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.
Which space named after Polish mathematician Wacław Sierpiński doesn’t belong? Image: Evelyn Lamb, based on images by Beojan Stanislau, Johannes Rössel, George Hart, and Tai-Danae Bradley.
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.
IQ test always worried me with the “which one doesn’t belong’ questions. You could usually find at least two perfect sensible and obvious answers. eg 3 curved shapes and one straight-sided figure (odd one out the straight sided figure) but, at the same time, 3 of the shapes filled in with black and one left in outline. (the outline figure), Then sometimes to complicate it even more maybe 3 would have bilateral summetry, and one quadrilateral symmetry, etc. I always thought is just showed how dumb the IQ test setters were!
The way I would approach this in a math class I was teaching would be to have my students discuss what the next term would be. The obvious answers are that the sequence is geometric with 2n or that it’s an arithmetic sequence where you add n to each term where n is the number the term is in the sequence. This would mean that the obvious next terms would be 8 or 7. However, I wouldn’t tell my students this. I would have them try and figure it out for themselves. In my opinion it’s best to not just give the answer, but promote mathematical thinking and the process behind it. I think it’s more important for students to understand the process so they can replicate the problem with different numbers and come up with a sensible answer. That way they truly understand the problem instead of just knowing the answer. In mathematics understanding the process is more important than just understanding the answer.