A History of the New Math (and lessons for CS Ed)

Spines of New Math paperbacks from the 1960s (courtesy wikimedia.org)

Spines of New Math paperbacks from the 1960s (courtesy wikimedia.org)

Many of us remember the New Math from personal experience. I do from elementary school in the 1970s in West Hurley, NY.

I loved it. I learned that the decimal system is arbitrary and numbers could be expressed in any base. That was fascinating.

Of course, I was the kid who learned his times tables for fun.

The New Math emphasized understanding the rule-systems that underlie numbers. In elementary school, it constructed the very concept of number with set theory rather than by rote counting.

There wasn’t a focus on students being able to do arithmetic computations. This upset people, and by the 1970s, the New Math was under attack.

The “back to basics” movement re-established an emphasis on computations in the 1980s.

As described by Christopher J. Phillips in his book The New Math: A Political History (The University of Chicago Press, 2015), it’s not a coincidence that this is the same decade in which the country elected Ronald Reagan as president.

Phillips cogently makes the case that the rise and fall of the New Math movement traces our cultural mores and larger political beliefs about who should be making decisions in our society.

Going back two thousand years, Phillips shows how the argument about how mathematics should be taught has been a proxy for a conversation about how people should be taught to think.

For the developers of the New Math, their approach would help American citizens be critical and creative thinkers—what was required to counter the Cold War threat of a dominant Soviet Union.

Indeed, the federal funding that was leveraged in the 1950s to build the New Math movement was appropriated as literally a matter of national defense. This was followed by the Elementary and Secondary Education Act in the 1960s, which continued the federal government’s role in fostering national education curricula.

The consensus that the federal government should be deciding what’s taught in our nation’s schools frayed with the cultural changes in the 1960s and collapsed with the horrors of Vietnam in the 1970s.

As we work towards making computer science a first-class citizen in the pantheon of school teaching and learning, what lessons can we draw from the rise and fall of the New Math?

Computer science is a liberal art—not just a vocational skill. It’s true that becoming accomplished as a software developer is a path to a good career, including good pay. And it’s true that there is a social justice dimension to broadening participation in computing—everyone should discover whether they love computing and then have access to these career paths.

But the reason to institutionalize computer science in K-12 is deeper than that. It’s because computing is beautiful and powerful—like all forms of knowing and doing.

We must go beyond the zero-sum game. One of our big challenges is creating time for teaching and learning computing. We don’t want to create winners (computer science) and losers (other areas of study).

It seems clear that infusion approaches—integrating computing into other subjects—will be an important part of the future.

It’s a team effort. One of the big take-aways from Phillips’ book was the reach of the School Mathematics Study Group—the organization that was created to develop and support the New Math. Curriculum writers from all over the country were involved in creating the reference texts; these individuals then served in leadership roles in the adoptions in their home states.

Most importantly, now we live in a time where everyone’s involved in curriculum decisions, particularly parents.

We need everyone together to make this happen.

P.S. I highly recommend Christopher Phillips’ book. His writing is clean and compelling, and the story is engaging and compact. He also published an essay-length version of his thesis in the New York Times on December 3, 2015.

8 thoughts on “A History of the New Math (and lessons for CS Ed)

  1. Hi, Fred,

    Excellent points about the political aspects of the New Math movement. I didn’t even add it up (in decimal or binary) that the Back to Basics movement was (and still is) encouraged by the political establishment that understands an educationally limited electorate is in their best interest.

    I was a math teacher and now I’m a vocal advocate of computer use in math classrooms. I wrote a book, Hacking Math Class with Python to promote that idea. Every day I speak with somebody who works for an institution whose website is full of words like “progressive,” “innovative,” even “revolutionary” but whose conditioning and fear get them a math class indistinguishable from those in the 1800s except for whiteboards instead of blackboards.

    You’re right, we CS types need to learn from the fate of the New Math movement. I’ll check out Phillips’ book.


    Peter Farrell

  2. Fred, Great post! I, too, am a child of the New Math which ultimately led me to a math degree and a love of number theory. The New Math is, naturally, one of the foundations of my AP Computer Science class. Twenty years of students have now heard me exhort them to “Give Fibonacci his due but let’s move on to Gauss!” They seem to tolerate it well. Let’s hope that computer science will, at some point, find a place in the math curriculum of our high schools, a place where I have always believed it belongs. Thanks again! David

  3. Ah, yes! I remember (and also loved) the New Math. If we know *why* something works, we don’t have to rely so much on memorizing it, because we can recreate it if we forget it. (I’m not referring to multiplication facts — it’s just silly to have to reconstruct those every time we need them.) But New Math probably went a bit too far in expecting all kids to understand all of the “whys,” which are sometimes be more challenging than rote learning.

