What is "Reform Math"? Who promotes "Reform Math"? Who opposes "Reform Math"?

It is well-known that there is a major national debate about the way math is taught. At present the agenda is agressively dominated by the proponents of "reform math". It should be better-known that the development, promotion, and implementation of "reform math" curricula is led by a relatively small but powerful group of "education researchers", who are generally not trained as mathematicians or scientists. The entire "reform math" industry has been sustained since the early 1990's by billions of dollars of governmental grant funding.

On the other side, the leading opponents of the "reform math"movement are often accomplished research mathematicians, who generally do not have a substantial financial or career stake in the debate.

Table of contents:

• Understanding "Reform Math" and the "Math Wars"
• Who's who in the math wars? Follow the money trail
• Additional sources of information on the Math Wars

Understanding "Reform Math" and the "Math Wars"

Glossary: The chain of interconnected concepts and terms advocated by the dominant "reform math" movement:

• Reform math:
  • Gained prominence in the 1990's. De-emphasizes computational skills, emphasizes imprecisely defined "concepts".
• Standards-based curriculum:
  • "standards" generally refers to a series of documents issued by the NCTM, the primary advocacy group for reform math
• Research-based curriculum:
  • promoted by "researchers" in "Mathematics Education", generally not based on research in mathematics or science.
• NSF-funded or NSF-supported curriculum:
  • instructional material developed and promoted with support of multi-million dollar grants from the Education (EHR) branch of the NSF, not the mathematics (DMS) or science branches of the NSF
• New new math
  • reform math started as a response to the original "new math" which was dominant from the early 60's through the late 80's. The original "new math" was criticized for being overly rigorous and demanding, the "new new math" is criticized for going too far in the opposite direction.
• Inquiry-based or investigation-based curriculum:
  • emphasizes unguided "explorations" by students. One weakness of inquiry-based curricula is unequal individual participation in group "explorations".

The reform math movement has raised many legitimate objections from a range of qualified experts:

For almost two decades, mathematics education in K-12 classrooms has been driven by unsupported pedagogical theories constructed in our schools of education and propagated by the National Council of Teachers of Mathematics (NCTM). Their curricular and pedagogical "vision" for mathematics education reform, articulated in the two NCTM standards documents (1989 and 2000), has dominated local, state and federal education decision-making and policies, as well as public discussions, and press coverage. But many parents, mathematics experts, and K-12 teachers of mathematics do not share this vision.

A well-informed group of education stakeholders rejects the NCTM doctrine and model for mathematics reform. The expertise and viewpoints of this diverse group, comprised of mathematicians and scientists, K-12 teachers of mathematics, educational researchers, and concerned parents across our nation has been regularly eclipsed and marginalized by the dominant voice of mathematics educators in our schools of education and of NCTM officials. This constituency's expertise is often entirely absent from the decision-making process. We are members of that constituency, and are part of an informal bipartisan grassroots coalition of advocates for authentic reforms in mathematics education.

(From Ten Myths About Math Education And Why You Shouldn't Believe Them, by Karen Budd, Elizabeth Carson, Barry Garelick, David Klein, R. James Milgram, Ralph A. Raimi, Martha Schwartz, Sandra Stotsky, Vern Williams, and W. Stephen Wilson)

Studies purporting to support the claims of the "reform math" movement are often unscientific and systematically flawed, and generally not viewed as credible by objective experts:

(The reform movement)... began in 1989 with the publication of Curriculum and Evaluation Standards for School Mathematics (generally known as “The NCTM Standards”) by the National Council of Teachers of Mathematics [5]. The National Science Foundation (NSF) subsequently funded the development and implementation of thirteen elementary, middle, and high school mathematics curricula based on these Standards, programs variously referred to as “reform,” “Standards- based,” or “NSF-sponsored” by their publishers and others. Many of these programs have been controversial. In particular, there has been concern that the NSF-sponsored curricula moved from pilot testing to large-scale implementation without sufficient independent evaluations of their efficacy in preparing students for college mathematics and science courses. Although studies of the effectiveness of these curricula have yielded promising conclusions (see, for example, the collection of such evaluations in [17]), most have been conducted by persons associated with their writing or implementation. A recent National Research Council (NRC) report, On Evaluating Curricular Effectiveness [8], also expresses concerns about the methodological adequacy of these studies. (page 905)

