This
is a
preprint of an article that appeared in the
BSHM
Bulletin: Journal of the British Society for the History of
Mathematics, Volume 22, Issue 1, p. 22-33 (2007), (c)
Taylor & Francis. The
definitive version is available at: http://dx.doi.org/10.1080/17498430601148762 The BSHM
Bulletin may be found online at:
http://www.tandf.co.uk/journals/titles/17498430.asp

** **

**A quarter
century of US 'math
wars' and political partisanship**

David Klein

California State University, Northridge, USA

This article traces the history of the US 'math wars' from 1980, and discusses the political polarizations that fuelled and resulted from the disagreements.

*Keywords*: math wars; progressive
education;
politics

* *

*2000
Mathematics Subject Classifications*: 01A60, 01A61, 97-03, 97B99

**Introduction**

Treatises on education and its social implications span at least two millennia. Since the18th century, two major strands within this genre may be identified: progressive education and classical education.[1] The latter traces its origins to Plato, who argued that education for a just society requires the reinforcement of the rational over the instinctive and emotional aspects of human nature. Systematic instruction and practise are part of the classical tradition. They are also essential components of Asian and other non-Western educational systems.

The hallmarks of progressive education, by contrast, are naturalistic, child-centred instruction and discovery learning. Progressive education is an outgrowth of the Romantic Movement with roots going back to Jean Jacques Rousseau. John Dewey and William Heard Kilpatrick were instrumental in ensuring the dominance of progressive education theory in teachers colleges through most of the 20th century.[2] In the variant promoted by Kilpatrick, who was especially influential in mathematics education, subjects would be taught to students based on their direct practical value, or if students independently wanted to learn them.[3]

The history of US mathematics education of the past quarter century cannot be separated from these historical strands, nor from contemporary political and economic influences. A distinctive feature of the 1990s and early years of the 21st century was the association of right and left wing political ideologies with competing mathematics education programmes and their advocates.[4]

Particular textbooks and curricular programmes were the focal points of disagreement. Examples have been identified and described elsewhere.[5] Sometimes referred to as 'constructivist',[6] those textbooks and programmes were aligned with, promoted by, and in some cases endorsed in writing[7] by the National Council of Teachers of Mathematics (NCTM), the leading organization for pre-collegiate mathematics education in the US. In opposition to the use of these progressivist school programmes, organizations of parents sprang up across the US, and worked in collaboration with university mathematicians and other academics. The resulting 'math wars' of the 1990s often fractured along political lines. But it was the events of the 1980s that spawned the controversies of the succeeding decade.

**Seeds
of Reform: the 1980s**

In
a long series of documents published by the NCTM, three have been
especially
influential: *An* *Agenda
for Action* (1980), *Curriculum and
Evaluation Standards for School Mathematics* (1989), and
*Principles and
Standards for School Mathematics* (2000). The
latter two are referred to respectively
as the* 1989 NCTM Standards* and the *2000
NCTM Standards*, or just *Standards* when the
context is
clear.

*An* *Agenda
for Action* paved the way for major
trends of the 1990s.[8] It
recommended that problem solving
be the focus of school mathematics. It asserted that 'difficulty with
paper-and-pencil computation should not interfere with the learning of
problem-solving strategies'. Technology would make problem solving
available
to students without basic skills. According to the report, 'All
students
should have access to calculators and increasingly to computers
throughout
their school mathematics program', including elementary school
students. The
report called for 'decreased emphasis on such activities
as...performing paper
and pencil calculations with numbers of more than two digits'.

*An
Agenda for Action* also argued
that 'emerging programs that prepare users of
mathematics in non-traditional areas of application may no longer
demand the
centrality of calculus. . .' The de-emphasis of calculus would later
support
the move away from the systematic development of its prerequisites:
algebra,
geometry, and trigonometry. The 'integrated' high school mathematics
books of
the 1990s contributed to this tendency. While those books contained
parts of
algebra, geometry, and trigonometry, these traditional subjects were
not
developed systematically, and often depended on student 'discoveries'
that were
incidental to solving 'real world problems'.

