What Happened to ‘New Math’?
‘New math’ is remembered as “a dismal mistake”, and has been called “one of the worst ideas of the 20th century” — but, to many of the brightest minds in education and mathematics, it seemed like a good idea at the time. So, where did ‘new math’ come from, and what went wrong? And sixty years later, what has it taught us about the nature of education reform?
The following is a transcript of the documentary, with a bibliography at the end.
Amidst the turmoil and change of the 1960s, an experiment was playing out in schools across America: students and teachers were opening fresh textbooks and learning “modern mathematics”, also known as “new math”.
None of the mathematics itself was particularly new. However, it was a radical new approach to teaching the subject; an ambitious attempt to modernise an outdated math curriculum with an enlightened emphasis on understanding rather than rote memorization.
Under new math, children were taught abstract, obscure mathematics previously reserved for older students; including set theory, how to count in different number bases, and that these are not “numbers”, but “numerals”.
‘The new math’ curriculum was developed in a number of countries with varying success, but it was nowhere more hotly debated — or swiftly rejected — than in America. Well-received at first,‘new math’ faced a backlash there in the mid-1960s that led to its rapid demise.
By the 1970s, new math’s reputation had cratered, and it was branded a “dismal mistake”. Time Magazine called new math “one of the worst ideas of the 20th century,” and it’s been occasionally lampooned in popular culture:
Tom Lehrer: Some of you who have small children may have perhaps been put in the embarrassing position of being unable to do your child’s arithmetic homework because of the current revolution in mathematics teaching known as the New Math…
Clip: The Incredibles 2:
Dash: That’s not the way you’re supposed to do it, dad. They want us to do it this way.
Bob: I don’t know that way. Why would they change math? Math is math. Math is math!
♬ New math, new-hoo-hoo math,
It won’t do you a bit of good to review math!
It’s so simple, so very simple,
That only a child can do it! ♬
Christopher Phillips: I think that for certain people of a certain age, everyone knows about the new math and they feel traumatized by it.
Professor Christopher Phillips wrote a book about new math.
Asher: I’m curious what got you interested in the new math to begin with? You wrote a whole book about it.
Chris: It became for me, a kind of microcosm of much bigger questions that I thought were really, really interesting.
Questions like: what role should experts have in designing the curriculum? Should mathematics be taught as a set of concrete facts and techniques to be memorized, or as an abstract logical system to be understood? And, perhaps most importantly, why should children learn math to begin with? The history of new math traces society’s evolving answers to these fundamental questions.
With new math’s spoiled reputation, it’s easy to overlook that — like many stories of historic failure — it seemed like a good idea at the time. To understand how new math went from a promising revolution of math instruction to nearly universally reviled, we need to rewind.
New math was born out of a long period of soul-searching for American education that had been churning for decades, and really came to a boil after the Second World War with what was widely considered to be a failed curriculum.
With its numerous scientific innovations, the Second World War had demonstrated the importance of science like never before. Afterwards, scientific prowess became a national priority; seen as essential not only for progress, but for survival in a race for technological supremacy between emerging global superpowers.
Math, especially, was seen in a new light; proving itself useful for more than just doing taxes or counting change. As “the language of the sciences”, mathematics could launch rockets, crack uncrackable codes, and produce the most powerful weapon the world had ever seen. It was generally understood that the postwar world would be defined by such innovations, and that mathematics would play a key role.
Meanwhile, the uses for math were also expanding. The war had advanced many novel applications for math, making the subject relevant to many more people than before.
American government and military officials knew that in order to compete with adversaries like the Soviet Union, they needed an unrivaled, state-of-the-art math curriculum; one that would prepare students to take on the unpredictable challenges of an increasingly complicated world.
The problem was, the existing curriculum was not up to that task.
Clip: America is awakening to the fact that her schools are ill-equipped for today, inadequate for the future.
There was growing concern about the state of American math education. Military officials were alarmed by basic math deficiencies among draftees during the war, requiring additional training for what they should have learned in school. Two reports on education in 1940 concluded that for many students math had been neglected, and called for a revitalized curriculum.