(From "A Study of Core-Plus Students Attending Michigan State University", American Mathematical Monthly, December 2006 (and reprinted online), by Thomas Parker and Richard O. Hill)

The strong objections of the Mathematics community to the "reform math" movement elicited some token concessions from the NCTM, which did not meaningfully address the important concerns that had been raised. A revision of the NCTM standards is known as "PSSM" - Principles and Standards for School Mathematics:

by the end of the 1990s enough mathematicians—notable among them Richard Askey, the late Han Sah, and Hung-Hsi Wu—had developed a loathing for NCTM doctrine that managed to attract the attention of NCTM itself. Other opposition has also emerged, mainly from parents’ groups enraged at the NCTM-blessed mathematics programs beginning to spread in their schools.

PSSM continues to abhor direct instruction in, among other things, standard algorithms, Euclidean geometry, and the uses of memory. Though like its predecessor it has the word “standards” in its title, it is not a set of standards in the usual meaning of the term, for it refuses to say what exactly a child should learn in thirteen years of schooling. Long division? Quadratic formula? How to compute the quotient of two fractions? (See p. 218 of PSSM for an enlightening discussion.) Proof of a theorem on inscribed angles? Trigonometric identities? PSSM will neither affirm or deny, lest it seem to dictate content.

“Explore”, “develop”, and “understand”, and their variants, are much more prominent in the text than “know”, “prove”, and “remember”.

I warn you that these “principles and standards” cannot be appreciated by reading only a few pages. In the small the document sometimes sounds good. But if PSSM in the large informs our vision, then self-esteem is better than knowledge, dictionaries can replace a ready (memorized?) vocabulary, and higher-order thinking skills will boil stones into soup.

(From Ralph Raimi, Letter to the Notices of the American Mathematical Society, February 2001)

The opposition of the mathematics and science community to "reform math" came to a crescendo with the publication of the landmark open letter to Education Secretary Riley. The letter was published as a paid advertisement in the Washington Post on November 18, 1999. An online version of the Riley letter is available, and makes for very interesting reading.

The letter is a protest in the strongest possible terms to an October 1999 endorsement of ten "reform math" curricula issued by a Department of Education panel. More than 200 prominent mathematics and science experts strongly protested the competence, objectivity, and conclusions of the panel endorsing the reform math curricula. The list includes seven Nobel Laureatues and Fields Medalists (the Mathematics equivalent of the Nobel Prize), as well as mathematics department chairs from many top U.S. universities, as well as some state and national education leaders.

It is significant to note that two of then ten "reform math" curricula that were strongly condemned in the letter to Secretary Riley are now in use at Columbia Public Schools! These are CMP (Connected Mathematics Program, grade 6-8) and Core-Plus (Contemporary Mathematics in Context, grades 9-12).

Unfortunately, the "reform math" movement continued to dominate the debate about the teaching of mathematics across the United States. Predictably, as the number of schools adopting "reform math" curricula has increased, so have the problems.

In an effort to understand and address the problems, the U.S. Department of Education announced a National Mathematics Advisory Panel on April 18, 2006. The final report of the panel was released on March 13, 2008, and the full report as well as excerpts are available online at:

Foundations for Success: Report of the National Mathematics Advisory Panel.

The general conclusion of the panel:

"This Panel, diverse in experience, expertise, and philosophy, agrees broadly that the delivery system in mathematics education—the system that translates mathematical knowledge into value and ability for the next generation—is broken and must be fixed. " (p xiii)

The "reform math" movement claims to support its arguments with "mathematics education research". However, the National Mathematics Advisory Panel pointedly and specificly warns that a large proportion of the "mathematics education research" does not meet the usual scientific criteria for research validity and applicability:

"As in all fields of education, the large quantity of studies gathered in literature searches on important topics in mathematics education is reduced appreciably once contemporary criteria for rigor and generalizability are applied." (p xxvi )

Officially "The NCTM Welcomes National Math Panel’s Focus on Strengthening Math Education", so the the Panel's strong and unambiguous conclusion about the poor quality of "mathematics education research" was a conundrum. As usual, the NCTM masterfully rose to a thorny public relations challege with the following cleverly misleading response:

"While much is known about effective mathematics teaching, the National Math Panel was limited in the range of research that it was permitted to consider."

Translation for the reader unfamiliar with "education research": The National Panel was not permitted to use "the large quantity of studies gathered in literature searches on important topics in mathematics education" because these studies failed to meet the standard scientific "criteria for rigor and generalizability".

