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Suggested Citation:"Front Matter." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

High School Mathematics At Work

Essays And Examples For The Education Of All Students

MATHEMATICAL SCIENCES EDUCATION BOARD

CENTER FOR SCIENCE, MATHEMATICS, AND ENGINEERING EDUCATION

NATIONAL RESEARCH COUNCIL

NATIONAL ACADEMY PRESS
WASHINGTON, D.C.
1998

Suggested Citation:"Front Matter." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

NATIONAL ACADEMY PRESS
2101 Constitution Avenue, NW Washington, DC 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.

The National Research Council (NRC) is the operating arm of the National Academies Complex, which includes the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The National Research Council 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 Wulf, President of the National Academy of Engineering, also serve as chairman and vice chairman, respectively, of the National Research Council.

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 Pew Charitable Trusts. Any opinions, findings, or recommendations expressed in this report are those of the authors and do not necessarily reflect the views of the Pew Charitable Trusts.

Library of Congress Cataloging-in-Publication Data

High school mathematics at work : essays and examples for the education of all students / Mathematical Sciences Education Board.

p. cm.

Includes bibliographical references and index.

ISBN 0-309-06353-1 (pbk.)

1. Mathematics—Study and teaching (Secondary)—United States. I. National Research Council (U.S.). Mathematical Sciences Education Board.

QA13.H54 1998

510'.71'273—ddc21

98-19669

Permission for limited reproduction of portions of this book for education purposes but not for sale may be granted on receipt of a written request to the National Academy Press, 2101 Constitution Avenue, NW, Washington, DC 20418.

Additional copies of this report may be purchased from the
National Academy Press,
2101 Constitution Avenue, NW, Lock Box 285, Washington, DC 20055. (800) 624-6242 or (202) 334-3313 (in the Washington Metropolitan Area). This report is also available online at http://www.nap.edu.

Printed in the United States of America

Copyright 1998 by the National Academy of Sciences. All rights reserved.

Suggested Citation:"Front Matter." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

National Research Council

Center for Science, Mathematics, and Engineering Education

Mathematical Sciences Education Board

Hyman Bass (MSEB Chair)

Columbia University

Glenda T. Lappan (MSEB Vice Chair)

Michigan State University

Sherry Baca

Prescott Unified School District

Deborah Ball

University of Michigan

Benjamin Blackhawk

St. Paul Academy and Summit School

Sadie Bragg*

Borough of Manhattan Community College

Gail F. Burrill

University of Wisconsin, Madison

Patricia Campbell

University of Maryland

Shari Coston*

Arkansas Education Renewal Consortium

Ingrid Daubechies

Princeton University

Shelley K. Ferguson

California Mathematics Project

Melvin D. George

University of Missouri

Roger E. Howe

Yale University

Bruce Jacobs*

Oakland Electronic Commerce Resource Center

Lee Jenkins

Enterprise School District, Redding, CA

Rick Jennings

Yakima School District, Yakima, WA

Harvey B. Keynes*

University of Minnesota

James R. C. Leitzel*

University of New Hampshire

Tony Q. Martinez*

Leander High School, Leander, TX

Pamela Matthews

American University

David Moore

Purdue University

Mari Muri

State of Connecticut Department of Education

Richard Normington

Pacific Bell

Mark Saul

Bronxville Public Schools

Richard Schoen

Stanford University

Edward A. Silver

University of Pittsburgh

William Tate

University of Wisconsin, Madison

Susan S. Wood

J. Sargeant Reynolds Community College

Margaret H. Wright*

AT&T Bell Laboratories

Project Staff

Rodger Bybee Executive Director,

CSMEE

Joan Ferrini-Mundy Director,

MSEB

Bradford Findell Program Officer/Editor

Daniel Goroff Division Director,

Post-secondary Policy and Practice

Kathleen Johnston Editorial Associate

Gale Moore Financial & Administrative Associate

Doug Sprunger Senior Project Assistant

Project Consultants

Susan Forman

Cathy Kessel

Lynn Arthur Steen

*  

Member until June 1997

Suggested Citation:"Front Matter." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

National Research Council

Center For Science, Mathematics, And Engineering Education

High School Mathematics at Work Task Force

Hyman Bass

Columbia University

Bruce Jacobs

Oakland Electronic Commerce Resource Center

Tony Q. Martinez

Leander High School, Leander, TX

Pamela Matthews

American University

Patrick McCray

G. D. Searle & Co.

Karen Dee Michalowicz

The Langley School, McLean, VA

Henry O. Pollak

AT&T Bell Labs (retired)

Jack Price, Chair

California State Polytechnic University

Alan H. Schoenfeld

University of California, Berkeley

Daniel Teague

North Carolina School of Mathematics & Science

Suggested Citation:"Front Matter." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

High School Mathematics at Work Reviewers

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:

George Campbell Jr.

