This past month I taught a course, "Paradoxes & Infinities," in Hong Kong through the Center for Talented Youth, a gifted & talented program through Johns Hopkins University.
My lasting impression, a few days after completion, is that there still are some great ways to teach advanced math to advanced students. The organization and the logistics of the program itself had some some issues; but these were not negative enough to mollify my experience.
The course is an intensive three week program. The curriculum is math and logic based with paradoxes as the connective tissue. In order to discuss many paradoxes one needs to have a basic understanding of set theory (Russell's paradox), probability (Monty Hall paradox) and sequences (Achilles & the Tortoise) with some other topics sprinkled in. We also studied cardinality, symbolic logic, game theory, combinatorial games and the structure of the real numbers. Each day I, or my TA Raymond, would present brain teasers and puzzles. The combination of all these topics and activities lead to lots of fun but was, at times, a bit overwhelming.