national standards: a new dimension in professional leadership

454 Part I� Background� Crosswhite

National Standards: A New Dimensionin Professional LeadershipF. Joe CrosswhitePast President NCTMProfessor EmeritusThe Ohio State University

The intent of this article is to present an overview of the National Councilof Teachers of Mathematics* (NCTM) Curriculum and Evaluation Standardsfor School Mathematics (NCTM. 1989). This is the first component of themore comprehensive Standards Project that will also address the areas ofteaching, teacher education, and the evaluation of teaching. A working draftof these companion standards is now in circulation under the title,Professional Standards for Teaching Mathematics. After extensive review andrevision, the teaching standards will be released at the NCTM annual meetingin 1991.Throughout its history, the NCTM has provided leadership in matters of

curriculum, instruction, and teacher education. That has been its primarypurpose. Thus, in one sense, the Standards Project is simply an extension ofthis pattern of leadership. The current effort to develop, disseminate, andwork toward the implementation of a comprehensive set of national standardsfor school mathematics, however, is a significant departure from earlierNCTM efforts.To understand the Council’s motivation for developing national standards

or to judge their appropriateness, one needs to consider the context withinwhich this project evolved. The documentary history that foreshadows andsurrounds this project may help to put it in perspective. Space does not permita full elaboration of how these documents anticipate and color the currenteffort; however, a study of these documents will reveal that the Standardsshould be viewed more as evolutionary than revolutionary.

In the mid-1970s, there was a growing concern among professionals inmathematics education that the school curriculum was being narrowed bywhat has been called the Back to Basics movement. That movement seemed tocontinue a cyclic pattern of overreaction that has characterized the history ofschool mathematics in this country. What has been seen as an excessiveemphasis in one direction during one generation has been replaced in the nextby an equally unbalanced emphasis in an opposing direction. Suchpolarizations have been counterproductive. School mathematics has sufferedfrom a vacillation between what the National Advisory Committee onMathematics Education called "false dichotomies." In the words of theirreport, we allow ourselves to be "manipulated into false choices between the

School Science and MathematicsVolume 90 (6) October 1990

Part I�Background�Crosswhife 455

old and the new in mathematics, skills and concepts, the concrete and theabstract, intuition and formalism, structure and problem solving, inductionand deduction" (NACOME. 1975). These are indeed false choices. Schoolmathematics programs should seek reasonable balance between the elements ineach pair, and yet, those kinds of choices have characterized cycles in schoolmathematics.The National Council of Supervisors of Mathematics was reacting to the

narrowing effect on curriculum of the Back to Basics movement in the NCSMPosition Paper on Basic Mathematical Skills (NCSM, 1978). At essentially thesame time, and with similar motivation, the NCTM made the commitment todevelop a set of recommendations for school mathematics of the 1980s thatbecame the Council’s An Agenda for Action (NCTM, 1980). Each of thesedocuments may be seen as a progenitor of the Standards Project. They callfor a more balanced approach to curriculum and instruction and areconceptually quite consistent with the new standards. In fact, attempts toevaluate the impact of the NCTM Agenda became one of the immediatemotivations for the Standards. The Agenda was written at a level of generalitythat proved difficult to translate into criteria for program evaluation. The newstandards were intended to define criteria of excellence that would providemore specific guidelines for curriculum and instruction and a more assessablebase for evaluation.

Subsequent to the release of the NCTM Agenda, there was an explosion ofconcern for science and mathematics education in US schools. This wassignaled most dramatically by the National Commission on Excellence inEducation in A Nation at Risk: The Imperative for Educational Reform(NCEE, 1983). This was quickly followed by a spate of national commentarygenerally critical of conditions in our schools and of science and mathematicseducation particularly. This climate of national concern was reinforced byemerging data from international comparative studies of student achievement,e.g., from the Second International Mathematics Study (Crosswhite, 1985).Curriculum was specifically identified as a contributor to an unacceptableachievement pattern for US students in The Underachieving Curriculum:Assessing US School Mathematics from an International Perspective(McKnight, 1987). Based on this and other studies, a symposium oninternational comparative studies sponsored by the Mathematical SciencesEducation Board crystallized the national concern even as early drafts for theCurriculum and Evaluation Standards for School Mathematics were beingwritten. All of this created an atmosphere that is now much more receptive tothe notion of national standards for school curricula than has historically beentrue in the United States.

