> 2) Money needs to support that. Which means for Math, the money for math teachers needs to be competitive with research departments of banks, and very different for different subjects, which seems offensive to schools and government in general. If teaching positions aren't competing with other professional careers in the subject matter, it will never work. This will, of course, mean that many science teachers make more than a school principal and even a district administrator. Deal with it.
I believe this to be a heavily US-centric view, Estonia and Finland do not pay more for math teachers than they could get in banks' research departments but still manage to get competent teaching across most school subjects.
Things work outside of the US, the issue is the US does not want to look outside and adapt itself to incorporate what's been learnt from other systems. It's a "do the US way or no way" attitude, and it's slowly eroding to become more a "no way" than any kind of "US way" of doing things.