One of the great things and the greatest faults of the Asian learning system is it's emphasis on drilling. You're right drilling is meant to be for reinforcement, not introduction.

There seems to be 1 way of thinking about learning: do it and do it and do it again. Which *does* work for math, science or other predictable subjects.

And it does work for some areas of language. Conjugation for example-when done properly. The problem is you get students and teachers who try to memorize and then drill absolutely everything.