AUTHOR AND BIBLIOGRAPHIC DATA

NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS

The NCTM Commission on Standards for School Mathematics

Thomas A. Romberg, Chair

Iris M. Carl               Christian R. Hirsch

F. Joe Crosswhite          Glenda Lappan

John A. Dossey             Dale Seymour

James D. Gates             Lynn A. Steen

Shirley M. Frye            Paul R. Trafton

Shirley A. Hill            Norman Webb

Members of the Working Groups

K-4                        9-12

Paul R. Trafton, Chair     Christian R. Hirsch,Chair

Hilde Howden               Sue Ann McGraw

Mary M. Lindquist          Gerald R. Rising

Edward C. Rathmell         Harold L. Schoen

Thomas E. Rowan            Cathy L. Seeley

Charles S. Thompson        Bert K. Waits


5-8                        Evaluation

Glenda Lappan, Chair       Norman Webb, Chair

Daniel T. Dolan            Elizabeth Badger

Joan F. Hall               Diane J. Briars

Thomas E. Kieren           Thomas J. Cooney

Judith E. Mumme            Tej N. Pandey

James E. Schultz           Alba G. Thompson


Project Assistant

E. Anne Zarinnia

Library of Congress Cataloging-in-Publication Data

National Council of Teachers of Mathematics. Commission on Standards for School Mathematics. Curriculum and evaluation standards for school mathematics / prepared by the working groups of the Commission on Standards for School Mathematics of the National Council of Teachers of Mathematics. p. cm. "June 1989." Bibliography: p. ISBN 0-87353-273-2 1. Mathematics--Study and teaching. 2. Curriculum evaluation. I. Title. QA11.N29 1989 510'.71--dc20 89-9421 CIP

Copyright (c) 1989 by

THE NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS, INC.

1906 Association Drive, Reston, Virginia 22091

All rights reserved

Printed in the United States of America

Sixth printing 1993

Permission to photocopy limited material from the Curriculum and Evaluation Standards for School Mathematics is granted for educational purposes. Permission must be sought for commercial use of content from this publication, when the material is quoted in advertising, when portions are used in other publications, or when charges for copies are made. Use of material from the Curriculum and Evaluation Standards for School Mathematics , other than those cases described, should be brought to the attention of the National Council of Teachers of Mathematics.

PREFACE

In 1986, the Board of Directors of the National Council of Teachers of Mathematics established the Commission on Standards for School Mathematics as one means to help improve the quality of school mathematics. This document, which is the product of the commission's efforts, contains a set of standards for mathematics curricula in North American schools (K-12) and for evaluating the quality of both the curriculum and student achievement. As school staffs, school districts, states, provinces, and other groups propose solutions to curricular problems and evaluation questions, these standards should be used as criteria against which their ideas can be judged.

The standards were drafted during the summer of 1987 and revised during the summer of 1988 by the members of four Working Groups, each representing a cross section of mathematics educators, including classroom teachers, supervisors, educational researchers, teacher educators, and university mathematicians. They were appointed by John Dossey, president of NCTM. Their work was authorized and reviewed by the NCTM Commission on Standards for School Mathematics , coordinated by Thomas A. Romberg and assisted by E. Anne Zarinnia. All who worked on the project thank the Utah Council of Teachers of Mathematics. Their hospitality both summers made our work easier and more enjoyable.

The revisions were based on copious and helpful reactions to the working draft of this document gathered during the 1987-88 school year. We thank all who contributed comments. This final document is considerably stronger and more coherent because of the careful reviews and thoughtful suggestions that were provided. In fact, we are confident this document represents the consensus of NCTM's members about the fundamental content that should be included in the school mathematics curriculum and about key issues concerning the organization and implementation of student and program evaluation.

The Standards is a document designed to establish a broad framework to guide reform in school mathematics in the next decade. In it a vision is given of what the mathematics curriculum should include in terms of content priority and emphasis, The challenge we issue to all interested in the quality of school mathematics is to work collaboratively to use these curriculum and evaluation standards as the basis for change so that the teaching and learning of mathematics in our schools is improved.

ACKNOWLEDGMENT

This document is significant because it expresses the consensus of professionals in the mathematical sciences for the direction of school mathematics in the next decade. It is also significant because it represents the total commitment of the National Council of Teachers of Mathematics to provide the leadership and resources for this vitally important work. The investment of time, money, and human efforts in the development of the Curriculum and Evaluation Standards for School Mathematics spans the terms of at least three presidents and boards of directors. Each one of us is proud to have been closely associated with the efforts.

We particularly acknowledge the outstanding leadership of Thomas A. Romberg, who chaired the Commission on Standards for School Mathematics, directed the writing project, and reported the deliberations to the profession. The Council is grateful to him, the members of the working groups, the project assistant, the Mathematical Sciences Education Board, and the thousands of other individuals and groups who offered their reactions to the initial draft.

Also, we give our special gratitude to the Headquarters staff, who supported the development and participated in the production throughout the entire process. All these activities were ultimately facilitated and guided by our executive director, James D. Gates, to whom we give our heartfelt appreciation.

F. Joe Crosswhite, President 1984-1986

John A. Dossey, President 1986-1988

Shirley M. Frye, President 1988-1990

ENDORSERS

The following mathematical science organizations join with the National Council of Teachers of Mathematics in promoting the vision of school mathematics described in the Curriculum and Evaluation Standards for School Mathematics:

• American Mathematical Association of Two-Year Colleges
• American Mathematical Society
• American Statistical Association
• Association for Women in Mathematics
• Association of State Supervisors of Mathematics
• Conference Board of the Mathematical Sciences
• Council of Presidential Awardees in Mathematics
• Council of Scientific Society Presidents
• Institute of Management Sciences
• Mathematical Association of America
• Mathematical Sciences Education Board
• National Council of Supervisors of Mathematics
• Operations Research Society of America
• School Science and Mathematics Association
• Society for Industrial and Applied Mathematics

SUPPORTERS

The professional organizations listed below have added their support for the quality mathematics curricula and assessment criteria provided by the Curriculum and Evaluation Standards for School Mathematics:

• American Association of Physics Teachers
• American Association of School Administrators
• American Chemical Society
• American Federation of Teachers
• Association for Supervision and Curriculum Development
• Council for Basic Education
• Council for Exceptional Children
• Council of Chief State School Officers
• Council of the Great City Schools
• International Reading Association
• International Technology Education Association
• Junior Engineering Technical Society
• National Association for the Education of Young Children
• National Association of Biology Teachers
• National Association of Elementary School Principals
• National Association of Secondary School Principals
• National Association of State Boards of Education
• National Catholic Education Association
• National Congress of Parents and Teachers
• National Council for the Social Studies
• National Council of Teachers of English
• National Education Association
• National School Boards Association
• National Science Teachers Association
• National Society of Professional Engineers

ALLIES

The organizations listed below have agreed to serve as allies in our effort to improve the teaching and learning of mathematics as described in the Curriculum and Evaluation Standards for School Mathematics.