For one thing, the math curriculum was outdated; for the most part, K–12 math textbooks had barely changed since colonial times. The math being taught wasn’t incorrect, but outmoded, no longer adequate to prepare students for the modern world.
Chris: So in the 1930s and 40s, a lot of the math curriculum had devolved, as its critics would say, into what’s sometimes called life adjustment or progressive education.
Clip: Just what does life adjustment mean in education?
Florence Stratmeyer: To help children and youth develop the skills, the knowledge, the attitudes basic to intelligently dealing with immediate situations of everyday living.
Chris: So all of math essentially gets reduced to like business math or to measuring heights to see who’s taller like useful, but quite shallow.
The result of this trend was the general decline of rigorous school mathematics throughout the first half of the 20th century. Over this period, the percentage of high school students taking geometry and algebra fell dramatically, as more students enrolled in the simpler ‘general math’ classes. This was frustrating to many mathematicians.
Chris: Part of what they hated is that mathematics and calculation were thought to be the same thing. And mathematicians say the one thing I never do is calculate, like, why would I calculate? That’s not interesting at all.
… they wanted to say we do not want students to come away from math class thinking that this is what math is really about. These are basic skills. Sure. But it’s not really the essential bits of mathematics.
However, mathematicians didn’t have a say in how their field was portrayed in schools, since textbooks were written mostly by educators, not subject-matter experts, leading to a disconnect between school math and, well, math.
Blame also fell on how math was taught; with an emphasis on rote learning and memorization that had long been standard-fare in the math classroom. Critics considered this approach uninspiring at best, and student-repellent at worst.
There was also debate about why math was being taught. What was the point of math class — to teach a set of handy techniques useful for day-to-day life, to prepare students for college (even if they didn’t plan on going), or something else entirely?
Reformers believed that mathematics had a higher calling; that it was unique for its ability to cultivate modern, “intelligent citizens”, and to teach students how to arrive at their own conclusions, and how to think in the right way; life skills valued beyond the classroom, and especially in a democracy at odds with the rise of communism.
Chris: So one of the major questions broadly in the 1950s and 60s are what constitutes the sort of people who are democratic, free thinking Western people? The other is always the Soviets. It’s kind of the USSR versus the West.
But the idea is that the Soviet type is unthinking. It’s kind of they just take direction from above.
Clip: Communism: They are told what they must study, and held to it by inflexible discipline. They do not question.
And so if you tell them that two plus three is actually seven, they have to say that two plus three is seven.
But in the West, in this kind of sort of democratic way of learning mathematics, you still want students to know that two plus three isn’t seven. But you have to get them to know why it’s not seven instead of just saying it’s not seven, because the teacher told me.
And so math gets kind of caught up in this debate about how to get students to come to the right conclusions in the right way.
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.
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”.
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.”
What they did first was reform the high school curriculum — elementary reforms would come later — and they had their work cut out for them.
Chris: It’s really, really hard to change the school curriculum, especially in the U.S., just because every district and sometimes every school or every teacher gets to pick their own curricular materials and do things their own way.
Facing up to this challenge, SMSG assembled a coalition of mathematicians and high school teachers who got to work writing the new math textbooks.
When published, their textbooks were intentionally shoddy and paper-bound; meant to act as temporary ‘model textbooks’ to be copied and replaced by commercial publishers, with their bigger budgets and footholds in national markets; a strategy that served them well in high schools.
But all the new material presented a major hurdle: for the new textbooks to work, teachers had to be trained how to use them.
Chris: One of the fears of a lot of these reformers is that teachers themselves had not had much mathematics. And this is true to this day. And so if you’re trying to, you know, change the way the textbooks work by inserting a lot of higher level mathematics, it’s really hard to do that if the teachers themselves may not understand it.
In addition to writing textbooks, SMSG and other new math organisations mounted massive, nationwide teacher training programs in the late 50’s and early 60’s, paying teachers overtime to attend new math classes.
And so they’d be taught by some of the very best mathematicians in the country. And then the idea is that they would take back that excitement, these new ideas into the classroom and bring them to the students.
