You teach students math by putting them in a classroom and having them take notes while a lecturer talks about math. What skill are you actually training? How to take notes.

Also 'how to follow mathematical reasoning,' which can be even more insidious: they feel like they understood all the lectures but then see the exam and have no idea where to start.

In a different scenario they learn to solve problems by doing textbook exercises, spend four years acing courses, then get to grad school and realize they have no idea how to go about research.