__Brief Chronology and Dramatis Personae of The New Math____ __

__ __

**(1951‑1975, R.I.P.)**

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**