# Whatever Happened To New Math?

## In the early sixties it was going to revolutionize American education. By the early seventies it had confounded a generation of schoolchildren. Today it is virtually forgotten. But as we head toward another round of educational reforms, we should recall why it went wrong.

December 1990 | Volume 41, Issue 8

Its founding fathers are dead, its disciples scattered, its millions long spent. Yet countless Americans still carry the revolutionary message of new math in their memories, if not always close to their hearts. Now in their mid-thirties or forties, these “new math kids,” myself among them, were part of a learning crusade that in the 1950s and 1960s marched through schools across the nation. For many of us, new math was a disaster; for others, a godsend.

Before the results could even be measured, new math became a near religion, complete with its own high priests and heresies. Chief among the hierophants were the University of Illinois’s Max Beberman and Stanford’s Edward Begle. Together with mathematicians and educators at universities in New York, Indiana, Massachusetts, Minnesota, and Maryland, they took aim at the mindless rigidity of traditional mathematics. They argued that math could be exciting if it showed children the whys of problem solving rather than just the hows. Memorization and rote were wrong. Discovery, deduction, and limited drill were the best routes to arithmetical mastery.

In practice, this meant learning how different number systems worked, that the number 9 in the decimal, or base ten, system would be the number 100 in base three. It meant learning about the set, a grouping of things: a beach as a “set” of grains of sand, for example. It meant learning the difference between a number like 7 and its representation the numeral, which could be expressed many different ways—21 minus 14, 7 times 1, VII. It meant learning to draw rulerlike number lines and divide them into sections to discover fractional multiplication. It meant learning about frames—boxlike symbols used as substitutes for the x, y, z ’s of algebra. It meant learning a new language with terms like open sentence, complementation , and truth set . It meant, in essence, learning to discover the hidden patterns in mathematics before knowing what they were called and reasoning out solutions before knowing rules—all at an earlier age than had ever been attempted before.

Beberman also urged a conceptual overhaul of math education. Mathematics should be taught as a language, he said. And like language, it should be considered a liberal art, a key to clear thinking, and a logic for solving social as well as scientific problems.

No educational proposal, before or since, has won such wide and quick acceptance. PTAs, politicians, and textbook publishers stumbled over one another to endorse the new approach to what was probably the worst-taught subject in American schools. Many high school teachers also were ecstatic, even though new math required that they work harder, perhaps retrain, and drop the drill sergeant’s mask for that of the muse. When the Soviets launched Sputnik, in 1957, the small new-math experiment, previously confined to a few score schools, became a national obsession. Parents went to night school to learn the new approach. The press hailed the reformers as the guiding geniuses of the most important curriculum change since Pythagoras.

By the mid-1960s more than half the nation’s high schools had adopted some form of the new-math curriculum. The figure jumped to an estimated 85 percent of all schools, kindergarten through grade twelve, a decade later. As Robert Davis, founder of the elementary-school program known as the Madison Project and now a professor at Rutgers University, said at the time, “U.S. math literacy can no longer be a matter of God and heredity.”

Now, almost thirty years later, we are hearing the saune lament about our mathematical skills and the same call for educational mobilization. Why? Where did new math go? And what happened to all those schoolchildren ready to experience, as one writer called it, “the wonder of why”?

If they were, like me, high school freshmen in 1964, they may have developed a lifelong aversion to anything associated with new math. Or they may have gone on to become brilliant mathematicians. The differences in experience and outcomes were as varied as the nation’s geography and, most important, only as good as the teachers. But what new math became is not what it was intended to be. In fact, there never was just one new math.

The need for curriculum change was apparent to educators everywhere after World War II. Wartime experience had shown that many high school graduates were too illiterate in math to be trained in radar and navigation. Scientific discoveries and new technology made such illiteracy a threat to America’s future.

Yet everywhere would-be reformers looked, orthodoxy reigned. Population growth and a national shortage of mathematics teachers had forced everyone from coaches to homemaking instructors to the blackboard. Few distinguished themselves. Often inadequately trained, these teachers relied heavily on rules-and-rote textbooks that in many ways had changed little since colonial times. Mathematics was presented not as a human enterprise but as a static subject about which everything was known, including a handy bag of computational tricks—like “carrying” and “borrowing” numbers. (Borrow from where?)