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Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

How Students Learn

HISTORY, MATHEMATICS, AND SCIENCE IN THE CLASSROOM

Committee on How People Learn, A Targeted Report for Teachers

M. Suzanne Donovan and John D. Bransford, Editors

Division of Behavioral and Social Sciences and Education

NATIONAL RESEARCH COUNCIL OF THE NATIONAL ACADEMIES

THE NATIONAL ACADEMIES PRESS
Washington, D.C.
www.nap.edu

Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

THE NATIONAL ACADEMIES PRESS
500 Fifth Street, N.W. Washington, D.C. 20001

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.

This study was supported by Award No. R215U990024 between the National Academy of Sciences and the U.S. Department of Education. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the organizations or agencies that provided support for the project.

Library of Congress Cataloging-in-Publication Data

National Research Council (U.S.). Committee on How People Learn, A Targeted Report for Teachers.

How students learn : history, mathematics, and science in the classroom / Committee on How People Learn, A Targeted Report for Teachers ; M. Suzanne Donovan and John D. Bransford, editors.

p. cm.

"Division of Behavioral and Social Sciences and Education."

Includes bibliographical references and index.

ISBN 0-309-07433-9 (hardcover) — ISBN 0-309-08948-4 (pbk.) — ISBN 0-309-08949-2 (pbk.) — ISBN 0-309-08950-6 (pbk.) 1. Learning. 2. Classroom management. 3. Curriculum planning. I. Donovan, Suzanne. II. Bransford, John. III. Title.

LB1060.N38 2005

370.15′23—dc22

2004026246

Additional copies of this report are available from the
National Academies Press,
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Printed in the United States of America.

Copyright 2005 by the National Academy of Sciences. All rights reserved.

Suggested citation: National Research Council. (2005). How Students Learn: History, Mathematics, and Science in the Classroom. Committee on How People Learn, A Targeted Report for Teachers, M.S. Donovan and J.D. Bransford, Editors. Division of Behavioral and Social Sciences and Education. Washington, DC: The National Academies Press.

Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

THE NATIONAL ACADEMIES

Advisers to the Nation on Science, Engineering, and Medicine

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. Wm. 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. Harvey V. Fineberg 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. Wm. A. Wulf are chair and vice chair, respectively, of the National Research Council.

www.national-academies.org

Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
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Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

COMMITTEE ON HOW PEOPLE LEARN: A TARGETED REPORT FOR TEACHERS

JOHN D. BRANSFORD (Chair),

College of Education, University of Washington

SUSAN CAREY,

Department of Psychology, Harvard University

KIERAN EGAN,

Department of Education, Simon Fraser University, Burnaby, Canada

SUZANNE WILSON,

School of Education, Michigan State University

SAMUEL S. WINEBURG,

Department of Education, Stanford University

M. SUZANNE DONOVAN, Study Director

SUSAN R. MCCUTCHEN, Research Associate

ALLISON E. SHOUP, Senior Project Assistant

ELIZABETH B. TOWNSEND, Senior Project Assistant

Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
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Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

Preface

This book has its roots in the report of the Committee on Developments in the Science of Learning, How People Learn: Brain, Mind, Experience and School (National Research Council, 1999, National Academy Press). That report presented an illuminating review of research in a variety of fields that has advanced understanding of human learning. The report also made an important attempt to draw from that body of knowledge implications for teaching. A follow-on study by a second committee explored what research and development would need to be done, and how it would need to be communicated, to be especially useful to teachers, principals, superintendents, and policy makers: How People Learn: Bridging Research and Practice (National Research Council, 1999). These two individual reports were combined to produce an expanded edition of How People Learn (National Research Council, 2000). We refer to this volume as HPL.

In the present book, the goal is to take the HPL work to the next step: to provide examples of how the principles and findings on learning can be used to guide the teaching of a set of topics that commonly appear in the K-12 curriculum. As was the case in the original work (1999), the book focuses on three subject areas: history, mathematics, and science. Each area is treated at three levels: elementary, middle, and high school. Distinguished researchers who have extensive experience in teaching or in partnering with teachers were invited to contribute the chapters. The committee shaped the goals for the volume, and commented—sometimes extensively—on the draft chapters as they were written and revised. The principles of HPL are embedded in each chapter, though there are differences from one chapter to the next in how explicitly they are discussed.