Less well-known, but concurrent with A Nation at Risk, is the report of theNational Science Board Commission on Precollege Education in Mathematics,Science, and Technology (NSB, 1983). This report, titled Educating Americans

for the 21st Century, identifies many of the curricular issues addressed in the


456 Part I�Background�Crosswhite

NCTM Standards. Of particular relevance is the paper. The MathematicalSciences Curriculum K-12: What is Still Fundamental and What is Not(CMBS, 1983), that was prepared as source material for the commission. Thereports of two national conferences, School Mathematics: Options for the1990s (Romberg, 1984) and New Goals for School Mathematics (CBMS,1984), should also be acknowledged as immediate precursors of the NCTMStandards. Each contains recommendations that are fleshed out in theCurriculum and Evaluation Standards for School Mathematics. To fullyappreciate the evolution of the Standards and to understand why they havethose characteristics that will be described later in this article, one needs toreview these antecedents. The Standards and their motivation are also clarifiedby contemporaneous documents, such as Everybody Counts (MSEB, 1989)and Reshaping School Mathematics (MSEB, 1990).The Curriculum and Evaluation Standards for School Mathematics may

also be studied with greater perspective when one realizes how and why thiseffort represents a new dimension in professional leadership. The Standardsproject stands in contrast to earlier NCTM efforts and to those of otherprofessional organizations in several ways.

Never before has a professional organization of teachers undertaken thetask of specifying national standards for school curricula in its discipline. Infact, in the formative stages of this project, we were widely advised not to usethe word standards or in any other way to suggest that we might beadvocating a national curriculum. The US tradition of local control of schoolscaused many to have difficulty separating the notion of national leadershipfrom the spector of federal control. It was not easy for some, even among theNCTM membership, to see that national professional standards need not, andin fact they do not, pose a threat to local autonomy. The NCTM Standardsdescribe a vision for school mathematics; they do not prescribe a curriculum.Local options and local initiatives will determine how well and to what extentthat vision will be realized. There can be wide variation in specific approachesto curriculum consistent with the standards.The near concurrent development of standards for school mathematics

curriculum, for teaching and teacher education, and for the evaluation of bothteaching and learning represents a far more comprehensive effort than anyearlier NCTM undertaking. Parallel efforts in other professional organizationsmake the current level of attention to mathematics education even moreencompassing. For example, the NCTM is working closely with theMathematical Association of America to develop new standards for themathematical preparation of teachers, the Mathematical Sciences EducationBoard has developed a supporting rationale and framework that augments theNCTM Standards (MSEB, 1990), and the Board on Mathematical Sciences (incollaboration with several mathematical organizations) is addressing issues ofreform in collegiate mathematics. The comprehensive nature of these efforts,and the degree of cooperation among them, should create an overall integrity


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that will cause the several sets of new standards to be mutually consistent andsupportive. The Curriculum and Evaluation Standards for School Mathe-matics should be seen as one element in a much more comprehensive reformmovement. In isolation, some aspects of the Standards may seem unattainableor even unwise. When viewed in the context of supporting change in allaspects of mathematics education, or even more broadly as part of a systemicchange in education itself, the Standards seem more immediately realistic.Even standing alone, the new Curriculum and Evaluation Standards for

