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Which One Doesn’t Belong? A Shapes Book and Teacher’s Guide, by Christopher Danielson

From The Objective Standard, Vol. 11, No. 4.

dw-shapes

Which One Doesn’t Belong? A Shapes Book and Teacher’s Guide, by Christopher Danielson. Portland, ME: Stenhouse Publishers, 2016. 111 pp. $33.33

Earlier this year, at an annual meeting for math teachers, Dan Meyer gave a fascinating talk on how to get children to love and succeed at mathematics.1 The talk was fascinating in part because it challenged some popular pedagogical views. Meyer observed, for example, the futility of trying to motivate students by merely identifying mathematical relationships in nature, or saying that math will be useful in their future careers, or formulating word problems with objects to which students might relate. By themselves, said Meyer, such tactics fail to interest many students in math and can even turn them off to the subject.

Most of all, however, the talk was fascinating because it offered positive ways to engage children in an immensely useful subject. Among other things, it showed the importance of not starting formally, with precise definitions about something very abstract, but rather of starting informally, with something perceptual that raises interesting questions and gets students wondering and debating about what the answers might be.

The process Meyer advocated does not ignore the more careful measurements or more precise definitions that help ultimately to answer questions raised. Rather, it saves those for later, focusing initially on ensuring that students become interested not only in the answers but also in the journey toward their discovery.

Since hearing this talk, I’ve been implementing the ideas with my son, and I’ve been on the lookout for resources that might be of assistance. One of the best resources I have found is Which One Doesn’t Belong? A Shapes Book and Teacher’s Guide by Christopher Danielson.

As its title suggests, the book presents sets of shapes and asks of each, which shape is different from the others in the set. There are other shape-comparison books on the market, but this one involves an important difference. As Danielson explains:

In this book, the question “Which one doesn’t belong?” is ambiguous: there isn’t just one answer. In fact, any one of the shapes on any one of the pages can be the one that doesn’t belong. All choices are correct, which shifts the focus to justification. Which One Doesn’t Belong? isn’t about guessing the right answer; it’s about expressing mathematical relationships precisely in order to communicate with others. (p. 3)

One of the pages, for example, has a small blue square in the upper left, a large red square in the upper right, a small red square sitting on one of its corners in the lower left, and a small red rectangle in the lower right. Which one doesn’t belong? Well, that depends on whom you ask—and what he focuses on. . . .

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Endnotes

1. http://blog.mrmeyer.com/2016/nctm16-beyond-relevance-real-world-stronger-strategies-for-student-engagement/.