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

271 Pages·2000·1.69 MB·English

by  National Research Council, National Convocation on Mathematics Education in the Middle Grades

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
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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
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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-
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