School Mathematics are more comprehensive than earlier NCTM curriculumguidelines. The new standards address the school mathematics program for allstudents at all grade levels. Curriculum guidelines have usually addressed asubset of the student population, a restricted range of grade levels, or both,and never have curriculum guidelines been so immediately coupled withguidelines for evaluation. The simultaneous development of standards in thesetwo closely-related areas is both a recognition of the degree to whichtraditional testing practices have had a stagnating influence on curriculum andof the fact that some aspects of the new vision for school mathematics willsimply require nontraditional methods of assessment.The process by which these new standards have been and are being

developed also represents a new dimension in NCTM’s professionalleadership. Past NCTM curriculum guidelines or other position statementshave been developed by relatively small committees and approved by theBoard of Directors. In the current effort, drafts of the standards have beensubmitted to extensive mail review, have been the subject of discussion atmany NCTM meetings and at meetings of affiliated groups, and have beenreviewed independently by both professionals and nonprofessionals in regionalforums conducted by the Mathematical Sciences Education Board. Thus, wecan expect that the Standards more nearly reflect a professional consensusthan any similar NCTM statements developed in the past. Moreover, becauseof the extensive review of working drafts and the subsequent revision based onthose reviews, there is likely to be a wider sense of ownership among theNCTM membership that will be a critical factor in local implementation.The commitment to invest the Councils resources and energies as fully in

the implementation of the Standards as it has in their development also standsin contrast to earlier efforts. Too often curriculum guidelines have simplyappeared in one of the NCTM publications with the apparent expectation thatnothing further need be done to ensure their impact in the schools. In theStandards project, a major effort is being made to generate a grass rootsreform movement as well as to work with test and textbook publishers tomake appropriate materials available to support that reform. Regionalconferences are now underway that will make models and materials availableto a number of local implementation teams in each state. Together with theexpense incurred in development and initial dissemination, the commitment topursue this project through the implementation stage will require a financial



commitment unprecedented in NCTM or any other professional organizationof teachers in a given subject field. The magnitude of the Standards, both inconceptual and financial terms, certainly does extend the dimensions ofprofessional leadership.

I have digressed from my assigned task, to describe key features of theCurriculum and Evaluation Standards for School Mathematics, because I feelit is important that these be studied with perspective. They are part of themost comprehensive leadership effort the National Council of Teachers ofMathematics has ever undertaken. More than that, they are part of a largerreform movement that encompasses all aspects of mathematics education at alllevels, and they have developed in the context of an even larger educationalreform movement that may affect the fundamental conditions of schoolingwithin which mathematics teaching and learning occurs. The Standards haveevolved in a climate of national concern about mathematics achievement.They were written to reflect recent developments in the mathematical sciencesand their applications. They are based on a new vision of what it will mean tobe mathematically literate in this information age. They are responsive to

developing computing technologies and cognizant of their potential impact onboth curriculum and instruction. Finally, they describe a balanced curriculum,not a continuation of a pattern of misguided overreaction. In short, theCurriculum and Evaluation Standards for School Mathematics should not beread as just another set of curriculum guidelines.

The Curriculum and Evaluation Standards for School Mathematics

The Standards are intended as criteria that can be used to judge the qualityof a mathematics curriculum or methods of evaluation. They are statementsabout what should be valued in a school mathematics program. They are notintended to be prescriptive. They do not outline topics for a particular gradelevel, and they do not constitute a scope and sequence chart. Instead, theypresent a holistic vision of school mathematics that defines new goals, setsnew national expectations, and creates a framework for reform at the locallevel.A central basis for the Standards is consideration of what it will mean to be

mathematically literate in an information society, a society that will requireworkers to understand the complexities and technologies of communication, toask questions and formulate problems, to assimilate unfamiliar information,and to work cooperatively in teams as well as independently. Henry Pollak’ssummary of the mathematical expectations for new employees in today’sindustries is cited in the Standards as illustrative of these new demands:

1. The ability to set up problems with the appropriate operations.2. Knowledge of a variety of techniques to approach and work on

problems.3. Understanding of the underlying mathematical features of a problem.4. The ability to work with others on problems.


Part I�Background�Crosswhife 459

5. The ability to see the applicability of mathematical ideas to common andcomplex problems.

6. Preparation for open problem situations, since most real problems arenot well-formulated.

7. Belief in the utility and value of mathematics. (NCTM, 1989, p. 4)The contrast between the skills and understandings implicit in theseexpectations and those acquired by students working independently on routinesets of drill and practice exercises is the basis for several of the major themesin the new curriculum standards.

