Brief Chronology and Dramatis Personae of The New Math
Like most historical movements, the "new math" is not a single phenomenon, and the words have been applied to developments that sometimes contradicted one another. The phrase is most generally applied to the introduction of certain kinds of formal language in school mathematics instruction, words and phrases such as "set", "open sentence", "base‑n" and "distributive law," where they previously had been used only among mathematicians ‑‑ if there. Another indicator was the careful insistence on distinguishing between "number" and "numeral", and indeed saying everything else in a more precise way than had been customary in school‑rooms. Of course, exact wording was only the indicator of what new things the reformers wished to teach, and not the substance. It was not only new language and logic, but several new mathematical topics, that entered many curricula at the time. Examples: proofs of certain algebraic facts from axioms for a field, and the development of the real (and complex) number systems as extensions of the more intuitive counting number system. The sixties was also the era in which probability and vectors entered high‑school topics to some degree. But more characteristic of the reform was not the new subject‑matter but the emphasis on the axiomatic, logical structure of mathematics, even at the earliest levels, and a consequent downgrading (by many enthusiastic teachers and textbooks) of exercise in routine manipulations.
AAAS American Association for the Advancement of Science
AMS American Mathematical Society
CEEB College Entrance Examination Board
CSMP Comprehensive School Mathematics Program
CUPM Committee on the Undergraduate Program in Mathematics (of the MAA)
DOE Department of Education (usually federal, as in USDOE)
ERIC Educational Resources Information Center
HEW Department of Health, Education and Welfare
MAA Mathematical Association of America
MINNEMAST Minnesota Mathematics and Science Teaching Project
NCTM National Council of Teachers of Mathematics
NDEA National Defense Education Act
NIE National Institute of Education
NSF National Science Foundation
NIH National Institutes of Health
OE Office of Education (federal), predecessor of DOE.
OEEC Organization for European Economic Cooperation
SAT Scholastic Aptitude Test (administered by the CEEB)
SMSG School Mathematics Study Group
UICSM University of Illinois School Mathematics Program
UMMaP University of Maryland Mathematics Project
1950 Establishment of the NSF by Congress
1951 Establishment of University Of Illinois project (UICSM) in school mathematics, headed by Max Beberman. This project dealt only with grades 9‑12, and became famous by the late 1950s.
1953 First NSF Summer Institute, at Boulder, Colorado, designed to upgrade the mathematical competence of liberal arts college mathematics teachers. The NSF Institutes program later expanded, under the direction of Russell Phelps, to concentrate on secondary school teachers, both in summer Institutes and part‑time academic year Institutes as well, especially after 1957, when many of the Institutes were associated with particular New Math curriculum projects.
1955 Formation of the Commission on Mathematics of the CEEB (Albert Tucker, chairman). Though there had been innumerable commissions and reports before this one, going back to 1900, the CEEB report (1959) was actually influential. It offered a detailed curriculum for college‑bound 9‑12 students, including much solid mathematics as well as some of the "new math" terminology. The CEEB Report, while not a curriculum project as such, influenced all later curriculum developments for secondary schools, and, though this was not its expressed purpose, earlier grades as well.
1957 Soviet "Sputnik" launched in October persuades Congress to unload unprecedented millions of dollars under the NDEA of the following year, for science education via NSF grants and OE grants.
1958 Establishment of School Mathematics Study Group (SMSG), the largest and best financed of all the NSF projects of the era, by the combined efforts of the AMS, MAA and NCTM. It was headed by Edward G. Begle, Associate Professor of mathematics at Yale, who after a few years became Professor of Education at Stanford, to which he moved the entire project. SMSG published a complete K‑ 12 curriculum and then some. These books were not commercial, though thousands of copies of its mimeographed texts were sold. Mainly, SMSG invited commercial publishers to take advantage of SMSG texts and experience in producing their own.
1958 Publication of two papers in The Mathematics Teacher, one by Kline and one by Meder, attacking and defending the proposals of the CEEB Commission and the introduction of abstraction into school mathematics generally. These papers outlined the positions that would continue to divide the mathematical community during the whole of the New Math era.
1958 David A. Page begins The Arithmetic Project with Carnegie Foundation support at the University of Illinois; Page had formerly been Beberman’s assistant at UICSM.
1959 Publication of the long-awaited Report (and Appendices) of the CEEB Commission on Mathematics
1959 The “Wood's Hole Conference” (at the Oceanographic Institute there), a meeting of noted scientists, mathematicians, psychologists and others on the general topic of improving science education. Though the conference had been initiated by Jerrold Zacharias, a physicist, the proceedings were ultimately summarized by the psychologist Jerome Bruner in a short book (1962) called The Process of Education, in which the structural elements in all learning were emphasized as essential for understanding the whole.
1959 An OEEC conference of mathematicians and educators (Marshall Stone, Chairman) takes place at Royaumont, in France. Jean Dieudonné's keynote address, famously characterized by his line, "Euclid Must Go!", urged vector space methods instead of the current synthetic system, and the tone of his talk favored more logic and abstraction in school math in general. The conference was also attended by Begle and other Americans. The history of "new math" in Europe from this point on resembles that in the USA, but is not an imitation of it, and was not uniform across Europe any more than it was across the U.S.A.
