Well, wizarding education remains utterly awful! Literally every single subject other than Herbology has led to Hazel having to invent her own ways to do things, no?
While undoubtedly a way to stretch one's magic skills, it's telling that only one class has actually been able to teach her rather than force her to teach herself (and do so far faster than is sensible).
Her inability to understand the house point system is... interesting, although it doesn't quite make sense to me. It's obviously supposed to speak to her immature individualism, but I feel that at least her experience with, say, the werewolves should have taught her about group benefit and detriment.