The
*1989 NCTM Standards* described
general standards for the bands of grades: K-4,
5-8, and 9-12. It promoted the views of *An Agenda for Action*, but with
greater
elaboration. The grade level bands included lists of topics that were
to
receive 'increased attention' and others for 'decreased attention'. The
K-4
band called for greater attention to 'Operation sense', 'Use of
calculators
for complex computation', 'Collection and organization of data',
'Pattern
recognition and description', 'Use of manipulative materials', and
'Cooperative
work'.

Slated for decreased attention were 'Long division', 'Paper and pencil fraction computation', 'Rote practice', and 'Teaching by telling'. Topics listed for decreased attention in grades 5-8 included: 'Relying on outside authority (teacher or an answer key)', 'Manipulating symbols', 'Memorizing rules and algorithms', and 'Finding exact forms of answers'.

As
in *An Agenda for Action*, the *Standards
*put strong emphasis on the use of
calculators throughout all grade levels. On page 8, the *Standards* proclaimed,
'The new
technology not only has made calculations and graphing easier, it has
changed
the very nature of mathematics...' The NCTM therefore recommended that,
'appropriate calculators should be available to all students at all
times'.

The
*Standards* reinforced
the general themes of progressive education by advocating
student centred, discovery learning. The utilitarian justification of
mathematics was so strong that both basic skills and general
mathematical
principles were to be learned almost invariably through 'real world'
problems. Mathematics for its own sake was not encouraged.

The
arguments in support of these changes took two major themes: social
justice in
the form of challenging racial and class barriers on the one hand, and
the
needs of business and industry on the other.[9] The
following passage
from Alan Schoenfeld's, *The Math Wars*, (page 255)
is representative:

... lack of access to mathematics is a barrier – a barrier that leaves people socially and economically disenfranchised. For these reasons, noted civil rights worker Robert Moses declared that "the most urgent social issue affecting poor people and people of color is economic accessÉ. I believe that the absence of math literacy in urban and rural communities throughout this country is an issue as urgent as the lack of registered Black voters in Mississippi was in 1961."

The
needs of business were described on page 3 of the *1989 NCTM
Standards*:

Traditional notions of basic mathematical competence have been outstripped by ever-higher expectations of the skills and knowledge of workers . . . employees must be prepared to understand the complexities and technologies of communication, to ask questions, to assimilate unfamiliar information, and to work cooperatively in teams. Businesses no longer seek workers with strong backs, clever hands, and "shopkeeper" arithmetic skills.

Arguments
for social justice and business needs were often conjoined, as on page
9 of the
*Standards*:

If all students do not have an opportunity to learn this mathematics, we face the danger of creating an intellectual elite and a polarized society. The image of a society in which a few have the mathematical knowledge needed for the control of economic and scientific developments is not consistent either with the values of a just democratic system or with its economic needs.

*Everybody
Counts*,
a 1989 report of the National Research Council, not only restated the
same
themes, but offered the *1989 NCTM Standards* as the
solution:

Through the *Standards*, parents
and teachers will be able
to understand in concrete terms what a school mathematics program might
look
like if it is to serve our national objectives adequately. (page 89)

The
confluence of social justice
themes, attendance to the needs of business, and the promise of
conceptual
understanding of mathematics for *all* students
gave the NCTM's agenda the
momentum it needed. Business, government, and labour unions could all
find
something to like in the proposal. By the beginning of the final decade
of the
20th century, the NCTM's vision for mathematics education was
unstoppable.

**NCTM
Reform and Counter-Reform: the 1990s and Beyond**

Even
though the NCTM was not a governmental agency, its standards played the
role of
national standards. Virtually all state standards were modelled on the *1989
NCTM Standards*.
California's 1992 Mathematics Framework was, if anything, even more
extreme. For example, it instructed, 'Calculators are the "electronic
pencils" of today's world...In every grade calculators can be issued to
students just as textbooks are. A reasonable goal is to make
calculators
available at all times for in-class activities, homework, and tests.'
California's progressive education policies would lead to public
opposition later
in the decade.

