It would have helped if my E&M class had been more than triple integrals and geometry.

Idk - would it kill physics profs to graph shit in Desmos so you can visualize some of these fields? Or start with simple examples? I know how to do a partial fraction decomp, but if I’m spending all of my time on tedious algebra and then fuck up the integral in such a way that I accidentally made something that looks like what Papa Wolfram gives you when you ask him to integrate 1/(x^5 + 1) - then you don’t know if you did fuck up or not, because maybe there’s some trick or this has significance and blargggggh.

(You could get partial credit on tests in quantum by explaining that you knew your answer was incorrect because it was negative when it wasn’t supposed to be or vice versa - test average was usually about 11%.)

I wanted to become a physics teacher specifically, just because I hated the way I was taught physics so much. (I hate the way chemistry is taught too, but I also hate chemistry. Unfortunately, I’ve only got to teach physics as a sort of concessionary “elective” that they tossed SPED students and the basketball star in…)

imagining fields (not forces,

Yeah that thing. Except that they were dubbed "magnetic lines of force". Also, I remember it being separately explained that even though they were called that, they didn't represent the direction of force (of course not, or you'd not need the right-hand-rule and left-hand-rule).

Looking at the iron shavings though, it seemed more like low potential energy regions/ stable regions.

Also it give a feeling of being analogous to fringe patterns.