Academic priorities 244

Spending some time on foundations, sure. Forcing students to memorize and regurgitate a proof, dubious. Having them reguritate the proof on an exam, I think not -- that's a waste of time.

Rigor, definitely an exposure is needed. Demonizing non-zero infinitesimals because of unfamiliarity with non-standard analysis and hyper-reals, that's just an indication of teacher incompetence (or bigotry). Spending 90+% of a calculus course for NON-mathematicians on proofs, a waste of time.

Exposure to mathematical rigor is useful for all, watering beginners in it serves no useful purpose (except, perhaps, ego-boo for sadists). My S.B. is theoretical math, all my other degrees are EE -- been on both sides of the fence, both as student and as instructor (undergraduate and grad. student level). I enjoyed the theoretical mathematics courses I took. I enjoyed the other math courses I took also, but I also learned enough to recognize the differences and the reasons for them. As I've said elsewhere, I've found what I learned as a theoretical math. major invaluable as a engineer, but I also needed other things to succeed as an engineer which the theory courses often completely failed to connect to.

So I agree with you, but still think there is considerable room for improvement in educational practices, both grade school and university (and probably that does not shock you).