In fact, the "reform math" movement has actively resisted the usual scientific criteria, insisting on "their own" criteria even if those are rejected by mainstream scientists and educators.

A very interesting manifesto of the "reform math" movement is the paper "An Agenda for Research Action in Mathematics Education: Beginning the Discussion", published in the Journal for Research in Mathematics Education, 2004, vol 35, no 2, p 74-80, and prominently reprinted on the NCTM website. The paper is authored by the "NCTM Research Committee" (including Robert Reys of the MU College of Education, and member of the CPS Secondary Mathematics Task Force). Annotated excerpts follow:

"The Research Committee is a major standing committee of the NCTM, entrusted to advise the NCTM Board of Directors ..."

The NCTM wants to expand even further its power over "federal policy and funding":

"The call presented in this article introduces a set of issues for broader discussion among the community of mathematics educators that makes the case for the NCTM to play a more central role in shaping federal policy and funding than it currently employs."

The paper touts success of the NCTM standards (two different versions) as enabling the "mathematics education community" to effectively seize control of the national debate.

"The 1989 Curriculum Standards and the 1991 Professional Teaching Standards were consensus statements that enabled the mathematics education community to define for itself what is important and what critical concerns in curriculum, evaluation, assessment, teaching and technology would be central to the Council (NCTM)."

The paper acknowledges the validity of much of the major criticism leveled against the "reform math" movement:

"As critics have pointed out, the body of mathematics education does not provide evidence that is compelling enough to support many important educational and programmatic decisions at the school and system level (Carnine & Gersten 2000; Whitehurst 2003). Too often, research in mathematics education does not contribute consciously to an interconnected body of practice-oriented research nor do the results of one study signal the next step in making progress toward answering an important and practical problem. This results in little cumulative evidence for practitioners and policymakers to address the effectiveness of instructional strategies and curricula. On the political front the desire for research to address these concerns has raised questions about the quality and rigor of research in mathematics education, spawned the creation for the ERIC Clearinghouses, and engaged the government in defining its own standards for educational research."

Remarkably, the paper then forcefully argues to mobilize the "reform math" movement to reject the concerns of everyone outside the movement itself:

"We must also project an agenda for action by which we can define our own direction, our own standards of rigor, and our own central research questions..." (orignal emphasis)

This argument appears to have been persuasive. Indeed the "reform math" movement seems to have rejected most of the legitimate concerns of mathematicians, scientists, and sadly, also those of students, parents, and teachers.

Incredibly, past NCTM President Johnny Lott characerizes all opponents of his group's positions as "stalkers", whether they be individual experts, parent groups, or governmental entities. From 'Calling Out' the Stalkers of Mathematics Education:

"When the word stalker is used, different images come to mind: a hunter, a shadower, or possibly a person who follows another person with the intent to harm. In recent years, a kind of stalking, lurking menace has focused on the field of mathematics education. It is time to confront this presence and "call it out" for what it is."

"This menace to mathematics education has appeared in three guises: the expert who uses position or power in an attempt to denigrate the field; people who use half-truths, fear, and innuendo to try to control public opinion, school boards, and other agencies that work with mathematics education; and, finally, federal agencies that use money to bend state and local school systems to their will."

"We can put a stop to the stalking and coercion of mathematics education by individuals, groups, and governments ...."

The "reform math" movement certainly continues to make a forceful effort to "put a stop" to all opposition (which Lott calls "stalking and coercion") with no consideration of the origin or validity of the opposition. It is amazing that members of this powerful group like to think of themselves as victims of a "kind of stalking, lurking menace" to help justify their own determined bullying of "public opinion, school boards, and other agencies".

Who's who in the math wars? Follow the money trail

The NSF (National Science Foundation) has traditionally supported research in science and mathematics. NSF grant support for science and mathematics is one indicator of standing in the community of peer scientists and mathematicians. Many of the prominent critics of "reform math" are accomplished mathematicians, and accordingly many have a strong record of NSF grant support for mathematics (DMS is the Division of Mathematical Sciences in the NSF organization).