    I remember that our Algebra I textbook included the derivation of the quadratic formula. (I could “sort of” follow it, but I certainly couldn’t have reproduced it at that point.) I’m sure it was included for enrichment — it was on a couple of pages with a different-colored background — and I don’t remember our teacher even mentioning it. (And I’m willing to bet that most of my classmates have no recollection at all of having seen that in the textbook. Only a true math geek would have taken note.)

    But I wish that, instead of throwing it all out, the “powers that be” had kept more of the core ideas of New Math (teaching the “whys,” set theory, etc.) I often see Venn diagrams used to explain all sorts of things — and not just in math and science — they give simple visual depictions of systems of things or ideas. Maybe they’re primarily in publications written by baby boomers, for whom they’re second nature. But when do today’s kids learn about them? They’re not in the Common Core Math Standards, which include the word “union” only once, in the context of probability. “Data sets” and “solution sets” are mentioned several times, but “intersection” is usually in the physical sense (as in the intersection of lines or curves).

  4. I would like to speak uniquely to this as someone who has degrees in mathematics, computer science, and math/CS Education. I also have experience both as a teacher and as a mathematical software developer. And I was taught the new math.

    I also loved the new math. But I *should* have loved the new math. The new math was great for the kids who are gifted in those areas. For those who were not so gifted, it was a little obtuse. In the era of the new math, we produced some great mathematicians, and also some frustrated students and parents.

    The problem is not the new math/old math. The problem is trying to use a “one size fits all” approach to education.

    Quite honestly, I worry about trying to force computer science education on children who are struggling to learn basic math.

    I learned computer science at age 12 when my father handed me a BASIC manual. He was teaching CS in high school at the time. Was I hungry for it? Certainly. I learned from a dry textbook with little access to a computer. And when I did have access, it was through a teletype machine with no screen.

    Should we be teaching CS at a younger age? Yes. Should we improve access? Yes.

    But we have to look at every child individually and try to move that child toward a better future. Certainly give every child opportunity, but focus on providing what each child needs at that moment.

    • Gosh, this was a great post. I, 2, was a child of new math … all of my books in HS (’67) were paperbacks with SMSG on the back. But enough history… I really liked what you said about the differentiation of kids. At our school , an urban and diverse school in KY, we have a four year sequence that includes Intro to CS, Python, CSP and AP CS A – JAVA. I teach all but the JAVA. Some of our kids crave what we offer and some crave to get out. Our biggest problem is that once a student is in our track it is hard for them to leave (and for others to get in). The two of us that run this program struggle with how to best offer CS to everyone in a fitting fashion and still deal with pretty large numbers of kids. So your last line about focusing on what each child needs at the moment is compelling… Thanks

  5. Fascinating and useful history lesson! Yet while New Math may have disappeared from curricula – perhaps for being too radical — efforts to reform math education have continued, and the pendulum swings back and forth. When I was teaching middle school math in the early 2000s, the curriculum materials changed 3 times during the 4 years I taught in NYC. We went from a very “progressive” curriculum called Math in Context to a more traditional Houghton-Mifflin textbook, and to a “middle-of-the-road” program called Impact Mathematics. So perhaps this lesson from history is to recognize the swings between efforts to reform and efforts to react / pull back.

    Another important factor in reform efforts is buy-in. Perhaps the New Math and other previous reforms also failed due to lack of investment in getting stakeholders like teachers and parents to buy into it. Institutions like schools don’t react well to sudden changes. If teachers are forced to teach new material in a new way, they will likely try to stuff the new content into old ways, or give it a try, perhaps have a bad or mixed experience, and say that the old materials / old ways are better. Only a few would naturally emerge with new vision and new attitudes + beliefs.

    When I was a younger teacher trying to teach math in a way I didn’t learn, it took some very intensive PD for me to get those a-ha moments to realize why this new way of teaching and learning is so potentially powerful. Yet it was also fraught with risks because it meant transforming the school and classroom culture and leaving well-trod paths of traditional ways of interactions between learners, a recasting of my teaching role, etc. Students resisted it, or misunderstood, or took advantage of my struggles and experimentation. Sadly, the experiment ended with the change of the superintendent and the rise of high-stakes standarized testing.

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