[zukzuk]

This! I learned more trigonometry in 2 weeks when I was tasked with a digital signal processing project than I did in years and years of (objective-less) schooling.

An important addendum to this is that the objective has to be closely tied to the work — the feedback loop for learning and then seeing some results from that learning has to be tight.

I think this may be why in school grades were not a good objective, for me anyway. They were just too distant a reward from the work.

[jonhendry18]

Someone should make a big diagram, showing a variety of "cool things" that require math or which knowing the math helps to use, and the chain of math techniques and areas that lead to it - with granularity finer than "calc III".

Sort of like a Civilization tech tree, but for applications of mathematics. "If you want to do 3D graphics, learn this but also this which leads to this which leads to this."

That way students can say "I'm hating Taylor series but if I learn that I can use it in X" or "This is hard but if I get through it I can learn quaternions and do Y" or whatever.

[halayli]

Exactly! That's the context I was considering as well (including school)

Schools do a pretty bad job at providing context to the problem. What we are taught are solutions. And these solutions came from problems that were objectives to the authors. I need to "live" the problem and relate to it to understand the motivation behind the solutions.