The NY Times has an article (Brain Calisthenics for Abstract Ideas) that discusses how to learn. It advocates more rote learning of a certain kind.
The article starts with the subject "graphs and equations": a subject that many find hard to master. As the article goes:
For about a month now, Wynn, 17, has been practicing at home using an unusual online program that prompts him to match graphs to equations, dozens upon dozens of them, and fast, often before he has time to work out the correct answer. An equation appears on the screen, and below it three graphs (or vice versa, a graph with three equations). He clicks on one and the screen flashes to tell him whether he’s right or wrong and jumps to the next problem.
“I’m much better at it,” he said, in a phone interview from his school, New Roads in Santa Monica, Calif. “In the beginning it was difficult, having to work so quickly; but you sort of get used to it, and in the end it’s more intuitive. It becomes more effortless.”
Of course he is not learning the theory but a kind of shortcuts. But is that wrong? Chess masters don't calculate every possible move. They see a situation and somehow they "know" how to react. The same applies to many experts.
Maybe those endless exercises at rote-learning schools are not so senseless as any presume.