Calculus for a New Century: A Pump Not a Filter

276 Pages·1987·8.521 MB·English

by  L. Steen

C A L C U L US
f or a
NEW CENTURY
A PUMP, NOT A FILTER
A National Colloquium
October 28-29, 1987
Edited by Lynn Arthur Steen for
The Board on Mathematical Sciences and
The Mathematical Sciences Education Board of
The National Research Council
National Academy of Sciences
National Academy of Engineering
Institute of Medicine
Mathematical Association of America
The image used on the cover of this book and on the opening
pages of each of its seven parts shows a periodic minimal
surface discovered in 1 987 by Michael Callahan, David
Hoffman, and Bill Meeks III at the University of
Massachusetts. This computer generated image was created
by James T. Hoffman, ©1 987.
The questions from the AP calculus test in the Examination
section are reproduced with the permission of The College
Entrance Examination Board and of Educational Testing
Service, the copyright holder.
© 1 988 by the Mathematical Association of America.
Permission for limited reproduction of these materials for
educational purposes but not for sale is granted.
Library of Congress Card Number 87-063378
ISBN 0-88385-058-3
Printed in the United States of America
Current printing (last digit) 6 5 4 3 2 1
Calculus for a New Century
A Pump, Not a Filter
Preface ix Bernard L. Madison
Introduction xi Lynn Arthur Steen
Colloquium
Plenary Presentations
Calculus for a New Century 3 Frank Press
Castles in the Sand 4 Ronald G. Douglas
Calculus of Reality 6 Robert M. White
Calculus Today 10 Lynn Arthur Steen
Calculus Tomorrow 14 Thomas W. Tucker
Views from Client Disciplines
Views from Client Disciplines 18 Cathleen S. Morawetz
Calculus for Engineering Practice 18 W. Dale Compton
Calculus in the Biological Sciences 20 Henry S. Horn
Calculus for Management: A Case Study 21 Herbert Moskowitz
Calculus and Computer Science 23 Anthony Ralston
Calculus for the Physical Sciences 25 James R. Stevenson
Views from Across Campus
A Chancellor's Challenge 27 Daniel E. Ferritor
National Needs 29 Homer A. Neal
Now is Your Chance 30 Michael C. Reed
Involvement in Calculus Learning 32 Linda B. Salamon
Calculus in the Core of Liberal Education 35 S. Frederick Starr
Responses
Mathematics as a Client Discipline 41 George E. Alberts
Calculus and the Computer in the 1990's 42 William E. Boyce
The Role of the Calculator Industry 43 Michael Chrobak
Calculus: Changes for the Better 44 Ronald M. Davis
Imperatives for High School Mathematics 45 Walter R. Dodge
An Effective Class Size for Calculus 46 John D. Fulton
Don't! 48 Richard W. Hamming
Evolution in the Teaching of Calculus 49 Bernard R. Hodgson
Collective Dreaming or Collaborative Planning 51 Genevieve M. Knight
Calculus—A Call to Arms 52 Timothy O'Meara
Surprises 53 William M. Priestley
Calculus for a Purpose 54 Gilbert Strang
Yes, Virginia ... 55 Sallie A. Watkins
Reports
Calculus for Physical Sciences 59 Jack M. Wilson and Donald J. Albers
60 Ronald D. Archer and James S. Armstrong
Calculus for Engineering Students 62 Donald E. Carlson and Denny Gullick
63 Charles W. Haines and Phyllis O. Boutilier
65 Carl A. Erdman and J. J. Malone
Calculus for the Life Sciences 66 William Bossert and William G. Chinn
Calculus for Business and Social Science Students 68 Dagobert L. Brito and Donald Y. Goldberg
