|
Items in cart [0] |
Questions? Call 888-624-8373 |
| Copyright © 2009. National Academy of Sciences. All rights reserved. Terms of Use and Privacy Statement |
Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page R1
Mathematics
Education
in tho
huddle Grades
Teaching lo Meet the Needs of
Middle Grades [earners and lo
Maintain High Expectations
Proceedings of a National Convocation arc! Action Conferences
Center for Science, Mathematics, and Engineering Eclucation
National Research Council
NATIONAL ACADEMY PRESS
Washington, DC
OCR for page R2
NOTICE: The project that is the subject of this report was approved by the Governing Boa rcl of the
National Research Council, whose members are drawn from the councils of the National Acaclemy of
Sciences, the National Acaclemy of Engineering, ancl the Institute of Meclicine. The members of the
committee responsible for the convocation ancl report were chosen for their special competences ancl with
regard for appropriate balance.
The Center for Science, Mathematics, ancl Engineering Eclucation (CSMEE) was established in 1995 to
provide coordination of all the National Research Council's education activities ancl reform efforts for
students at all levels, specifically those in kindergarten through twelfth Oracle, undergraduate institutions,
school-to-work programs, ancl continuing eclucation. The Center reports directly to the Governing Boa rcl
of the National Research Council.
The Convocation ancl Action Conferences about which these proceedings report were funded by a grant
from the U.S. Department of Eclucation with additional funding from the American Eclucational 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 Eclucation.
Library of Congress Cataloging-in-Publication Data
Mathematics education in the middle Oracles: teaching to meet the needs
of middle Oracles learners ancl to maintain high expectations:
proceedings of a national convocation and action conferences / Center
for Science, Mathematics, ancl Engineering Eclucation, National Research
Council.
p. cm.
Includes bibliographical references.
ISBN 0-309-06797-9 {pink.)
1. Mathematics Stucly ancl teaching IMiclclle school) Unitecl
States Congresses. 1. Center for Science,Mathematics, ancl Engineering
Eclucation.
QA13 .M156 1999
510'.72 clc21
99-050765
Aclclitional copies of this report are available from National Acaclemy Press, 2101 Constitution Avenue,
N.W., Lock Box 285, Washington, DC 20055. Call {8001 62~-62~2 or {2021 33~-3313 {in the
Washington metropolitan area).
This report is also available online at htip://www.nap.eclu.
Printed in the Unitecl States of America
Copyright 2000 by the National Acaclemy of Sciences. All rights reserved.
OCR for page R3
National Acaclemy of Sciences
National Acaclemy of Engineering
Institute of Meclicine
National Research Council
The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished
scholars engaged in scientific ancl engineering research, cleclicatecl to the furtherance of science ancl
technology ancl to their use for the general welfare. Upon the authority of the charter granted to it by the
Congress in 1863, the Acaclemy has a mandate that requires it to advise the federal government on
scientific ancl technical matters. Dr. Bruce M. Alberts is president of the National Acaclemy of Sciences.
The National Academy of Engineering was established in 1 96A, under the charter of the National
Acaclemy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its
administration ancl in the selection of its members, sharing with the National Acaclemy of Sciences the
responsibility for advising the federal government. The National Acaclemy 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 Acaclemy
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 Acaclemy of
Sciences by its congressional charter to be an adviser to the federal government ancl, upon its own
initiative, to identify issues of medical care, research, ancl eclucation. Dr. Kenneth 1. Shine is president of
the Institute of Meclicine.
The National Research Councilwas organized by the National Academy of Sciences in 1916 to associate
the broad community of science ancl technology with the Acaclemy's purposes of furthering know~eclge ancl
advising the federal government. Functioning in accordance with general policies determined by the
Acaclemy, the Council has become the principal operating agency of both the National Acaclemy of
Sciences ancl the National Acaclemy of Engineering in providing services to the government, the public,
ancl the scientific ancl engineering communities. The Council is administered jointly by both Acaclemies ancl
the Institute of Meclicine. Dr. Bruce M. Alberts ancl Dr. William A. Wulf are chairman ancl vice chairman,
respectively, of the National Research Council.