The California Mathematics Council, an affiliate of the NCTM, sent a letter to the California Board of Education dated April 17, 1996 citing an ordered list of 13 basic skills 'desired by Fortune 500 companies' with computation in 12th place. It praised the 1992 California Framework for addressing the needs of business:

* *

Equally
impressive is that these changes in the way
we teach mathematics are supported by the business community. *What
Work
Requires of Schools: A SCANS Report for America 2000* concludes
that students
must develop a new set of competencies and new foundation skills. It
stresses
that skills must be learned in context, that there is no need to learn
basic
skills before problem solving, and that we must reorient learning away
from
mere mastery of information toward encouraging students to solve
problems. . .
Learning in order to know must never be separated from learning to do.

Through
the 1990s, funding for textbooks aligned to the *Standards* flowed from
the National
Science Foundation (NSF) and corporate foundations.[10] Parents
were the first to object, especially in California,[11] and
they formed grassroots organizations[12] to pressure
schools to use other
textbooks, or allow parental choice. NCTM aligned books and programmes
were
criticized for diminished content and lack of attention to basic
skills. The
elementary school programmes required students to use their own
invented
arithmetic algorithms in place of the standard algorithms of
arithmetic.
Calculator use was encouraged to excess and integrated even into
kindergarten
lessons. Student discovery group work, at all grade levels, was the
preferred
pedagogy, but in most cases, projects were aimless or inefficient.
Statistics
and data analysis were overemphasized repetitiously at all grade levels
at the
expense of algebra and more advanced topics. Mathematical definitions
and
proofs for the higher grades were deficient, missing entirely, or even
incorrect.[13] Critics
openly derided
constructivist programmes in their schools as 'dumbed-down', and
described the
genre as, 'fuzzy math', 'new-new math', or 'whole math', in analogy
with the
failed reading pedagogy known as 'whole language learning'.

Some
of the widely used programmes aligned to the *Standards* did not
even include
textbooks, since books might interfere with student discovery. *MathLand*, a K-6
programme, was
one such example, and it was nearly devoid of mathematical content.[14]
Nevertheless, by 1997 *MathLand* was adopted
by 60% of the state's public elementary
schools, according to its publishers,[15] and was one
of many NCTM aligned
programmes in use across the US. Promotional materials for *MathLand* cited the
same SCANS
report and Fortune 500 ordered list of topics.

The
views of most American mathematicians involved in these debates were
similar to
those of their British counterparts, who were simultaneously confronted
by the
same issues in public education.[16] Criticisms
by mathematicians on
both sides of the Atlantic were well articulated in a 1995 report
entitled*
Tackling the Mathematics Problem, *commissioned
jointly by the London Mathematical
Society, the Institute of Mathematics and its Applications, and the
Royal
Statistical Society*,* as seen in
the following excerpts:

In recent years English school mathematics has seen a marked shift of emphasis, introducing a number of time-consuming activities (investigations, problem-solving, data surveys, etc.) at the expense of 'core' technique. In practise, many of these activities are poorly focused; moreover, inappropriate insistence on working within a context uses precious time and can often obscure the underlying mathematics...

[W]e have also seen implicit 'advice' ... that teachers should reduce their emphasis on, and expectations concerning, technical fluency. This trend has often been explicitly linked to the assertion that "process is at least as important as technique". Such advice has too often failed to recognise that to gain a genuine understanding of any process it is necessary first to achieve a robust technical fluency with the relevant content...

In parallel with these changes in emphasis, evidence that many English pupils were unable to solve standard problems involving, for example, decimals, fractions, ratio, proportion and algebra ... was interpreted by many curriculum developers and those responsible for defining national curricula, as meaning that such topics were 'too hard' for most English pupils in the lower secondary years.

