Designing Mathematics or Science Curriculum Programs

A Guide for Using Mathematics and Science Education Standards

Committee on Science Education K-12 and the Mathematical Sciences Education Board

Center for Science, Mathematics, and Engineering Education

National Research Council

NATIONAL ACADEMY PRESS
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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards Designing Mathematics or Science Curriculum Programs A Guide for Using Mathematics and Science Education Standards Committee on Science Education K-12 and the Mathematical Sciences Education Board Center for Science, Mathematics, and Engineering Education National Research Council NATIONAL ACADEMY PRESS Washington, D.C.

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council (NRC), 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 NRC is the operating arm of the National Academies, which includes the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The NRC was organized in 1916 by the National Academy of Sciences to associate the broad community of science and technology with the Academy's purposes of furthering knowledge and providing impartial advice to 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 Alberts, president of the National Academy of Sciences, and Dr. William A. Wulf, president of the National Academy of Engineering, are chairman and vice chairman, respectively, of the NRC. The Center for Science, Mathematics, and Engineering Education (CSMEE) was established in 1995 to provide coordination of all the NRC's education activities and reform efforts for students at all levels, specifically those in kindergarten through 12th grade, undergraduate institutions, school-to-work programs, and continuing education. The Center reports directly to the Governing Board of the NRC. This study by the Mathematical Sciences Education Board and the Committee on Science Education K-12 of CSMEE was conducted under a grant from the National Science Foundation (ESI-9355774) to the National Academy of Sciences/NRC. Any opinions, findings, and conclusions or recommendations expressed in this report are those of the authors and do not necessarily reflect the views of the National Science Foundation. Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards is available for sale from the 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, DC metropolitan area). It is also available at http://www.nap.edu. International Standard Book Number 0-309-06527-5 Printed in the United States of America. Copyright 1999 by the National Academy of Sciences. All rights reserved.

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards THE CENTER FOR SCIENCE, MATHEMATICS, AND ENGINEERING EDUCATION COMMITTEE ON SCIENCE EDUCATION K-12 Jane Butler Kahle (Chair), Department of Teacher Education, Miami University, Oxford, OH J. Myron Atkin, School of Education, Stanford University, Stanford, CA Caryl Edward Buchwald, Department of Geology, Carleton College, Northfield, MN George Bugliarello, Polytechnic University, Brooklyn, NY Beatriz Chu Clewell, The Urban Institute in Washington, Washington, DC William E. Dugger, Technology for All Americans, Blacksburg, VA Norman Hackerman, The Robert A. Welch Foundation, Houston, TX Leroy Hood, University of Washington, Seattle, WA William Linder-Scholer, SciMathMN, Roseville, MN Maria Alicia Lopez Freeman, Center for Teacher Leadership in Language and Status, California Science Project, Monterey Park, CA John A. Moore, University of California, Riverside, CA Darlene Norfleet, Flynn Park Elementary School, University City, MO Carolyn Ray, Urban Systemic Initiative, Cleveland, OH Cary Sneider, Boston Museum of Science, Boston, MA Rachel Wood, Delaware State Department of Public Instruction, Dover, DE Robert Yinger, School of Education, Baylor University, Waco, TX

