One Point of View: NCTM's Curriculum and Evaluation Standards: What They Are and WhyThey Are NeededAuthor(s): Thomas A. RombergSource: The Arithmetic Teacher, Vol. 35, No. 9 (May 1988), pp. 2-3Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193402 .

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One Point OF X7ÍGCO

NCTM's Curriculum and Evaluation Standards: What They Are and

Why They Are Needed By Thomas A. Romberg

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During this past year, NCTM has produced a working draft of a set of curriculum and evaluation Standards for school mathematics (Commission on Standards for School Mathematics of the National Council of Teachers of Mathematics 1987). As chair of the Commission, I have been asked to respond to four questions.

What are standards?

The Oxford American Dictionary de- fines a standard as "a thing or quality or specification by which something can be tested or measured" or "the required level of quality" (1980, 666). For the Commission, a standard spec- ifies criteria to be used to judge the quality of the mathematics curriculum and methods of evaluation.

What is the purpose of standards?

Historically, three reasons have been cited for groups formally to adopt a set of standards: (1) to ensure quality, (2) to indicate goals, and (3) to pro- mote change. For this Commission, all three reasons are of equal impor- tance.

First, standards are often used to ensure that the public is protected from shoddy products. For example, a druggist is not allowed to sell a drug unless it meets certain very rigid stan- dards that include both control of how it was produced and evidence of its

Thomas Romberg teaches at the University of Wisconsin- Madison, WI 53706. He is pres- ently chairman of the NCTM's Commission on Standards for School Mathematics. He is inter- ested in research on the teaching and learning of mathematics.

effectiveness. Standards in this sense should be considered minimal criteria for quality. They set necessary, but not sufficient, conditions for produc- ing desired results.

Second, standards are often used as a means of expressing goals or expec- tations. For example, the standards for tests developed by the American Psychological Association in 1974 de- scribe the kind of documentation that publishers should provide about the reliability and validity of each test. Standards in this sense are statements of expectations.

Third, standards are often set or revised to lead a group toward some new desired goal or goals. This intent is to improve or update practices when necessary. In this sense, stan- dards should be seen as "criteria for excellence" rather than minimal stan- dards. They are based on a profes- sion's informed vision of what should be done given current knowledge and experience.

Once the NCTM Standards have been produced in their final form, it is expected that some groups will use them as criteria for what should be, whereas others will compare products and procedures with the Standards.

Why are standards for school mathematics needed?

For the NCTM Commission, the de- velopment of Standards as statements of expectations or as "criteria for ex- cellence" to produce change was our focus for several reasons; at the heart of them all is the fact that our society is emerging into a new age - the Infor- mation Age. Schools and, in particu-

lar, school mathematics must reflect the important consequences of this new age if our students are to be adequately prepared to live in the twenty-first century. Thus, the curric- ular and evaluative Standards we set have been written to foreshadow those expectations. Our vision of the future is based on the fact that during the past quarter century, a new tech- nology has evolved that replaces the human and mechanical means of com- munication, the printed page, letters, and so on, with electronic means by which information can be shared al- most instantly with persons any- where. Information is the new capital and the new raw material. Communi- cation is the new means of produc- tion. Furthermore, of all the subjects now taught in schools, none have changed as much as mathematics as a result of the new technology. The calculator and computer have influ- enced both what is important within the discipline and expanded the use of mathematics in other areas.

To reflect these changes, the NCTM Standards have been based on five goals for all students:

Becoming a mathematical problem solver. The development of each stu- dent's ability to solve problems is essential if he or she is to be a produc- tive citizen. We strongly endorse the first recommendation of An Agenda for Action (National Council of Teachers of Mathematics 1980, 2): "Problem solving must be the focus of school mathematics."

Learning to communicate mathe- matically. The development of a stu-

2 Arithmetic Teacher

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denťs power to use mathematics in- volves learning the signs, symbols, and terms of mathematics. This goal is best accomplished in problem situa- tions in which the student has an opportunity to read, write, and dis- cuss ideas in which the use of the language of mathematics is natural.