President and CEO, NACME, Inc., New York, NY

Arthur Eisenkraft

Science Coordinator, Bedford Public Schools, Bedford, NY

Jane D. Gawronski

Superintendent, Escondido Union High School District, Escondido, CA

Cindy Hannon

State Mathematics Specialist, Maryland State Department of Education

Harry Kesten

Professor of Mathematics, Cornell University, Ithaca, NY

Ron Latanision

Chairman, MIT Council on Primary and Secondary Education, Professor of Material Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA

Douglas H. O'Roark

Mathematics Teacher, Lincoln Park High School, Chicago, IL

Diane Resek

Professor of Mathematics, San Francisco State University, San Francisco, CA

Judah L. Schwartz

Professor of Education ,Harvard University, and Emeritus Professor, Engineering Science & Education, Massachusetts Institute of Technology, Cambridge, MA

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.

Suggested Citation:"Front Matter." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×
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Suggested Citation:"Front Matter." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

Foreword: Mathematics for a Modern Age

ZELL MILLER

Governor of Georgia

Now more than ever, our daily lives are directly affected by mathematics. I'm not just talking about the grades students get or how many mathematics classes they have to take. I'm talking about answering the phone, faxing a document, or driving a car. I'm talking about buying medicine for your family, building a house, and listening to music. Mathematics has also helped bring us things that indirectly affect us, like the discoveries of DNA, weather patterns, and how to use light as a surgical tool. It has helped us walk on the moon, create microchips, and transmit images across thousands of miles. With mathematics, we design models to test our ideas and refine them, from nerve impulses to human behavior, volcanoes to food. Mathematics is everywhere. But mathematics has always been around, and the concepts it uses have always helped us.

So why is mathematics so much more important to our lives now than it was then? Years ago, in the eras of the abacus or slide rule, information took a lot longer to sort through, but now it is easy to chart a course, assay a risk, or compare statistics. Information is more abundant than ever. You can find answers about everything from world politics to school lunches almost as soon as you think of the questions.

This new speed of access to volumes of information obviously brings good

Page viii Cite
Suggested Citation:"Front Matter." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

things—like better medical information, better building materials, and more diverse options in business and education. The down side to all of this is that as easily as there can be information, there can be misuse of information.

So what does this mean for our children? More than ever, they need to be mathematically savvy. Learning to think and reason mathematically is the only way our children can be sure that they are in control, not being controlled.

More practically, almost every job these days requires at least some elementary understanding of mathematics. In fact, many of the jobs that keep our country competitive and successful in the global market are jobs that require more than basic mathematics comprehension. Not that everyone needs to be able to program a computer or predict the stock market, but with the vastly increased speed of statistical calculation (and manipulation) and easier and faster global communication, our children need to know what a number means, where it came from, and how best to judge its veracity.

As the Governor of Georgia, I take all of this pretty seriously. I know the importance of bringing businesses to my state to create jobs for Georgians. The world, however, is their marketplace; to be healthy, competitive, and economically secure, our citizens must understand mathematics. They need to become comfortable with the notion of mathematics as a tool for life.

GOVERNOR ZELL MILLER was elected Governor of the state of Georgia in 1990. Since taking office, his love of teaching and commitment to education has resulted in one of the most ambitious agendas to improve public education in this century. Governor Miller's public career includes service at virtually every level of government: as mayor, as a member of the state senate, as lieutenant governor, and now as Governor. He is currently Chairman of the Education Commission of the States. He has also chaired the Southern Governors' Association, the Appalachian Regional Commission, and the Council of State Governments. Governor Miller keynoted the 1992 Democratic National Convention in New York and chaired the Platform Drafting Committee for the 1996 Democratic National Convention in Chicago.

