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Real-Life Math and Teacher Training: Cures for 'Innumeracy'?

The United States has produced inspiring, fresh ways to teach math, but has dropped the ball on implementing them.

That's a key message of a New York Times magazine piece that's making the rounds. It tells the story of a Japanese teacher who found success using radical teaching methods inspired by American "reformers." But he was shocked to find when he moved here that U.S. math teachers weren't using the methods themselves.

The article is adapted from a forthcoming book, Building a Better Teacher, by Elizabeth Green, chief executive of Chalkbeat. Green writes: 

It wasn't the first time that Americans had dreamed up a better way to teach math and then failed to implement it. The same pattern played out in the 1960s, when schools gripped by a post-Sputnik inferiority complex unveiled an ambitious 'new math,' only to find, a few years later, that nothing actually changed. ... The trouble always starts when teachers are told to put innovative ideas into practice without much guidance on how to do it. In the hands of unprepared teachers, the reforms turn to nonsense, perplexing students more than helping them. 

This scenario, she goes on to say, is playing out again with the Common Core State Standards in math. While the standards are well-intended, she reports, the teacher training so far has been "weak and infrequent," and principals are unprepared to provide support. And despite labels claiming common-core alignment, many textbooks haven't undergone substantial changes, Green writes.

Math Sense-Making

Working from the premise that Americans suffer from "innumeracy" (which plenty of readers are likely to take issue with), Green lays out what that "better way to teach math" looks like. It's a combination of what the Japanese teacher learned from the National Council of Teachers of Mathematics and other reformers in the 1980s and what the common-core standards are trying to do.

Students should learn math in a way that mimics what they do in real life. Teachers should move from encouraging "answer-getting"—memorizing procedures and algorithms—to focusing on "sense-making"—letting students struggle through problems and make mistakes, so that they'll come to understand the "whys" of math on their own.

There are numerous (pun intended) champions of this approach. Three years ago, I wrote about Dan Meyer, a math educator who presented a widely viewed TED Talk on why sense-making is so crucial and how to use it in the math classroom. And as I wrote in March, many teachers are beginning to rethink how they present new concepts—for instance, through inquiry rather than memorization—under the common-core standards. (Though as Bill McCallum, a lead writer of the math standards, recently told me, the emphasis on conceptual understanding doesn't mean students shouldn't also memorize procedures.) In fact, every time I write about this, I get comments from teachers who say they've been teaching this way all along.

However, the first step toward better math teaching for all is better professional development. "Left to their own devices, teachers are once again trying to incorporate new ideas into old scripts, often botching them in the process," Green writes. "No wonder parents and some mathematicians denigrate the reforms as 'fuzzy math.' In the warped way untrained teachers interpret them, they are fuzzy."

New standards themselves, no matter how much emphasis they put on conceptual understanding, will not be the change that improves our country's math skills, she argues. But new standards plus better training could do the trick. 

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