out of the box” methods.
Sometimes advanced kids aren’t very good at explaining their “out of the box” methods, and that is something they need to learn how to do. Common Core places more emphasis on explaining how a problem was solved than previous standards. This is a skill that is probably more important to kids who will go on to advanced math than people who will mainly only use math for knitting, making consumer purchase decisions, etc.
I recall one time I was grading timed math tests for my son’s 2nd grade class. The class was doing something similar to the Number Talks I explained earlier, even though that was long before Common Core. (“Come up with an equation that equals today’s date.”) My son proposed something with negative numbers or a square root or something–he saw that part of the day as his challenge to show off. His explanation must have been particularly confusing, because the teacher looked questioningly at me, and I nodded to confirm that what he’d done and tried to explain worked.