I was a math + physics major in college, but I work at an outfit that has a lot of engineers. In my observation, most of them are weak at math -- they got through it OK in college but it didn't come alive for them, which is probably not their fault. And as they start their careers, they can easily get productive enough without using their math, whereupon they forget it pretty quickly.

This isn't a slam on anybody -- these are bright and capable people, and I envy their success.

A handful of people, maybe 10%, gravitate towards the problems that involve math. Maybe they took a personal interest in math while in school, or maybe they're using math to cover up a shortfall in some other area. They become the "math people" in the department, and everybody brings quantitative engineering problems to them. I'm one of the math people, not even officially an engineer, but I volunteer to solve problems that other people hate. I'm actually not as successful in my career as some of the engineers, but at the same time, I'm doing OK considering that I got a more esoteric degree.

I think we could teach math in a way that's more relevant to the people who might actually use it, without detracting from what makes math come alive for math people. Let's teach more computation and proofs, perhaps from the git-go. Computation is how most people solve problems anyway. Proofs offer a much richer palette of ideas and styles than memorized "forms" and algorithms.

Granted, any reform of math education suffers the same pitfall as contemporary and historical methods: Massive attrition. This is the huge unsolved problem in math education.