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Kent HainesI loved the entire section on the mittens problem, but one moment that struck me in particular was when Maya brought up the problem, unprompted, a week later and shared a new mathematical idea.
We often talk about giving kids openmiddle problems in math class as a way to improve engagement and intrinsic motivation. I agree with all of that and have seen it in my classroom. But I think this vignette about Maya shows another benefit of asking open questions: Kids spend more time doing math than they otherwise would.
When I was a kid, I remember one day when we spent math class hunting for $1 Words. We changed every letter in a word to the number that matched its place in the alphabet (A=1, B=2, C=3 etc) and then added the digits. If we got a perfect 100, that was a $1 Word. My name, Kent, (11 + 5 + 14 + 20) is sadly not worth a dollar.
Since that lesson in 3rd grade, I have spent countless hours idly converting letters to numbers and adding them. As a kid I would do this on long road trips, searching billboards and bumper stickers for those perfect words. I still do this when trapped in a PD session that I hate.
Because of this habit, I’ve done thousands and thousands of addition problems, many more than I was ever expected to do in math classes. I was always seen as a kid who just “got math” in school, but maybe I’m just a kid who spent more time than everyone else doing math. You want to find the best piano player in your school? Find the kid who has spent the most hours playing the piano.
All of that to say, Maya showed in that moment that she was one of those kids who thinks about math for fun. She’s the type to solve a problem and then keep gnawing on it at home, in bed, at dinner, and then notice something new.
But I don’t think Maya is special in that regard, and I don’t think I am either. I think that just about any kid will chew on a mathematical idea if they are given an interesting reason to do so. I’ve already seen it with my 4 year old son, who routinely brings up old math questions I’ve asked him (How can you show me eight fingers?) with new insights (There’s 4 and 4, but there’s also 5 and 3!)
So this is one of my goals, as a parent and as a teacher. Give my kids experiences with math that are perplexing and engaging, so that when their minds wander, they wander in a mathematical direction. Because every minute they spend daydreaming about math is like playing another scale on the piano. Bit by bit, they’re learning how to play a sonata.

Kent,
Thank you so much for sharing these thoughts. I think you’re really on to something. It’s complicated too, because I know Maya’s spending those hundreds and thousands of hours doing math, and so the gap widens. Part of addressing access and equity needs to be getting into kids’ heads so they too are doing lots of math outside the math block. That sounds really hard. Worth doing though.
Tracy

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