Math Misadventures With the Common Core

The Common Core makes for strange bedfellows.  I found myself resonating with Mark Rice who wrote about the Common Core at The Huffington Post; a publication where I rarely agree with commentary provided.  Rice is a professor and chair of the Department of American Studies at St. John Fisher College in Rochester, NY.  Rice wrote about his 8-year-old daughter who was struggling with math.

The Common Core might turn out to be one of the best reforms in K-12 education in decades. It’s all still pretty new and its cumulative impact on the intellectual development of students might turn out to be a great thing. What I know right now, though, is that it is asking third graders to approach math in ways that seem terribly unsuited to them.

I don’t just mean things like the worksheet that included a rectangle divided into six sections with written instructions asking students to shade one-fifth of it…

No, I’m not talking about the typographical error on an official New York State Common Core third-grade math worksheet, though such a boneheaded mistake does little to inspire confidence.

What I mean by math problems unsuited to third-graders are ones that go something like this: Two kids are served brownies. One kid, “Julian,” eats one-half of a small brownie and the other kid, “Debbie,” eats one-eighth of a big brownie. Julian claims that he ate more than Debbie (because one-half is more than one-eighth). The students are asked to explain why Julian’s claim is false, using words and pictures, and then use words and pictures to make that supposedly false statement into a true statement.

I guess that what the students are supposed to realize is that because the brownies are different sizes (though what kind of adult would cut unequal-sized brownies for kids?), one-half isn’t necessarily bigger than one-eighth. That’s true, but without knowing the size of each brownie, there really isn’t enough information to determine which brownie piece is bigger. Maybe Julian really did eat more than Debbie.

More to the point though, is this question: How in the world is that problem supposed to help a third-grader learn fractions? Third-graders are concrete thinkers and they are just learning the basics of fractions. Why throw in a poorly-written word problem that asks them to explain an abstract concept such as the idea that one-eighth of a larger whole may be bigger than one-half of a smaller whole? Until they fully understand the basics of halves and eighths — and unless there is a picture showing the relative sizes of each whole — such abstractions only muddy the waters of learning.

Then there is the problem of dividing a “whole” into two “halves,” calling each half a new whole, and then asking the students to divide the new whole into new halves. My daughter looked at the problem and she knew that she wasn’t seeing two new wholes. She was seeing two halves of the original whole that still stared back her from the page.