This worked well in high schools. By one estimate, at least half of the nation’s high schools were teaching some new math by the mid-1960s, rising to an estimated 85% a decade later,and the reception was, at first, generally positive.
Chris: High school new math, by and large, was a huge success. People don’t even sometimes remember that new math reformed the way high school teaching was done, because what they focus on are the elementary school math. And then that was much harder to change.
With high school reforms accomplished, and the reformers feeling pretty good about themselves, elementary school new math felt like the natural next step. Reformers believed that to effectively change how students think about math — and for math to teach them how to think properly — they needed to intervene at earlier grades, when students are first introduced to the subject.
Armed with the psychological justification of Bruner and Piaget, even more NSF funding, and perhaps a touch of hubris, SMSG began writing elementary new math textbooks in the early 1960s. And this is where things started going wrong for new math.
Elementary schools would pose especially tough resistance to the methodical, comprehensive reforms that high schools had experienced. There are a number of factors that undermined new math’s adoption in elementary schools. Perhaps the most important was the failure to adequately train elementary teachers; while roughly half of high school teachers had received new math training by 1965, just 5% of elementary school teachers had.
There were a number of reasons why so few elementary teachers were trained. For one thing, there was the sheer number of them; elementary teachers outnumbered high school teachers nationally by 8-to-1. Even with the NSF’s budget for reform programs, teacher-training was a daunting task. On top of that,
Chris: Elementary school teachers had almost no mathematics as a general rule. They had maybe one or two mathematics classes in college and there were so many of them, they couldn’t be retrained adequately. So it’s a huge logistical problem.
As generalists, elementary teachers also had little incentive to participate in exhaustive, extracurricular training for just one of several subjects they taught each day.
Elementary teachers were also rarely consulted in the design of the new curriculum, largely because they were not represented by a formal, national organisation like high school math teachers were. This failure to collaborate with elementary teachers meant they often had little understanding of the theory and reasoning behind the new curriculum, and was met with resistance because it implicitly challenged their competence and authority as educators.
There’s one more important factor here, and that’s the rushed rollout of commercial new math textbooks. While SMSG was toiling away, meticulously designing their model curriculum like they’d done in high schools, there had been a surge in demand for elementary school new math textbooks nationwide.
The reason behind this surge has to do with quirks of the school textbook market. To oversimplify a bit, in America, the textbooks adopted by just a few big states — such as California and Texas — can effectively determine the textbooks available to the rest of the country because their large populations mean they can make or break the publishers’ bottom-line.
When both of these states selected new math textbooks state-wide by 1964, publishers responded by churning out textbooks boasting new math buzzwords like ‘sets’, ‘discovery’, and ‘structure’ on their covers. One textbook executive in 1965 put it this way: “anyone not in new math can count himself out of the mathematics textbook business.”
This new math gold rush in the mid-1960s meant that the commercial publishers didn’t have time to wait for teachers to be adequately trained, or for SMSG to finish their model curriculum.
As a result, many of these commercial new math textbooks bore only a superficial resemblance to SMSG’s carefully designed curriculum,61 and they were criticized for lacking substance, including sections on the requisite new math concepts — particularly “sets” — without concern for the reasoning behind them.
All of these factors led to a rushed and uneven adoption of the new curriculum in elementary schools. Bearing the brunt of these confounding and chaotic circumstances were the teachers, who received the new curriculum with confusion and frustration, describing it as a “bomb” dropped on their classrooms. How were they supposed to effectively teach material they didn’t even properly understand themselves?
Many students were just as confused by new math,
Clip: There’s No Time for Love, Charlie Brown
Linus: New math is too much for me.
Lucy: You’ll get onto it. It just takes time.
Linus: Not me. I’ll never got onto it. How can you do new math problems with an old math mind?
Parents may have been most confused of all; frequently voicing concern over the strange, unfamiliar math homework their children were bringing home. Supplementary training materials were published to ease the transition to the new curriculum for parents and teachers, but as far as they were concerned, it was too little, too late — and the elementary curriculum had gone “too far too fast.”
