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Calculus for a New Century: a Pump, Not a Filter

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Calculus for a New Century: a Pump, Not a Filter DOCUMENT RESUME ED 300 252 SE 050 088 AUTHOR Steen, Lynn Arthur, Ed. TITLE Calculus for a New Century: A Pump, Not a Filter. Papers Presented at a Colloquium _(Washington, D.C., October 28-29, 1987). MAA Notes Number 8. INSTITUTION Mathematical Association of America, Washington, D.C. REPORT NO ISBN-0-88385-058-3 PUB DATE 88 NOTE 267p. AVAILABLE FROMMathematical Association of America, 1529 18th Street, NW, Washington, DC 20007 ($12.50). PUB TYPE Viewpoints (120) -- Collected Works - Conference Proceedings (021) EDRS PRICE MF01 Plus Postage. PC Not Available from EDRS. DESCRIPTORS *Calculus; Change Strategies; College Curriculum; *College Mathematics; Curriculum Development; *Educational Change; Educational Trends; Higher Education; Mathematics Curriculum; *Mathematics Instruction; Mathematics Tests ABSTRACT This document, intended as a resource for calculus reform, contains 75 separate contributions, comprising a very diverse set of opinions about the shap, of calculus for a new century. The authors agree on the forces that are reshapinc calculus, but disagree on how to respond to these forces. They agree that the current course is not satisfactory, yet disagree about new content emphases. They agree that the neglect of teaching must be repaired, but do not agree on the most promising avenues for improvement. The document contains: (1) a record of presentations prepared fcr a colloquium; (2) a collage of reactions to the colloquium by a variety of individuals representing diverse calculus constituencies; (3) summaries of 16 discussion groups that elaborate on particular themes of importance to reform efforts; (4) a series of background papers providing context for the calculus colloquium; (5) a selection of final examinations from Calculus I, II, and III from universities, colleges, and two-year colleges around the country; (6) a collection of reprints of documents related to calculus; and (7) a list of colloquium participants. '.PK) *********************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. ******************************************************k**************** CALCULUS for 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 1987 by Michael Callahan, David Hoffman, and Bill Meeks IIIat the University of Massachusetts. This computer generated image was created by James T. Hoffman, ''',1987. 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. r 1988 by the Mathematical Association of America. Permission for lirmied 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 4 Calculus for a New Century A Pump, Not a Filter Preface .;z 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 iv 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 Genevie,,e M. Knight CalculusA 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 Gul lick 63 Charles W. Haines and Phyllis 0. 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. Es linger 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 n 0 TABLE OF CONTENTS 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 andUri 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-MA A 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 State University. SEYMOUR V. PARTER, Professor of Mathematics, University of Wisconsin. ANDREW M. GLEASON, Hollis Professor of Mathe- maticks and Natural Philosophy, Harvard Univer- HENRY 0. POLLAK, Bell Communications Research, sity. (Retired). JEROME A. GOLDSTEIN, Professor of Mathematics, STEPHEN B. ROD!, 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. GILFEATHER, 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 Erector, Mathemat- ical Sciences in the Year 2000, National Research ical Sciences Education Board, National Reseaich Council. Council. BERNARD L. MADISON, Director, Mathematical Sci- ALFRED B. WILLCOX, Executive Director, Mathemat- ences in the Year 2000, National Research Council.
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