As public opposition increased in the US, debates became more polarized along political lines. Mushrooming press accounts of bizarre classroom projects and deficient textbooks led to open ridicule by columnists, especially conservatives, and involvement of politicians. Generally, the politicians most sympathetic to the criticisms were Republican. However, as part of the Congressional debate on education legislation, Democratic Senator Robert Byrd made searing criticisms of the mathematics education reform movement from the Senate floor. He focused on a particular textbook,[17] scorned by critics as 'Rainforest Algebra'. The Congressional Record of June 9, 1997 includes the following passages from his speech:

Mr. President, over the past decade, I have been continually puzzled by our Nation's failure to produce better students despite public concern and despite the billions of Federal dollars... I took algebra instead of Latin when I was in high school. I never had this razzle-dazzle confusing stuff...

This odd amalgam of math, geography and language masquerading as an algebra textbook goes on to intersperse each chapter with helpful comments and photos of children named Taktuk, Esteban, and Minh. ... I still don't quite grasp the necessity for political correctness in an algebra textbook. Nor do I understand the inclusion of the United Nations Universal Declaration of Human Rights in three languages or a section on the language of algebra which defines such mathematically significant phrases as, "the lion's share," the "boondocks," and "not worth his salt."

... From there we hurry on to lectures on endangered species, a discussion of air pollution, facts about the Dogon people of West Africa, chili recipes and a discussion of varieties of hot peppers...what role zoos should play in today's society, and the dubious art of making shape images of animals on a bedroom wall, only reaching a discussion of the Pythagorean Theorem on page 502.

Falling
back on the theme of social justice, progressive educators cast the
critics as
politically right wing, and presented the disagreements to journalists
as a
conflict between conservative traditionalists who demanded basic skills
and
progressive reformers who advocated conceptual understanding.

Many conservatives did indeed rally in opposition to the progressive maths of the NCTM, for example, Lynne Cheney, Chester Finn, Rush Limbaugh, Phyllis Schlafly, and Thomas Sowell. However, not all opponents were conservative. Three of the four founders of the parents group, Mathematically Correct, described themselves as liberal Democrats as did Elizabeth Carson, the leader of NYC HOLD, which by the beginning of the 21st century had emerged as the leading opposition group to NCTM aligned programmes. Following a presentation to the California Board of Education, Abigail Thompson, a mathematics professor at the University of California at Davis

. . .was invited to speak at a local Republican convention. A liberal Democrat, Thompson was stunned. Mathematicians tend to jump into such issues with both feet, she says, "and then they find themselves labeled as right-wing conservatives. And it's pretty hilarious. I don't know any mathematicians who are right-wing conservatives."[18]

Alfie
Kohn, an advocate of progressive education, criticized parental
opposition in
an April 1998 Phi Delta Kappan article entitled, *Only for My Kid:
How
Privileged Parents Undermine School Reform*. He
observed, 'It is common
knowledge that the Christian Right has opposed all manner of
progressive
reforms', but he also identified the subversive role played by liberal
parents
opposed to the reform curricula:

Jeannie Oakes, author of Keeping Track, calls them "Volvo vigilantes," but that isn't quite accurate – first, because they work within, and skillfully use, the law; and second, because many of them drive Jeeps. They may be pro-choice and avid recyclers, with nothing good to say about the likes of Pat Robertson and Rush Limbaugh; yet on educational issues they are, perhaps unwittingly, making common cause with, and furthering the agenda of, the Far Right.

Like other progressives, Kohn reinforced the dichotomy of basic skills versus conceptual understanding, but he also advanced another dichotomy: doing what is best for learning versus doing what is best for admission to universities:

. . . more than one observer of the "math wars" has wondered whether we are witnessing a debate over pedagogy or about something else entirely. Are parents really trying to deny that encouraging students to figure out together what lies behind an algebraic formula is more valuable than getting them to memorize algorithms or slog through endless problem sets? Do they seriously doubt that such an approach is better preparation for higher math in college? Or does parental opposition really just reflect the fear that more sophisticated math instruction might be less useful for boosting SAT scores and therefore for getting students into the most elite colleges? Math reformers who counterpose merely doing arithmetic with really understanding (and being able to apply) mathematical principles may be missing the more pertinent contrast, which is between doing what is best for learning and doing what is best for getting my child into the Ivy League.

