national research council national convocation

Proceedings of a National Convocation and Action ConferencesCenter for Science, Mathematics, and Engineering Education National Research Council NATIONAL ACADEMY PRESS Washington, DC Mat

Proceedings of a National Convocation and Action Conferences

Center for Science, Mathematics, and Engineering Education

National Research Council

NATIONAL ACADEMY PRESS

Washington, DC

Mathematics

Education

in the Middle Grades

Teaching to Meet the Needs of Middle Grades Learners and to Maintain High Expectations

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.

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 Academy of Sciences

National Academy of Engineering

Institute of Medicine

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, Maryville 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

The National Academy of Sciences

gratefully acknowledges the U.S

De-partment of Education for its generous

financial support of the Convocation and

Action Conferences and these

proceed-ings, the American Educational

Re-search Association for its additional

financial support and co-sponsorship of

the Convocation and Action

Confer-ences, and the National Middle School

Association and National Council of

Teachers of Mathematics for their

co-sponsorship of the Convocation and

Action Conferences Any opinions,

findings, and conclusions or

recommen-dations expressed in this material are

those of the authors and do not

neces-sarily reflect those of the funders

We would like to acknowledge the

staff at the National Research Council’s

(NRC) Center for Science,

Mathemat-ics, and Engineering Education

(CSMEE) for their efforts in putting the

Convocation and Action Conferences

together In particular, Tina Winters

was instrumental in overseeing

logisti-cal arrangements for the meetings, and

in organizing these proceedings for

review and publication She was

sup-ported in her efforts by Kirsten

Acknowledgments

Sampson Snyder and Doug Sprunger

Others who provided on-site support were Kristance Coates and DeVonne Robertson

We are grateful to the members of the Program Steering Committee for their oversight in planning of the programs for the Convocation and Action Confer-ences We would also like to thank Anthony Jackson for his contributions to the program planning and his assistance with resources for the Convocation

Additional thanks go to Deborah Loewenberg Ball, Hyman Bass, and Sandra Wilcox for their instrumental roles in the organization of the Action Conference on the Professional Devel-opment of Teachers of Mathematics in the Middle Grades, the Action Confer-ence on the Nature and Teaching of Algebra in the Middle Grades, and the Action Conference on Research in the Teaching and Learning of Mathematics

in the Middle Grades, respectively We also wish to acknowledge the speakers and discussion group facilitators for their contributions and leadership that gave substance to the discussion

It should be noted that these proceed-ings have been reviewed by individuals

chosen for their diverse perspectives and technical expertise, in accordance with procedures approved by the NRC’s Report Review Committee The pur-pose of this independent review is to provide candid and critical comments that will assist the NRC in making the published report as sound as possible and to ensure that the report meets institutional standards for objectivity, evidence, and responsiveness to the study charge The content of the review comments and draft manuscript remains confidential to protect the integrity of the deliberative process

We wish to thank the following individuals for their participation in the review of this report:

Gilberto Cuevas, University of Miami Nina Koltnow, Sidwell Friends School Sidney L Rachlin, East Carolina University

Marlyn Spivak, Jack London Middle School

While these individuals have provided many constructive comments and suggestions, responsibility for the final content of this report rests solely with the authoring committee and the NRC

GAIL BURRILL

Project Director, Mathematics Education

in the Middle Grades

Learning mathematics in the middle

grades is a critical component in the

education of our nation’s youth The

mathematics foundation laid during

these years provides students with the

skills and knowledge to study higher

level mathematics during high school,

provides the necessary mathematical

base for success in other disciplines such

as science, and lays the groundwork for

mathematically literate citizens A

variety of evidence suggests that the

mathematics education landscape is

shifting and evolving rapidly Below

average mathematics achievement

scores for grade eight U S students as

reported in the Third International

Mathematics and Science Study (TIMSS)

(U.S Department of Education, 1996)

stimulated national concern leading to a

variety of activities and proposals

focus-ing attention on mathematics education

Data from the National Assessment of

Educational Progress (NAEP) (National

Center for Education Statistics, 1997)

indicates that while the nation has

demonstrated progress over time, the

achievement levels for all students are

not yet satisfactory Research about

mathematics education has begun to

have implications for classroom practice

States are setting high standards for

student achievement and aligning their

assessments with those standards The National Council of Teachers of

Math-ematics (NCTM) is preparing Principles

and Standards for School Mathematics, an

updated version of its previous standards

documents: Curriculum and Evaluation

Standards for School Mathematics,

(NCTM, 1989); Professional Standards for

Teaching Mathematics, (NCTM, 1991);

and Assessment Standards for School

Mathematics, (NCTM, 1995).

As educators focus on improving mathematics education, they face a variety of issues The problems of middle grades mathematics education are substantial and differ from those at the elementary and secondary levels

There are issues about:

• Content What mathematics content

is appropriate? How can the charac-terization of the U.S mathematics curriculum as a “mile wide, inch deep” be addressed? How can the mathematics curriculum be strength-ened yet respect the development issues so central to middle grades students? What is the nature of algebra at the middle grades and how does it influence the curriculum?

•How middle grades students learn mathematics What is the

balance between conceptual

under-Preface

standing and practice? What is the role of manipulatives in helping students learn? How do students build understanding of a concept over time?

•Teaching mathematics at the middle grades To what extent

do teacher background and prepara-tion specifically for the teaching of mathematics have an impact on what students learn? How can the issue of specialist versus generalist be re-solved? What teaching practices are most effective with middle grades students? How can teachers help students grow as individuals yet ensure that they learn mathematics?

•School organization and its relation to the teaching and learning of mathematics How

does the study of mathematics fit into the “house” concept? What are the characteristics of school structures that promote mathematics learning?

Are cross-disciplinary teams compat-ible with vertical articulation? What are the effects of school organization, scheduling, and philosophy on the mathematics program?

•Research How can the knowledge

gained from research be used to improve teaching and learning of mathematics in the middle grades?

How can an agenda for continued research that builds on the state of the field as well as moves the thinking forward be framed? What help do teachers need to translate research into practice? How might teachers become researchers themselves as

they reflect on their practice and on ways to improve?

These issues contribute to the challenge of improving mathematics education at the middle grades Change in schools and in teaching practice has been slow to occur Evidence is mixed about the ef fects and directions of ef for ts to improve mathematics education Engaging the community at large in conversa-tion about their goals and perspec-tives is a critical step to help the nation raise the bar and maximize opportunities for all middle grades children in its schools The dialogue and shared visions that occurred at the Convocation—plenar y sessions, panels, and small group discus-sions—can set the stage for making a dif ference

REFERENCES

National Center for Education Statistics (1996).

Pursuing excellence: A study of U.S eighth grade mathematics and science teaching, learning, curriculum, and achievement in international context Washington, DC: Author.

National Council of Teachers of Mathematics.

(1989) Curriculum and evaluation standards

for school mathematics Reston, VA: Author.

National Council of Teachers of Mathematics.

(1991) Professional standards for teaching

mathematics Reston, VA: Author.

National Council of Teachers of Mathematics.

(1995) Assessment standards for school

mathematics Reston, VA: Author.

Reese, C.M., Miller, K.E., Mazzeo, J., & Dossey,

J.A (1997) NAEP 1996 mathematics report

card for the nation and the states Washington,

DC: National Center for Education Statistics.