That might be true in theory. In practice, the bosses run the union.
Besides, my point is that the teachers' unions are run by people who think math is big and scary.
The NYC teachers union is a weird beast. The rank and file is very active. And the bosses have to kowtow to them. I have a friend in it and there was an open revolt regarding the last pay increase.
On the other hand, the amount on money they control gives them huge power over guys like Bloomberg. During the 1970s, it was the unions that bailed out NYC in the financial crisis with deals done late at night.
p.s. Why do you think Bloomberg put Klein -- a corporate lawyer -- in charge of the schools?