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**

Congressional Record of the US Senate, Robert Byrd, ‘A Failure to Produce Better Students,’ Senate, June 9, 1997, p S5393.

Hirsch E D, *The Schools We Need: Why We Don’t Have Them*, New York, New York, Double Day, 1996.

Hirsch E D, Romancing the Child, *Education Next* (Spring 2001) 34-39

www.educationnext.org/2001sp/34.html. Accessed on 22 August 2006.

Jackson, A, The math wars: California battles it out over mathematics education (Part II). *Notices of the American Mathematical Society*, *44*(7), (1997) 817-823.

Klein, D, ‘Big business, race, and gender in mathematics reform’, (appendix) in Steven Krantz, *How to Teach Mathematics*, American Mathematical Society (1999) 221-232.

Klein, D, Math problems: why the US Department of Education’s recommended math programs don’t add up*. American School Board Journal*, Volume 187, No. 4, (2000) 52-57. www.mathematicallycorrect.com/usnoadd.htm. Accessed on 22 August 2006.

Klein, D, et al, *The state of the state math standards 2005*, Washington, D. C., Thomas B. Fordham Foundation, 2005, 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.

Wu, H, The mathematics education reform: why you should be concerned and what you can do, *American Mathematical Monthly* 104 (1997), 946-954.

Wu, H, Basic skills versus conceptual understanding: a bogus dichotomy in mathematics education* American Educator*, American Federation of Teachers, Fall 1999.

[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*