Page viii Cite
Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

Taking this next step to elaborate the HPL principles in context poses a potential problem that we wish to address at the outset. The meaning and relevance of the principles for classroom teaching can be made clearer with specific examples. At the same time, however, many of the specifics of a particular example could be replaced with others that are also consistent with the HPL principles. In looking at a single example, it can be difficult to distinguish what is necessary to effective teaching from what is effective but easily replaced. With this in mind, it is critical that the teaching and learning examples in each chapter be seen as illustrative, not as blueprints for the “right” way to teach.

We can imagine, by analogy, that engineering students will better grasp the relationship between the laws of physics and the construction of effective supports for a bridge if they see some examples of well-designed bridges, accompanied by explanations for the choices of the critical design features. The challenging engineering task of crossing the entrance of the San Francisco Bay, for example, may bring the relationship between physical laws, physical constraints, and engineering solutions into clear and meaningful focus. But there are some design elements of the Golden Gate Bridge that could be replaced with others that serve the same end, and people may well differ on which among a set of good designs creates the most appealing bridge.

To say that the Golden Gate Bridge is a good example of a suspension bridge does not mean it is the only, or the best possible, design for a suspension bridge. If one has many successful suspension bridges to compare, the design features that are required for success, and those that are replaceable, become more apparent. And the requirements that are uniform across contexts, and the requirements that change with context, are more easily revealed.

The chapters in this volume highlight different approaches to addressing the same fundamental principles of learning. It would be ideal to be able to provide two or more “HPL compatible” approaches to teaching the same topic (for example, the study of light in elementary school). However, we cannot provide that level of specific variability in this already lengthy volume. Nevertheless, we hope that common features across chapters, and the variation in approach among the chapters, are sufficient to provide instructive insights into the principles laid out in How People Learn.

This volume could not have come to life without the help and dedication of many people, and we are grateful to them. First and foremost, the committee acknowledges the contributions of Robbie Case, who was to have contributed to the mathematics chapters in this volume. Robbie was at the height of a very productive career when his life came to an unexpected end in May 2000. Robbie combined the very best in disciplinary research and attention to the incorporation of research findings into classroom tools

Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

to support teaching and learning. In this respect, he was a model for researchers interested in supporting improved educational practice. The mathematics chapters in this volume are marked by Robbie Case’s influence.

The financial support of our sponsors, the U.S. Department of Education and the President’s Circle of the National Academy of Sciences, was essential. We appreciate both their support and their patience during the unexpectedly long period required to shape and produce so extensive a volume with so many different contributors. Our thanks to C. Kent McGuire, former assistant secretary of the Office of Education Research and Improvement for providing the initial grant for this project, and to his successor and now director of the National Institute for Education Sciences, Grover J. Whitehurst; thanks are due as well to Patricia O’Connell Ross, Jill Edwards Staton, Michael Kestner, and Linda Jones at the Department of Education for working with us throughout, and providing the time required to produce a quality product.

This report is a somewhat unusual undertaking for the National Research Council in that the committee members did not author the report chapters, but served as advisers to the chapter authors. The contributions of committee members were extraordinary. In a first meeting the committee and chapter authors worked together to plan the volume. The committee then read each draft chapter, and provided extensive, and remarkably productive, feedback to chapter authors. As drafts were revised, committee members reviewed them again, pointing out concerns and proposing potential solutions. Their generosity and their commitment to the goal of this project are noteworthy.

Alexandra Wigdor, director of the Division on Education, Labor, and Human Performance when this project was begun, provided ongoing guidance and experienced assistance with revisions. Rona Brière brought her special skills in editing the entire volume. Our thanks go to Allison E. Shoup, who was senior project assistant, supporting the project through much of its life; to Susan R. McCutchen, who prepared the manuscript for review; to Claudia Sauls and Candice Crawford, who prepared the final manuscript; and to Deborah Johnson, Sandra Smotherman, and Elizabeth B. Townsend, who willingly provided additional support when needed. Kirsten Sampson Snyder handled the report review process, and Yvonne Wise handled report production—both challenging tasks for a report of this size and complexity. We are grateful for their help.

