*nods* Algebra/galois theory was proofs, and I remember having to think about that one a lot. (That professor was great, I loved his class.) I took at least two? more math classes that were supposed to be proof-based, but I don't remember enough about them now to actually remember a whole lot about what kinds of problems we got. (And one of them was the ill-fated topology, where I'm sure the problem sets should have been proofs, but B and I basically learned the whole class the month before exams and then I, at least, forgot everything about it. I don't remember in the faintest what we did about the problem sets given that we weren't learning anything. Possibly the professor forgot to give us homework??)

you feel strongly about problem sets and pedagogy, and I would like to hear your thoughts.

These thoughts are not very profound (although surprisingly controversial), it's that there seems to be this strain in elementary education of NOT giving problem sets at all, even for (especially for, it seems like) skill-building, which is just ludicrous. (I totally am on board, of course, with giving problems that are more interesting than extremely dry drill -- but you can't just not practice the skills.) My kids' school has tried to do it this way, though Good Math Teacher has always tried to push back, and it looks like in the last couple of years there has been more pushback.

ETA: Early elementary math, of course, is another beast entirely, where a lot of the applicable concepts you can practice in ways other than written problem sets.