OCR for page R4
OCR for page R5
NATIONAL CONVOCATION ON MATHEMATICS EDUCATION
IN THE MIDDLE GRADES
Program Steering Committee
Eclwarcl 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
Ben jamin Blackhawk, Mathematics Teacher, St. Paul Acaclemy and Summit School, Crystal, MN
Susan S. Woocl, Professor of Mathematics, J. Sargeant Reynolds Community College, Richmoncl, VA
Representatives, American Educational Research Association
Robert Linn, Distinguishecl Professor of Eclucation, University of Coloraclo, Boulcler, CO
Sanclra Wilcox, Associate Professor of Teacher Eclucation, Michigan State University, East Lansing, Ml
Representatives, National Council of Teachers of Mathematics
Catherine Brown, Associate Professor of Curriculum and Instruction, Indiana University, Bloom
Karen Longhart, Mathematics Teacher, Flatheacl High School, Kalispell, MT
Representatives, National Middle School Association
Sam Chattin, Science Teacher, William H. English Miclclle School, Scottsberg, IN
Katherine Rasch, Dean and Professor of Eclucation, Maryville University, Chesterfielcl, MO
Member-At-Large
Shirley Sagawa, Executive Director, Learning First Alliance, Washington, DC
National Research Council Staff
Gail Burrill, Project Director
Roclger Bybee, Executive Director, CSMEE
Kristance Coates, Project Assistant
Joan Ferrini-Muncly, Associate Executive Director, CSMEE
Braclforcl Finclell, Program Officer
DeVonne Robertson, Program Assistant
Kirsten Sampson Snycler, Aclministrative Officer
Doug Sprunger, Senior Project Assistant
Tina Winters, Senior Project Assistant
*NAG: Member of the National Acaclemy of Sciences
ington, IN
OCR for page R6
OCR for page R7
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 renect 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. Inparticular,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
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.
A(l(litional thanks go to Deborah
Loewenberg Ball, Hyman Bass, anti
Sandra Wilcox for their instrumental
roles in the organization of the Action
Conference on the Professional Devel-
opment of Teachers of Mathematics in
the Mi(l(lle Gra(les, the Action Confer-
ence on the Nature and Teaching of
Algebra in the Mi(l(lle Gra(les, anti the
Action Conference on Research in the
Teaching anti Learning of Mathematics
in the Mi(l(lle Gra(les, respectively. We
also wish to acknowle(lge 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
OCR for page R8
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 wait 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 Lon(lon Mi(l(lle
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 Eclucation
in the Miclclle Gracles
OCR for page R9
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
skins 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
shining 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 ah 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,
(NCI~M, 19891; Professional Standardsfor
Teaching Mathematics, (NCI~M, 19911;
and Assessment Standardsfor School
Mathematics, (NCI~M, 19951.
As educators focus on improving
mathematics education, they face a
variety of issues. The problems of
middle grades mathematics education
are substantial anti (1iffer 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 wi(le, inch
(leep" be a(l(lresse(l? How can the
mathematics curriculum be strength-
ened yet respect the development
issues so central to mi(l(lle gra(les
students? What is the nature of
algebra at the mi(l(lle gra(les anti how
(toes it influence the curriculum?
· How micIcIle gracIes stucIents
learn mathematics. What is the
balance between conceptual un(ler
OCR for page R10
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
micIcIle gracIes. 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 arc! its
relation to the teaching arc!
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,
sche(luling, anti 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 buil(ls 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 renect 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 an(1 in teaching
practice has been slow to occur.
Evidence is mixed about the effects
and directions of efforts 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 anti maximize
opportunities for all mi(l(lle gra(les
chil(lren in its schools. The (lialogue
anti share(1 visions that occurre(1 at
the Convocation plenary sessions,
panels, anti small group (liscus-
sions can set the stage for making a
lifference.
