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Suggested Citation:"Front Matter." National Research Council. 2001. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10050.
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Knowing and Learning Mathematics for Teaching

Mathematics Teacher Preparation Content Workshop Program Steering Committee

Center for Education

Mathematical Sciences Education Board

National Research Council

NATIONAL ACADEMY PRESS
Washington, D.C.

Suggested Citation:"Front Matter." National Research Council. 2001. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10050.
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NATIONAL ACADEMY PRESS
2101 Constitution Avenue, N.W. Washington, D.C. 20418

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 Grant No. DUE-9706060 between the National Academy of Sciences and the National Science Foundation. 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.

International Standard Book Number 0-309-07252-2

Library of Congress Catalog Card Number 00-110978

Additional copies of this report are available from

National Academy Press,
2101 Constitution Avenue, N.W., Lockbox 285, Washington, D.C. 20055; (800) 624-6242 or (202) 334-3313 (in the Washington metropolitan area); Internet, http://www.nap.edu

Printed in the United States of America

Copyright 2001 by the National Academy of Sciences. All rights reserved.

Suggested Citation:"Front Matter." National Research Council. 2001. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10050.
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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.

Suggested Citation:"Front Matter." National Research Council. 2001. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10050.
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Suggested Citation:"Front Matter." National Research Council. 2001. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10050.
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MATHEMATICS TEACHER PREPARATION CONTENT WORKSHOP PROGRAM STEERING COMMITTEE

Deborah Loewenberg Ball, Chair,

University of Michigan

Richard Askey, *

University of Wisconsin-Madison

Hyman Bass, *

Columbia University

Genevieve Knight,

Coppin State College

Mark Saul,

Bronxville High School

Deborah Schifter,

Education Development Center, Inc.

Olga Garcia Torres,

Tucson Unified School District

Staff

Rodger Bybee, Executive Director,

Center for Science, Mathematics, and Engineering Education (CSMEE)

Joan Ferrini-Mundy, Associate Executive Director,

CSMEE

Gail Burrill, Project Director

Bradford Findell, Program Officer

Kirsten Sampson Snyder, Reports Officer

Doug Sprunger, Senior Project Assistant

Danna Brennan, Project Assistant

*

Member of the National Academy of Sciences

Suggested Citation:"Front Matter." National Research Council. 2001. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10050.
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MATHEMATICAL SCIENCES EDUCATION BOARD (MSEB) 1998-1999

Hyman Bass, Chair, *

Columbia University

Jere Confrey, Vice Chair,

University of Texas at Austin

Richard A. Askey, *

University of Wisconsin-Madison

Sherry Baca,

Prescott Unified School District

Deborah Loewenberg Ball,

University of Michigan

Benjamin Blackhawk,

St. Paul Academy and Summit School

Richelle Blair,

Lakeland Community College

Patricia Campbell,

University of Maryland

Ingrid Daubechies, *

Princeton University

Karen Economopoulos,

TERC

Susan Eyestone,

National Parent Teachers Association

Lee Jenkins,

Antioch Unified School District

Glenda T. Lappan,

Michigan State University

Miriam Masulo,

IBM Corporation

David Moore,

Purdue University

Mari Muri,

Connecticut Department of Education

Richard Normington,

TQM Services Group

Mark Saul,

Bronxville Public Schools

Richard Schoen,

Stanford University

Edward A. Silver,

University of Pittsburgh

William Tate,

University of Wisconsin-Madison

Jerry Uhl,

University of Illinois at Urbana-Champaign

Susan S. Wood,

J. Sargeant Reynolds Community College

Staff

Joan Ferrini-Mundy, Director, through June, 1999

Gail Burrill, Director

Bradford Findell, Program Officer

Sonja Atkinson, Administrative Assistant

*

Member of National Academy of Sciences

Suggested Citation:"Front Matter." National Research Council. 2001. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10050.
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Dedication

James R. C. Leitzel was a member of the Mathematical Sciences Education Board (MSEB) from 1994 to 1997. Jim's contributions to mathematics education are vast and diverse, but one of his principal commitments was to the improvement of teacher preparation and professional development. He was an articulate advocate for the Board's initiatives in this area. Jim served on the Professional Development of Teachers of Mathematics Working Group that contributed to the National Council of Teachers of Mathematics' Professional Standards for Teaching Mathematics and was the editor of the Mathematical Association of America's Call for Change: Recommendations for the Mathematical Preparation of Teachers of Mathematics. Jim's dedication to teachers and their growth as mathematics teachers also extended to those in his classes at The Ohio State University, the University of Nebraska-Lincoln, and the University of New Hampshire and to the many mathematics educators for whom he became a mentor. Jim passed away in 1998 but left a legacy of concern, care, and nurturing for teachers and teaching. In recognition of his contributions both to the MSEB and to the mathematics education community, we dedicate this book to him.

