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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 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 Mathematical Sciences Education Board was established in 1985 to provide a continuing national capability to assess the status and quality of education in the mathematical sciences and is concerned with excellence in education for all students at all levels. The Board reports directly to the Governing Board of the National Research Council.
Development, publication, and dissemination of this report were supported by a grant from The Carnegie Corporation of New York. Any opinions, findings, or recommendations expressed in this report are those of the authors and do not necessarily reflect the views of The Carnegie Corporation of New York.
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THE NATIONAL ACADEMIES
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 recognizes 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 RESEARCH COUNCIL
CENTER FOR SCIENCE, MATHEMATICS, AND ENGINEERING EDUCATION
MATHEMATICAL SCIENCES EDUCATION BOARD
JULY 1, 1998 - JUNE 30, 1999
HYMAN BASS (MSEB Chair)
JERE CONFREY (MSEB Vice Chair)
University of Texas at Austin
RICHARD A. ASKEY
University of Wisconsin-Madison
Prescott Unified School District
University of Michigan
St. Paul Academy and Summit School
Lakeland Community College
University of Maryland
National Parent Teachers Association
Antioch Unified School District
GLENDA T. LAPPAN
Michigan State University
Connecticut Department of Education
TQM Services Group
Bronxville Public Schools
EDWARD A. SILVER
University of Pittsburgh
University of Wisconsin-Madison
University of Illinois at Urbana-Champaign
SUSAN S. WOOD
J. Sargeant Reynolds Community College
RODGER BYBEE Executive Director,
CSMEE, through June, 1999
SUZANNE WOOLSEY Acting Executive Director,
JOAN FERRINI-MUNDY Director,
MSEB, through June, 1999
GAIL BURRILL Director,
BRADFORD FINDELL Program Officer/Editor
GALE MOORE Financial & Admin. Associate
This report has 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 purpose of this independent review is to provide candid and critical comments that will assist the authors and 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 remain 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:
University of Nottingham, England
Memphis City Schools
EDWARD T. ESTY
Chevy Chase, MD
Education Development Center, Inc.
While the individuals listed above have provided many constructive comments and suggestions, responsibility for the final content of this report rests solely with the authoring committee and the NRC.
Table of Contents
The development of this manuscript owes much to many. At New Standards, I am especially indebted to Pam Beck, Phil Daro, Elizabeth Stage, Dick Stanley, and Bokhee Yoon who provided encouraging comments on various drafts. In addition, the support of Bob Agee, Harold Asturias, and Mishaa Degraw is warmly acknowledged. I would also like to thank Claudia Alfaro for her help in producing this manuscript.
Members of the Balanced Assessment Project also played a role in the development of the ideas addressed here. I would like to thank Alan Schoenfeld, Sandy Wilcox, Judi Zawojewski, Alan Bell, Hugh Burkhardt, Rita Crust, John Gillespie, Daniel Pead, Richard Phillips, and Malcolm Swan.
It would not be practicable to name each of the teachers and mathematics educators who have contributed to this work. A special word of acknowledgment is due, however, to Diane Briars, Steve Leinwand, Joanne Mosier, Marge Pettit, as well as Dot Dow and her staff in the mathematics department at Dublin High School.
At the NRC, I would like to thank Joan Ferrini-Mundy for giving me the opportunity to collect together and write down these ideas that have been percolating over the last 10 years. Special thanks are also due to Gail Burrill and Brad Findell for their help editing each draft of this booklet and in coordinating its review and production. This manuscript benefited immensely from the comments of the reviewers, who, of course, remained anonymous to me throughout the process.
Finally, I would like to acknowledge the loving help, support, and encouragement that I received throughout from Andrew Bell.
University of California, Office of the President
Curriculum reform, performance assessment, standards, portfolios, and high stakes testing—what's next? What does this all mean for me in my classroom? Many teachers have asked such questions since mathematics led the way in setting standards with the publication of the Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 1989). This seminal document and others that followed served as catalysts for mathematics education reform, giving rise to new initiatives related to curriculum, instruction, and assessment over the past decade. In particular, approaches to classroom, school, and district-wide assessment have undergone a variety of changes as educators have sought to link classroom teaching to appropriate assessment opportunities.
Since the publication of Everybody Counts (National Research Council [NRC], 1989), the Mathematical Sciences Education Board (MSEB) has dedicated its efforts to the improvement of mathematics education. A national summit on assessment led to the publication of For Good Measure (NRC, 1991). This statement of goals and objectives for assessment in mathematics was followed by Measuring Up (NRC, 1993a), which provided prototypical fourth-grade performance assessment tasks linked to the goals of the NCTM's Curriculum and Evaluation Standards. Measuring What Counts (NRC, 1993b) demonstrated the importance of mathematics content, learning, and equity as they relate to assessment. The MSEB is now prepared to present perspectives on issues in mathematics education assessment for those most directly engaged in implementing the reform initiatives on a daily
basis—classroom teachers, school principals, supervisors, and others in school-based settings.
The MSEB, with generous support and encouragement from the Carnegie Corporation of New York, seeks to bring discussion of assessment to school- and district-based practitioners through an initiative called Assessment in Practice (AIP). Originally conceived as a series of "next steps" to follow the publication of Measuring Up and For Good Measure, the project, with assistance from an advisory board, developed a publication agenda to provide support to teachers and others directly involved with the teaching and assessment of children in mathematics classrooms at the elementary, middle, and high school levels.
Through a pair of resource booklets, AIP presents an exploration of issues in assessment. These booklets are specifically designed to be used at the school and school district level by teachers, principals, supervisors, and measurement specialists. Because these booklets are commissioned works, the opinions and recommendations they contain are those of the authors and not necessarily of the MSEB or the NRC. The first booklet, Learning About Assessment, Learning Through Assessment, written by Mark Driscoll and Deborah Bryant, discusses ways to assist teachers in learning about assessment and how student work can be a rich resource in professional development. This booklet, Keeping Score, written by Ann Shannon, discusses issues to be considered while developing high-quality mathematics assessments. Much of the raw material and analysis in this booklet grew out of the author's work with two projects, New Standards and Balanced Assessment, that are intended to produce mathematics assessments supporting the NCTM Standards. The publication of this booklet is not an NRC or MSEB endorsement of these projects, but rather a suggestion that many of the ideas may be useful to people who are rethinking the roles that assessment has played in mathematics education.
As we continue in our efforts to understand the implications of standards-based curriculum, instruction, and assessment, it is critical that teachers and others involved with the practice of instruction have the opportunity to reflect on how to best achieve the ultimate goal of improving student learning in mathematics. The MSEB welcomes this opportunity to provide resources in the area of assessment.
Hyman Bass, Chair
Mathematical Sciences Education Board