Whatever Happened To New Math?

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An important feature of the SMSG effort was the classroom testing of its courses and a recognition that what worked for some students might not work for all. From Chicago to San Jose, from black neighborhoods to cow towns, hundreds of thousands of children became part of a vast national experiment, all driven by the need to yank the country out of its deep and dangerous math rut. I was one of those SMSG children, and I knew I was in trouble from day one.

Enrolled in public school in the ninth grade for the first time since kindergarten, I was willing to accept that this was “Protestant” math. Yet nothing the nuns had taught me—except maybe discipline in the face of the unknown—could have prepared me for my first encounter with sets. This was not math as I had experienced it. The freedom of it all scared me. Where were the rules?

My teacher kept explaining that we were learning why things were so. I just wanted to know the answers. When told that the answers and the rules would reveal themselves, I felt like the Apostle Thomas after the Resurrection—very doubtful. As we moved into number lines, positive and negative numbers, and graphing equations, I panicked. No one in my family could help. I was the youngest and the lone new-math kid. Only the patience of a wonderful tutor helped me survive.

The democratizing of new math ensured that problems like mine would be repeated, for while many parents around the country did take advantage of special training sessions (like a “space-age” closed-circuit television course for parents in Iowa, financed by the Ford Foundation), most had no such opportunity. They felt befuddled by their children’s homework and embarrassed when they couldn’t explain why 1 plus 1 didn’t always equal 2. Max Beberman might have been willing to answer telephone calls at home, but few others were. The new-math revolution that the “pied piper of mathematics” had helped create was, by the early 1960s, no longer small, confined, or in any single person’s control.

Nor were the textbooks. At the beginning of the decade, commercial textbook publishers sensed the change in math education—and the potential profits—and leaped to meet the demand. Even the UICSM textbooks, produced loose-leaf by the University of Illinois Press, went commercial in 1962.

The trick for the publishers was to figure out how radical to be. The SMSG sample texts offered a guide, but companies were free to do everything from calling the old math new to pasting new math on the old, blending the two, or joining the revolution completely. Some companies offered careful and sound efforts. Others churned out a confusing hodge-podge. Before the sixties were over, an estimated six hundred different math textbooks had gone into use around the country, from kindergarten on up.

In their haste to jump on the new-math bandwagon, school districts frequently forgot the expensive lesson that Beberman had learned: Teachers must be nurtured and retrained in new-math techniques. Many teachers balked. They didn’t understand new math or why they were supposed to teach a roundabout way to answers that rules and procedures produced instantly. And for every first-grade teacher who introduced Cuisenaire rods—colored blocks used for the tactile discovery of fractions and division—a frightened traditionalist refused to budge.

Beberman heard their distress and gamely spoke out on their behalf. He knew that if new math was taught badly because teachers were unprepared, and if drills were mistakenly abandoned as unnecessary, children would not learn basic computation. At the 1966 meeting of the National Council of Teachers of Mathematics, he condemned what was happening as an “abortion of the [new math] revolution” and suggested that a major national scandal was in the offing.

Critics, generally ignored until now, began to find their way into the same newspaper and magazine articles that had once been so effusive. Morris Kline, chairman of the mathematics department at New York University, complained the loudest and longest, charging that new math was hopelessly abstract, elitist, confusing, and impractical. (His 1974 book Why Johnny Can’t Add was considered by some to be new math’s coup de grâce .) The satirist Art Buchwald joined the fray with an essay titled “Why Parents Can’t Add.” Tom Lehrer wrote a song about new-math subtraction—a song Beberman good-naturedly previewed to make sure it was mathematically correct—with lines like “The important thing is to understand what you’re doing, not get the right answer.”

 

While no critic advocated a return to the old days, each of the barbs had just enough truth to wound. For the first time, new-math proponents faced a restless audience. Reassuringly, the CEEB made the new-math standards part of its testing program in 1965, while RCA began preparing an eight-album new-math record set.

I changed high schools that same year and took geometry the old way. Old or new, high school math seemed strenuous, not particularly practical. But I was in the minority. Before long practicality became the measure by which all new math was judged. Applications—balancing a checkbook, paying your taxes—were something parents understood, and teachers ignored them at their peril. As Kline wrote, “Math serves ends and purposes and should be applied to show what it can accomplish.”