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Mathematics Education in the Middle Grades: Teaching to Meet the Needs of Middle Grades Learners and to Maintain High Expectations PDF

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Mathematics Education in the Middle Grades Teaching to Meet the Needs of Middle Grades Learners and to Maintain High Expectations Proceedings of a National Convocation and Action Conferences Center for Science, Mathematics, and Engineering Education National Research Council NATIONAL ACADEMY PRESS Washington, DC NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the convocation and report were chosen for their special competences and with regard for appropriate balance. The Center for Science, Mathematics, and Engineering Education (CSMEE) was established in 1995 to provide coordination of all the National Research Council’s education activities and reform efforts for students at all levels, specifically those in kindergarten through twelfth grade, undergraduate institutions, school-to-work programs, and continuing education. The Center reports directly to the Governing Board of the National Research Council. The Convocation and Action Conferences about which these proceedings report were funded by a grant from the U.S. Department of Education with additional funding from the American Educational Research Association. Any opinions, findings, or recommendations expressed in this report are those of members of the steering committee or participants in the Convocation and Action Conferences and do not necessar- ily reflect the views of the U.S. Department of Education. Library of Congress Cataloging-in-Publication Data Mathematics education in the middle grades : teaching to meet the needs of middle grades learners and to maintain high expectations : proceedings of a national convocation and action conferences / Center for Science, Mathematics, and Engineering Education, National Research Council. p. cm. Includes bibliographical references. ISBN 0-309-06797-9 (pbk.) 1. Mathematics—Study and teaching (Middle school)—United States—Congresses. I. Center for Science, Mathematics, and Engineering Education. QA13 .M156 1999 510'.72—dc21 99-050765 Additional copies of this report are available from National Academy Press, 2101 Constitution Avenue, N.W., Lock Box 285, Washington, DC 20055. Call (800) 624-6242 or (202) 334-3313 (in the Washington metropolitan area). This report is also available online at http://www.nap.edu. Printed in the United States of America Copyright 2000 by the National Academy of Sciences. All rights reserved. National Academy of Sciences National Academy of Engineering Institute of Medicine National Research Council The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Bruce M. Alberts is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recog- nizes the superior achievements of engineers. Dr. William A. Wulf is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Kenneth I. Shine is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy’s purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Bruce M. Alberts and Dr. William A. Wulf are chairman and vice chairman, respectively, of the National Research Council. NATIONAL CONVOCATION ON MATHEMATICS EDUCATION IN THE MIDDLE GRADES Program Steering Committee Edward Silver, Chair, Professor and Senior Scientist, Learning Research Development Center, University of Pittsburgh, Pittsburgh, PA Representatives, Mathematical Sciences Education Board Hyman Bass (NAS)*, Professor of Mathematics, Columbia University, New York, NY Benjamin Blackhawk, Mathematics Teacher, St. Paul Academy and Summit School, Crystal, MN Susan S. Wood, Professor of Mathematics, J. Sargeant Reynolds Community College, Richmond, VA Representatives, American Educational Research Association Robert Linn, Distinguished Professor of Education, University of Colorado, Boulder, CO Sandra Wilcox, Associate Professor of Teacher Education, Michigan State University, East Lansing, MI Representatives, National Council of Teachers of Mathematics Catherine Brown, Associate Professor of Curriculum and Instruction, Indiana University, Bloomington, IN Karen Longhart, Mathematics Teacher, Flathead High School, Kalispell, MT Representatives, National Middle School Association Sam Chattin, Science Teacher, William H. English Middle School, Scottsberg, IN Katherine Rasch, Dean and Professor of Education, Maryvile University, Chesterfield, MO Member-At-Large Shirley Sagawa, Executive Director, Learning First Alliance, Washington, DC National Research Council Staff Gail Burrill, Project Director Rodger Bybee, Executive Director, CSMEE Kristance Coates, Project Assistant Joan Ferrini-Mundy, Associate Executive Director, CSMEE Bradford Findell, Program Officer DeVonne Robertson, Program Assistant Kirsten Sampson Snyder, Administrative Officer Doug Sprunger, Senior Project Assistant Tina Winters, Senior Project Assistant *NAS: Member of the National Academy of Sciences v Acknowledgments The National Academy of Sciences Sampson Snyder and Doug Sprunger. gratefully acknowledges the U.S. De- Others who provided on-site support partment of Education for its generous were Kristance Coates and DeVonne financial support of the Convocation and Robertson. Action Conferences and these proceed- We are grateful to the members of the ings, the