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The New Math: A Political History
An era of sweeping cultural change in America, the postwar years saw the rise of beatniks and hippies, the birth of feminism, and the release of the first video game. It was also the era of new math. Introduced to US schools in the late 1950s and 1960s, the new math was a curricular answer to Cold War fears of American intellectual inadequacy. In the age of Sputnik and increasingly sophisticated technological systems and machines, math class came to be viewed as a crucial component of the education of intelligent, virtuous citizens who would be able to compete on a global scale.
In this history, Christopher J. Phillips examines the rise and fall of the new math as a marker of the period’s political and social ferment. Neither the new math curriculum designers nor its diverse legions of supporters concentrated on whether the new math would improve students’ calculation ability. Rather, they felt the new math would train children to think in the right way, instilling in students a set of mental habits that might better prepare them to be citizens of modern society―a world of complex challenges, rapid technological change, and unforeseeable futures. While Phillips grounds his argument in shifting perceptions of intellectual discipline and the underlying nature of mathematical knowledge, he also touches on long-standing debates over the place and relevance of mathematics in liberal education. And in so doing, he explores the essence of what it means to be an intelligent American―by the numbers.
In this history, Christopher J. Phillips examines the rise and fall of the new math as a marker of the period’s political and social ferment. Neither the new math curriculum designers nor its diverse legions of supporters concentrated on whether the new math would improve students’ calculation ability. Rather, they felt the new math would train children to think in the right way, instilling in students a set of mental habits that might better prepare them to be citizens of modern society―a world of complex challenges, rapid technological change, and unforeseeable futures. While Phillips grounds his argument in shifting perceptions of intellectual discipline and the underlying nature of mathematical knowledge, he also touches on long-standing debates over the place and relevance of mathematics in liberal education. And in so doing, he explores the essence of what it means to be an intelligent American―by the numbers.
224 pages, Hardcover
First published November 7, 2014
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February 20, 2025I'd heard the standard narrative about New Math.
It was an ambitious new curriculum, driving at real conceptual understanding. But it spread too fast to classrooms, where unready teachers made a hash of it. The project thus soured from "well-meaning reform" to "roundly mocked fiasco."
This narrative isn't wholly wrong. But Phillips enriches and complicates it in three ways.
1. What was New Math?
First, he illuminates exactly what new math was. Top-down, federally funded, and led by professional mathematicians, its goal was not "conceptual understanding" per se. The hope was to inculcate a special kind of thinking, characteristic of modern math: reasoning about abstract structures and logical systems. This kind of thinking, reformers argued, was what the U.S. needed to defeat the USSR in the so-called "cold war of the classrooms."
2. Primary vs. Secondary
Second, Phillips separates primary (K-6) and secondary (7-12) grades, because the two stories differ sharply.
In middle and high schools, new math was pretty much a success. Mathematicians and teachers wrote the curriculum together, in big, collaborative, NSF-funded teams. They produced model textbooks (which helped to seed the commercial textbook market) and wove together networks of teachers to advocate for the new curriculum. By 1965 almost half of math teachers had received training in the new approach. New Math lives on in high school textbooks today.
The fiasco was at the primary level. Classroom teachers contributed almost nothing to the curriculum, and were not impressed or pleased when the new textbooks landed. A grassroots "back to basics" backlash formed, and won the day. Also, although Phillips is restrained in his evaluation, the primary-level materials seem pretty terrible to me. (A set-theoretic definition of addition as forming unions of sets... for 7-year-olds?!)
3. The Stakes
Third, and most engrossingly, Phillips analyzes the hidden assumption of the whole New Math debate: that math education creates lifelong intellectual habits.
In short, that math class shapes all thinking.
The reformers worried that rote drill would create a nation blindly deferential to authority. They wanted the opposite: a nation of creative, analytical mini-mathematicians. Meanwhile, their "back to basics" opponents took the opposite view: that rote drill would breed discipline, diligence, and healthy respect for authority, while New Math would breed a feckless, disobedient generation unable to tell true from false, right from wrong.
But here's the key: for both supporters and opponents, New Math was not about test scores, achievement gaps, calculation abilities, or other more familiar concerns. It was about the kind of thinking a democratic society needed to thrive.
I can't help wondering if both the reformers and the anti-reformers had it all wrong. Maybe math education isn't about the intellectual habits of a free society.
Maybe math education is just about math. Those stakes seem high enough!
All in all, a fabulous little history, and worth the time for any teacher who wants to inspect the politics behind our visions of the classroom.
