[cma]

I don't think just doing everything from first principles is reasonable. Building up the natural numbers from set theory etc. would just be frustrating for kids.

Like trying to teach them their native language by grammar diagrams etc. instead of immersion

http://en.wikipedia.org/wiki/Language_immersion

Math is not exactly the same as natural language, but there are tradeoffs to doing it one way or the other and there needs to be balance.