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards MATHEMATICAL SCIENCES EDUCATION BOARD Hyman Bass (Chair), Department of Mathematics, Columbia University, New York, NY Jere Confrey (Vice Chair), Department of Curriculum and Instruction, University of Texas at Austin, Austin, TX Richard A. Askey, Department of Mathematics, University of Wisconsin at Madison, Madison, WI Sherry Baca, Prescott Unified School District, Dexter Family Literacy and Resource Center, Prescott, AZ Deborah Loewenberg Ball, University of Michigan, Ann Arbor, MI Benjamin Blackhawk, St. Paul Academy and Summit School, St. Paul, MN Richelle Blair, Lakeland Community College, Kirtland, OH Patricia Campbell, University of Maryland, College Park, MD Ingrid Daubechies, Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ Karen Economopoulos, TERC, Cambridge, MA Susan Eyestone, National Parents Teachers Association (PTA), Minneapolis, MN Lee Jenkins, Enterprise School District, Redding, CA Glenda T. Lappan, Connected Mathematics Project and Department of Mathematics, Michigan State University, East Lansing, MI Miriam Masullo, T.J. Watson Research Center, IBM Corporation, Yorktown Heights, NY David Moore, Department of Statistics, Purdue University, West Lafayette, IN Mari Muri, Bureau of Curriculum and Instructional Programs, Connecticut Department of Education, Hartford, CT Richard Normington, TQM Services Group, Sacramento, CA Mark Saul, Bronxville Public Schools, Bronxville, NY Richard Schoen, Department of Mathematics, Stanford University, Stanford, CA Edward A. Silver, University of Pittsburgh, Pittsburgh, PA William Tate, Department of Curriculum and Instruction, University of Wisconsin at Madison, Madison, WI Jerry Uhl, Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL Susan S. Wood, J. Sargeant Reynolds Community College, Richmond, VA

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards COMMITTEE TO DEVELOP A GUIDE FOR DESIGNING MATHEMATICS AND SCIENCE CURRICULUM PROGRAMS Cathy Seeley (Chair), Texas Statewide Systemic Initiative, University of Texas at Austin-Dana Center, Austin, TX Judy L. Capra, Jefferson County Public Schools, Wheat Ridge, CO Glenda T. Lappan, Connected Mathematics Project and Department of Mathematics, Michigan State University, East Lansing, Ml Jack Price, Center for Mathematics and Science Education and Equity and Technology, California State Polytechnic University, Pomona, CA Scott Samsel Stowell, Spokane School District No. 81, Spokane, WA

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards NATIONAL RESEARCH COUNCIL STAFF Rodger Bybee, Executive Director, Center for Science, Mathematics, and Engineering Education (CSMEE) Joan Ferrini-Mundy, Associate Executive Director, CSMEE; Director, Mathematical Sciences Education Board (MSEB), CSMEE Susan Loucks-Horsley, Division Director, K-12 Policy and Practice, CSMEE Harold Pratt, Director, Science Projects, CSMEE Tom Rowan, Project Consultant Kathleen Johnston, Project Consultant Alfred G. Young, Administrative Assistant, K-12 Policy and Practice, CSMEE Terry K. Holmer, Senior Project Assistant, Undergraduate Science Education, CSMEE Sally S. Stanfield, Editor, National Academy Press Dawn M. Eichenlaub, Production Manager, National Academy Press

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards REVIEWERS This report has been reviewed in draft form by individuals chosen for their diverse perspectives and technical expertise, in accordance with procedures approved by the National Research Council's (NRC's) Report Review Committee. The purpose of this independent review is to provide candid and critical comments that will assist the institution 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 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:Rick Billstein, University of Montana, Billings, MT Jere Confrey, University of Texas at Austin, Austin, TX Walter Denham, Mathematics Education Consultant, Fair Oaks, CA Alice Krueger, High Plains Consortium, Aurora, CO Michael Lang, Phoenix Urban Systemic Initiative, Tempe, AZ Lyn Richbart, New York State Education Department, Albany, NY Cary Sneider, Boston Museum of Science, Boston, MA Bonnie Ward, Chestertown, MD, Public Schools, Chestertown, MD 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 National Research Council.

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards Contents     PREFACE   xi     INTRODUCTION   1     Purpose of This Report   1     Curriculum Programs: A National Perspective   2     Curriculum Programs: The Potential   8     Assumptions Underlying This Report   13     COMPONENTS OF COHERENT MATHEMATICS AND SCIENCE EDUCATION CURRICULUM PROGRAMS   17     Goals of K-12 Mathematics and Science Curriculum Programs   17     Content Standards   20     Curriculum Framework   24     Instructional Materials that Support the K-12 Standards   29     PROCESS FOR DESIGNING A CURRICULUM PROGRAM   31     Establishing Goals and Standards   32     Building a Common Vision   33     Drafting a K-12 Curriculum Framework   34     Identifying Core Instructional Materials   35     Refining the Curriculum Framework   37     Evaluating the Curriculum Program   42     Building Consensus Among the Stakeholders and Obtaining Approval   44     APPENDIX A   47     Implementing a Mathematics or Science Curriculum Program         APPENDIX B   50     Mapping the NSES for Structure of Matter (K-12)         APPENDIX C   51     Mapping the NCTM Standards for the Topic of Statistics (K-12)         REFERENCES   53

