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THE MATH WARS By Robert E. Reys Despite the difficulties in designing, testing, and marketing new mathematics curricula, the need for significant improvement in student learning requires us to overcome these difficulties, Mr. Reys notes. All interested parties should stop trying to defend the past and work together to improve children's mathematics education for the future. |
THE continuing controversy regarding standards-based mathematics curricula developed with support from the National Science Foundation has produced a range of reactions from mathematicians, mathematics educators, parents, and other interested parties. The recent clashes in the California "Math Wars" remind us that the battle continues to consume much energy and emotion that could be used for better purposes.1 Differences of opinion with regard to what is important to learn and how it should be taught are nothing new in mathematics education.2 And at the heart of the discussion are the written curricula (i.e., the textbooks) that American students use in their mathematics classes. This is the issue I want to reflect on here.
As a mathematics educator old enough to have taught from several books produced by the School Mathematics Study Group (one of the "new math" curricula in the 1960s), I am now in my fifth decade of witnessing the continuing evolution of mathematics curricula. I have also been a co-author of a successful K-8 mathematics textbook series, which gave me firsthand experience with some of the challenges involved in developing a comprehensive mathematics program within the highly competitive, market-driven U.S. publishing environment.
During my career in higher education, I have had the opportunity to live in several countries, such as Mexico, Japan, and Sweden, where my children attended local schools. These adventures provided a rare but valuable opportunity to learn something about schools and curriculum materials in other countries. Today, I am involved in the National Science Foundation Show-Me Project (www.showmecenter.missouri.edu) that is dedicated to the dissemination and implementation of standards-based math curricula for middle schools.
Together, these experiences have provided professional growth and shaped my knowledge base. I share them with readers so that they will know the perspective from which I now reflect on the current controversies surrounding the reform of the mathematics curriculum.
In many ways, the United States is unique in its approach to education. My international perspective has enabled me to see both the virtues and the dangers of some of our traditional practices. For example, the United States is the only industrialized country that does not use the metric system, and it is one of the few countries that teaches separate courses in algebra and geometry. This means that curricular recommendations regarding the metric system made by Thomas Jefferson and included in a 1923 report by the Mathematical Association of America, titled The Reorganization of Mathematics in Secondary Education, have yet to be implemented. Clearly, significant curricular change is difficult and slow. Major pedagogical change in mathematics teaching presents even more challenges.
Developing Mathematics Textbooks
The mathematics textbook market in the U.S. is vast, and a number of factors facing the industry make seeking improvements very difficult. Among these are the following: 1) there is no national curriculum; 2) every state has its own state frameworks that influence what mathematical content is taught and when; 3) about half of the states are "adoption states," in which state committees review and approve textbooks; 4) the rest are "open states," in which each district, or sometimes school, chooses its own textbooks; 5) most districts adopt new mathematics books within a five- to seven-year cycle, but there is no single time (month or year) when all schools are adopting textbooks; 6) the availability of technology, including calculators and computers, varies greatly, so assuming the existence of a basic core of technology across all schools is risky; and 7) a serious shortage of certified mathematics teachers and a lack of deep mathematical knowledge among many who do teach limit the types of mathematics curricula that can be developed.
Together these factors translate into a need for textbook publishers, who are driven by sales, to produce materials that are available continuously, marketable in states with vastly different frameworks, and usable by teachers with a wide range of mathematical knowledge and preparation. Complicating the issue further, decisions about curriculum are often made by people with very limited backgrounds in mathematics.
These conditions severely restrict the long-term development of products. And they help explain why mathematics textbooks, even though prepared by different publishers, are often almost indistinguishable. In fact, the amount of deviation from the norm (i.e., from the leading seller) increases the likelihood that any new program will be rejected by states and districts. The bandwagon mentality is certainly alive and well in textbook production. The cost of developing and marketing completely new mathematics programs is very high, running into the tens of millions of dollars for an elementary mathematics program. Rather than create programs that are significantly different from the current best seller, the typical publisher examines the best sellers and emulates their strongest features. While this approach is safe and less risky, it limits significant change and ignores what children need.
The same factors that inhibit commercial textbook publishers from making significant changes have also made it more difficult to implement the vision portrayed in the National Council of Teachers of Mathematics (NCTM) publication Curriculum and Evaluation Standards for School Mathematics.3 Recognizing that publishers are reluctant to make the significant changes articulated in the NCTM standards, the National Science Foundation (NSF) supported a number of K-12 mathematics curriculum projects in an effort to produce programs that reflect the vision of the standards. (See "NSF-Funded Standards-Based Curriculum Projects," page 257.) These curricula have been the subjects of much discussion in recent years.
Debating Standards-Based Curricula
The improvements in mathematics education initiated by the release of the first version of the NCTM standards have stimulated more than controversy. Indeed, there is now widespread enthusiasm and much energy devoted to helping improve school mathematics instruction. And the mathematics curricula developed with NSF funds have served as a focal point for much of the recent debate.4 Ads and opinion pieces in prominent media outlets have brought an unprecedented level of national attention to mathematics education.
One major concern that has surfaced in these debates has been whether these standards-based mathematics curricula are being used in schools without adequate testing regarding their impact on student learning. This is a legitimate concern. In other fields, untested products would never be released for public use. For example, pharmaceutical companies must follow rigorous research procedures that include animal testing and documenting potential side effects before testing on humans can even begin. Then additional documentation on the human tests is required before permission is granted to make a product commercially available. Even with these testing procedures, the long-term consequences of a drug may not be known for many years.