It was an ambitious new curriculum, driving at real conceptual understanding. But it spread too fast to classrooms, where unready teachers made a hash of it. The project thus soured from "well-meaning reform" to "roundly mocked fiasco."
This narrative isn't wholly wrong. But Phillips enriches and complicates it in three ways.
1. What was New Math?
First, he illuminates exactly what new math was. Top-down, federally funded, and led by professional mathematicians, its goal was not "conceptual understanding" per se. The hope was to inculcate a special kind of thinking, characteristic of modern math: reasoning about abstract structures and logical systems. This kind of thinking, reformers argued, was what the U.S. needed to defeat the USSR in the so-called "cold war of the classrooms."
2. Primary vs. Secondary
Second, Phillips separates primary (K-6) and secondary (7-12) grades, because the two stories differ sharply.
In middle and high schools, new math was pretty much a success. Mathematicians and teachers wrote the curriculum together, in big, collaborative, NSF-funded teams. They produced model textbooks (which helped to seed the commercial textbook market) and wove together networks of teachers to advocate for the new curriculum. By 1965 almost half of math teachers had received training in the new approach. New Math lives on in high school textbooks today.
The fiasco was at the primary level. Classroom teachers contributed almost nothing to the curriculum, and were not impressed or pleased when the new textbooks landed. A grassroots "back to basics" backlash formed, and won the day. Also, although Phillips is restrained in his evaluation, the primary-level materials seem pretty terrible to me. (A set-theoretic definition of addition as forming unions of sets... for 7-year-olds?!)
3. The Stakes
Third, and most engrossingly, Phillips analyzes the hidden assumption of the whole New Math debate: that math education creates lifelong intellectual habits.
In short, that math class shapes all thinking.
The reformers worried that rote drill would create a nation blindly deferential to authority. They wanted the opposite: a nation of creative, analytical mini-mathematicians. Meanwhile, their "back to basics" opponents took the opposite view: that rote drill would breed discipline, diligence, and healthy respect for authority, while New Math would breed a feckless, disobedient generation unable to tell true from false, right from wrong.
But here's the key: for both supporters and opponents, New Math was not about test scores, achievement gaps, calculation abilities, or other more familiar concerns. It was about the kind of thinking a democratic society needed to thrive.
I can't help wondering if both the reformers and the anti-reformers had it all wrong. Maybe math education isn't about the intellectual habits of a free society.
Maybe math education is just about math. Those stakes seem high enough!
All in all, a fabulous little history, and worth the time for any teacher who wants to inspect the politics behind our visions of the classroom.
January 12, 2016
Best book about math I've ever read. As a person who missed the New Math era, I've frequently wondered what all the hubbub was about (especially as a math teacher). This book is a great introduction and analysis of the phenomenon generally known as New Math. As the subtitle says, the author explains the political background of the movement, not only in terms of government, but also in terms of educational philosophy. It was great learning of the origins and history of mathematical organizations such as NCTM, the MAA, and the AMA.
Style-wise, the book is written at a higher level of language than I was used to reading, but I grew to appreciate the precision of language. The author came across as mostly objective, but it was clear that he is fairly sympathetic to the New Math cause. With good evidence. It was most interesting to learn of the distinction between the creation and reception of the high school curriculum versus the elementary curriculum developed by the School Mathematics Study Group (at the time, a division of the National Science Foundation). I also appreciated the level of detail with which the author explained the content - specific enough for one to understand, but not so much to be dreary.
This is a book I would recommend to all math teachers. To understand the history and development of today's curriculum, and to learn from the mistakes and successes of the past, this book is a great resource.
Style-wise, the book is written at a higher level of language than I was used to reading, but I grew to appreciate the precision of language. The author came across as mostly objective, but it was clear that he is fairly sympathetic to the New Math cause. With good evidence. It was most interesting to learn of the distinction between the creation and reception of the high school curriculum versus the elementary curriculum developed by the School Mathematics Study Group (at the time, a division of the National Science Foundation). I also appreciated the level of detail with which the author explained the content - specific enough for one to understand, but not so much to be dreary.
This is a book I would recommend to all math teachers. To understand the history and development of today's curriculum, and to learn from the mistakes and successes of the past, this book is a great resource.