Prominent opponents of reform math - a cross section

The "reform math" movement gained influence in the early 1990's, when the Education (EHR) branch of the NSF started dispensing multi-million dollar grants for "math education", and has tenaciously worked to keep the money flowing. In contrast, the Mathematics (DMS) branch of the NSF generally does not administer education grants, and they judges grants by very different criteria. The recipients of the Education (EHR) grants, who are generally not mathematicians, prominently advertise their own work as "NSF-funded" or "research-based", and frequently use this distinction as a cudgel to marginalize dissenting opinions or competing curricula.

In short, the effects of large-scale and often indiscriminate funding of "reform math" projects by the NSF education division (EHR) has actually been viewed as harmful by many mathematicians. The following is excerpted from a May 7, 2002, email sent by Prof. Wilfried Schmid (Mathematics Dept., Harvard) to U.S. Representatives Nick Smith (Chairman, House Subcommittee on Research) and Sherwood Boehlert (Chairman, House Committee on Science):

"The NSF Directorate for Education and Human Resources (EHR) has caused tremendous damage to mathematics education in the United States. I say this with a sense of sorrow, since the science-directed activities of the NSF have done much to maintain and extend the US lead in science and mathematics research."

How much does the NSF spend on Mathematics Education? The NSF estimates that $1.8 billion was spent by the EHR directorate on 1,277 Mathematics Education projects in the time frame 1994-2002. This constitutes approximately 36 percent of the EHR spending during this period. This information comes from the internal audit The Mathematics Education Portfolio Brief, NSF 05-03, Item 1, page 10. (Also, see the organizational chart, figure 2 page 5, for an overview of some of the major players in "mathematics education" and their affiliations.) The FY 2007 budget for the EHR directorate is $796.7 million. If one assumes that the percentage for Mathematics Education has held constant at 36 percent, the NSF would have spent approximately $287 million on Mathematics Education in FY2007.

Although the wisdom of NSF education funding is itself subject to debate, the cumulative dollar value of NSF Education Support does serve as an effective indicator for identifying some of the leading figures in the "research-based" mathematics education movement. Many of the leading proponents of "reform math" are members of an elite club, let us call it the "ten-million dollar club", having been principal investigators or co-investigators on NSF education grants totaling more than $10,000,000. It is worth considering how these enormous amounts of money, and the associated professional prestige, are influencing the national debate on the teaching of mathematics. No one seems to have asked the following question:

• What is an appropriate level of public disclosure, or recusal for conflict of interest, for a member of the ten-million dollar club acting as an "objective expert" in advisory or decision making roles?

Prominent advocates of reform math - a cross section of the "ten million dollar club"

The MU (University of Missouri) College of Education is a major national center for advocates of "inquiry-based" and "research-based" methods in mathematics and science education. The list of MU College of Education faculty with multi-million dollar education grant support includes^*:

Barbara Reys - $25,150,773 on 7 NSF education grants

Robert Reys - $18,193,249 on 13 NSF education grants

Kathryn Chval - $13,693,416 on 3 NSF education grants

Fran Arbaugh - $7,902,368 on 5 NSF education grants

James Tarr - $7,037,981 on 2 NSF education grants

Sandra Abell - $4,773,073 on 8 NSF Education grants

Doug Grouws - $3,407,016 on 5 NSF Education grants

John Lannin - $2,610,009 on 3 NSF Education grants

In fact, the Doctoral program Mathematics Education at MU (University of Missouri) ranked very highly in a recent national survey conducted by Robert Reys (MU Math Education) and several current and and former MU Math Education students. The survey was part of an article published in the AMS Notices Nov 2007. The full text of the article is available online.

Additional sources of information on the Math Wars

Much of the information on any "war" tends to advocate a particular viewpoint. Many of the opponents and proponents of "reform math" listed in the tables above have links promoting their views on education and mathematics.

Generally nonpartisan information

• The National Mathematics Advisory Panel is generally considered by all parties to be nonpartisan. The membership represents a cross-section of prominent advocates from both sides of the math wars. The report as well as excerpts are available online at:

Foundations for Success: Report of the National Mathematics Advisory Panel.