Learning to reason mathematical- ly. Making conjectures, gathering ev- idence, and building an argument to support such notions is fundamental to doing mathematics. In fact, the demonstration of good reasoning should be rewarded even more than students' ability to find correct an- swers.

Learning to value mathematics. The mathematics curriculum should include numerous and varied experi- ences related to the cultural, histori- cal, and scientific evolution of mathe- matics so that students can appreciate the role of mathematics in the devel- opment of contemporary society and explore relationships between mathe- matics and the disciplines it serves: physical and life sciences, social sci- ences, and humanities. Students should learn that mathematics is more than a collection of concepts and skills to be mastered. This goal's in- tent is to focus attention on the need for students' awareness of the interac- tion between mathematics and the his- torical situations from which it has developed and the impact that inter- action has on our culture and our lives.

Becoming confident in one's own ability. The mathematics curriculum should include numerous and varied experiences related to the human as- pects of the development of mathe- matics. This focus allows students to understand that mathematics is an in- vention of the human mind so that they learn to trust in their own math- ematical thinking. As a result of studying mathematics, students need to view themselves as capable of us- ing their growing mathematical knowledge to make sense of new problem situations in the world around them.

The Standards that have been pro- duced should be viewed as "facili-

tators of reform" toward these goals. In this sense they are a component of the mathematics education com- munity's response to the perceived crisis in education (National Commis- sion on Excellence in Education 1983; National Science Board Commission on Precollege Education in Mathe- matics, Science, and Technology 1983). Hence, the standards should reflect the national positions and re- sponses of the mathematical sciences education community to the per- ceived crisis (e.g., NCTM 1980; Con- ference Board of the Mathematical Sciences 1984; Romberg 1984).

How can one participate in this effort? We believe that NCTM is the appro- priate agency to develop a set of cur- ricular and evaluative Standards. For too long we have abdicated this re- sponsibility to others, including legis- lators, administrators, and textbook and test publishers. Knowledgeable mathematicians and educators, through the professional organization that best reflects their interests, should take responsibility for the de- velopment of Standards that closely affect their work and lives.

The working draft now available was produced by members of four working groups. The members were chosen by the President of NCTM, John Dossey, to reflect the broad range of interests within NCTM. Each working group included a teacher, a supervisor, a teacher educator, a re- searcher, and a mathematician. Thus, although the document reflects the input from a variety of sources, it is a working draft. If it is to represent the membership of NCTM, comment by all is necessary. The working groups will meet early in the summer of 1988 to make revisions based on the col- lected comments.

References

American Psychological Association. Stan- dards for Educational and Psychological Tests. Washington, D.C.: APA, 1974.

Commission on Standards for School Mathe- matics of the National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics. Working Draft. Reston, Va.: The Council, 1987.

Conference Board of the Mathematical Sci- ences. New Goals for Mathematical Sciences Education. Washington, D.C.: CBMS, 1984.

. Overview and Analysis of School Math- ematics, Grades K-12. Washington, D.C.: CBMS, 1975.

National Commission on Excellence in Educa- tion. A Nation at Risk: The Imperative for Educational Reform. Washington, D.C.: U.S. Government Printing Office, 1983.

National Council of Teachers of Mathematics. An Agenda for Action: Recommendations for School Mathematics of the 1980s. Reston, Va.: The Council, 1980.

National Science Board Commission on Precol- lege Education in Mathematics, Science, and Technology. Educating Americans for the 2 1st Century. Washington, D.C.: The Com- mission, 1983.

Oxford American Dictionary. New York: Ox- ford University Press, 1980.

Romberg, Thomas A. School Mathematics: Options for the 1990s. Chairman's Report of a Conference. Washington, D.C.: U.S. Gov- ernment Printing Office, 1984. W

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