High School Mathematics at Work: Essays and Examples for the Education of All Students

192 Pages·1998·1.16 MB·English

by  National Research Council (U. S.) Mathematical Sciences Education Board Staff

High School Mathematics at Work: Essays and Examples for the Education of All Students
http://www.nap.edu/catalog/5777.html
H S
IGH CHOOL
M
ATHEMATICS
W
AT ORK
ESSAYS AND
EXAMPLES FOR
THE EDUCATION OF
ALL STUDENTS
MATHEMATICAL SCIENCES EDUCATION BOARD
NATIONAL RESEARCH COUNCIL
CENTER FOR SCIENCE, MATHEMATICS, AND ENGINEERING EDUCATION
NATIONAL ACADEMY PRESS
WASHINGTON, D.C. 1998
Copyright © National Academy of Sciences. All rights reserved.
High School Mathematics at Work: Essays and Examples for the Education of All Students
http://www.nap.edu/catalog/5777.html
NATIONALACADEMY 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 Acad-
emy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The mem-
bers 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 Acad-
emy 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. Func-
tioning 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 engineer-
ing communities. The Council is administered jointly by both Academies and the Institute of Med-
icine. 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, under-
graduate 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 Consti-
tution Avenue, NW, Lock Box 285, Washington, DC 20055. [phone] or [phone] (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.
Copyright © National Academy of Sciences. All rights reserved.
High School Mathematics at Work: Essays and Examples for the Education of All Students
http://www.nap.edu/catalog/5777.html
NATIONAL RESEARCH COUNCIL
CENTER FOR SCIENCE, MATHEMATICS, AND ENGINEERING EDUCATION
MATHEMATICAL SCIENCES EDUCATION BOARD
Hyman Bass (MSEB Chair) David Moore
Columbia University Purdue University
Glenda T. Lappan (MSEB Vice Chair) Mari Muri
Michigan State University State of Connecticut Department of Education
Sherry Baca Richard Normington
Prescott Unified School District Pacific Bell
Deborah Ball Mark Saul
University of Michigan Bronxville Public Schools
Benjamin Blackhawk Richard Schoen
St. Paul Academy and Summit School Stanford University
Sadie Bragg* Edward A. Silver
Borough of Manhattan Community College University of Pittsburgh
Gail F. Burrill William Tate
University of Wisconsin, Madison University of Wisconsin, Madison
Patricia Campbell Susan S. Wood
University of Maryland J. Sargeant Reynolds Community College
Shari Coston* Margaret H. Wright*
Arkansas Education Renewal Consortium AT&T Bell Laboratories
Ingrid Daubechies PROJECT STAFF
Princeton University
Rodger Bybee
Shelley K. Ferguson
Executive Director, CSMEE
California Mathematics Project
Joan Ferrini-Mundy
Melvin D. George
Director, MSEB
University of Missouri
Bradford Findell
Roger E. Howe
Program Officer/Editor
Yale University
Daniel Goroff
Bruce Jacobs*
Division Director, Postsecondary Policy and
Oakland Electronic Commerce Resource
Practice
Center
Kathleen Johnston
Lee Jenkins
Editorial Associate
Enterprise School District, Redding, CA
Gale Moore
Rick Jennings
Financial & Administrative Associate
Yakima School District, Yakima, WA
Doug Sprunger
Harvey B. Keynes*
Senior Project Assistant
University of Minnesota
James R. C. Leitzel* PROJECT CONSULTANTS
University of New Hampshire
Susan Forman
Tony Q. Martinez*
Cathy Kessel
Leander High School, Leander, TX
Lynn Arthur Steen
Pamela Matthews
American University
*Member until June, 1997
iii
Copyright © National Academy of Sciences. All rights reserved.
High School Mathematics at Work: Essays and Examples for the Education of All Students
http://www.nap.edu/catalog/5777.html
NATIONAL RESEARCH COUNCIL
CENTER FOR SCIENCE, MATHEMATICS, AND ENGINEERING EDUCATION
HIGH SCHOOL MATHEMATICS AT WORK TASK FORCE
Hyman Bass Karen Dee Michalowicz
Columbia University The Langley School, McLean, VA
Bruce Jacobs Henry O. Pollak
Oakland Electronic Commerce Resource AT&T Bell Labs (retired)
Center Jack Price, Chair
Tony Q. Martinez California State Polytechnic University
Leander High School, Leander, TX Alan H. Schoenfeld
Pamela Matthews University of California, Berkeley
American University Daniel Teague
Patrick McCray North Carolina School of Mathematics &
G. D. Searle & Co. Science
iv
Copyright © National Academy of Sciences. All rights reserved.
High School Mathematics at Work: Essays and Examples for the Education of All Students
http://www.nap.edu/catalog/5777.html
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 partici-
pation in the review of this report:
George Campbell Jr. Ron Latanision
President and CEO, NACME, Inc., Chairman, MIT Council on Primary and
New York, NY Secondary Education, Professor of Material
Arthur Eisenkraft Science and Engineering, Massachusetts
Institute of Technology, Cambridge, MA
Science Coordinator, Bedford Public Schools,
Bedford, NY Douglas H. O’Roark
Jane D. Gawronski Mathematics Teacher, Lincoln Park High
School, Chicago, IL
Superintendent, Escondido Union High School
District, Escondido, CA Diane Resek
Cindy Hannon Professor of Mathematics, San Francisco
State University, San Francisco, CA
State Mathematics Specialist, Maryland State
Department of Education Judah L. Schwartz
Harry Kesten Professor of Education, Harvard University,
and Emeritus Professor, Engineering
Professor of Mathematics, Cornell University,
Science & Education, Massachusetts
Ithaca, NY
Institute of Technology, Cambridge, MA
While the individuals listed above have provided many constructive comments and sug-
gestions, responsibility for the final content of this report rests solely with the author-
ing committee and the NRC.
v
Copyright © National Academy of Sciences. All rights reserved.
High School Mathematics at Work: Essays and Examples for the Education of All Students
http://www.nap.edu/catalog/5777.html
Copyright © National Academy of Sciences. All rights reserved.
High School Mathematics at Work: Essays and Examples for the Education of All Students
http://www.nap.edu/catalog/5777.html
F : M
OREWORD ATHEMATICS
M A
FOR A ODERN GE
ZELL MILLER
GOVERNOR OF GEORGIA
N
ow more than ever, our daily lives are directly affected by mathematics.
I’m not just talking about the grades students get or how many mathe-
matics 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
FOREWORD
vii
Copyright © National Academy of Sciences. All rights reserved.
High School Mathematics at Work: Essays and Examples for the Education of All Students
http://www.nap.edu/catalog/5777.html
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 ele-
mentary 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 economi-
cally 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 agen-
das 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 gov-
ernor, 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.
HIGH SCHOOL MATHEMATICS AT WORK
viii
Copyright © National Academy of Sciences. All rights reserved.
High School Mathematics at Work: Essays and Examples for the Education of All Students
http://www.nap.edu/catalog/5777.html
A
CKNOWLEDGMENTS
F
or 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 Techni-
cal 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 teach-
ing and learning through standards-based assessment tasks. The growing inter-
est in school-to-work issues, however, led to our giving this theme major promi-
nence. With this new focus, Lynn Arthur Steen and Susan Forman designed the
ACKNOWLEDGMENTS
ix
Copyright © National Academy of Sciences. All rights reserved.