Ah, that's a fair point. Most math textbooks are not that great pedagogically—perhaps I was just projecting how I think mathematical ideas should be introduced

Ah, that's a fair point. Most math textbooks are not that great pedagogically—perhaps I was just projecting how I think mathematical ideas should be introduced :). I'm definitely trying to do this myself: whenever I teach an abstract concept (more from PL than math), I've started to explicitly note both the formal definition and why it's interesting or relevant. Many explanations of abstract concepts I run into forget one of these components or the other, and it never ends well...