Curriculum and Evaluation Standards for School Mathematics has been hailed as the exemplar of what is needed in all curricular areas if we are to reform American education during the coming decade (National Council of Teachers of Mathematics 1989). As chair of the commission that produced this 258-page document, my intent here is to provide an account of how the mathematical sciences education community developed the Standards.
Origin of the Standards
The strategy we used came about as a result of two conferences held in 1983 in response to the perceived crisis in education, as voiced in A Nation at Risk and Educating Americans for the Twenty-First Century. The first conference was sponsored by the Conference Board of the Mathematical Sciences and funded by the National Science Foundation; the other was jointly sponsored by the National Council of Teachers of Mathematics (NCTM) and the University of Wisconsin and funded by the U.S. Department of Education. The dozen or so recommendations contained in the reports of both meetings were strikingly similar. Each suggested the development of a “new content framework” for the K–14 mathematics curriculum.
In 1986 the National Council of Teachers of Mathematics organized the Commission on Standards for School Mathematics to prepare a draft document. Composed of classroom teachers, supervisors, mathematics educators, and mathematicians, the Commission formed four working groups, one each to address curriculum for grades K–4, 5–8, 9–12, and a group to address evaluation. In developing the draft, the groups consulted reports and background papers related to the calls for reform; a variety of research reports; recent state curriculum documents (California, Oregon, Wisconsin); curriculum documents from other countries (Australia, The Netherlands, Japan, The United Kingdom); and two summary papers outlining the perspectives and the tasks to which we were committed.
- The Standards were created as a consequence of scholarly review and analysis.
- Review and consensus involving many groups were paramount in the process.
- Using its own resources, a professional organization produced the document. No authority to develop standards was demanded by a governmental agency or corporate group. The professional community decided it was needed and took the initiative.
The Reform Vision
- Teaching mathematics to “all students” emphasizes that anyone who is to be a productive citizen in the 21st century must be mathematically literate—including not only “talented white males” but all underrepresented groups.
- “More mathematics” implies that all students need to learn more than how to manipulate arithmetic routines. At present, nearly half of American students never study any mathematics beyond arithmetic.
- “Often different mathematics” indicates that all students need to learn concepts from algebra, geometry, trigonometry, statistics, probability, discrete mathematics, and even calculus.
- “To learn” means more than to memorize and repeat. Learning involves investigating, formulating, representing, reasoning, and using appropriate strategies to solve problems, and then reflecting on how mathematics is being used.
- “Revised” instruction implies that teachers and students need to envision mathematics classrooms as discourse communities where conjectures are made, arguments presented, strategies discussed, and so forth.
The content that all students should have an opportunity to learn is described in detail in Curriculum and Evaluation Standards for School Mathematics. To capture the importance of both technical and reflective knowledge, we chose the term mathematical power, which envisions a citizenry and society empowered by mathematics. For the individual, mathematical power means having the experience and understanding to participate constructively in society. For a culture to be mathematically powerful, its citizens must have the understanding and experience to undertake the routine tasks of everyday life, to operate as a democratic society, and to progress as a civilization. This means the acquisition, in society, of a critical mass of understanding, experience, and attitude, in addition to a substantial range of special expertise.
Thus, students need to learn to value mathematics, to reason and communicate mathematically, and to become confident in their power to use mathematics coherently to make sense of problematic situations in the world around them. Hence, the Standards advocate the application of four basic standards to all of the content standards proposed: mathematics as problem solving, mathematics as reasoning, mathematics as communication, and mathematical connections (making linkages within mathematics and between mathematics and the real world).
The Reform Strategy
The Commission's intent to develop a document titled Standards was deliberate. According to the Oxford American Dictionary, a standard is “a thing or quality or specification by which something can be tested or measured,” “the required level of quality,” or “a distinctive flag” (1980, p. 666). For us, a standard specified criteria to judge the quality of the mathematics curriculum and methods of evaluating it. In order to judge quality, we decided that there must be agreed-upon expectations. Thus, standards become statements about what is valued.