General Goals for Students

Emerging from the view of mathematical literacy, five general goals arearticulated for all students. It is particularly important to note that theopportunity for all students to achieve these goals to the best of their ability isat the heart of the NCTM vision of a quality mathematics program. Theintent of these general goals, and of the Standards themselves, is that eachstudent gain mathematical power, which is defined to be the ability to explore,conjecture, and reason logically, as well as the ability to use a variety ofmathematical methods to solve nonroutine problems. The five general goalsare that the student will:

1. Learn to value mathematics. Students should have numerous and variedexperiences related to the cultural, historical, and scientific evolution ofmathematics so that they can appreciate the role of mathematics in thedevelopment of our contemporary society and explore relationships amongmathematics and the disciplines it serves�the physical and life sciences, thesocial sciences, and the humanities.

2. Become confident in their own ability. Students need to see themselves asbeing capable of using their growing mathematical power to make sense ofnew problem situations in the world around them. They should see that doingmathematics is a common, familiar human activity. Having success ex-periences in a variety of real-life mathematical environments can help studentslearn to trust their own mathematical thinking.

3. Become a mathematical problem solver. Problem solving is the processthrough which students discover and apply the power and utility ofmathematics. Skill in problem solving is the hallmark of mathematical literacyand is essential to productive citizenship. To develop such skill, students neednot only to work frequently with problems that are easily resolved, but onothers that may require hours, days, or even weeks to solve. Some problemsmay be relatively simple exercises to be accomplished independently; othersshould involve small groups or an entire class working cooperatively.

4. Learn to communicate mathematically. To express and expand theirunderstanding of mathematics, students need to learn to use the signs,symbols, and terms of mathematics. This goal is best accomplished in thecontext of problem solving that involves students in reading, writing, and



talking in the language of mathematics.5. Learn to reason mathematically. Making conjectures, gathering evidence,

and building an argument to support a theory are fundamental to doingmathematics. Sound reasoning should be valued as much as the ability to findright answers.

Assumptions About Mathematics

The first consideration in preparing each of the curriculum standards was itsmathematical content. The standards are based on three assumptionsconcerning mathematics. First, is that knowing mathematics is doingmathematics. It is clear that the fundamental concepts and procedures of somebranches of mathematics should be known by all students, but the value ofinformational knowledge is in the extent to which it is useful in the course ofsome purposeful activity. Mathematics instruction should persistentlyemphasize "doing" rather than simply "knowing that." This assumptioncauses the Standards to envision a much more active role for students both inthe development and in the application of mathematical processes.

Second, some aspects of doing mathematics have changed in recent years.The computer’s ability to process large sets of information have broadened theareas in which mathematics is applied. Quantitative techniques have permeatedalmost all intellectual activities. Areas such as business, economics, linguistics,biology, medicine, and the social and life sciences have become much moremathematical. The fundamental mathematical ideas needed in these areas,however, are not necessarily those studied in the traditional algebra-geometry-precalculus-calculus sequence, a sequence designed with engineering andphysical science applications in mind.

Third, changes in technology and the extended applications of mathematicshave resulted in growth and change in the discipline of mathematics itself. It issaid that more than half of all mathematics known has been invented sinceWorld War II. The new technology not only has made calculations andgraphing easier, it has changed the very nature of the problems important tomathematics and the methods mathematicians use to investigate suchproblems. Because technology is changing mathematics and its uses, theStandards are based on the belief that:

1. Appropriate calculators should be available to all students at all times.2. A computer should be available in every classroom for demonstration

purposes.3. Every student should have access to a computer for individual and group

work.4. Students should learn to use the computer as a tool for processing

information and performing calculations to investigate and solve problems.The Standards do not argue that the availability of calculators eliminates

the need for students to learn algorithms. Some proficiency with paper-and-pencil computational algorithms is important, but such knowledge shouldgrow out of problem situations that create a need for the algorithms.



Furthermore, when one needs to calculate to find an answer, informed choicesshould be made between estimation, mental computation, paper-and-pencilalgorithms, and the use of a calculator.

