Hi mmom,
Here's my very cynical view as a person with kids aged 11-15. Take it for what any random stranger's opinion is worth....
My kids have been to various schools and I have a large number of math books (I collect them). What I've observed is that mathematics education in the United States is generally fair to poor. Overall, all the mainstream textbooks I've seen aim generally at teaching kids how to perform operations rather than teaching understanding of concepts and how different ideas fit together and relate to other areas. The schools follow this lead. If you hear phrases like "skills based," you're probably hearing, "learn the algorithm and move on." They pretend that writing an essay about addition is teaching concepts. I disagree....
Most of the teachers I've met at the K-8 level don't really understand mathematics; the 9-12 teachers are, well, less bad. K-5 teachers are known for having a poor understanding of the subject. So, combine poor knowledge with bad textbooks and IMO, the odds are against finding someone who'll really reach your son (and at his age, if you do, you'll say goodbye to that person after one year).
The Common Core/CC was supposed to fix a lot of these problems, but whoever was in charge left the implementation to the big ed textbook/testing companies. So they took a thoughtful set of standards and turned them into a dog's dinner of continued bad textbook mathematics.
I've read a lot about the CC; if implemented properly, it would be a gifted kid's dream. The lowest grade levels focus on concepts like the number line and equivalence and "addition is combining things." The idea is to weave these ideas into everything through the upper elementary grades and beyond. I'm not sure that's happening.
If you want some really good stuff on K-8 mathematics, try
this page (belongs to a CC author).
Use the stuff for teachers to teach the child. Instead of a private school, you could consider saving some money by keeping your son in a public school and hiring a mathy tutor who can go through this stuff with him.