70 Gerald Egerer and Raymond J. Cannon, Jr.
Calculus for Computing Science Students 71 Paul Young and Marjory Blumenthal
Encouraging Success by Minority Students 74 Rogers J. Newman and Eileen L. Poiani
Role of Teaching Assistants 76 Bettye Anne Case and Allan C. Cochran
Computer Algebra Systems 78 John W. Kenelly and Robert C. Eslinger
79 Paul Zorn and Steven S. Viktora
Objectives, Teaching, and Assessment 81 Alphonse Buccino and George Rosenstein
83 Philip C. Curtis, Jr. and Robert A. Northcutt
84 Lida K. Barrett and Elizabeth J. Teles
Issues
Innovation
Calculus Reform: Is it Needed? Is it Possible? 89 Gina Bari Kolata
Recent Innovations in Calculus Instruction 95 Barry A. Cipra
Science, Engineering, and Business
Calculus for Engineering 104 Kaye D. Lathrop
The Coming Revolution in Physics Instruction 106 Edward F. 'Redish
Calculus in the Undergraduate Business Curriculum 112 Gordon D. Prichett
Calculus for the Biological Sciences 116 Simon A. Levin
TABLE OF CONTENTS υ
Teaching and Learning
The Matter of Assessment 122 Donald W. Bushaw
Calculus Reform and Women Undergraduates 125 Rhonda J. Hughes
Calculus Success for All Students 129 Shirley M. Malcom and Uri Treisman
The Role of Placement Testing 135 John G. Harvey
Institutional Concerns
Calculus from an Administrative Perspective 141 Richard S. Millman
Innovation in Calculus Textbooks 145 Jeremiah J. Lyons
Perspective from High Schools 149 Katherine P. Layton
A Two-Year College Perspective 154 John Bradburn
Calculus in a Large University Environment 157 Richard D. Anderson
Mathematical Sciences
A Calculus Curriculum for the Nineties 162 David Lovelock and Alan C. Newell
Computers and Calculus: The Second Stage 168 R. Creighton Buck
Present Problems and Future Prospects 172 Gail S. Young
Examinations
Final Examinations for Calculus I 179
Final Examinations for Calculus II 194
Final Examinations for Calculus III 207
Readings
A Special Calculus Survey: Preliminary Report 215 Richard D. Anderson and Don Loftsgaarden
Two Proposals for Calculus 216 Leonard Gillman
Calculus in Secondary Schools 218 NCTM-MAA Joint Letter
Calculators in Standardized Testing of Mathematics 219 College Board-MAA Recommendations
NSF Workshop on Undergraduate Mathematics 221
Transition from High School to College Calculus 224 Donald B. Small
Calculators with a College Education? 229 Thomas Tucker
Who Still Does Math with Paper and Pencil? 231 Lynn Arthur Steen
Computing in Undergraduate Mathematics 233 Paul Zorn
Participants
Calculus for a New Century: Participant List 243

National Research Council
Task Force on Calculus
RONALD G. DOUGLAS (CHAIRMAN), Dean, College of PETER D. LAX, Professor of Mathematics, Courant
Physical Sciences and Mathematics, State Univer- Institute of Mathematical Sciences, New York Uni-
sity of New York, Stony Brook. versity.
LIDA K. BARRETT, Dean, College of Arts and Sci-
ARTHUR P. MATTUCK, Professor of Mathematics,
ences, Mississippi State University.
Massachusetts Institute of Technology.
JOHN A. DOSSEY, Professor of Mathematics, Illinois
SEYMOUR V. PARTER, Professor of Mathematics,
State University.
University of Wisconsin.
ANDREW M. GLEASON, Hollis Professor of Mathe-
HENRY O. POLLAK, Bell Communications Research,
maticks and Natural Philosophy, Harvard Univer-
(Retired).
sity.
JEROME A. GOLDSTEIN, Professor of Mathematics, STEPHEN B. RODI, Chair, Division of Mathematics
Tulane University. and Physical Sciences, Austin Community College.
Supporting Staff
LAWRENCE H. Cox, Staff Director, Board on Mathe- PETER L. RENZ, Associate Director, Mathematical
matical Sciences, National Research Council. Association of America.
FRANK L. GlLFEATHER, Consultant to the Board on LYNN ARTHUR STEEN, Consultant to the Task Force
Mathematical Sciences, University of Nebraska. on Calculus, St. Olaf College.
THERESE A. HART, Research Associate, Mathemat- MARCIA P. SWARD, Executive Director, Mathemat-
ical Sciences in the Year 2000, National Research ical Sciences Education Board, National Research
Council. Council.
BERNARD L. MADISON, Director, Mathematical Sci- ALFRED B. WILLCOX, Executive Director, Mathemat-
ences in the Year 2000, National Research Council. ical Association of America.
Board on Mathematical Sciences
PHILLIP GRIFFITHS (CHAIRMAN), Provost, Duke Uni- JOSEPH J. KOHN, Professor of Mathematics, Prince-
versity. ton University.