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards Preface Because the curriculum a student studies has a major effect on what she or he will learn in school, the design and implementation of curriculum programs is a high priority for local, state, and federal education agencies. Accordingly, the National Science Foundation (NSF) has designated the use of high-quality, standards-based mathematics and science curricula as important components of the systemic initiatives it funds at the local, state, and regional levels. The NSF not only wants states and districts to select high-quality instructional mathematics and science materials but also to assemble them in a coherent way within and across grade levels in a manner that has the greatest potential for improving student achievement. The NSF's interest in enhancing student learning in mathematics and science motivated the agency to ask the National Research Council's (NRC) Center for Science, Mathematics, and Engineering Education (CSMEE) to develop a guide to help state- and district-level mathematics and science curricula developers design multi-year curriculum programs. In making its request, the NSF was aware of the importance and difficulty of developing coherent curriculum programs that provide students with the opportunity to learn mathematics and science in a continuous, interconnected, and cumulative way throughout their schooling, kindergarten through high school. The NSF asked for the guide to be based on the National Council of Teachers of Mathematics' (NCTM) Curriculum and Evaluation Standards for School Mathematics1 and the NRC's National Science Education Standards (NCTM, 1989; NRC, 1996b). The guide was to be designed for use with local and state frameworks and curriculum guidelines by school districts engaged in the work of standards-based improvement efforts. Generally, districts have a number of instructional materials from which to choose but little or no guidance in 1   In 1998, the NCTM released a discussion draft of its latest standards effort. It is entitled Principles and Standards for School Mathematics: Discussion Draft (NCTM, 1998).

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards determining how to assemble the materials to create coherent curriculum programs in either mathematics or science. After CSMEE's receipt of the NSF's request, the Third International Mathematics and Science Study (TIMSS) began to release the results of its assessments of and contextual research into three student populations at the fourth-grade, eighth-grade, and the final year of secondary school levels. In addition to student achievement, TIMSS specifically collected data on the curriculum documents and textbooks used in the various nations participating in the study. Data were also collected from the results of surveys of students, teachers, school officials, and national officials. The mathematics and science curricula in the countries involved in the study were thoroughly analyzed, and a number of inferences were made about the relationships between student achievement and the curriculum. Although a causal connection has not been established between the TIMSS achievement results and curriculum, the possible relationship raises provocative questions about the mathematics and science curricula in the United States and provides new lenses through which to study and, hopefully, to improve them. In response to the NSF's request for a curriculum program design guide, the Mathematical Sciences Education Board (MSEB) and the Committee on Science Education K-12 (COSE K-12), both within CSMEE, joined forces to form the Committee to Develop a Guide for Designing Mathematics and Science Curriculum Programs. The members of this committee are listed on page v of this report. In developing this guide, the committee found a common thread between the NSF's concern that curriculum programs lack coherence and questions raised by TIMSS data about the mathematics and science curricula in the United States. In responding to this finding, this guide takes the position that learning is cumulative over time and, therefore, curriculum programs in the United States should be designed to be more coherent over time. This guide outlines the components of coherent programs in mathematics or science, proposes criteria by which their quality can be judged, and suggests a process for developing them. Cathy Seeley Chair, Committee to Develop a Guide for Designing Mathematics and Science Curriculum Programs Harold Pratt Study Director Center for Science, Mathematics, and Engineering Education

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Designing Mathematics or Science Curriculum Programs: A Guide for Using Mathematics and Science Education Standards Designing Mathematics or Science Curriculum Programs

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