Suggested Citation:"Front Matter." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

Acknowledgments

For over ten years the Mathematical Sciences Education Board (MSEB) has worked to support the improvement of mathematics education. The work of the Board becomes visible largely through publications, beginning with Everybody Counts (1989) and Reshaping School Mathematics (1990). High School Mathematics at Work builds on this prior work. Like Measuring Up (1992), it contains student tasks; like Mathematical Preparation of the Technical Work Force (1995), it highlights the mathematics needed for careers.

High School Mathematics at Work was developed through the efforts of more people than can be named individually here. We gratefully acknowledge the generous financial support of the Pew Charitable Trusts, and thank both Robert Schwartz for his special encouragement with this project when he was Director of their Education Programs, as well as Janet Kroll for her continuing interest and support as our program officer.

The project was launched as a 12th grade sequel to Measuring Up through the initiative of Linda P. Rosen. The MSEB first envisioned that this sequel would illuminate some features of high-quality high school mathematics teaching and learning through standards-based assessment tasks. The growing interest in school-to-work issues, however, led to our giving this theme major prominence. With this new focus, Lynn Arthur Steen and Susan Forman designed the

Suggested Citation:"Front Matter." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

project, secured funding, collected mathematical examples, commissioned essays, and worked with the Task Force, first as members of the MSEB staff and later as consultants. We also thank Daniel Goroff for his leadership during a period of staff transition.

Examples of mathematical tasks were solicited over a period of two years from a wide variety of sources, as described in Appendix A. From the hundreds of examples that were contributed, the Task Force selected about two dozen for inclusion, wrote first drafts of those mathematical examples, and identified essay topics and authors. The resulting collection of examples and essays was molded into its current form by Bradford Findell, serving as editor, under the guidance of Glenda Lappan, Alan Schoenfeld, and Harvey Keynes, with the assistance of Cathy Kessel, and with substantial input from Deborah Ball, Sadie Bragg, Gail Burrill, Shari Coston, Shelley Ferguson, Melvin George, Rick Jennings, Jim Leitzel, Tony Martinez, Pamela Matthews, Patrick McCray, and Jack Price.

Of course, no project of this size could ever come to completion without the contributions of support staff. Thanks especially to Sharon O'Donnell for her help collecting the essays and examples and to Catherine Bell and Doug Sprunger for their help with the review process. We must also thank Sally Stanfield, Linda Humphrey, and the staff at the National Academy Press for their support and patience with the complex evolution of this project.

HYMAN BASS, CHAIRMAN

Mathematical Sciences Education Board

References

National Research Council. (1989). Everybody counts: A report to the nation on the future of mathematics education. Washington, DC: National Academy Press.

National Research Council. (1990). Reshaping school mathematics: A philosophy and framework for curriculum. Washington, DC: National Academy Press.

National Research Council. (1993). Measuring up: Prototypes for mathematics assessment. Washington, DC: National Academy Press.

National Research Council. (1995). Mathematical preparation of the technical work force. Washington, DC: National Academy Press.

Additional thanks for the many efforts and suggestions offered by the following people:

Jennifer Bemis, John Bishop, Judy Estep, Jim Fey, Carol Findell, Kent Findell, Irene Gable, Jim Gates, Mary Hornyak, Ramona Irvin, Jay Labov, Patrice Legro, Diane Mann, Bob Naismith, Harold Pratt, Kirsten Sampson, Harold Shoen, Kevin Sullivan, Jan Tumoi, Phil Wagreich, Tina Winters, and Judi Zawojewski.

Suggested Citation:"Front Matter." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

Table of Contents

Foreword: Mathematics for a Modern Age
Zell Miller, Governor of Georgia

 

vii

Acknowledgments

 

ix

Introduction

 

1

PART ONE
Connecting Mathematics With Work and Life

 

 

 

 

Overview

 

9

1

 

Mathematics as a Gateway to Student Success
Dale Parnell, Oregon State University

 

14

2

 

Market Launch
Rol Fessenden, L. L. Bean, Inc.