The
arguments were strained. The 'traditional curriculum' was accused of
being too
focused on basic skills at the expense of understanding, or more
concisely, of
being 'dumbed-down'. Thus, progressive programmes were putatively
'better
preparation for higher math in college'. Yet, elite universities
expected a
traditional curriculum as preparation for admission. The unstated
implication
is that elite universities favoured a lower level of understanding over
the
concept-rich programmes that the NCTM claimed to offer *all* students.
But this was
hard to reconcile with criticisms of the NCTM reform by top university
mathematicians. After all, mathematicians devote their lives to
mathematical
concepts. How could they be opposed to conceptual understanding of
mathematics?

In
*The Math Wars* Schoenfeld
also describes the traditional curriculum as elitist and
portrays the math wars as a battle between equality and elitism:

. . . the traditional curriculum bore the recognizable traces of its elitist ancestry: The high school curriculum was designed for those who intended to pursue higher education. (page 267)

The *Standards*, buttressed
by NCTM's call for
"mathematics for all" and the equity agenda in *Everybody Counts*, clearly
sat in the
education-for-democratic-equality [camp]. . . In contrast, . . . the
traditional curriculum was a vehicle for . . . the perpetuation of
privilege. .
.Thus the *Standards *could be
seen as a threat to the current social order. (page
268)

. . . the traditional curriculum, with its filtering mechanisms and high dropout and failure rates (especially for certain minority groups) has had the effect of putting and keeping certain groups "in their place." (page 281)

These powerful indictments demanded radical solutions. Mathematics reform was social reform, and that meant redefining K-12 mathematics to make it more accessible. The resulting decline of K-12 mathematical content had obvious repercussions for universities. Hung-Hsi Wu expressed concerns of mathematicians when he wrote:

This reform once again raises questions about the values of a mathematics education ... by redefining what constitutes mathematics and by advocating pedagogical practices based on opinions rather than research data of large-scale studies from cognitive psychology.

The reform has the potential to change completely the undergraduate mathematics curriculum and to throttle the normal process of producing a competent corps of scientists, engineers, and mathematicians.[19]

The
term 'traditional' was never clearly defined in the debates. The NCTM
aligned
programmes were easy to define simply by listing them, and it is true
that some
specific 'traditional' mathematics programmes favoured by parents and
mathematicians could also be identified, but it is unclear what
tradition, if
any, they followed. Some of the secondary school mathematics books
favoured by
'traditionalists' dated back to the 'new math' period of the 1950s and
60s, at
which time they were considered anything but traditional. Others, like *Saxon
Math*,
included innovations such as review of previous topics within each
problem set. The strongest tradition in US education is progressivism
itself, not the
challenges to it.

The conflict between reformers and the California public reached a turning point in 1997. Under a Republican governor, the California Board of Education rejected the reform-oriented draft standards from one of its advisory committees, the Academic Standards Commission. The Commission majority, knowing the Board was opposed to their NCTM aligned draft,

delayed presenting it ... for the required Board approval until the very last minute allowed by law, foreclosing effective debate within the Commission at its final meeting and expecting that the deadline of January 1, 1998 for the Board's final decision would also prevent the Board's changing much of what they were springing in October... But the success of this hardball politics was foiled by the rapid response of the (forewarned) Board, which appointed four mathematicians [Gunnar Carlsson, Ralph Cohen, Steve Kerckhoff, and R. James Milgram] at Stanford University [to rewrite the draft]. [20]

In a few weeks the Stanford mathematicians rewrote the standards, correcting more than 100 mathematical errors, and eliminating all pedagogical directives. The document was approved in December 1997 by the State Board. California's new standards were clear, coherent, and met the criteria set by the California legislature to be competitive with mathematics standards of the highest performing countries in mathematics education.[21]

The
reaction from mathematics reformers was swift. The lead story in the
February
1998 News Bulletin of the NCTM, *New California Standards Disappoint
Many,* charged, 'Over protests
from business, community, and education leaders, California's state
board of
education unanimously approved curriculum standards that emphasize
basic skills
and de-emphasize creative problem solving, procedural skills, and
critical
thinking'. Joining the educational progressives, the state-wide chairs
of the
Academic Senates of the public colleges and universities in California
issued a
joint statement condemning California's standards and claimed that 'the
consensus position of the mathematical community' was against them.

