[hackinthebochs]

The problem comes from the teachers, who themselves don't really know the subject. They know it as a set of rules, and thus thats how they teach it. Get teachers who actually know the material and the problem will mostly solve itself.

A more practical solution would be to change how the books themselves are written. Math is taught as just a set of rules to be memorized. We've lost the fact that math was motivated by real problems that real people had. We need to teach it in a problem-analysis-solution manner rather than "here are some rules and now here are some contrived problems for practice".