Tangential, but I think people tend to underestimate just how important and deep mathematical fundamentals are in general. The relatively "simple" notions on which we build all other mathematical concepts, such as equality, relation, function, symmetry, associativity etc. actually have incredible depth to them. Too often, I think teachers and texts gloss over these notions instead of plumbing their philosophical depth and implications (statements like "the proof falls out automatically" or "the proof is obvious" or "the proof is a natural consequence" are a real disservice to learners). Both set theory and category theory are illustrations of just how far you can go with a few of these ideas (category theory, for instance, is basically entirely built up around the notion of a function and only two other ideas, identity and associativity—yet these three "simple" ideas alone are enough to construct a theory rich enough to model all the other branches of mathematics!)
Understanding mathematics is really understanding how to start approaching metamathematics. What does it mean to distinguish one class of things from another? What does it mean to say something has a property? That a property is reflected or preserved? These are the sorts of questions that are fruitful. It makes sense that the spaced repetition approach can help because it might necessarily force you to continue thinking about (and thus questioning) a concept you'd otherwise have taken for granted or not plumbed to sufficient depth. Too often, we fail to recognize how complicated "simple" things really are.
> Too often, I think teachers and texts gloss over these notions instead of plumbing their philosophical depth and implications
I have a few questions:
What level of teacher?
Are you a maths teacher/teaching academic?
My understanding of Maths education in the west is that they essentially spend the whole time attempting to get children to the point where they can do precalc and that any attempt at reform is eventually defeated by conservative engineers running a concerted political campaign to convince the voting public that set theory and category theory are a leftist conspiracy.
My experience of university mathematics was that set theory was assumed knowledge (fair, it has managed to stay in the curriculum), same with category theory (lol).
I would say that if it weren’t for the rise of the computer and the prevalence of relational databases in the late 20th C they would have managed to cut all non-precalc out entirely.
Understanding mathematics is really understanding how to start approaching metamathematics. What does it mean to distinguish one class of things from another? What does it mean to say something has a property? That a property is reflected or preserved? These are the sorts of questions that are fruitful. It makes sense that the spaced repetition approach can help because it might necessarily force you to continue thinking about (and thus questioning) a concept you'd otherwise have taken for granted or not plumbed to sufficient depth. Too often, we fail to recognize how complicated "simple" things really are.