April 30, 2026
As a non-parent, non-teacher, as the relation of an expert on education, as someone comically useless at arithmetic, I am very weirdly fascinated by changes and mutations in curriculum and standards etc. As someone taught in between "New Math" and "Common Core", so in the "Back to Basics" "Good Old Fashioned Way", I often wonder if there is any chance that I might not have to sit down with a pencil and paper to get the answer to 48 x 92. (Math people love to lament that, uniquely, non-math people will loudly, and "proudly", proclaim their badness at math. This is in fact not unique in the slightest -- ask people if they can draw sometime -- and also a lie: nobody on earth is "proud" that they can't do math.) What if I'd learned starting with sets, like in New Math? What if I learned to estimate and use tricks to simplify problems like in modern "common core" math? Who knows! I did like geometry, not insofar as it involved shapes and drawings as you might expect, but because I thought doing proofs was interesting, although (as far as I remember) too time-consuming for me to get homework done on time.
Even more interesting is the reaction of other people to changes like this. Generally, people hate how they were taught, and rage about it; but when they hear someone teaches another way, they fly into an even more extravagant rage. Maybe it's because I know for a fact that I would not be able to do my own old math homework from the 80s and 90s, and would have to relearn it even if my kids were taught exactly the same as me, but I'm pretty unsympathetic to the Mr. Incredibles of the world. I have opinions of course -- a confirmed Luddite, I think all video, touchscreen, internet, and for the love of God AI shit does not belong in school; even back in the days of computer lab, I knew that simply sitting around computers did not make me learn anything and all we did was play games, which is fun but not educational, unless it was "edutainment" software, which was neither fun nor educational -- but I find most people proudly reactionary when it comes to school. Every fucking redditor has listened to "Sold a Story" and almost none of them has the first fucking clue what "phonics" means; I've seen them say that people don't argue rationally online because they didn't learn phonics, we need phonics because just being able to read the words out loud is not enough! What they know is that phonics is anti-woke reading, and Mississippi does it so here's mud in your eye liberals!!, and conservative moralizing about education, as Phillips ably documents, is a perpetual undercurrent rolling along beneath the educational trends that come around.
Unfortunately this book also follows a heinous academic trend, the hideous practice of announcing "in this chapter, I argue", for the benefit of people who do not read but skim, aka grad students. It is nearly unreadably repetitive in places, while at the same time frustratingly scanty in terms of long or detailed quotations or examples. I read the whole book in a single (albeit horrendously delayed) trip from San Francisco to Montreal, because it is very short; the depth and detail just isn't there in terms of what exactly New Math consisted of, what its critics didn't like about it, etc. There's a lot more random/more-or-less pointless examples from antiquity onward of philosophers moralizing about education, or so it felt, than in-depth presentation of the actual subject matter, and this being a modern history book by a modern academic there is absolutely no attempt to even suggest to the reader any material "novelistic" reality like what the New Math guys looked like or what kind of classrooms the kids sat in etc. It can take your breath away, just what a colorless, odorless, backrooms-esque non-world History takes place in, for academics. I can't do more than "it was OK".
Which is too bad because ultimately the revelations of this "political history" are quite interesting. New Math was born of the fear of communism, and for the entire postwar 20th Century America defined itself against communism more than anything else. It is always interesting to read old 50s stuff where they assumed that, of course, communism was more rational and economically sound, but god dammit we in America are a land of dreamers, individualists who dance to the beat of our own drum, we believe man cannot live on bread alone! and to contrast that with how, now that we think of communism as an "objective failure" economically, it is the leftists who are airy-fairy impractical romantics and capitalism the Cold Equations that must be accepted as the Law of Nature. Similarly, the progress of NEW MATH, which came from the belief that, of course, Ivan was better at math than Johnny, but he only learned by rote, and could not understand the whys and wherefores, or creatively apply his knowledge to new situations; if his teacher told him 2+2=5 he would of course believe it!! (Phillips naturally quotes the odious Orwell on this.) So Johnny had to learn to understand math first, and like a good creative individual American come, by his own effort, to the correct answer; if he made a mistake along the way that threw the answer off, it's not a big deal because the process, free and rational and basic, was sound. (Phillips naturally quotes the delightful, though in this case quite misguided, Tom Lehrer.) By the 70s, nobody really gaf about the Worldwide Threat of Communism anymore, having lost so many thousands for no reason in Asia, and the reactionaries had gathered strength to say actually, to prevent Johnny from growing his hair out and listening to that devil music, he needs to shut the fuck up and not think but believe me when I say 2+2=5 because that's the way we did things back in my day. And both of these arguments were anti-socialist conservatives; and both were calling their way "discipline". It was history that changed around the New Math; and curriculum is very slow to change, compared to history.