American Educational Re- Program Steering Committee for their search Association for its additional oversight in planning of the programs financial support and co-sponsorship of for the Convocation and Action Confer- the Convocation and Action Confer- ences. We would also like to thank ences, and the National Middle School Anthony Jackson for his contributions to Association and National Council of the program planning and his assistance Teachers of Mathematics for their co- with resources for the Convocation. sponsorship of the Convocation and Additional thanks go to Deborah Action Conferences. Any opinions, Loewenberg Ball, Hyman Bass, and findings, and conclusions or recommen- Sandra Wilcox for their instrumental dations expressed in this material are roles in the organization of the Action those of the authors and do not neces- Conference on the Professional Devel- sarily reflect those of the funders. opment of Teachers of Mathematics in We would like to acknowledge the the Middle Grades, the Action Confer- staff at the National Research Council’s ence on the Nature and Teaching of (NRC) Center for Science, Mathemat- Algebra in the Middle Grades, and the ics, and Engineering Education Action Conference on Research in the (CSMEE) for their efforts in putting the Teaching and Learning of Mathematics Convocation and Action Conferences in the Middle Grades, respectively. We together. In particular, Tina Winters also wish to acknowledge the speakers was instrumental in overseeing logisti- and discussion group facilitators for cal arrangements for the meetings, and their contributions and leadership that in organizing these proceedings for gave substance to the discussion. review and publication. She was sup- It should be noted that these proceed- ported in her efforts by Kirsten ings have been reviewed by individuals vii chosen for their diverse perspectives Gilberto Cuevas, University of Miami and technical expertise, in accordance Nina Koltnow, Sidwell Friends School with procedures approved by the NRC’s Sidney L. Rachlin, East Carolina Report Review Committee. The pur- University pose of this independent review is to Marlyn Spivak, Jack London Middle provide candid and critical comments School that will assist the NRC in making the While these individuals have provided published report as sound as possible many constructive comments and and to ensure that the report meets suggestions, responsibility for the final institutional standards for objectivity, content of this report rests solely with evidence, and responsiveness to the the authoring committee and the NRC. study charge. The content of the review comments and draft manuscript remains confidential to protect the integrity of GAIL BURRILL the deliberative process. Project Director, Mathematics Education We wish to thank the following in the Middle Grades individuals for their participation in the review of this report: viii Preface Learning mathematics in the middle assessments with those standards. The grades is a critical component in the National Council of Teachers of Math- education of our nation’s youth. The ematics (NCTM) is preparing Principles mathematics foundation laid during and Standards for School Mathematics, an these years provides students with the updated version of its previous standards skills and knowledge to study higher documents: Curriculum and Evaluation level mathematics during high school, Standards for School Mathematics, provides the necessary mathematical (NCTM, 1989); Professional Standards for base for success in other disciplines such Teaching Mathematics, (NCTM, 1991); as science, and lays the groundwork for and Assessment Standards for School mathematically literate citizens. A Mathematics, (NCTM, 1995). variety of evidence suggests that the As educators focus on improving mathematics education landscape is mathematics education, they face a shifting and evolving rapidly. Below variety of issues. The problems of average mathematics achievement middle grades mathematics education scores for grade eight U. S. students as are substantial and differ from those at reported in the Third International the elementary and secondary levels. Mathematics and Science Study (TIMSS) There are issues about: (U.S. Department of Education, 1996) stimulated national concern leading to a • Content. What mathematics content variety of activities and proposals focus- is appropriate? How can the charac- ing attention on mathematics education. terization of the U.S. mathematics Data from the National Assessment of curriculum as a “mile wide, inch Educational Progress (NAEP) (National deep” be addressed? How can the Center for Education Statistics, 1997) mathematics curriculum be strength- indicates that while the nation has ened yet respect the development demonstrated progress over time, the issues so central to middle grades achievement levels for all students are students? What is the nature of not yet satisfactory. Research about algebra at the middle grades and how mathematics education has begun to does it influence the curriculum? have implications for classroom practice. • How middle grades students States are setting high standards for learn mathematics. What is the student achievement and aligning their balance between conceptual under- ix

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