REFERENCES
National Center for Education Statistics. (1996~.
P?`rsavingexcellence:Ast?`dyof U.S. eighth grace
mathematics and science teaching, learning,
cavrric?`l?`m, and achievement in international
context. Washington, DC: Author.
National Council of Teachers of Mathematics.
(1989~. Cavrric?`l?`m and evaluation standards
for school mathematics. Reston, VA Author.
National Council of Teachers of Mathematics.
~lg9ly. Professional standardsfor teaching
mathematics. Reston, VA Author.
National Council of Teachers of Mathematics.
(1995). Assessment standardsfor school
mathematics. Reston, VA Author.
Reese, C.M., Miller, KE., Mazzeo, J., & Dossey,
J.A. (1997). NAEP 1996 mathematics report
cardfor the nation and the states. Washington,
DC: National Center for Education Statistics.
OCR for page R11
ACKNOWLEDGMENTS
· ~
V11
PREFACE
1X
LETTER FROM THE PROGRAM STEERING COMMITTEE
1
EXECUTIVE SUMMARY
5
PARTICIPANT OBSERVATIONS
14
CONVOCATION PAPERS AND DISCUSSION SUMMARIES
19
Teaching anc! Learning Mathematics at the MicIcIle GracIes:
Setting the Stage
Mathematics in the Middle: Building a Firm Foundation
of Understanding for the Future Glenda Lappan
The Middle School Learner: Contexts, Concepts, and
the Teaching Connection Thomas Dickinson
Content arc! Learning Issues in the MicIcIle GracIes
Renections on Middle School Mathematics Nancy Doda
Mathematics Content and Learning Issues in the
Middle Grades Kathleen Hart
Summary of Small Group Discussion on Content and
Learning Issues in Middle Grades Mathematics
Teaching Issues in the MicIcIle GracIes
Using Video of Classroom Practice as a Too} to Study and
Improve Teaching Nanette M. Seago
Pane} Reactions to the "Cindy Video"
Teaching and Learning Mathematics in the Middle Grades:
Student Perspectives Linda Foreman
21
23
32
39
41
50
58
61
63
76
79
OCR for page R12
Pane} Response to Foreman Student Video
Summary of Small Group Discussion on Teaching Issues in
the Middle Grades
Organizational Issues in the Middle Grades
The Organization and Structure of Schools at the Middle Grades:
A Principal's Perspective Adapted from the Transcript of
Remarks by Stephen 0. Gibson
The Organization and Structure of Schools at the Middle Grades:
The Role of Development, Subject Matter, and Teacher
Professional Development Mary Kay Stein
Improving Achievement in the Middle Grades in Mathematics
and Related Areas: Lessons from the Project on High
Performance Learning Communities Robert D. Feiner et al.
Pane} Discussion on the Organization of Schools at the Middle Grades
Closing Remarks
Renections on the Convocation
Adaptedfrom the transcript of remarks by Edward Silver
ACTION CONFERENCES
90
92
95
97
101
111
125
129
131
141
Action Conference on the Nature and Teaching of Algebra in
the Middle Grades
Action Conference on Research in the Teaching and Learning of
Mathematics in the Middle Grades
Action Conference on the Professional Development of
Teachers of Mathematics in the Middle Grades
APPENDICES
143
160
168
i. Convocation and Action Conference Agendas
2. Biographical Information on Convocation and Action
Conference Speakers
3. Convocation and Action Conference Participant Lists
4. Marcy's Dots
5. Discussion Session Worksheets
6. Background Paper for the Convocation: What Is Sth Grade
Mathematics: A Look from NAEP John Dossey
7. Resources
179
189
215
239
245
247
253
OCR for page R13
Mathematics
Ellueation
in Who
Middle Grades
OCR for page R14