Format of the Curriculum Standards

The 40 curriculum standards divide the discussion of curriculum contentinto three grade-level groups: (a) kindergarten through 4, (b) grades 5 through8, and (c) grades 9 through 12. Each standard has four components:

1. The identification of a topic in mathematics to be explored at thosegrade levels.

2. A statement of expected student activities relative to that topic.3. A Focus Section that elaborates a rationale for that standard.4. A Discussion Section that includes examples meant to convey the spirit

of the standard.Two general principles guided the statements of activities. First, that

activities should grow out of problem situations; and second, that learningoccurs through active involvement with mathematics. Traditional teachingpractices that focus on manipulating symbols and practicing algorithms as aprelude to problem solving ignore the fact that knowledge often emerges fromproblems. This suggests that instead of the expectation that skill incomputation must precede word problems, experiences in problem solving helpto develop the ability to compute. The Standards reject the conception oflearning as a process in which students passively absorb information, storing itfor retrieval as individual fragments resulting from repeated practice andreinforcement. Instead, they subscribe to a constructive, active view oflearning in which students approach a new task with prior knowledge,assimilate new information, and construct their own meanings. This view oflearning demands variation in instruction that should include opportunities for(a) appropriate project work, (b) group and individual assignments, (c)discussion between teacher and students and among students, (d) practice onmathematical methods, and (e) exposition by the teacher. This view oflearning is reflected in the verbs chosen to describe student actions in theStandards, e.g.. to investigate, to formulate, to find, to explore, to verify.

Prior to grade 9, there is no differentiation of expectations for students.The content of each standard is considered appropriate for all students. It isthe mathematical content perceived to be needed by all productive citizens. Todeny any subset of students the opportunity to learn this body of mathematicswould be to invite an intellectual elite and a polarized society. The 9-12standards are differentiated, a core program is defined for all students, andextensions in the breadth and depth of treatment and in the applications ofthe core topics are suggested for college-bound students. The mathematics ofthe core program is sufficiently broad and deep so that student options forfurther study would not be limited. The expectation is that all students musthave the opportunity to encounter typical problem situations related to a


462 Part I�-Background�Crosswhite

range of important mathematical topics; however, their experiences may differin the pace at which they encounter these topics and in the vocabulary ornotation used, the complexity of the arguments, or the level of mathematicalrigor introduced.

Content of the Curriculum Standards

The first three curriculum standards for each grade level segment deal with(a) problem solving, (b) communication, and (c) reasoning. Details vary acrossgrade levels with respect to what is expected both of students and ofinstruction. This variation reflects the developmental level of the students,their mathematical background, and the specific mathematical topics they areencountering; however, it is clear that each of these areas should be addressedthroughout the school curriculum with increasing levels of sophistication.The fourth curriculum standard at each level is titled Mathematical

Connections. This label was chosen to convey the belief that, although it isnecessary to teach specific concepts and procedures within a given topic area,mathematics must be approached as a whole. The internal connectionsbetween the concepts, principles, and procedures of the several branches ofmathematics must be the object of direct instruction. Students should emergefrom school mathematics with a global and interconnected view ofmathematics, not a compartmentalized view. The external connections ofmathematics to other disciplines and to the real world are equally important.Thus, conscious attempts to relate the mathematics a student studies to otherareas they are encountering in the school curriculum and to their out-of-schoolenvironment should be frequent and pervasive.

These first four curriculum standards are so illustrative of the flavor andspirit of the Standards that examples, collapsed across the several grade levelsegments, seem appropriate here.

1. Mathematics as Problem Solving. This standard emphasizes activitiesthat enable students to:

a. Use problem-solving approaches to investigate and understandmathematical content.

b. Recognize and formulate problems arising in everyday andmathematical situations.

c. Develop and apply a variety of strategies to solve problems, withemphasis on multi-step and nonroutine problems.

d. Verify and interpret results with respect to the original problem.e. Acquire confidence in using mathematics meaningfully.

2. Mathematics as Communication. Focuses student attention on developingand using language and symbols to:

a. Model situations using oral, written, concrete, pictorial, graphical, andalgebraic representations.

b. Reflect on and clarify their own thinking about mathematical ideasand situations.