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Suggested Citation:"Front Matter." National Research Council. 2001. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10050.
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Suggested Citation:"Front Matter." National Research Council. 2001. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10050.
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Acknowledgments

We would like to acknowledge the staff at the National Research Council 's (NRC) Center for Science, Mathematics, and Engineering Education (CSMEE) for their efforts in putting the Workshop together. In particular, Doug Sprunger was instrumental in overseeing arrangements for the meeting and in arranging these proceedings for review and publication. Onsite support was also provided by Kirsten Sampson Snyder and Tina Winters.

We are grateful to the members of the Program Steering Committee for their oversight in planning the program for the Workshop. We also wish to acknowledge the speakers and in particular the discussion group leaders for their contributions and leadership that gave substance to the discussion.

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 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:

Shelly Ferguson, National Council of Teachers of Mathematics

Kay McClain, Vanderbilt University

Albert Otto, Illinois State University

Tad Watanabe, Towson State University

Laura van Zoost, University of Western Michigan

While the individuals listed above have provided many constructive comments and suggestions, responsibility for the final content of this report rests solely with the steering committee and the National Research Council.

Gail Burrill

Project Director

Mathematical Sciences Education Board

Suggested Citation:"Front Matter." National Research Council. 2001. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10050.
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Suggested Citation:"Front Matter." National Research Council. 2001. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10050.
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 What Kinds of Mathematical Knowledge Matter in Teaching?

 

65

   

 Perspectives from a Mathematician
Alan Tucker

 

66

   

 Perspectives from a Mathematics Educator
Deborah Schifter

 

69

   

 Perspectives from the Community College
Gladys Whitehead

 

72

 

 

HOW CAN TEACHERS DEVELOP SUCH MATHEMATICAL KNOWLEDGE?

 

75

   

 Investigating Alternative Approaches to Helping Teachers Learn Mathematics

 

77

   

 Student Curriculum Materials: Japanese Teachers' Manuals
Shin-ying Lee

 

78

   

 Student Curriculum Materials: Investigations in Number, Data, and Space
Marco Ramirez

 

86

   

 Case Materials
Carne Barnett

 

90

   

 Programs and Practices
Deborah Schifter, Virginia Bastable, and Jill Bodner Lester

 

94

   

 Video as a Delivery Mechanism
Bradford Findell, Deborah Loewenberg Ball

 

98

   

 Promising Approaches for Helping Prospective Elementary Teachers Learn Mathematics for Teaching

 

105

   

 Looking at Textbooks
Richard Askey

 

106

   

 The Professional Growth of a Classroom Teacher
Carol Midgett

 

116

   

 The Importance of Mathematical Content
Alice Gill

 

119

   

 NSF and Teacher Preparation Programs
James Lightbourne

 

122

   

 Where Are We? Moderator's Summary
Joan Ferrini-Mundy

 

125

   

 Concluding Remarks
Deborah Loewenberg Ball

 

127

 

 

DISCUSSION GROUP REPORTS

 

129

   

 Question #1

 
   

 Discussion Group #1

 

131

   

 Discussion Group #10

 

133

   

 Question #2

 
   

 Discussion Group #2

 

137

   

 Discussion Group #9

 

140

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There are many questions about the mathematical preparation teachers need. Recent recommendations from a variety of sources state that reforming teacher preparation in postsecondary institutions is central in providing quality mathematics education to all students. The Mathematics Teacher Preparation Content Workshop examined this problem by considering two central questions:

  • What is the mathematical knowledge teachers need to know in order to teach well?
  • How can teachers develop the mathematical knowledge they need to teach well?

The Workshop activities focused on using actual acts of teaching such as examining student work, designing tasks, or posing questions, as a medium for teacher learning. The Workshop proceedings, Knowing and Learning Mathematics for Teaching, is a collection of the papers presented, the activities, and plenary sessions that took place.

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