• The Christian Science Monitor newspaper ran a series of articles in 2000 titled "The Math Meltdown". This series was recognized by a national reporting award:

2000: National Awards for Education Reporting
Education Writers Association, 2nd place
The Math Meltdown, Recipients: Marjorie Coeyman, Mark Clayton, and Amelia Newcomb

The Math Meltdown - table of contents and links to each of the articles

• "What Works" clearinghouse from the U.S. Department of Education: provides "high-quality reviews of the effectiveness of replicable educational interventions (programs, products, practices, and policies) that intend to improve student outcomes."
• ERIC clearinghouse from the U.S. Department of Education: provides "Bibliographic records of education literature plus a growing collection of full text"

Opposition to "reform math":

• Mathematically Correct
• David Klein was one of the authors of letter to Sec. Riley
  • very good overview of the 'math wars',
  • on the harmful effects of NSF Education grants
• Richard Askey was one of the authors of letter to Sec. Riley
  • on education
  • on assessment
• Hung-Shi Wu - references on mathematics education; Wu was also one of the authors of letter to Sec. Riley
• NYChold
• (local connection) Columbia Parents for Real Math - includes Petition signed by over 600 Columbia residents

Advocacy for "reform math":

• NCTM - National Council of Mathematics Teachers - the primary advocacy organization for "reform math"
  • (local connection) Education Material Committee (EMC) members include Robert Reys and Barbara Reys of the MU College of Education
    • members of groups overseen by EMC include Fran Arbaugh and Doug Grouws from MU, and James Hiebert from Delaware
• Deborah Ball
• Joan Ferrini-Mundy published the article "Principles and Standards for School Mathematics: A Guide for Mathematicians" in the September 2000 AMS Notices. Her resume also includes:
  • Director of the NSF Division of Elementary, Secondary, and Informal Education (DRL) within the EHR Directorate (Education and Human Resources). The DRL alone manages a portfolio of 820 active education grants in excess of a billion dollars, specifically $1,092,429,655 (database search 4-1-08). This works out to an average award in excess of a million dollars per grant, specifically $1,332,231.
  • Principal investigator or co-investigator on 10 education grants from the NSF EHR Directorate totaling $38,516,092
  • chaired the Writing Group for NCTM 2000 Principles and Standards for School Mathematics
  • served on the Board of Directors of the NCTM
  • served as Ex-officio member of the National Mathematics Advisory Panel
• (local connection) Robert Reys - current projects
• Ruth Parker's lecture "Engaging Parents and the Public" (LSC PI Meeting 1999)
• James Hiebert 's lecture "Effective Mathematics Teaching: What does the research say?" (CSUN 2007)
• (local connection) The Show-me Center describes itself as "A National Science Foundation project supporting implementation of standards-based middle grades mathematics curricula".
• • The Show-Me Center Staff consists of the following University of Missouri faculty:
    • Director: Barbara Reys
    • Co-Directors: Fran Arbaugh, Ira Papick, Robert Reys, James Tarr
  • Specifically, the Show-me center "provides information and resources needed to support selection and implementation of standards-based middle grades mathematics curricula. ... The phrase "standards-based" is used here to refer to implementation of recommendations regarding mathematics curriculum and instructional practice outlined in the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics (1989), Professional Standards for Teaching Mathematics (1991) and the Principles and Standards for School Mathematics (2000). "
  • Connected Math (CMP) is one of the four "reform math" middle school curricula promoted directly by the Show-Me center. CMP is the curriculum adopted by Columbia Public Schools for grades 6-8. The principal author of CMP is Glenda Lappan (former NCTM president, NCTM Lifetime Achievement Alumni Award). Glenda Lappan also led the Show-Me Center team that developed the document Implementing Standards-Based Mathematics Curricula: Preparing The Community, The District, And Teachers

(Note from September 08: The Show-me Center links here are via the Internet Archive to reflect site that was online in April 08. Comparing the current Show-me Center site with the April 08 version shows some serious revisions of history. For example, the center is now retroactively relabeled as "A National Science Foundation
Implementation and Dissemination Project: Middle School Mathematics", conspicuously removing "standards-based" .)

• Mathematically Sane: Who is in charge? Why are they hiding?
• From the Mathematically sane Mission statement: "We are a national grass-roots group of teachers, administrators, teacher educators, parents, and mathematicians who are concerned about the future of mathematics education. We are self-financed and have no affiliation with any other organization, either non-profit or for-profit. ... We are not publicizing the names of those organizing the effort in order to focus attention on the content rather than on the individuals involved."
• A bit of investigation reveals that W. Gary Martin has been able to juggle several hats while remaining in the shadows:
  • Mathematically Sane "founding member and webmaster", but not named on the site
  • Principal Investigator on an active NSF education grant in the amount of $9,377,887
  • former NCTM "Chief Education Officer"
  • former NCTM "Director of Research"