California
mathematicians put a stop to the rumour of a consensus in the
mathematics
community against the state's standards. More than 100 mathematics
professors
from colleges and universities in California added their names to an
open
letter in support of the California standards. The signatories included
chairs
of the mathematics departments at the California Institute of
Technology,
Stanford, and several state universities. Jaime Escalante, portrayed in
the
movie* Stand and Deliver,* also added
his name in support.[22] The
conflict was more than just a theoretical disagreement. At stake was
the use
of NCTM aligned textbooks in California, the biggest market in the
nation.

California proceeded to develop state-wide tests and a system for textbook adoptions that included review panels of mathematicians and classroom teachers. Thus, California became the national base for opposition to the NCTM reform movement.

In
October 1999, the US Department of Education released a report
designating 10
mathematics programmes as 'exemplary' or 'promising'. Several of the
programmes on the list, including *MathLand,* had been
sharply criticized by
mathematicians and parents for much of the decade. The imprimatur of
the US
government carried by these controversial programmes threatened not
only to
undermine California's new direction in mathematics education, it could
marginalize criticisms of the NCTM aligned textbooks nationwide.

Within
a month of the release of the Education Department's report, more than
200
university mathematicians added their names to an open letter to
Secretary
Riley calling upon him to withdraw those recommendations.[23] The
list of signatories included seven Nobel laureates and winners of the
Fields
Medal, the highest international award in mathematics, as well as
mathematics
department chairs of many of the top universities in the US, and a few
state
and national education leaders. The* *open letter
was published on 18
November 1999 as an ad in the Washington Post, paid for by the Packard
Humanities Institute.[24]

Within
days the NCTM responded to the mathematicians' open letter with its own
letter
to Secretary Riley in which the organization explicitly endorsed all of
the
'exemplary' and 'promising' programmes.[25]
Nevertheless, in the
following years, the mathematicians' letter continued to be a useful
tool for
parents opposed to NCTM aligned textbooks. Recognizing its utility,
NCTM
President Johnny Lott in January 2004 posted a denunciation of the open
letter
on the NCTM website, under the title, *"Calling Out" the Stalkers
of Mathematics Education,* in which he
wrote:

Consider people who use half-truths, fear, and innuendo to control public opinion about mathematics education. As an example, look at Web sites that continue to use a public letter written in 1999 to then Secretary of Education Richard Riley by a group of mathematicians and scientists defaming reform mathematics curricula developed with National Science Foundation grants. . . A small group continues to use the letter in an attempt to thwart changes to mathematics curricula.[26]

Resistance
through the end of the century to abandoning the NCTM style textbooks
in some
California school districts was considerable. One case resulted in
front page
newspaper coverage. A critic of the California standards, Guillermo
Mendieta,
threatened a hunger strike on behalf of NCTM aligned mathematics
programmes.
Mendieta was the Director of Mathematics Education for the Achievement
Council,
a non-profit organization that addressed educational inequities. At
stake was
whether the Los Angeles Unified School District (LAUSD) would use
California
state approved textbooks or continue with 'integrated math' in
secondary
schools, along with *MathLand *and similar
programmes in elementary schools. Mendieta was supported by a coalition
that included the NCTM, Center X within
the University of California at Los Angeles, and various Latino and
African
American Organizations. LAUSD School Board President Genethia Hayes
also
extended her support to Mendieta and declared, 'I will advocate as hard
as I
can with my colleagues to make sure this particular door never gets
shut for
children of color. I really do see this as an issue of social justice'.[27]

One of the advocates for California approved textbooks was Barry Simon, the mathematics chair and IBM Professor of Mathematics and Theoretical Physics at the California Institute of Technology. Simon asserted that basic skills are essential to mathematics and counselled against redefining algebra via the NCTM aligned programmes in order to increase passage rates. Confronting the social justice arguments of the progressivists, he countered, 'If anyone is racist or sexist, it is those who claim that women and minorities are unable to deal with traditional mathematics'.[28] Others gave similar advice. Nevertheless, Mendieta's arguments carried the day. LAUSD's use of state approved textbooks was thus delayed until 2001.

