I wish I could go back and learn math the way you want it to be taught. My math experiences consist of my (engineer) Dad getting upset and offended because I couldn't understand algebra. Still have a mental block against it.
Of course, in my high school, math was taught by football coaches who had to have a teaching credit in order to maintain their coaching status....
In my high school the best math teacher was a quiet man who assigned homework and gave clear explanations but wasn't particularly "good with kids;" he made a tremendous difference in my brother's life without any interest in his life beyond the classroom.
The math teacher who won all the awards was not a good classroom teacher -- his lectures were full of distractions and his homework was dull -- but he tried to get to know every student personally, and if you stayed after school with questions, he was an excellent one-on-one tutor. But he demanded friendship in return for tutelage. It was important to him to know how you were doing or feeling; how were you getting along in your adolescence. Any time you want to talk (including the middle of class, which was why his lectures were always scattered)... a lot of students really liked him.
I refused on general principles to see him after class, and I never liked his ways, which I found smarmy. Part of his legacy was that I never visited any of my college profs during office hours, assuming that I'd be required to be social with them if I did. I thus lost out on thousands of dollars worth of education.
Touchy-feely won the day back then, but eventually the quiet man who actually taught math won a national teacher's award.
Maybe they should (maybe they did) set up some triage system so they can funnel the kids who respond positively to a real classroom to teacher A and all the other kids to teacher B.
My best friend is a mathematician, and he's wonderful at explaining incredibly complicated stuff so that a person disinclined in the mathular area really is fascinated. I love it when he talks to me about what he's currently studying...