Historically, groups have adopted standards to (1) assure quality, (2) indicate goals, and (3) promote change. The NCTM Commission on Standards was created to achieve each of these three objectives. In the United States, any group or individual can produce and sell a mathematics textbook, test, or curriculum guide. Although most such efforts are well intentioned, the recent proliferation of manipulatives, software, and modules have made minimal curricular standards a necessity. The Commission focused on the development of standards as statements of expectations or as “criteria for excellence.” However, part of our broader strategy was to provide mathematics teachers “a distinctive flag” to justify their demands for change.
- Before any plan can proceed, a need for change must be established. First, evidence must be presented that the current system is not effective. Second, planners must decide whether the problem is the result of a lapse in quality control, a design flaw, or a combination of both (Cuban 1988). Third, if a new design is needed, planners must be aware of the traditions that have to be challenged. The need for a new blueprint for mathematics education has been well documented.
- Vision is a key factor if a new design is needed. Design change involves not only eliminating or replacing inadequate materials or practices, but creating a new system. Realizing a vision necessarily includes consideration of values, goals, and standards. The Standards were designed to fulfill this vision.
- Planning includes involving everybody in a system or school in arriving at consensus about the details of long- and short-range plans (with timetables) for change. It is at this step that demand is created.
- The next step involves identifying specific elements of the system to be targeted for change (curriculum materials, instructional methods, examinations, teachers, technology) and prioritizing them.
- Any system depends on suppliers. In a supply-and-demand society, schools must demand that suppliers (textbook publishers, testing companies, staff developers, university teacher education programs) contribute the ingredients necessary for the desired changes in elements.
- Then it is time to operationalize the new materials, procedures, and programs. Feedback from this trial phase is matched with the vision and the plan for judgment, and revisions may be made.
- Finally, a product (a curriculum, an instructional procedure, assessment materials) is developed. In economics, a product is judged of good quality if it satisfies customer needs while making the company a profit. In education, quality should be judged in terms of what students are able to do and whether this meets society's needs. Again, via feedback, we now return to the vision and our goals and objectives to update or revise the vision, plans, specific elements, and so forth.
Our intent is that school staffs at all levels use this seven-step strategy to develop a reform curriculum for K–12 mathematics. In particular, each mathematics teacher must understand the need for change, own the vision, participate in planning, become a spokesperson for the demands for new products and processes, try out new materials, and judge student progress toward the reform vision. Teachers need to understand the critical role they play in curriculum reform efforts.
Status of the Standards
Implementation of the Standards means a numbers of things need to occur: using the documents to plan change, making demands of suppliers, enhancing the professional status of mathematics teachers and educators, and empowering teachers to voice their views. Planning for change in education takes place on at least three organizational levels.
Reform initiatives at the national level are being influenced by the Standards. They were a focal point in the Bush administration's strategy for school reform and were adopted by the National Education Goals Panel. At the state level, reform plans should go beyond goal statements and general expectations to curricular frameworks for schools. Several states (California and Texas, for example) have recently produced frameworks based on the Standards, and several others are in the process of developing them. In addition, many states (19, at last count) have initiated new assessment practices, in part to align testing with the goals of the reform effort.
At the local district level, plans for change should go beyond specifying materials and resources to designating how teachers and students should interact with them. It is encouraging that many districts have formed curriculum committees; however, it is hard to estimate how many of these districts have developed implementation plans.
The evidence that the demands for change are being heard is clear. The National Science Foundation is funding a variety of curriculum and teacher enhancement projects. The Department of Education is encouraging the use of Eisenhower funds to assist teachers in developing new materials. California, Texas, and other states are urging publishers to develop new texts to meet their frameworks. In fact, at current professional meetings, book publishers are claiming either that their current materials meet the criteria set forth in the Standards or that they are developing new materials to meet them. Test publishers, too, are busy developing new instruments to be aligned with the Standards.
The professional status of mathematics teachers and educators and their empowerment has also been enhanced. The creation of the Mathematical Sciences Education Board (another of the recommendations) has provided the mathematics community with a national agency to represent its constituents. Membership in national and local mathematics teachers' organizations is at an all-time high, and attendance at meetings has set records every year. Finally, an increasing number of mathematics teachers are being asked to testify at hearings and serve on national and state committees dealing with mathematics education.
