A few weeks ago, my school asked me to give a 10-minute speech to our 400 youngest students, a sort of farewell address before I return to my American homeland.
Ten minutes isn’t very long, but it is roughly 297 times their average attention span, and I didn’t want to bore them. So I asked my class of 12-year-olds: What should I talk about?
Here’s how the conversation went:
Then they sort of yelled indiscriminately for a while, which I suppose was my own fault for riling them up. You might as well feed them sugar right before bedtime.
Seeking greater pliability and innocence, I asked my class of 11-year-olds. This is how that went:
Then they spent the afternoon giggling, for which, once again, I can only blame myself.
After this, I realized what I wanted to talk to them about: them. After all, it’s not just me who finds that this age-group ping-pongs between “charmingly ungovernable” and “utterly feral.” Everybody seems to share that feeling.
The world isn’t quite sure what to do with 11-to-13-year-olds.
I’ve been having a little argument with five-years-ago me. The question is this:
Five-years-ago me? Throw his drink in your face. He’d tell you that rote thinking is the bane of his working days, that deep understanding is the whole point of learning mathematics. He’d tell you: No black boxes, ever.
Today-me is less convinced. Don’t working mathematicians, from the ground floor all the way up to Andrew Wiles, sometimes use black boxes? Isn’t it common sense that sometimes you need to use tools that you can’t build for yourself?
I’m still wary of equipping students with black boxes, but these days I’m willing to do it, so long as three conditions are met. I hesitate to share this crude checklist, knowing my colleagues out there in the profession will have wiser ways to frame the tradeoffs. (After all, aren’t checklists too binary, too black-and-white, for an idea as elusive and shaded as “understanding”?)
Nevertheless, my checklist goes something like this:
NOTE: These are 100% subjective and 110% definitive.
Historians will look back at this period and ask, “What mass lunacy gripped these people, that so many of them sought pleasure in running long distances?” Their books will have titles like “The 21st-Century Illness: How Marathons Brought Civilization on the Brink” and “26-Mile Masochism: Had They Not Heard of Cars and Bicycles?” and “Running in Giant Meaningless Circles: You Were Right All Along, Ben.” Then they will go play dodgeball, because the future is a better place.