PETER BICKEL, Professor of Statistics, University of CATHLEEN S. MORAWETZ, Director, Courant Insti-
California, Berkeley. tute of Mathematical Sciences, New York Univer-
HERMAN CHERNOFF, Professor of Statistics, Harvard sity.
University. ALAN NEWELL, Chairman, Department of Mathemat-
RONALD DOUGLAS, Dean, College of Physical Sci- ics, University of Arizona.
ences and Mathematics, State University of New RONALD PYKE, Professor of Statistics, University of
York, Stony Brook. Washington.
E.F. INFANTE, Dean, Institute of Technology, Univer- GuiDO WEISS, Professor of Mathematics, Washington
sity of Minnesota. University.
WILLIAM JACO, Professor of Mathematics, Oklahoma SHMUEL WINOGRAD, Mathematical Sciences Depart-
State University, Stillwater. ment, IBM T.J. Watson Research Center.
νιιι
Mathematical Sciences Education Board
SHIRLEY A. HILL (CHAIRMAN), Curators Profes- California.
sor of Mathematics and Education, University of
STEVEN J. LEINWAND, Mathematics Consultant,
Missouri—Kansas City.
Connecticut State Department of Education.
J. MYRON ATKIN, Professor, School of Education, GAIL LOWE, Principal, Acacia Elementary School,
Stanford University.
California.
C. DIANE BISHOP, State Superintendent of Public
PEGGY C. NEAL, Burney Harris Lyons Middle
Instruction, Arizona Department of Education. School, Georgia, (Retired).
DAVID BLACKWELL, Professor of Statistics, University
HENRY O. POLLAK, Bell Communications Research,
of California—Berkeley.
New Jersey, (Retired).
IRIS M. CARL, Elementary Mathematics Instruction
JACK PRICE, Superintendent of Schools, Palos Verdes
Supervisor, Houston Independent School District.
Peninsula Unified School District, California.
RICHARD DE AGUERO, Director of Student Activities,
ANTHONY RALSTON, Professor of Computer Science
Miami Senior High School, Florida.
and Mathematics, State University of New York,
WILLIAM J. DENNIS, JR., Senior Research Fellow, Buffalo.
National Federation of Independent Business, Inc.
LAUREN B. RESNICK, Learning, Research and Devel-
JOHN A. DOSSEY, Professor of Mathematics, Illinois opment Center, University of Pittsburgh.
State University.
STEPHEN B. RODI, Division Chairperson, Mathemat-
JAMES T. FEY, Professor of Curriculum & Instruction ics and Physical Sciences, Austin Community Col-
and Mathematics, University of Maryland. lege.
SHIRLEY M. FRYE, Director of Curriculum & Instruc- YOLANDA RODRIGUEZ, Mathematics Teacher, Martin
tion, Scottsdale School District, Arizona. Luther King Open School, Massachusetts.
ANDREW GLEASON, Hollis Professor of Mathematicks FREDERICK A. ROESCH, Senior Vice President,
and Natural Philosophy, Harvard University. Global Electronic Marketing, Citibank, N.A.
NEAL GOLDEN, Chairman, Computer Science Depart- THOMAS ROMBERG, Professor, Department of Cur-
ment, Brother Martin High School, Louisiana. riculum & Instruction, University of Wisconsin,
KENNETH M. HOFFMAN, Professor of Mathematics, Madison.
Massachusetts Institute of Technology. TED SANDERS, Superintendent of Education, Illinois.
DAVID R. JOHNSON, Chairman, Department of Math-
LYNN ARTHUR STEEN, Professor of Mathematics, St.
ematics, Nicolet High School, Wisconsin.
Olaf College.
ANN P. KAHN, Past-President, The National PTA.
DOROTHY S. STRONG, Director of Mathematics,
DONALD L. KREIDER, Professor of Mathematics and Chicago Public Schools.
Computer Science, Dartmouth College. NELLIE C. WEIL, Past-President, National School
MARTIN D. KRUSKAL, Professor of Mathematics and Boards Association.
Astrophysical Sciences, Princeton University.
CALVIN J. WOLFBERG, Past-President, Pennsylvania
KATHERINE P. LAYTON, Beverly Hills High School, School Boards Association.