I just finished a PhD in math at a top department, but not one that placed much emphasis on graduate student teaching. Grad students here teach only as TAs, and the training is minimal. I got great student evaluations, but I realize this was due more to holding lots of office hours and making study guides than to any real pedagogical brilliance on my part.
Next year I'll start a postdoc at a similarly research-oriented place, and I'd like to be a more effective instructor. The question is: where do I start? What are some good survey books or articles that would bring me (partially) up to speed on best practices for teaching university-level math? My formal knowledge of good teaching strategies is essentially nil.
I'll have the chance to teach a range of undergraduate courses. I realistically won't have the ability (or longevity, or experience...) to make sweeping changes in e.g. the way the calculus classes are taught, but I'd like to do the best I can within the current framework. I may also have the chance to design a one-off mid-level undergrad course from scratch, so something touching on course development would be helpful.