By the early 1970s, the fate of new math was sealed.
After the problematic launch in elementary schools, the backlash against new math really took off. After 1965, numerous critical articles were published in the likes of Newsweek and Time, voicing concern that students of new math weren’t learning basic arithmetic.
Even some of new math’s early pioneers felt the curriculum had gone too far. One claimed that the new math’s abstract concepts “have no place in elementary school mathematics.” Max Beberman himself — the “father of new math” — spoke out against it, disturbed by the curriculum’s neglect of computation skills and inadequate teacher training.
Renowned physicist Richard Feynman, reviewing textbooks for adoption in California, criticized new math’s use of “overly pedantic, confusing” language, its emphasis on precision at the expense of clarity, and for lacking relevance and purpose.
Probably the most scathing critique of new math was a book published in 1973 by mathematician Morris Kline, called Why Johnny Can’t Add. Kline had been a staunch critic of new math since its beginnings in the 1950s, when he called it “much too difficult and, more important, thoroughly meaningless to the student.” Speaking for many applied mathematicians, Kline faulted the influence of pure math for steering the curriculum toward what he considered to be meaningless abstraction.
Vindicated by the backlash against new math, he called it an “irresponsible innovation”, and implicated the new curriculum as the cause of declining math test scores across the country. This became one of the loudest critiques of the new curriculum.
In reality, the correlation between new math and the declining scores was dubious at best. In the late sixties, test scores were declining in many subjects, not just math; likely the result of the growing number of students.77 There was even some evidence in favour of new math, indicating that in some cases it might stabilize or even improve test scores and better prepare students for college.
Such nuance was lost on popular critique, though, and this was just the beginning of the end. The sixties and early seventies experienced tectonic social, cultural, and political shifts in the wake of Watergate and the Vietnam War, which undermined public trust in the government, institutions, and technocrats.
Chris: Maybe experts after Vietnam are not the ones we should be trusting. Maybe we should instead be trusting our local pastors. We should be trusting those teachers that we know. We should be trusting our kind of local institutions, not these far away academic elite, hoity toity Harvard mathematicians who both got us into Vietnam and got us the new math.
By that time, new math had been swept up in Lyndon Johnson’s domestic reform program known as The Great Society; rebranding the curriculum as just another failed government initiative lambasted by conservatives in the late 1960s and early 1970s.
And so there’s a huge backlash against lots of these elite top-down programs.
Richard Nixon: I say it’s time to quit pouring billions of dollars into programs that have failed in the United States of America.
And the new math kind of gets caught up in that. The kind of curriculum reform, folks swing against it really intensely.
There was also a shift in belief about how math ought to be instructed, and what constituted the ‘right’ way of thinking. Instead of emphasising understanding, critics in the seventies believed that the math curriculum needed to return to its roots — to re-instill traditional values by going “back to basics” and focusing again on ‘practical’ math and computation skills.
Chris: And this becomes a rallying cry on the right in the 1970s. But the idea is that we don’t want students to be creative. We want students to be drilled and disciplined. We want them to get the right answer when we tell them the right answer.
Meanwhile, amidst the backlash, funding for new math programs like SMSG began to dry up, some of it siphoned away for the war in Vietnam. Mathematicians disentangled themselves from curriculum reform, passing the reins back to educators, and the new math reformers dispersed, moving on to address other priorities such as unequal access to high-quality education.
Chris: After they leave, there’s no one really left to defend the curriculum because the teachers, they would love to go back, in many cases, to the math they know. And then the educational reformers themselves in the 1970s are much more concerned with African-American education, with disenfranchised groups around the country, and some of the failures of liberal reforms. And so there’s no one left to defend the new math.
Despite its reputation, to classify new math as a complete failure is an oversimplification. It may not have accomplished all of its lofty goals, but new math did have a lasting impact on the curriculum — and it sparked a national conversation about education reform that continues today.
Chris: So the new math never really goes away. This is one of the dirty little secrets of the new math.
And what happens by and large, in the late 1960s, early 1970s, is that it simply just becomes a part of education.
