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.
This experience was both difficult and rewarding for me. It took me a few days to realize that the students are still children. They need different motivation than university students, or, at least, different degrees of motivations. Oddly, they became more interested when the topics became more abstract. We watched some videos about Cantor and the "great problems" of pure mathematics. This caught their imagination. They became engaged with cardinality and the real numbers once it was put in this context.
Some material was not that interesting to them. To my surprise 😉 they were not that absorbed by the convergence of sequences. I thought they would like the pattern recognition. What I realized was they like the "puzzle" aspect of it but, to them, the motivation was missing. It was another "just because" topic.
It was a lot of work yet rewarding. I am not sure I would do it again. This is because of the opportunity cost more than the experience I had. Hong Kong is fantastic. I had a great time visiting various temples and malls. There are lots of malls. So many malls. There was lots of shopping going on. In malls. All the malls. Four story labyrinths with the largest Apple store and most opulant jewelry dealers I have ever seen. I highly recommend the islands for an escape. But if you like shopping you can find some malls.
For people that are interested in G&T development I think CTY has a lot to offer. I did think the caliber of the student would be a bit higher but they were still great students with lots of potential. And, I was allowed to develop and change the course as I saw fit. This worked out nicely for everyone.
Lastly, I want to point out, for those that are not aware, the beating the US education system takes. I travel a lot and, of course, live abroad so I hear disparaging remarks often. But it's different coming from 11 - 13 year old children. My TA Raymond, who teaches in New York, shared this story with the kids:
"Ok, I have to show something that my college students do in the US," he said as he turned to the board.
He wrote a version of this on the board:
And the students roared with laughter. There were comments like "they do what?" And, "how could they do that?"
These are accelerated students and so their perspective is different. However, this "story" stayed with them the entire three weeks. They openly mock our K-12 system while dreaming of coming to our universities. I do not have any solutions but it is embarrassing having to try to explain why we are so bad at educating ourselves. Hopefully this changes soon.