I was involved in math education for a few years. Asking "why" questions to students can often lead you nowhere. There's a tendency to believe that mathematical reasoning is obvious and that successful math education just requires a paradigm shift or "correct pedagogy." Maybe? I think it's more complicated than that. I don't think most students would be successful in an environment which turns math into an investigation, even though as adults we see that as being incredibly fruitful.
I think if you dump thousands of dollars into any program, you'll see some improvement in your kid's education. Money buys expertise, support, attention, and cohesiveness.
Oh yeah, I forgot to mention: I interviewed at a Russian School of Math while I was finishing my degree. The guy gave me a math test at a coffee shop. It's funny because they clearly have their own way of teaching the "how." I remember solving some of their basic problems and being told "we teach it like this instead."
