At the risk of utterly derailing this with irrelevant discussion: path-dependent systems are particularly tricky for some people IMHO. I think in a more state-based way, and my first rigorous dive into path-dependent calculation was during my chemical engineering degree -- I learned to be extremely vigilant about memorizing what was path-dependent and triple-checking if that affected the situation I was calculating.
I do wish there was more rigorous exposure to them at lower levels of education and younger age. Because while I'm perfectly capable of handling path-dependent systems with proper focus and effort, my brain doesn't feel "native" when deriving solutions around those spaces - it feels similar to being "fluent enough" in another language. I feel this way about a lot of things -- I really feel I'd have been happier and more fulfilled if I'd been immersed in super rigorous first-principles education beginning around age 8-9. I didn't do well with things like "memorize this procedure for doing long division" and did much better with conceptual derivations of physics/math/science/historical arcs, etc.