Teaching mathematics not in a constructive way is extremely harmful. One have to wipe out all the previously acquired superstitions, all that high school crap out of the students minds before reinstating a proper, constructive knowledge there. Which raises the question - what was the point of filling the minds with all that crap in the first place?

Same thing with languages, there are schools which approach foreign languages formally, starting with grammar and all that. Some of that schools are known for training spies, for example, which is sort of an indication of their quality.