Why Johnny Can’t Add Without a Calculator

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June 25 2012 6:00 AM

Why Johnny Can’t Add Without a Calculator

Technology is doing to math education what industrial agriculture did to food: making it efficient, monotonous, and low-quality.

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If you learn how to multiply 37 by 41 using a calculator, you only understand the black box. You’ll never learn how to build a better calculator that way.

Photograph by Thinkstock.

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When Longfellow Middle School in Falls Church, Va., recently renovated its classrooms, Vern Williams, who might be the best math teacher in the country, had to fight to keep his blackboard. The school was putting in new “interactive whiteboards” in every room, part of a broader effort to increase the use of technology in education. That might sound like a welcome change. But this effort, part of a nationwide trend, is undermining American education, particularly in mathematics and the sciences. It is beginning to do to our educational system what the transformation to industrial agriculture has done to our food system over the past half century: efficiently produce a deluge of cheap, empty calories.

I went to see Williams because he was famous when I was in middle school 20 years ago, at a different school in the same county. Longfellow’s teams have been state champions for 24 of the last 29 years in MathCounts, a competition for middle schoolers. Williams was the only actual teacher on a 17-member National Mathematics Advisory Panel that reported to President Bush in 2008.

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Williams doesn’t just prefer his old chalkboard to the high-tech version. His kids learn from textbooks that are decades old—not because they can’t afford new ones, but because Williams and a handful of his like-minded colleagues know the old ones are better. The school’s parent-teacher association buys them from used bookstores because the county won’t pay for them (despite the plentiful money for technology). His preferred algebra book, he says, is “in-your-face algebra. They give amazing outstanding examples. They teach the lessons.”

The modern textbooks, he says, contain hundreds of extraneous, confusing, and often outright wrong examples, instead of presenting mathematical ideas in a coherent way. The examples bloat the books to thousands of pages and disrupt the logical flow of ideas. (For instance, the standard geometry book for Fairfax County, which is used in schools around the country, tries to explain what a mathematical point is by analogy to pixels on TV screens, which are not in fact point-like.) Teachers at other schools in the county have told him that they would rather use the old books, too, but their principals would kill them. Other teachers have told me the same about new technologies—they, like Williams, think the technologies are ineffectual, but lack his courage to oppose them.

According to an October 2011 report, 89 percent of high school math teachers think their students are ready for college-level mathematics. But only 26 percent of post-secondary teachers think the students are ready once they get there.

This shortfall in mathematical preparation for college-bound students has existed for a long time, but it is being exacerbated by the increased use of technology. College-level math classes almost never use graphing calculators, while high-school classes invariably do. College professors want their students to understand abstract concepts; technology advocates claim their products help teach students such abstractions, but in practice they simply don’t.

Take the Promethean, one of the two interactive whiteboards the school uses. When I asked a Longfellow science teacher what she could do with the Promethean she couldn’t do on the blackboard, the first thing she showed me was a music video featuring a Rube Goldberg machine. She did not intend this ironically.

The second thing she showed me was a drawing of an electric circuit in which wires connect a light bulb to a battery. When the circuit was closed, the bulb lit up. This drawing goes to the heart of the technological disconnect. Her students like it when the bulb lights up, she says, because it reminds them of a video game. But this shortcut is dangerous. Learning how to visualize—as required when an electric circuit is drawn on a blackboard—is vital for developing the ability to think abstractly. You also have to make students manipulate real circuits with real batteries, with real wires that connect them and sometimes break. Showing them a toy circuit in computer software is an unhappy middle ground between these two useful teaching exercises: You neither learn how to trouble-shoot in the real world, nor do you think clearly about how electrons work.