In the history of education, waves of curricular reform have swept across U.S. public schools. In nearly all instances, these waves occurred because of larger political, economic, and social issues facing the nation. One of those reform waves occurred between the late-1950s and early-1970s called “The New Math.” The trigger for the New Math (and companion tidal surges for a “New Biology” and “New Social Studies”) was the Soviet Union’s launching of the satellite called “Sputnik” in 1957.

In the then “Cold War” between the U.S. and the Soviet Union, “Sputnik” announced to U.S. policymakers that somehow Russian scientists and mathematicians were far ahead of American ones and something had to be done with K-12 and higher education curriculum and instruction to catch up. As had happened often in American schools, every national problem has as part of its solution, changing what happens in classrooms. So a “space race” ensued. Schools became a second front in the “Cold War” between the U.S. and the Soviet Union.

And that is the background for the introduction of the New Math in U.S. public schools beginning in the late-1950s and extending into the mid-1970s. As these curricular changes settled into the schools, teachers, parents, and students became key actors in the implementation of the “New Math.”

**What Was the New Math?**

Instead of memorizing rules and constant number drills as traditionally was done in elementary and secondary school math instruction, one writer described the reform this way:

*[M]athematicians and educators at universities in New York, Indiana, Massachusetts, Minnesota, and Maryland, t… 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.*

I*n 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.*

Unfortunately, both teachers and parents were unfamiliar with these new concepts and details of the “new math” thus creating difficulties in how much of it was actually taught, much less, learned.

Consider Peanuts and Lucy cartoons:

**How Many Teachers Taught the New Math?**

It is hard to say. I examined many articles and books to answer the question. What I did discover is that there was no initial plan or program to train secondary and elementary school teachers to teach the “New Math.” Keep in mind, that nearly all teachers of math, especially in elementary schools, had minimal or no training in teaching math other than having taken a few courses in college. Teachers, then, were largely unprepared for the new texts and reform rhetoric surrounding the “New Math.”

One study done in the late-1970s of U.S. schools looked at schools that had embraced the “New Math.” The researchers concluded:

*Despite the”new math” thrust, and although it is evident that the number and variety of mathematics courses offered insecondary schools has increased since 1955, there appears to be little change in mathematics instruction in grades K-12. Few efforts were made to educate elementary or secondary teachers concerning the new changes in content and methodology with the result that the single textbook is still the primary source of mathematics curricula with most teachers using no instructional materials except the texbook and chalkboard.*

In 1974, a *New York Times’*s article reported that: “…an estimated 85 percent of elementary and secondary schools in the United States teach the “New Math.” But that estimate doesn’t answer my question about how many teachers taught the “New Math” since an elementary school of 25 teachers might have two dozen teachers conducting “New Math” lessons or a quarter of the staff or only one delivering such lessons. And in secondary schools where there were math departments, one, five, or none of the teachers may have embraced the innovation.

Because of the lack of classroom data, answering the question with any confidence is beyond my grasp.

**What Did a “New Math” Lesson Look Like in Elementary and Secondary Schools?**

A few photos and YouTube videos may help answer the question:

Consider that new texts became available:

There are two YouTube videos about changes in the math curricula in high school and elementary school. They include vignettes of what occurred in classroom lessons. The videos can be found at: https://www.youtube.com/watch?v=lvEcFJANVQo

Overall, “New Math” instruction, given the limits of the data, remained teacher-centered and textbook-driven, often involving student work on a chalkboard. The “New Math”seldom triggered changes in the teacher’s familiar repertoire of techniques in delivering content and skills. Lecturing and using textbook problems to introduce new concepts and frequent drills and quizzes solidified what was learned.

**The Aftermath of the New Math**

Yes, like previous curricular reforms that rushed across America’s thousands of districts, the “New Math” had disappeared by the late-1960s. Subsequent curricular reform movements such as “Back to Basics”in the 1970s, the quest for rigorous standards following *A Nation at Risk* report in 1983, and the subsequent adoption of Common Core standards led to new curricula in both math and other academic subjects.

But a residue of the “New Math” remained in classrooms. Some teachers in some schools in some districts continued to use “new math” textbooks. As more and more of fervent “New Math” teachers retired, the curriculum reform, weakly imbedded in America’s classrooms to begin with, disappeared. In 1989 and later in 2000, the National Council of Teachers of Mathematics (NCTM) published curricular and instructional standards aligned with the movement to toughen academic standards and guide different levels of math instruction. Since 2010, the Common Core standards contain guidance for math curricula and instruction.

Nary a mention of the “New Math” appeared in these documents. Like many school reforms, it had become a footnote, an asterisk in the history of math curricula.

[Comment] When I was in sixth grade, about 1962, my class had New Math. I couldn’t stand math before that, all those boring drills, but I absolutely LOVED New Math. (I remember those thick yellow softcover textbooks with typewriter printing and special symbols drawn in by hand.) I loved learning about different number bases (and converting between base 10 and base 7, 12, etc) and how Egyptians and Mayans wrote numbers and stuff like that. It was the first time I was introduced to the notion that math could actually be fun. I have heard that the reason it was abandoned was that most teachers didn’t know how to teach it. Too bad.

Ah, Birdfriender, boosters of the New Math could have used your words then. As the post makes clear, unprepared teachers proved to be a significant factor in the demise of the New Math. Thanks for taking the time to comment.

New math is alive (unfortunately) and has morphed into realistic mathematics. And it doesn’t work!

I’d like to read more, Paul. Could you expand your comment?

Just look at the ‘work’ of Jo Boaler and the criticism of it. Also, see maybe:

https://www.cis.org.au/publication/myths-that-undermine-maths-teaching/

and by me with Dick Clark and John Sweller:

Click to access 2010-SwellerClarkKirschner.pdf

Click to access EJ909939.pdf

Many thanks, Paul. I forgot the work of Jo Boaler–my error. Will look at the other one.

I forwarded this message to another Professor Shan at National Central University in Taiwan. He is an expert in mathematics education and a member of the Mathematics Curriculum Standards Committee.

He told me that some of the material suggested by SMSG (School Mathematics Study Group) is still here in high school mathematics, such as the theory of “sets” and “vectors”. Please forgive me for being bad at math! However, I do remember learning these things when I was in high school in 1966-1969. By the way, our school system has been 6-3-3 for decades.

He also told me that one of the important members of the SMSG, Prof. Edward Begle, is from Stanford. He gave me the obituary about Prof. Begle. Please see the following website:https://www.nytimes.com/1978/03/03/archives/prof-edward-g-begle-chief-proponent-of-new-math-understanding-of.html

W. J. Shan from Taiwan

Thanks for your comment on the New Math of the 1960s and forwarding it to a colleague.

There was a fair amount of teacher training and some NSF funding. I can’t find it now, but there’s a good writeup by one of the key architects.

The set theory and distributive/commutative stuff definitely did permeate down, felt it myself in the 70s and (I think) kids still get it some. Note that Dick Feynman had an excellent critisism of the set theory stuff…said it really wasn’t key in most physics and engineering, not in the way the reformers thought it was firming up math. He was also critical of the number versus numeral distinctions as opposed to just learning more conventional arithmetic/algebra.

Hey, thanks for recalling the criticism of the “New” math of those years.