When I was young, I really wanted to be a parent; nowadays I thank God that I am not one. I think it would have worked out if I had had a child back then, although life for parents was starting to get annoying (already the panic about kids playing outside unsupervised); but nowadays it is absolutely terrifying. I have no idea how you can prevent your kid from screen addiction, AI dependence, alt-right Twitch streamers with an audience exclusively of 8-year-olds, any of it, without going full Captain Fantastic and (even assuming the rosy view of homeschooling in that movie) leaving them weird and isolated and creepy. But I think if they were in public school, and not allowed (or encouraged, by tech companies long grasping "charitable" fingers) to use AI (which will definitely tell them 2+2=5 at some point) they would get a better math education than I did, because of the New New Math of "Common Core". And regardless of trendy podcasts and whether they were taught phonics in kindergarten, I could definitely handle teaching them to read (even I, who absolutely did not learn by phonics alone, and could always tell who did because of how they sounded out every word, back in second grade). Too bad that reading, that is to say from start to finish, not as a "discipline" but a pleasure, is so discouraged for the academics of the world, and results in garbage writing like in this book.
Even more interesting is the reaction of other people to changes like this. Generally, people hate how they were taught, and rage about it; but when they hear someone teaches another way, they fly into an even more extravagant rage. Maybe it's because I know for a fact that I would not be able to do my own old math homework from the 80s and 90s, and would have to relearn it even if my kids were taught exactly the same as me, but I'm pretty unsympathetic to the Mr. Incredibles of the world. I have opinions of course -- a confirmed Luddite, I think all video, touchscreen, internet, and for the love of God AI shit does not belong in school; even back in the days of computer lab, I knew that simply sitting around computers did not make me learn anything and all we did was play games, which is fun but not educational, unless it was "edutainment" software, which was neither fun nor educational -- but I find most people proudly reactionary when it comes to school. Every fucking redditor has listened to "Sold a Story" and almost none of them has the first fucking clue what "phonics" means; I've seen them say that people don't argue rationally online because they didn't learn phonics, we need phonics because just being able to read the words out loud is not enough! What they know is that phonics is anti-woke reading, and Mississippi does it so here's mud in your eye liberals!!, and conservative moralizing about education, as Phillips ably documents, is a perpetual undercurrent rolling along beneath the educational trends that come around.
Unfortunately this book also follows a heinous academic trend, the hideous practice of announcing "in this chapter, I argue", for the benefit of people who do not read but skim, aka grad students. It is nearly unreadably repetitive in places, while at the same time frustratingly scanty in terms of long or detailed quotations or examples. I read the whole book in a single (albeit horrendously delayed) trip from San Francisco to Montreal, because it is very short; the depth and detail just isn't there in terms of what exactly New Math consisted of, what its critics didn't like about it, etc. There's a lot more random/more-or-less pointless examples from antiquity onward of philosophers moralizing about education, or so it felt, than in-depth presentation of the actual subject matter, and this being a modern history book by a modern academic there is absolutely no attempt to even suggest to the reader any material "novelistic" reality like what the New Math guys looked like or what kind of classrooms the kids sat in etc. It can take your breath away, just what a colorless, odorless, backrooms-esque non-world History takes place in, for academics. I can't do more than "it was OK".
Which is too bad because ultimately the revelations of this "political history" are quite interesting. New Math was born of the fear of communism, and for the entire postwar 20th Century America defined itself against communism more than anything else. It is always interesting to read old 50s stuff where they assumed that, of course, communism was more rational and economically sound, but god dammit we in America are a land of dreamers, individualists who dance to the beat of our own drum, we believe man cannot live on bread alone! and to contrast that with how, now that we think of communism as an "objective failure" economically, it is the leftists who are airy-fairy impractical romantics and capitalism the Cold Equations that must be accepted as the Law of Nature. Similarly, the progress of NEW MATH, which came from the belief that, of course, Ivan was better at math than Johnny, but he only learned by rote, and could not understand the whys and wherefores, or creatively apply his knowledge to new situations; if his teacher told him 2+2=5 he would of course believe it!! (Phillips naturally quotes the odious Orwell on this.) So Johnny had to learn to understand math first, and like a good creative individual American come, by his own effort, to the correct answer; if he made a mistake along the way that threw the answer off, it's not a big deal because the process, free and rational and basic, was sound. (Phillips naturally quotes the delightful, though in this case quite misguided, Tom Lehrer.) By the 70s, nobody really gaf about the Worldwide Threat of Communism anymore, having lost so many thousands for no reason in Asia, and the reactionaries had gathered strength to say actually, to prevent Johnny from growing his hair out and listening to that devil music, he needs to shut the fuck up and not think but believe me when I say 2+2=5 because that's the way we did things back in my day. And both of these arguments were anti-socialist conservatives; and both were calling their way "discipline". It was history that changed around the New Math; and curriculum is very slow to change, compared to history.