The impact of the Standards document since its publication three years ago has gone far beyond our expectations. However, the hard part of systemic change is yet to happen. Only when the plans and new products are being used in classrooms by teachers who own the philosophy and vision expressed in the Standards will real change begin to occur.
Challenges That Remain
To carry out the vision of a reformed school mathematics curriculum, policymakers and school staffs face a number of issues and problems.
The meaning of “standards”? To many persons, the term standards implies measuring student performance. Although not a serious issue, the use of the word to indicate a vision that mathematics teachers can rally around is unusual and requires explanation.
Nominal change. To appease demands for change, producers often change labels but not substance. For example, since 1990 the authors of the National Assessment for Educational Progress have claimed substantial changes in items in the test battery in light of the reform expectations. In fact, both the 1990 and 1992 batteries show little alignment with the NCTM Standards (Romberg et al. 1992).
What is mathematics? “Most of the population perceive mathematics as a fixed body of knowledge long set into final form. Its subject matter is the manipulation of numbers and the proving of geometrical deductions. It is a cold and austere discipline which provides no scope for judgment or creativity” (Barbeau, 1989, p. 2). The aims of teaching mathematics need to go beyond this narrow view to empower learners to create their own mathematical knowledge; to reshape mathematics, at least in school, to give all groups more access to its concepts and to the power its knowledge brings; and to bring the social contexts of the uses and practices of mathematics into the classroom. When mathematics is seen in this way, it can then be studied in living contexts that are meaningful to learners, including their languages, cultures, and everyday lives, as well as their school-based experiences.
The “saber-tooth tiger” content. Topics should be included because of their inherent worth, not because they have “always been part of the curriculum.” Peddiwell's (1939) satirical tale of continuing to teach students techniques to scare saber-tooth tigers with fire long after the tigers have become extinct is analogous to the continued expectation that students master interpolation of logarithms, square roots, long division, and myriad other routine procedures long after computers have automated them. Further, room needs to be made in the curriculum for new, or newly important, topics such as statistics or discrete mathematics.
Teacher independence and isolation. One tradition of schooling is that teaching happens behind closed doors (Metz 1978). Such independence allows teachers to take risks and be creative. Taken to an extreme, independence often leads to isolation. Porter (1988) refers to one consequence of independence as a curriculum “out of balance.” Elementary school mathematics is routinely taught in such a way that students are repeatedly exposed to the same content from one grade to the next, with skills typically receiving 10 times the emphasis given to either conceptual understanding or application. The reform vision sees as the norm a balanced curriculum arrived at via teacher collaboration, joint planning of lessons, and shared judgments about student performance.
- “Math is what we do to quiet kids down after recess.”
- “Drill on procedures teaches students how to follow rules.”
- “Success on a math test is essential for tracking.”
- “Math should not be fun. It teaches students about drudgery and failure.”
- “Curricular changes must improve standardized test scores.”
Isn't this a repeat of the “new math”? This is a natural question, given the failure of post-Sputnik attempts to develop a new mathematics curriculum. The answer is: NO! The “new math” was an elitist attempt by university mathematicians to better prepare college-bound mathematics students for a changed collegiate curriculum (Romberg 1990). The current movement focuses on mathematics for all students and is being organized by the teachers of mathematics at all levels.
How is this effort related to other reforms? Although the objectives of the mathematical sciences education community were developed independently of many other programs, if they embrace the same assumptions about subject matter content and pedagogy as other change plans, then they should be compatible. Systemic change based on the same ideas is needed.
A Vision and a Strategy
There is no question that the current school mathematics curriculum is out-of-date. The majority of American students do not have an opportunity to become empowered mathematically even though our culture demands mathematical literacy of its citizens. Creating new curriculums will take time, hard work, commitment, patience, and persistence.
In Curriculum and Evaluation Standards for School Mathematics, the mathematical sciences education community has proposed both a vision of a mathematics curriculum designed to meet the need and a strategy that districts and schools can follow to construct a curriculum consistent with this vision. For teachers, the Standards provide a flag to rally around as they fulfill their essential role in mathematics reform.