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c. Use the skills of reading, listening, viewing, and questioning tointerpret and evaluate mathematical ideas.

d. Appreciate the value of mathematical notation and its role in thedevelopment of mathematical ideas.

e. Realize that representing, discussing, reading, writing, and listening tomathematics are a vital part of learning and using mathematics.

3. Mathematics as Reasoning. Concentrates on leading students to:a. Draw logical conclusions about mathematics by recognizing and

applying inductive and deductive reasoning processes.b. Use mathematical models, facts, properties, and relationships to

validate and explain their own thinking.c. Make and evaluate mathematical conjectures and arguments.d. Appreciate the pervasive use and power of reasoning as a part of

mathematics.4. Mathematical Connections. Provides opportunities for students to make

connections within mathematics and between mathematics and other areas sothey can:

a. See mathematics as an integrated whole.b. Relate graphical, numerical, physical, algebraic, and verbal models or

representations.c. Recognize relationships among different topics in mathematics and

between mathematics and other curriculum areas.d. Value the role of mathematics in our culture and society.

For each grade level segment, nine or ten additional content standards arestated and discussed. Some of these share common or similar titles,emphasizing that some topics should be developed across a wider range ofgrade levels. Others emphasize specific content that needs to be fullydeveloped within that level.Of particular note at the 9-12 level is the recommendation for a common

core curriculum for all students. This is a major departure from recentpractice at the high school level where we have compartmentalized themathematics for college-preparatory students and have expected other studentsto explore quite different topics. The standards take the position thatdifferences among students entering high school, in mathematicalachievement, motivation, or intended goals, should be addressed byenrichment and extension of the proposed core content rather than bydeletion. A school curriculum in line with the NCTM Standards would permitall students to progress as far into the mathematics program as theirachievement in each topic area would allow.

Several important features are included in the introduction to each grade-level set of standards. The assumptions underlying the standards for thatgrade-level segment are explicitly stated. A summary of changes in contentand emphasis is given for each grade-level group. These summary lists are veryinformative as to shifts in emphases and the ways in which space and time can



be made available to accommodate new content and emphases. There is, inboth the introductory sections and in the elaboration on each standard,discussion of modes of instruction that are consistent with the spirit of thestandards.

The Evaluation Standards

Fourteen evaluation standards in three categories are presented in a sectionseparate from the curriculum standards. The first set of three evaluationstandards describes general assessment strategies related to the curriculumstandards. The next seven focus on how teachers might gather informationthat will help them improve instruction. These standards closely parallel thecurriculum standards. They deal with assessing mathematical power, problemsolving, communication, reasoning, mathematical concepts, mathematicalprocedures, and mathematical disposition, i.e., students’ attitudes aboutmathematics and their inclination to think and act in positive ways towardmathematics. Teachers can use these standards to make comprehensiveassessments of their students’ progress in mathematics. The final set of fourstandards relates to gathering evidence for program evaluation. These stan-dards are to be used by teachers, administrators, and policy makers to makejudgments about the quality of a school program in mathematics and theeffectiveness of instruction.

Teaching Standards

Standards for the teaching of mathematics, along with teacher educationand the evaluation of teaching, are now being developed by the NCTM. Thesestandards will address a full range of issues relating to mathematicsinstruction. Until they are available, one can find in the Curriculum andEvaluation Standards for School Mathematics quite a lot of guidance withrespect to teaching methods that are in the spirit of the new vision of schoolmathematics. These are either explicit in the discussion sections or they areimplied by the nature of the student activities recommended or in theexamples given.

A Vision of School Mathematics

The guest editors of this special issue asked me to describe what I wouldexpect schools to look like if the NCTM Standards become reality. That is aneasy task. If I visited a class in such a school, I would expect to see thefollowing:

1. A room fully equipped for mathematics instruction; with a computer forthe teacher to use in demonstrations, with other computers for student access,with an appropriate calculator for each student, with extensive resourcematerials including manipulatives, and with an arrangement and atmosphereconducive to activity learning.