When I was young, I really wanted to be a parent; nowadays I thank God that I am not one. I think it would have worked out if I had had a child back then, although life for parents was starting to get annoying (already the panic about kids playing outside unsupervised); but nowadays it is absolutely terrifying. I have no idea how you can prevent your kid from screen addiction, AI dependence, alt-right Twitch streamers with an audience exclusively of 8-year-olds, any of it, without going full Captain Fantastic and (even assuming the rosy view of homeschooling in that movie) leaving them weird and isolated and creepy. But I think if they were in public school, and not allowed (or encouraged, by tech companies long grasping "charitable" fingers) to use AI (which will definitely tell them 2+2=5 at some point) they would get a better math education than I did, because of the New New Math of "Common Core". And regardless of trendy podcasts and whether they were taught phonics in kindergarten, I could definitely handle teaching them to read (even I, who absolutely did not learn by phonics alone, and could always tell who did because of how they sounded out every word, back in second grade). Too bad that reading, that is to say from start to finish, not as a "discipline" but a pleasure, is so discouraged for the academics of the world, and results in garbage writing like in this book.
February 1, 2024
Interesting, but not what I expected. I would have liked to have seen more examples of what was being taught, since I started school at the very end of New Math.
November 9, 2024
This is a relatively brief but interesting history of the "new math" curriculum in its development, implementation, and downfall in the USA during the 60s and 70s. I have been teaching high school math for about two decades and recognize many parallels to the Common Core implementation, most of which have to do with the gaps between the people who understand the math and pedagogy, the people who are writing the textbooks, and the teachers who are told to implement the material without always having adequate support or training.
I thought it was quite interesting to learn how successful the New Math was at the high school level, which was the intended target of the curriculum's designers. Most of the failure stories you hear revolve around elementary school experience, and this book gets into the combination of that not being the intended audience plus the lack of support for school teachers and the undue influence of textbook publishers that led to the backlash and downfall of the New Math. There's an interesting bit at the end that ties the backlash to the New Math to the general turn against "big government" and the conservative turn that lead to the Reagan era.
Anyway, the short version is that this is a lot less mathy and a lot more history based. For me, as a math teacher, it was interesting to learn how much of what we continue to teach at the high school level was first introduced as part of the New Math.
I thought it was quite interesting to learn how successful the New Math was at the high school level, which was the intended target of the curriculum's designers. Most of the failure stories you hear revolve around elementary school experience, and this book gets into the combination of that not being the intended audience plus the lack of support for school teachers and the undue influence of textbook publishers that led to the backlash and downfall of the New Math. There's an interesting bit at the end that ties the backlash to the New Math to the general turn against "big government" and the conservative turn that lead to the Reagan era.
Anyway, the short version is that this is a lot less mathy and a lot more history based. For me, as a math teacher, it was interesting to learn how much of what we continue to teach at the high school level was first introduced as part of the New Math.
January 25, 2024
The subtitle here is key: this is a political history. It pays a lot of attention to who played what role and what they said and what was said about them, but less to the mathematical and pedagogic detail of the new math. This is of course good history, but not really what I expected when I picked up the book.
As a history it does a good job putting the new math reforms in context: its inception as a response to Sputnik and the cold war, its expansion as part of LBJ's great society, and the backlash from Nixon's silent majority. What I thought was the strongest point of the book was how it placed the new math as just one in the never-ending sequence of reforms and counter-reforms. It's not simply a swing of the pendulum, some things really do change permanently. The fight just moves in new directions.
As a history it does a good job putting the new math reforms in context: its inception as a response to Sputnik and the cold war, its expansion as part of LBJ's great society, and the backlash from Nixon's silent majority. What I thought was the strongest point of the book was how it placed the new math as just one in the never-ending sequence of reforms and counter-reforms. It's not simply a swing of the pendulum, some things really do change permanently. The fight just moves in new directions.
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