My high school math teacher used to give us extra classes that weren't directly connected to the curriculum. They were always about structure, elegance, and beauty. Quite a lot of time was also spent on history: who was studying what, when, and why. (Also there was a cult of Leonard Euler, which maybe is not so surprising if you did high school math.)

I found it to be the most important glue in my math education. In fact, all the natural science ought to be taught in this way. Kinda like Bill Bryson's Brief History of Everything, plus actual calculations.

We won a math contest in my last year. I was expecting it to stay interesting.

Unfortunately when I got to university math (and the rest of engineering) was taught in a very utilitarian way. There was very little context, just a lot of similar looking derivations.

I blame the exam culture. In a way it's good because it motivates you to learn something, but it's bad because you end up learning it in a way that isn't useful. At the end of your college days, you are unlikely to remember just how Stoke's theorem works or the coefficients in Runge-Kutta. That's just because the size of the curriculum is huge. But if you had a context, a set of stories about when and why something was studied, you'd have a much better chance of being able to recall that it even exists.