 

18

3

 

Integrating Vocational and Academic Education
Thomas Bailey, Columbia University

 

24

4

 

The Importance of Workplace and Everyday Mathematics
Jean E. Taylor, Rutgers University

 

30

5

 

Working with Algebra
Daniel Chazan, Michigan State University Sandra Callis Bethell, Holt High School

 

35

 

 

EMERGENCY CALLS

 

42

 

 

BACK-OF-THE-ENVELOPE ESTIMATES

 

45

 

 

SCHEDULING ELEVATORS

 

49

 

 

HEATING-DEGREE-DAYS

 

54

Suggested Citation:"Front Matter." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

PART TWO
The Roles of Standards and Assessments

 

 

 

 

Overview

 

59

6

 

Science and Mathematics Education: Finding Common Ground
Jane Butler Kahle, Miami University

 

63

7

 

SCANS and Mathematics—Supporting the Transition from Schools to Careers
Arnold Packer, Johns Hopkins University

 

67

8

 

Thinking about the SAT
William Linder-Scholer, SciMath Minnesota

 

70

9

 

Extended Response Tasks in International Contexts
John Dossey, Illinois State University

 

75

 

 

DRUG DOSAGE

 

80

 

 

MENTAL MATHEMATICS

 

83

 

 

BUYING ON CREDIT

 

87

PART THREE
Curricular Considerations

 

 

 

 

Overview

 

93

10

 

Fitting Tasks to Curriculum
Zalman Usiskin, University of Chicago

 

97

11

 

Mathematics as a Way of Thinking about Things
Albert A. Cuoco, Education Development Center

 

102

12

 

Preparing Students for Post-secondary Education
Harvey B. Keynes, University of Minnesota

 

107

 

 

LOTTERY WINNINGS

 

111

 

 

HOSPITAL QUALITY

 

115

 

 

ROUNDING OFF

 

119

 

 

RULES OF THUMB

 

123

Page xiii Cite
Suggested Citation:"Front Matter." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
×

PART FOUR
Implications For Teaching and Teacher Education

 

 

 

 

Overview

 

129

13

 

Pedagogical Implications for Problem-Centered Teaching
Glenda T. Lappan, Michigan State University

 

132

14

 

The Role of Complex Mathematical Tasks in Teacher Education
Gilbert J. Cuevas, University of Miami

 

137

15

 

Assessment Conversations as a Tool for Reform
Paul G. LeMahieu, University of Delaware and Department of Education Marshá T. Horton, Delaware Department of Education

 

141

 

 

ESTIMATING AREA

 

145

 

 

TIMING TRAFFIC LIGHTS

 

147

 

 

BUYING A USED CAR

 

153

PART FIVE
Epilogue

 

157

Appendixes

 

 

A

 

Sources of Problems and Tasks
Susan Forman and Lynn Arthur Steen

 

163

B

 

Task Force Members

 

167

Index

 

171

Suggested Citation:"Front Matter." National Research Council. 1998. High School Mathematics at Work: Essays and Examples for the Education of All Students. Washington, DC: The National Academies Press. doi: 10.17226/5777.
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Traditionally, vocational mathematics and precollege mathematics have been separate in schools. But the technological world in which today's students will work and live calls for increasing connection between mathematics and its applications. Workplace-based mathematics may be good mathematics for everyone.

High School Mathematics at Work illuminates the interplay between technical and academic mathematics. This collection of thought-provoking essays--by mathematicians, educators, and other experts--is enhanced with illustrative tasks from workplace and everyday contexts that suggest ways to strengthen high school mathematical education.

This important book addresses how to make mathematical education of all students meaningful--how to meet the practical needs of students entering the work force after high school as well as the needs of students going on to postsecondary education.

The short readable essays frame basic issues, provide background, and suggest alternatives to the traditional separation between technical and academic mathematics. They are accompanied by intriguing multipart problems that illustrate how deep mathematics functions in everyday settings--from analysis of ambulance response times to energy utilization, from buying a used car to "rounding off" to simplify problems.

The book addresses the role of standards in mathematics education, discussing issues such as finding common ground between science and mathematics education standards, improving the articulation from school to work, and comparing SAT results across settings.

Experts discuss how to develop curricula so that students learn to solve problems they are likely to encounter in life--while also providing them with approaches to unfamiliar problems. The book also addresses how teachers can help prepare students for postsecondary education.

For teacher education the book explores the changing nature of pedagogy and new approaches to teacher development. What kind of teaching will allow mathematics to be a guide rather than a gatekeeper to many career paths? Essays discuss pedagogical implication in problem-centered teaching, the role of complex mathematical tasks in teacher education, and the idea of making open-ended tasks--and the student work they elicit--central to professional discourse.

High School Mathematics at Work presents thoughtful views from experts. It identifies rich possibilities for teaching mathematics and preparing students for the technological challenges of the future. This book will inform and inspire teachers, teacher educators, curriculum developers, and others involved in improving mathematics education and the capabilities of tomorrow's work force.

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