2. A teacher who spends much of his or her time creating an active learning



environment; one who guides, questions, discusses, clarifies, and listens morethan they lecture or give directions.

3. A group of students who explore, investigate, discuss, reason, validate,represent, and construct mathematics as often as they practice algorithmicskills; students who work together in groups and communicate with each otherand with the teacher in the language of mathematics.

4. A curriculum that is rich in problem-solving activities; one that includesan integrated range of topics, that is connected from topic-to-topic and withthe world outside mathematics, that elicits reasoning and communication, thatis based more on mathematical concepts than algorithmic procedures, and onethat reflects emerging trends in mathematics and its applications.

I am sure there are rooms, teachers, students, and curricula that alreadyhave many of these features. I have seen some. If the NCTM Standards havethe impact they are hoped to have, such will become the rule rather than theexception.

References

Conference Board of the Mathematical Sciences. (1983). The mathematicalsciences curriculum K-12: What is still fundamental and what is not. InNational Science Board Commission on Precollege Education inMathematics, Science, and Technology, Educating Americans for the 21stcentury: Source materials (pp. 1-23). Washington, DC: National ScienceFoundation.

Conference Board of the Mathematical Sciences. (1984). New goals formathematical sciences education. Washington, DC: Author.

Crosswhite, F. J., et al. (1985). Second international mathematics study:Summary report for the United States.

Mathematical Sciences Education Board. (1989). Everybody counts: A reportto the nation on the future of mathematics education. Washington,DC: National Academy Press.

Mathematical Sciences Education Board. (1990). Reshaping schoolmathematics: A philosophy and framework for curriculum. Washington,DC: National Academy Press.

McKnight, C. C. et al. (1987). The underachieving curriculum: Assessing USschool mathematics from an international perspective. Champaign, 1L:Stipes.

National Advisory Committee on Mathematics Education. (1975). Overviewand analysis of school mathematics, grades K-12. Washington, DC:Conference Board of the Mathematical Sciences.

National Commission on Excellence in Education. (1983). A nation atrisk: The imperative for educational reform. Washington, DC: USGovernment Printing Office.

National Council of Supervisors of Mathematics. (1978). Position statementson basic skills. Mathematics Teacher, 71(2), 147-152.


466 Part I�Background�Romberg

National Council of Teachers of Mathematics. (1980). An agenda foraction: Recommendations for school mathematics of the 1980s. Reston,VA: Author.

National Council of Teachers of Mathematics. (1989). Curriculum andevaluation standards for school mathematics. Reston, VA: Author.

National Science Board Commission on Precollege Education in Mathematics,Science, and Technology. (1983). Educating Americans for the 21st century.Washington, DC: National Science Foundation.

Romberg, T. A. (1984). School mathematics: Options for the 1990s.Chairman’s report of a conference. Washington, DC: US GovernmentPrinting Office.

Evidence Which Supports NCTM’sCurriculum and Evaluation Standardsfor School MathematicsThomas A. RombergNational Center for Research in Mathematical Sciences EducationUniversity of Wisconsin-MadisonMadison, Wisconsin 53706

In March 1989, the Curriculum and Evaluation Standards for SchoolMathematics was released by the National Council of Teachers ofMathematics (NCTM). This document presents a vision of school mathematicsthat the authors argue is needed, makes sense, and that it is possible torealize. Whenever sweeping changes are called for in current practices,practitioners should be able to marshall evidence to support therecommendations. The purpose of this article is to present a summary of suchevidence for the necessity of reform in school mathematics.

It should be understood that during the two years it took to prepare theStandards and the extensive review of literature made in conjunction withthem, discussions were held with members of the Commission on Standardsfor School Mathematics and with members of the writing groups, and alibrary of materials was available to the writers. Thus, scholarly evidence wasconsidered in the preparation of the Standards.However, it also should be understood that the Standards is not a research

document, nor a set of text materials to be followed by teachers in classroomsto improve test scores, nor is it a piecemeal set of recommendations to makecurrent instruction in mathematics more efficient and effective. Rather, it was


national standards: a new dimension in professional leadership

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