Social
justice arguments in support of NCTM programmes continued into the new
century. The introduction to the book, *Rethinking Mathematics:
Teaching Social
Justice by the Numbers, *published in
2005, argued that,

Teachers cannot easily do social justice mathematics teaching when using a rote, procedure-oriented mathematics curriculum. Likewise a text-driven, teacher centered approach does not foster the kind of questioning and reflection that should take place in all classrooms, including those where math is studied. (page 4)

The
release of the *2000 NCTM Standards* had little
impact on nationwide
disagreements, beyond affirming the direction of the *1989 Standards*. The
revisions were
primarily rhetorical and the document did not differ substantially from
its
predecessor. More significant was the 'No Child Left Behind Act',
signed into
law with bipartisan support in 2002. Although flawed in many respects,
it asked
for challenging academic standards, high quality teachers, and imposed
annual
testing requirements on US schools. Perhaps even more significant was
the
creation in April 2006 of the 'National Mathematics Advisory Panel'
charged
with making policy recommendations to the President and Secretary of
Education
for the improvement of mathematics achievement of students. Of the 17
expert
panellists appointed by the conservative Bush administration, five were
signatories of the 1999 open letter to former Education Secretary
Riley. The
Expert Panel that recommended the 'exemplary' and 'promising'
mathematics programmes
in 1999 was appointed by a Democratic administration. The stark
difference
between the two expert panels reflects the political divide in the
maths wars.

**Concluding
Remarks**

Why did disagreements about school mathematics books in the US diverge according to left and right politics?

Part of the answer is historical. The roots of progressive education are intertwined with anti-authoritarian ideals from the Romantic Era. In addition, progressive educators, including a former NCTM president, argued that women and members of ethnic minority groups learn mathematics differently from white males.[29] Such views were harmonious with the politically liberal ethnic identity ideologies popular during this period, especially in universities. Taking into account the anti-elitism and social justice arguments surrounding constructivist mathematics programmes, it is then not surprising that multiculturalists and liberals would be attracted to the NCTM vision, even if they did not understand the mathematical issues involved. As those groups constituted parts of the electoral base for Democratic politicians, the latter would be reluctant to challenge the use of constructivist maths in schools.

The NCTM reform was an attempt to redefine mathematics in order to correct social inequities. To make mathematics more accessible to minority groups and women, progressive educators argued for programmes that eliminated basic skills and the intellectual content that depends on those skills. Ironically, progressivists' advocacy of such mathematics programmes for the supposed benefit of disenfranchised groups contributed to racial stereotyping, in contradiction to core progressive values.

In the course of the math wars, parents of school children and mathematicians who objected to the dearth of content were dismissed as right wing, but there is nothing inherently left wing about the NCTM aligned mathematics programmes. Neither the former Soviet Union nor other socialist countries participated in education programmes remotely like those promoted by the NCTM. Progressive maths is a purely capitalist phenomenon. Indeed, one of the promotional themes of the NCTM was to prepare students for the needs of business.

Ultimately, the injection of left and right ideologies into mathematics education controversies is counterproductive. The math wars are unlikely to end until programmes espoused by progressives incorporate the intellectual content demanded by parents of school children and mathematicians.

**Acknowledgments.** The author
would like
to thank Elizabeth Carson, Harry Hellenbrand, Ralph Raimi, Mary Rosen,
and
Sandra Stotsky for critical readings and suggestions.

**Bibliography**

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www.edexcellence.net/foundation/publication/publication.cfm?id=338.
Accessed on
22 August 2006.