But the "testing of textbooks" is very different from the "testing of drugs." With drugs, the independent variable (the drug being tested) can be carefully controlled, while the dependent variables are monitored closely. With mathematics textbooks, the dependent variable is student learning, and the independent variable is the mathematics curriculum. With textbooks it is not possible to place tight controls on the curricula, because the teacher, the students, the school contexts, and much more play critical roles in implementing the intended program. Therefore the treatment is immediately confounded by the teacher variable, as well as by countless other variables. Specific difficulties in conducting research related to curriculum abound and have been well stated.5
What does it mean to be effective? With drugs, effectiveness is more easily agreed upon than with educational programs. If a drug cures its intended ailment without undue negative side effects, it can be agreed that it is effective. However, with mathematics curriculum materials, determining what is effective depends on the evidence one values. Some people place the highest priority on skill development, so any evidence of improved skill is judged positively. Others may value understanding mathematical concepts, while still others may view problem solving as most important. While these goals are not mutually exclusive, obtaining valid and reliable evidence to support them all is very difficult. And as Judith Sowder points out, once this evidence is reported, its reception is greatly influenced by what people value and will accept as evidence.6
Impact of Mathematics Curricula
It has been suggested that standards-based mathematics curricula don't have a research base of student mathematical performance to support their use. Clearly, much research remains to be done and reported. However, the statement implies that traditional programs, which still make up the overwhelming majority of the programs in use, have a sterling record of success in promoting mathematics learning. Moreover, it ignores decades of poor performance documented by the National Assessment of Educational Progress (NAEP) and by three international assessments, the latest being the Third International Mathematics and Science Study (TIMSS). Furthermore, the lack of knowledge and understanding of mathematics discussed by Liping Ma is the by-product of mathematics programs that were in place long before standards-based mathematics curricula existed.7
People who demand research to document the effectiveness of reform curricula are either unaware of the history of student performance using the traditional curricula or choose to ignore more than 30 years of widely reported results. In fact, to assume that traditional mathematics programs have shown themselves to be successful is, according to James Hiebert, "ignoring the largest database we have." Hiebert goes on to say, "The evidence indicates that the traditional curriculum and instructional methods in the United States are not serving our students well."8
In arguing against the use of standards-based, NSF-supported curricula, some have alleged that children were used as guinea pigs for untried programs. This argument has strong emotional appeal. Who wants a child to be used as a guinea pig? Critics have advocated "stricter controls to prevent schools from using untested programs without the informed consent of parents and students."9 This claim is ironic on at least two counts. First, the traditional mathematics curriculum supported by the critics has not been tested for effectiveness, unless international assessments are used as the measure, in which case these curricula fall far short. Second, there has been unprecedented field-testing of these NSF-supported curricula over the past decade. They have been piloted, revised, field-tested in real classrooms, and revised again prior to their commercial availability. Data continue to be systematically collected, and feedback from the field is reflected in later editions. Research reporting on student achievement in a variety of grades is beginning to emerge.10 To criticize these curricula because of the philosophy they embody or the mathematical content of the materials is one thing. To suggest that they have not been extensively field-tested with teachers and students is blatantly untrue and irresponsible.
In fact, with very few exceptions, most widely used mathematics textbooks are not carefully researched and field-tested with children before they are sold to school districts. I base this assertion on my personal experience as well as on years of interacting with textbook authors. My own experience in co-authoring a textbook series was that, while every effort was made to create a product of the highest quality, publication deadlines made it impossible to do extensive field-testing. Lessons were written and edited and occasionally focus-tested with teachers. However, because of the market-driven nature of the textbook business, it was not possible to have teachers use the materials for several years and revise them based on student performance and feedback from teachers.
Calls for testing and documenting the impact of mathematics curricula will surely continue, and they should. However, the bar should be set at the same height for all publishers. If the developers of standards-based mathematics curricula are required to document the impact of those materials on student performance, then the same criterion should be applied to all companies producing mathematics textbooks for the same market. Of course, the prospects for such a requirement are dim.
Seizing the Opportunity
These are exciting times in mathematics education. Despite the difficulties in designing, testing, and marketing new mathematics curricula, the need for significant improvement in student learning requires us to overcome these difficulties. All interested parties should stop trying to defend the past and work together to improve children's mathematics education for the future.
The current curricular changes in mathematics education articulated in the recently released Principles and Standards for School Mathematics provide an opportunity for rich and substantive dialogue.11 We can all hope that mathematicians will use this document "as a tool for focused, constructive efforts to improve pre-K-12 mathematics education."12 If they do so, we can look forward to valuable discussions about ways to improve the mathematics education of our children. Opportunities to reflect on what we do and don't know and to explore new options are bound to emerge. And, in the process, mathematicians, mathematics educators, classroom teachers, and school administrators will be able to pool their collective wisdom and energies to develop mathematics programs that will help all students learn relevant and challenging mathematics throughout their school years. This is an important task that requires a united effort if we are to be successful, and nothing short of success is acceptable.
ROBERT E. REYS is a professor of mathematics
education, University of Missouri, Columbia.
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Last updated 8 November 2001
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