The open secret of math is that the hardest thing to do in it is count. -Andrei Zelevinsky

Last night I had the extraordinary privilege of teaching my first Math Circle class, to a group of 9- to 12-year-olds at Harvard. I think they had a blast. I KNOW I had a blast. The theme is counting, and we started out by discovering that all our names turned out to be four letters long. We then counted up the squares in this figure,

and once they settled that, we spent the rest of the hour following a diagonal. We came up with several good conjectures on the diagonal problem, and I’m very excited for next week; I expect they’ll nail it. There were a lot of great victories along the way—the youngest in the room really wanted to use fractions, and found a way when we had to enumerate different sizes of square—but the one that pointed the way forward for the rest of the course was when they confidently told me that the diagonal of a 1 million-by-1 million square would pass through 1 million grid cells. I pointed out that they had just effectively counted 1 million things in a couple of seconds. I thought that was cool. I hope they thought it was cool. I think they did.

I’m also excited for what this might teach me about my high school students. In this little laboratory where I’ve controlled out teenage apathy and uneven experience with algebra, I’ll be interested to see how natural it is (or isn’t) to start using abstractions and symbols. Great fun!