What Happened to ‘New Math’?
By: Asher Isbrucker
Tags: Education, History, Documentary, America, Mathematics

By the 1950s, the stage was set for reform. It was clear that the rapidly changing postwar world called for a new curriculum, and the convergence of pent-up frustrations with reshuffled national priorities in the 1950s sparked the true beginning of “new math.”

The first new math program began in 1951 as an experimental high school curriculum led by Max Beberman, a professor of education and gifted teacher sometimes called “the father of new math”. A visionary reformer, he believed that math should be taught more as a language than a science, considering the subject a liberal art and calling it “as creative as music, painting or sculpture.”

He encouraged students to think about problems and arrive at conclusions independently, drawing on principles of mathematics they’d learned before in order to ‘discover’ solutions for themselves — an approach he called “discovery learning,” which would become a hallmark of many ‘new math’ programs. Though his pioneering curriculum never achieved widespread adoption, in many ways his approach defined “new math” for reformers who came after.

The view of math as a creative endeavour became a core tenet of the new curriculum. Reformers were united by a desire to tear down the edifice of mathematics as a domineering, rigid, unchanging subject learned by repetitive drills in computation, believing that teachers should instead build understanding and appreciation of math’s core concepts. This approach wasn’t unanimously accepted.

Tom Lehrer: but in the new approach, as you know, the important thing is to understand what you’re doing rather than to get the right answer

But more on that later. Meanwhile, outside of the classroom, the field of mathematics had been split by a widening rift between two different approaches known as ‘applied’ and ‘pure’ mathematics.

Applied math was seen primarily as a tool, studied for its practical use in the real-world.

Chris: And for them the applications of mathematics are the key things. And so you learn mathematics in order to do physics. You learn mathematics in order to deploy statistics accurately, etc.

Pure math, on the other hand, is studied for its own sake, independent from real-world application, with a heavy emphasis on logic and deductive reasoning. ‘Pure’ mathematicians approach their field as a set of abstract, underlying ‘structures’, proving theorems generally far-removed from the physical world.

Chris: It needs to have no connection with reality at all. It’s much closer to art or to poetry than to physics.

These diverging schools of thought sparked heated debate among mathematicians as to the true nature of their field. Was math worth studying for its own sake, detached from the real world? Or was it purely practical; a tool for the applied sciences?

This division isn’t always so clear cut, and is sometimes contested by mathematicians, but in the 1950s it had a real impact on the curriculum. Pure math was often characterised by adherents as “modern mathematics” — implying that its counterpart was outdated, and that ‘pure math’ should be the basis of an updated curriculum, and the reformers agreed.

This naturally didn’t sit well with applied mathematicians, who became new math’s earliest and staunchest critics, objecting to its neglect of practical math in favour of what they called “uninspiring abstraction.”

Despite its name, ‘new math’ wasn’t particularly new mathematics — though many new math concepts were new to the classroom, they had been known for a long time. Instead, it was a new approach to teaching math, and a reshuffling of the manner and order in which it was introduced to classrooms in textbooks.

Chris: So think of the old math textbooks as you build up from the basics. And the basics would be basic arithmetic. And then you build up and eventually you put basic geometry into it and then you build up geometry and you put basic algebra and build up algebra.

The new math instead, what they wanted to start with are the structures that underlie all mathematics. And so the very first thing you learn is what is a set, and a set is a group of elements.

‘Set theory’ was one of the most pervasive new math topics, introduced in new math textbooks from K-12. The intent was to develop a better understanding of numbers as an abstract concept — portraying them as groups of objects (sets) rather than as arbitrary symbols.

Chris: And so you can start to kind of develop this intuition about numbers and about reasoning without ever talking about numbers themselves.

In new math classes, students learned modular arithmetic, used ‘frames’ to substitute for unknown values, counted using number lines, and perhaps most infamously, learned operations in number bases other than ten. The idea here was to elucidate underlying structures of math by demonstrating how it would work if, for example, we only counted up to seven — showing how place values count groups of the base number.

New math textbooks also introduced students to abstract principles of algebra like the commutative, associative, and distributive laws, (having to do with grouping and ordering operations), and were known for their precise language often criticized as pedantic — like distinguishing a ‘number’ from the numerals that represent it. In new math, students learn that these are all different ‘names’ for the number ‘seven’.

These are just a few out of many new math concepts; nearly all meant to emphasize the structure of math. But all the new material begged an important question: could students even learn it?

Chris: these reformers in the 1950s, they, of course, were concerned that their reforms were psychologically sound. They wanted to know whether their students could handle going from “two plus two is four” to thinking about sets.

… and they found reassurance in contemporary child psychology. It turned out that new math’s emphasis on ‘structure’ complemented a popular understanding of the developing mind as a set of structures, rooted in the work of psychologists Jean Piaget and Jerome Bruner.

Psychologists Jean Piaget & Jerome Bruner

Chris: the reigning idea of psychology that a lot of these reformers referred to said that, well, the reason why even a first grader can start to learn advanced mathematics is that advanced mathematics is structured the same way as the student’s mind. Of course, this is no longer the way we think about learning science, but at this one moment in time, they seemed to map on perfectly to each other.

This armed new math reformers with a psychological justification for their reforms, especially in the elementary schools. So, with some justified confidence, the reformers carried on.

As the 1950s drew to a close, such reform efforts were increasingly prioritized by the federal government. American officials were concerned about a lack of elite scientists and mathematicians, dubbed a “crisis” and seen as a matter of national security. In 1950, the National Science Foundation was established to promote scientific research and education, partially “to secure the national defense.” The NSF would bankroll the most prolific new math reforms in the sixties.

For educators and government officials, the stakes couldn’t have been higher. A 1953 issue of The Mathematics Teacher stated that “competence in mathematics widespread among our people is essential for the preservation of our society”.33 H.G. Rickover, a prominent US Navy Admiral during WWII and later a proponent for education reform, put it bluntly: “No matter what methods are chosen in the duel between the communist and the free world, education will… determine the outcome.”

Chris: The usual turning point of all this is the launch of Sputnik in 1957, the Russian satellite.

Clip: Today a new moon is in the sky: a 23-inch metal sphere placed in orbit by a Russian rocket.

With Sputnik, the world’s first artificial satellite, the Soviet Union beat America — and the rest of the world — into space. Being bested in such a dramatic manner sparked a crisis of confidence in American scientific superiority, and the flawed education system took much of the blame.

Chris: Now the failure of the curriculum became a failure in the global Cold War. And so, like many such moments, it became a really, really kind of easy excuse to flood these curricular developments with money.

And that’s exactly what happened. In 1958, Eisenhower signed the National Defense Education Act, which provided a windfall of funds for education reform initiatives, specifically in mathematics, sciences, and foreign languages. So began the “Cold War of the classrooms”.

A timeline of new math reform organisations in the 1950s.

By 1958 there were numerous organisations working on their own new math curricula, each taking a slightly different approach. One of these organisations, the School Mathematics Study Group, or SMSG, became the most influential and heavily funded organisation, and the de facto ‘leader’ of the new math movement in the 1960s.

SMSG was led by Edward Begle, a math professor spurred to action after helping his daughter with her math homework and finding her textbook “so revolting that [he] had to do something.”