1962 "Letter of 75 Mathematicians" (so-called, not the title of the paper) published in The American Mathematical Monthly, objecting to the current emphases on abstraction in school math projects, with reasons. Professor Morris Kline, of NYU, was the ringleader. Begle printed a spirited rejoinder in the same volume of the Monthly.
1963 The "Cambridge Conference" at Harvard, suggesting an extremely ambitious and abstract school mathematics program for ambitious or talented students, though not intended as a recommendation for the present day.
1963 Burt Kaufman incorporated Cambridge Conference ideas into his experimental program for gifted students at the Nova (FL) schools, which eventuated in CSMP and ultimately "MEGSSS"
1964 Max Beberman has second thoughts on abstraction on a mass scale as then being taught in the elementary grades, citing the danger of "raising a generation of kids who can't do computational arithmetic", in a pessimistic talk at an NCTM meeting in Toronto, as reported in the New York Times and elsewhere.
1965 Tom Lehrer sings The New Math at The Hungry i in San Francisco, and later records it, mocking the sacrifice of arithmetic (and accuracy) to New Math posturing, that elevates "understanding" above understanding.
1965 Congress establishes Regional Educational Laboratories and ERIC, as part of a comprehensive Elementary and Secondary Education Act, reorganizing OE to include a Bureau of Research overseeing many earlier programs.
1969 Richard Nixon takes office, sends budget to Congress omitting funds for the NSF Teachers' Institutes. These are restored by Congress, but killed for the following years.
1970 Nixon proposes establishment of a National Institute of Education (NIE), parallel with NSF and NIH, as a research vehicle for the education profession, to take over most of what the Dept of Education had been doing in the past in this line. All NSF curricular projects are closed down (or would be when the ending date of the current grant was to arrive) and mathematicians theretofore concerned with school mathematics begin returning to their previous pursuits.
1970 Max Beberman dies at age 45; UICSM is taken over by Robert B. Davis, who brings a different flavor to Illinois, more concerned with the psychology of learning than with the logical rigor and emphasis on structure that had theretofore characterized “new math” projects.
1972 NIE legislation finally passes. All curriculum programs financed through federal regional laboratories are reviewed in the process of transferring the successful ones from the (federal) DOE to the new NIE. Burt Kaufman's CSMP fails the test (allegedly because of its emphasis on the F. Papy "minicomputer"), presaging trouble for new math programs generally. (Actually, CSMP support was reinstated for a time, after protest and a second round of evaluation; but federal support died away soon after, though CSMP itself remains as one of the few new math initiatives to survive in commercial form.) Ed Begle drinks a toast to the SMSG, closing after 14 years, at the Exeter (UK) meeting of the International Congress of Mathematics Education. (NIE did not succeed in its attempt to wrest control of public education from the professional educators, as it turned out.)
1973 Publication of the book, Why Johnny Can't Add, by Morris Kline. A blast, generally regarded as the death knell of the New Math.
1975 Death Certificates for the New Math:
(a) The Conference Board of the Mathematical Sciences National Committee on Mathematical Education publishes a report in which the teaching profession and others are advised to use the phrase "new math" only as a reference to "a certain historical phenomenon" and not as a descriptor for new currents in mathematics education. R.I.P.
(b) The phrase "back to basics", referring to what would be the predominant current of the period 1975‑1990, has no particular origin, but it does describe a self‑conscious reaction to the 'set theory' and other axiomatics promulgated by most "new math" reformers, as evidenced by the fact that the NIE called a conference, NIE Conference on Basic Mathematical Skills, at Euclid, Ohio, October 4‑6, 1975. The participants included many of the leaders of the late "new math" as well as many who were to become more famous in the following generation's reaction; and the papers, while not condemning the "new math" explicitly, do offer advice to NIE concerning what the participants saw as the place of math education research and government policy for the post "new math" era.
Despite all the furor, the "new math" never ran very deep in American schools, and most textbooks either ignored it or included its ideas superficially or in garbled form. For a few years most commercial textbooks touted themselves as "new math", which they seldom were, and then they backed off. The same with the schools themselves, and their curriculum committees. Probably about 10% of American students were exposed to it in any significant way during its time, and all this despite the NSF‑financed teachers' Institutes, where thousands of teachers (grades 9‑12, mostly) took courses in modern mathematics in preparation, they thought, for teaching the new curricula.
On the other hand, some traces of these new topics did remain, and in looking at today's texts we still see in some of them a tip of the hat (at least) to "numeral", to "base‑n" computation, to "axioms for a field" and so on. The movements of history do not have clear‑cut beginnings and endings. Whatever failings the K‑12 garbling of modern mathematics in the 1960s suffered from, many of the topics were a necessary innovation and will necessarily remain in any good curriculum, if mathematics is to be understood at all. Furthermore, the account given above ignores the many other projects that made the decade of the 1960s so interesting in mathematics education. Some of the names listed below are associated with important projects of the times, usually centered at a single university, with experimental texts and classes but without the vast outreach of SMSG or the brilliant showmanship of Max Beberman. Others were frequent contributors to the research literature, or members of important committees, commissions or conferences, whose reports were influential. Except for Bruner, Piaget and Zacharias they were all mathematicians or mathematics educators. The identifying comments are far from full descriptions of their relevance to the New Math, and sometimes mention only one of their academic appointments, and in a few cases that mention is valid for a period more recent than the New Math era.
