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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.
241 pages, Paperback
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.
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.
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.
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