For example, sets are still commonly discussed in math textbooks, as are other new math concepts like the ‘commutative law’ (that order doesn’t matter when adding).
Since the 1960s, the reforms haven’t stopped. New math was just the opening act of what became known as “the math wars” — an ongoing series of curricular reforms rooted in debate about how and why students should learn mathematics.
Like new math before it, “back to basics” fell out of favour in the 1980s, replaced by newly introduced ‘standards’ to act as benchmarks for math proficiency. In 2009 came the Common Core Standards with a familiar emphasis on understanding mathematics, demonstrated not just by ‘showing one’s work’ but by explaining it. Common Core has received familiar blowback from confused and frustrated parents, earning the disdainful nickname of ‘the new new math’.
Chris: There’s just a fundamental disagreement among educators about the right way to teach something. So one legacy of the new math is just a reminder that learning math is always political. One goal is learning some math, of course, but there’s a much bigger goal. And so one legacy is that debates about how we learn math are always debates about how we learn to think.
Ronald Reagan: You found that our educational system is in the grip of a crisis…
In 1983, President Reagan’s National Commission on Excellence in Education published a report ominously titled A Nation at Risk, warning that:
“… the educational foundations of our society are presently being eroded by a rising tide of mediocrity that threatens our very future as a Nation and as a people…”
This sentiment, familiar to the postwar period anxiety that led to the new math reforms, indicates the timelessness of dissatisfaction with the state of education. The report goes on to propose a possible explanation, acknowledging:
“… the multitude of often conflicting demands we have placed on our Nation’s schools and colleges. They are routinely called on to provide solutions to personal, social, and political problems that the home and other institutions either will not or cannot resolve.”
A Nation at Risk reignited familiar angst about an imperfect education system falling short of society’s countless, often conflicting expectations. It’s a persistent disappointment that ebbs and flows, but never goes away. New math, “back to basics”, A Nation at Risk, and more recent federal initiatives like No Child Left Behind and Race to the Top all trace their roots to the perceived ‘failure’ of the education system — and the reforms that came before them — to live up to the nation’s conflicting ideals.
Barack Obama: It’s clear that doing the same old things will not get the job done for our kids.
As society continues to change at a rapid clip, so, too, do our expectations of our schools, burdened with the tall order of preparing children for a world yet unknown, for a future where there is no certainty. And in the face of that, the very nature of education is up for debate.
It’s a reminder that in one crucial respect, mathematics differs from the world it describes. In the perfectly ordered universe of mathematics, regardless of how you arrive at the solution, it’s either right or wrong. Such certainty is rare in the real world. If new math taught us anything, it’s that life’s messier endeavours — like education reform — can exist somewhere between success and failure; raising many more questions than they answer.
Baker, David, et al. “One Hundred Years of Elementary School Mathematics in the United States: A Content Analysis and Cognitive Assessment of Textbooks From 1900 to 2000.” Journal for Research in Mathematics Education, vol. 41, no. 4, 2010, pp. 383–423. JSTOR.
Feynman, Richard P. “The Textbooks for the “New” Mathematics.” Engineering and Science, vol. XXVIII, no. 6, 1965, pp. 9–15. Caltech Library, http://calteches.library.caltech.edu/2362/1/feynman.pdf
Garrett, Alan W. “Mathematics Education Goes to War: Challenges and Opportunities during the Second World War.” National Council of Teachers of Mathematics, 1999.
Hartnett, Kevin. “Meet the New Math, Unlike the Old Math.” Wired, 8 October 2016, https://www.wired.com/2016/10/meet-new-math-unlike-old-math/. Accessed 4 October 2020.
Hayden, Robert W. A history of the “new math” movement in the United States. Iowa State University, 1981. Iowa State University, https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=8426&context=rtd .
Kendig, Frank. “Does new math add up?” The New York Times, 6 January 1974, https://www.nytimes.com/1974/01/06/archives/does-new-math-add-up-new-math.html.
Phillips, Christopher J. The New Math: A Political History. The University of Chicago Press, 2015