Math feeds on itself. It takes a simple concept, and then examines it from a dozen points of view, seeing more and more structure in the idealized problems, both on formal and intuitive levels. As a result, having learned some math, you can more easily anticipate new structure in the new math, and in other problems, as on the intuitive level, it generalizes very well because of the simplicity of constructions that get studied.

Educators must know a great deal about the effect of mathematical sophistication. It's interesting how undergrad textbooks, even on the subjects I know nothing about, seem boring and longwinded, and it's often more instructive to just find a tutorial paper, tapping greater depth through keywords and references.