The thing is that the concepts are often not really that hard to understand. Differential calculus is actually really really simple. The concept is, I mean! But most math texts devote maybe one little chapter to the concept of it and then obscure that chapter with a difficult problem set about limits. That’s enough to turn anyone off!

Many math teachers learned under a regime that was all about sweating out tough problem sets and worrying about understanding the underlying concepts later.

This method tends to work well for a small subset of people who enjoy manipulating numerals and symbols. It loses people who COULD learn math but who aren’t suited to that kind of learning.

A step-by-step approach that uses visual techniques to teach concepts and treats problem sets as secondary (but necessary) can engage students and enthuse them by showing them exactly what they’re doing and why.

Obviously, for engineers, scientists, and mathematicians, good technique is critical, and I’m not saying we shouldn’t teach it, but we really need to step teaching technique as if it WERE math. Because it isn’t. And that deprives students who are led to believe otherwise.