Henry Alder Professor of mathematics at UC Davis, President of MAA in 1977
Carl B. Allendoerfer Professor of mathematics at U of Washington,
member of CEEB Commission (1955-1958), President of MAA in 1961
Frank B. Allen high school teacher, President of NCTM 1962‑64
Max Beberman Director of UICSM, high school teacher and professor of math education at U of Illinois
Ed Begle Director of SMSG, formerly professor of math at Yale, later professor of education at Stanford
Peter Braunfeld Professor of math education at U of Illinois
Kenneth E. Brown specialist for mathematics, OE (then within HEW)
Jerome Bruner psychologist, professor at Harvard, Chairman of the "Woods Hole Conference" on science education, 1959)
Robert B. Davis director of the Madison Project, professor of education at Syracuse, later at Illinois, etc.
Jean Dieudonné, French mathematician, friend of Bourbaki and spiritual father of "New Math" in Europe
Mary Dolciani, teacher and professor of math education at Hunter College, prominent writer of successful textbooks beginning with her work for SMSG
William L. Duren, Jr., professor of mathematics, later a Dean at U Virginia; Chairman of CUPM during the late 50s
Howard Fehr, professor at Columbia University Teachers College, President of NCTM 1956‑58, member of CEEB Commission
James T. Fey Professor of mathematics at Maryland
Hans Freudenthal Dutch mathematician, sometimes credited with having “saved Holland from the ‘new math’”, prolific author and editor of journal. Educational Studies in Mathematics
Andrew Gleason Professor of mathematics, Harvard
Peter Hilton Professor of mathematics at Cornell
Burt Kaufman, founder of CSMP (1967) and later full‑scale programs for gifted students
John Kelley, professor of mathematics at U Cal Berkeley, influential in SMSG
Jeremy Kilpatrick professor of math education at U of Georgia
Morris Kline professor of mathematics at NYU, author of books on the history and cultural aspects of mathematics, leading critic of “the new math”
John R. Mayor director of UMMaP, President of NCTM 1952‑54
Albert E. Meder, Jr. Administrative Dean at Rutgers, and Executive Director of the CEEB Commission (1955-1959)
Bruce Meserve professor of mathematics, associate of Max Beberman at Illinois in 1950s
Edwin Moise mathematician, SMSG author (geometry), later professor of education at Harvard
David A. Page professor of math education at U of Illinois, director of "The Arithmetic Project"
Frédérique Papy Belgian innovator of abstract materials for small children, influential in the USA partly through Burt Kaufman's CSMP
Jean Piaget Swiss developmental psychologist, especially of small children
Henry Pollak Mathematician at The Bell Telephone Labs
Gerald Rising professor of mathematics education at SUNY Buffalo
Paul Rosenbloom math professor at U Minnesota, Minnemast project director
Marshall Stone math professor at Harvard and Chicago, President of AMS in 1943
Patrick Suppes Professor at Stanford, logic, geometry project for elementary grades
Albert W. Tucker math professor at MIT, Chairman (1955-1958) of the CEEB Commission for College Preparatory Mathematics
Henry Van Engen professor of math education at U Wisconsin, editor of The American Teacher, member of CEEB Commission (1955-1958)
Herbert Vaughan logician and professor of mathematics at U of Illinois, co‑author of some UICSM materials
James Wilson director of the longitudinal study of SMSG results, professor of education at U Georgia
Jerrold Zacharias Professor of physics at MIT, director of PSSC, a physics curriculum project for high schools which was a model for later NSF initiatives in other fields.
There are so many mathematicians and teachers who participated in the writing projects of SMSG that it is pointless to list them here. There were many others, not part of experimental projects or commissions, who wrote influential commercial textbooks embodying or affecting to embody “new math” principles, or conducted NSF Summer Institutes for teachers, or commented from the sidelines. Nothing in school mathematics of the time escaped interpretation in terms of “new math”, one way or another.
Many of those named above have written articles, some polemic, some as classroom notes or reports of progress of one or another “newmath” project; these can mainly be found in the back volumes of The Mathematics Teacher (published by NCTM), the American Mathematical Monthly (published by MAA). It is a pleasant way to spend a few hours in a library having back volumes of these journals, to select those for (say) 1953, 1963 and 1973, to see what people were writing about the reforms of the time, and to note how the tone changes as the profession approached 1975 and 1980. There are other English language journals of mathematics education, including Hans Freudenthal's Educational Studies in Mathematics (Holland), but the two American journals named above are the most easily found in this country’s research libraries.
Ralph A. Raimi
Revised 26 August 2005