Klein,
D, 'A brief history of American K-12 mathematics education in the 20th
century', in James Royer (ed) *Mathematical cognition: a volume in
current
perspectives on cognition, learning, and instruction*,
Information Age
Publishing, 2003, 175 - 225

www.csun.edu/~vcmth00m/AHistory.html. Accessed on 22 August 2006

McKeown,
M, Klein, D, Patterson, C, * '*National
science foundation systemic initiatives: how
a small amount of federal money promotes ill-designed mathematics and
science
programs in k-12 and undermines local control of education', in Sandra
Stotsky
(ed), *What's at stake in the k-12 standards wars: a primer for
educational
policy makers*, New York,
Peter Lang Publishing, Inc., 2000, 313 - 369.

National
Research Council, *Everybody Counts: A Report to the Nation on the
Future of
Mathematics Education*, National
Academy Press, Washington, D.C., 1989

Raimi, R, *Uncivil
war, *in* Education Next* (Hoover
Institution, Stanford, CA,
Summer 2004). This is a review of *California Dreaming: Reforming
Mathematics
Education*
by Suzanne M. Wilson (Yale University Press, 2003, xvi+303 pages), and
may be
found in expanded form at http://www.educationnext.org/unabridges/20042/raimi.pdf. The review
as printed
is at http://www.educationnext.org/20042/81.html. Accessed
on 22 August
2006.

*Rethinking
mathematics: teaching social justice by the numbers*, (ed) Eric
Gutstein and Bob Peterson,
copyright 2005, Rethinking Schools Ltd.

Martin
Scharlemann *Open Letter on MathLand*, 11 October
1996.
http://mathematicallycorrect.com/ml1.htm. Accessed on 22 August
2006.

Schoenfeld,
A. The math wars, *Educational
Policy,*
Vol. 18 No. 1, (2004) 253-286.

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what you
can do, *American Mathematical Monthly* 104 (1997),
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mathematics education* American Educator*, American
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[1] For an elaboration of this dichotomy, see Hirsch, *Romancing
the
Child*

[2] See Hirsch, *The Schools We Need*, p.
71-79

[3] Klein, *A Brief History of Mathematics Education in
the 20th
Century *(*A Brief History*)

[4] For the sake of transparency, I identify myself as a socialist and a registered member of the Green Party.

[5] See Klein, *Math Problems*
and *A
Brief History*

[6] Constructivism in this context is a variant of
progressivism. See
Hirsch, *The Schools We Need*, p. 245

[7] See the appendix of *A Brief History*

[8] *A Nation at Risk*,
another important
document from this period, is discussed in *A Brief History*.

[9] These same themes appeared in *A Nation at Risk.*

[10] For more details, see *A Brief History*

[11] However, a group of parents of school children in
Princeton, New
Jersey, including Princeton University faculty, in 1991 objected to
progressivist programs and eventually founded their own Charter school.
See *A
Brief History*.

[12] Two of the most important were "Mathematically Correct" (www.mathematicallycorrect.com) and New York City HOLD (www.nychold.com)

[13] See for example, Klein, *Math Problems*

[14] See Scharlemann, *An Open Letter on MathLand*

[15] *Time*, August 25, 1997,
Suddenly,
Math Becomes Fun And Games. But Are The Kids Really Learning Anything?

[16] See for example Wu, *Basic Skills Versus Conceptual
Understanding: A Bogus Dichotomy in Mathematics Education*

[17] *Focus on Algebra, Addison-Wesley Secondary Math, An
Integrated
Approach*, Addison-Wesley, Menlo Park, CA,
1996.

[18] Quoted from Jackson,* **The math wars: California
battles it out over
mathematics education (Part II).*

[19] Wu, The Mathematics Education Reform

[20] Quoted from Raimi, *Review of the book California
Dreaming*

[21] See Klein et al, *The State of State Math Standards
2005*

[22] See *A Brief History*

[23] I am a co-author of that letter.

[24] It is posted at: mathematicallycorrect.com/nation.htm

[25] The letter appears in the appendix to *A Brief History*

[26] For a rebuttal, see www.mathematicallycorrect.com/rebutlott.htm

[27] Quoted from Richard Colvin, Debate Over how to Teach Math Takes Cultural Turn, Los Angeles Times, March 17, 2000

[28] Ibid

[29] See *Big Business*