1, 2, 4,…. What’s the next number in the sequence? I was a rule-follower as a kid, so I always got the “right” answer on questions like that, but they still bugged me. Sure, 8 would be predictable, but why couldn’t it be 7, 9, or 34 million, for that matter? It seemed like we were making an awful lot of assumptions about how sequences were going to behave without much evidence. Pattern recognition is an important part of doing math, but so is the skepticism that made me feel uneasy when I predicted what a sequence would do based on just a few beginning terms. Owen Elton describes why any answer would be “correct” using one of those awful Facebook “only 1 in a thousand will get it” math riddles that pops up every now and then.
Christopher Danielson’s book Which One Doesn’t Belong and Mary Bourassa’s blog of the same name would have been great for me as a kid. Each page in the book is a set of four shapes, and you have to say which one doesn’t belong. But any answer can be “right.” Each prompt can start a discussion of what traits the shapes/numbers/graphs have in common and do not. Instead of learning the one right answer and moving on, kids can discuss which answers jumped out at them and why. They can have open-ended conversations about math rather than just trying to find the one right answer.
I’ve seen posts about #wodb all over the #MTBoS, so I won’t even try to link to everyone who’s talked about using these prompts in the classroom, but I do want to mention Tracy Zager, who has a thoughtful post about using “which one doesn’t belong” in a second-grade classroom and the way open-ended math discussions can get both students and teachers thinking about what math words mean.
Danielson also writes the blog Talking Math with Your Kids, which aims to foster mathematical reasoning skills in early childhood by helping parents have low-stress conversations about math with their kids. Yes, please!
Helping parents have low-stress conversations about math with their kids is the aim of Bedtime Math, an app and blog. Each day it gives parents a fun prompt and some questions to start the discussion. I also love reading Malke Rosenfeld (currently blogging at Math in Unexpected Spaces) and Mike Lawler of Mike’s Math Page, who talk to their kids about math a lot. (I got nerdsniped yesterday by a fun area question from Lawler’s blog.)
I don’t have kids, so I’m mostly a bystander in talking math with kids, but I do have two young goddaughters. When we get together, we often count things together, and I hope as they grow up, I can keep talking with them about math in ways that are age-appropriate and fun. Reading blogs like Danielson’s, Zager’s, Rosenfeld’s, and Lawler’s and following the #tmwyk hashtag on Twitter are helpful for me when I’m thinking about how to talk with my goddaughters about math. I’m also partial to the #wodb hashtag. It’s just fun to see the cool mathematical “which one doesn’t belong” pictures created by both students and teachers. I’m hoping that in a few years, my goddaughters and I will be making some of them for ourselves.