I’m hard at work on the post I promised over a month ago on the history of algebra, which turned into a whole research project. In the meantime, a shout out:
I met Sam Coskey and Avital Oliver on a Chinatown bus from New York to Boston. All three of us were taking the day to go visit Bob and Ellen Kaplan’s math circle in Cambridge, MA. Avital and I had independently read Out of the Labyrinth and were excited enough about it to contact the Kaplans and ask to visit.
There I was, on the bus with two strangers, united by an interest in math education taking place outside the timeline and curricular demands of school. What was it like?
Avital is not professionally an educator but he is as intense and passionate about math education as anyone I know. He and Sam met in the math department at Rutgers. I am a little vague on the details of the story but after Sam finished his PhD they were both in NYC and started up The School of Mathematics: Avital rented an artist studio in a basement in Fort Greene, Brooklyn, they outfitted it as a (very alt/boho-feeling) classroom, and started holding free math classes on Saturday mornings for all comers. As I described before, these sessions always start with a simple, usually elementary-level question. Then they go wherever the participants take them. Sam and Avital’s roles are felt more than seen: every time I’ve been present, the conversation has magically turned into a deep exploration of important content (why do triangles with congruent angles have proportional sides? how would you write down numbers if you forgot the usual way? why do parallelograms with equal base and height have equal area? why is multiplication associative?), without being visibly directed almost at all.
Anyway, on the bus, after hearing what they were up to, I found myself in an intense conversation with Avital about the nature of mathematics and the purpose of math education. I had spent the prior year and a half rediscovering my own relationship with math by working page-by-page and problem-by-problem through Michael Artin’s Algebra textbook (which is awesome, btw). I was having my mind completely blown by algebra and was really excited about it. I had also started to be certain that I wanted my professional life to be concerned with giving students the opportunity to have an experience akin to the experience I was having. I saw that experience as being defined by rigorous but creative play in an imaginative wonderland (the mathematical universe). I described this as my goal. Enticing students into this wonderland by setting them up to see some really intriguing patterns, images, and connections, was my plan to accomplish it.
Avital said, “that’s not mathematics.” What was it then? “Some sort of pied-piper, luring-them-in-with-candy typed thing.” (I’m paraphrasing since I can’t remember exactly, but this is the idea.) To Avital, it’s not mathematics unless you’re trying to answer a question you already had. You’re not teaching mathematics unless you’re working with people to build tools to find answers they already wanted. (I’m sure you’ll recognize the spirit of this point of view in the work of Dan Meyer and Shawn Cornally, but Avital is the most uncompromising purveyor of it I’ve come across.)
It’s not like I was converted on the spot – oh, never mind, yeah, I’ll forget my whole plan and start over. But it’s been deeply valuable to me over and over again to put to myself “Avital’s challenge”: say an idea is beautiful and I want you to see this. What question could we entertain that would make this idea necessary? And why would you want to answer this question? How could I get you interested in this question? And, if the notion of you being interested feels at all strained, maybe this is not the idea I should be leading you to.
I think with that conversation Avital has won my personal “most influential conversation with a stranger on a bus” prize.
Avital moved to Israel last summer, and Sam took over leading the School of Math, which he does really beautifully. Sam is leaving NYC as well at the end of this academic year. The future of the School is unclear. So, if you live in NYC, you might want to check it out before the end of May. Classes are on Saturdays and start at 11. This coming saturday, Avital is briefly back in town from Israel, so this might be a good one to be there for.