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 Report Review Committee. The purpose of this independent review is to provide candid and critical comments that will assist the institution in making its published report as sound as possible and to ensure that the report meets institutional standards

Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×

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 thank the following individuals for their review of this report: Jo Boaler, Mathematics Education, School of Education, Stanford University; Miriam L. Clifford, Mathematics Department, Carroll College, Waukesha, Wisconsin; O.L. Davis, Curriculum and Instruction, The University of Texas at Austin; Patricia B. Dodge, Science Teacher, Essex Middle School, Essex Junction, Vermont; Carol T. Hines, History Teacher, Darrel C. Swope Middle School, Reno, Nevada; Janis Lariviere, UTeach—Science and Mathematics Teacher Preparation, The University of Texas at Austin; Gaea Leinhardt, Learning Research and Development Center and School of Education, University of Pittsburgh; Alan M. Lesgold, Office of the Provost, University of Pittsburgh; Marcia C. Linn, Education in Mathematics, Science, and Technology, University of California, Berkeley; Kathleen Metz, Cognition and Development, Graduate School of Education, University of California, Berkeley; Thomas Romberg, National Center for Research in Mathematics and Science Education, University of Wisconsin–Madison; and Peter Seixas, Centre for the Study of Historical Consciousness, University of British Columbia.

Although the reviewers listed above have provided many constructive comments and suggestions, they did not see the final draft of the report before its release. The review of this report was overseen by Alan M. Lesgold, University of Pittsburgh. Appointed by the National Research Council, he was responsible for making certain that an independent examination of this report was carried out in accordance with institutional procedures and that all review comments were carefully considered. Responsibility for the final content of this report rests entirely with the authors, the committee, and the institution.

John D. Bransford, Chair

M. Suzanne Donovan, Study Director

Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×
Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×
   

Appendix 3A:   Implications for Planning,

 

164

   

 Notes,

 

177

   

 References,

 

177

4

 

“They Thought the World Was Flat?”: Applying the Principles of How People Learn in Teaching High School History
Robert B. Bain

 

179

   

 Where to Begin? Transforming Topics and Objectives into Historical Problems,

 

181

   

 Designing a “History-Considerate” Learning Environment: Tools for Historical Thinking,

 

199

   

 Conclusion,

 

209

   

 Acknowledgments,

 

210

   

 Notes,

 

211

   

 References,

 

212

Part II:
Mathematics

 

 

5

 

Mathematical Understanding: An Introduction
Karen C. Fuson, Mindy Kalchman, and John D. Bransford

 

217

   

Principle #1:   Teachers Must Engage Students’ Preconceptions,

 

219

   

Principle #2:   Understanding Requires Factual Knowledge and Conceptual Frameworks,

 

231

   

Principle #3:   A Metacognitive Approach Enables Student Self-Monitoring,

 

236

   

 Next Steps,

 

243

   

 Notes,

 

246

   

 References,

 

246

   

 Suggested Reading List for Teachers,

 

256

6

 

Fostering the Development of Whole-Number Sense: Teaching Mathematics in the Primary Grades
Sharon Griffin

 

257

   

 Deciding What Knowledge to Teach,

 

259

   

 Building on Children’s Current Understandings,

 

267

   

 Acknowledging Teachers’ Conceptions and Partial Understandings,

 

279

   

 Revisiting Question 2: Defining the Knowledge That Should Be Taught,

 

281

   

 How Can This Knowledge Be Taught?: The Case of Number Worlds,

 

282

   

 What Sorts of Learning Does This Approach Make Possible?,

 

302

Page xiii Cite
Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×
Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×
Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
×


How Students Learn

HISTORY, MATHEMATICS, AND SCIENCE IN THE CLASSROOM

Suggested Citation:"Front Matter." National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press. doi: 10.17226/10126.
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How do you get a fourth-grader excited about history? How do you even begin to persuade high school students that mathematical functions are relevant to their everyday lives? In this volume, practical questions that confront every classroom teacher are addressed using the latest exciting research on cognition, teaching, and learning.

How Students Learn: History, Mathematics, and Science in the Classroom builds on the discoveries detailed in the bestselling How People Learn. Now, these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness.

Organized for utility, the book explores how the principles of learning can be applied in teaching history, science, and math topics at three levels: elementary, middle, and high school. Leading educators explain in detail how they developed successful curricula and teaching approaches, presenting strategies that serve as models for curriculum development and classroom instruction. Their recounting of personal teaching experiences lends strength and warmth to this volume.

The book explores the importance of balancing students’ knowledge of historical fact against their understanding of concepts, such as change and cause, and their skills in assessing historical accounts. It discusses how to build straightforward science experiments into true understanding of scientific principles. And it shows how to overcome the difficulties in teaching math to generate real insight and reasoning in math students. It also features illustrated suggestions for classroom activities.

How Students Learn offers a highly useful blend of principle and practice. It will be important not only to teachers, administrators, curriculum designers, and teacher educators, but also to parents and the larger community concerned about children’s education.

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