DOCUMENT RESUME
ED 066 875
EM 010 151
TITLE
INSTITUTI ON
SPONS AGENCY PUB DATE NOTE
Proceedings of the 1972 Conference on Computers in Undergraduate Curricula.
Georgia Inst, of Tech., Atlanta. ; Southern Regional Education Board, Atlanta, Ga.
National Science Foundation, Washington, D.C.
72
578p.
EDRS PRICE MF-J0.65 HC-$19.74
DESCRIPTORS Art Education; Biology; Business Education;
Chemistry; *Computer Assisted Instruction; Economics; Education; Engineering; Geography; Interinstitutional Cooperation; Language Instruction; Mathematics; Physics; Social Sciences; Speeches; Statistics; Teacher Education; Undergraduate Study
ABSTRACT
The 83 papers presented at the 1972 Conference on Computers in Undergraduate Curricula are reproduced in this volume. With computer science specifically excluded as an area of interest for the conference, papers fall under the following headings: biology, business, chemistry, economics, education, engineering, geography, languages and art, mathematics, physics, social sciences, statistics, and a general section on faculty training, software exchange, and shoestring facilities. (RH)
Proceedings of the § 1972 Conference on Computers
' 1 in Undergraduate Curricula
1 1 1
June 12, 13, 14, 1972 Atlanta, Georgia
Sponsored by the Southern Regional Education Board
in cooperation with the
Department of Continuing Education, Georgia Institute of Technology
Proceedings of the , 1972 Conference on Computers - in Undergraduate Curricula
June 12, 13, 14, 1972 Atlanta, Georgia
Sponsored by the Southern Regional Education Board
in cooperation with the
Department of Continuing Education, Georgia Institute of Technology wits support from the f.ational Science Foundation
U.S. DEPARTMENT OF HEALTH. EDUCATION & WELFARE OFFICE OF EDUCATION THIS DOCUMENT HAS 8EEN REPRO- DUCED EXACTLY AS RECEIVED FRO*,. THE PfiRSON OR ORGANIZATION ORIG- INATING IT POINTS OF VIEW OR OPIN- IONS STATED DO NOT NECESSARILY REPRESENT OFFICIAL OFFICE OF EDU CATION POSITION OR POLICY
Library of Congress Catalog Card Number 72-83189 Printed in the united Jtates of America Distributed by
the Southern Regional Education Board, Atlanta, Georgia
CONTENTS
lusmusiM EAUifcs
Nillian F. Atchison, University of Maryland Mfleport on Inter Qtti onal Pannls”
blOLDGl
SIMULATION OP BIOLOGICAL 5 I STEMS# I
Chairnan, Nary Jane Brannon, Huntingdon College
Thoias L. Iseahour, University of north Carolina
John C. Marshall
Howard D. Orr, St. Jlaf Collage
HThe Use of the Conputer in an Undergraduate Ecology Course”
Stephen B. Kessell, Aeherst College "Quantitative Ecology for Undergraduates”
Howard c. Howland, Cornell University
"Digital and Analog Conputing in General Aninal Physiology”
SIMULATION OF BIOLOGICAL SISTERS, II
Chairnan, Mary Jane Brannon, Huntingdon College
Ernest H- Salter, Cottey Junior College for tfonen Bar.ry L. Batenan
Gerald N. Pitts, University of Southwestern Louisiana HConputerized Ecology Simulation"
Davis S. Hinds Mary Ellen Burrows
Janes c. Horton, California State College "Computer Based Ingairy Investigations in Biology”
BUSINESS
BUSINESS AND ACCOUNTING
Chairnan, B. G- Duna, faireont State College
tfillian F. Bentz, University of Kansas
"Computer Assisted Algorithn Learning in Accounting”
Thomas L. Guthrie, Indiana University at Port Uayae "The Business Core Integrator at Indiana University”
Elbert B. Greynolds, Jr., Georgia state University "The Tine-Sharing Conputer and Intermediate Accounting”
Harley H. Courtney, University of Texas at Arlington "fieoote Tine-Sharing for Education in Business Planning and Control"
cHBHisray
CAI IN THE CHEMISTS Y CLAS3B00H
Chairnan, Charles Merideth, Ho rehouse College
J. J. La go wri i S. J. Castleberry
G. H. Culp, University of Texas at Austin
"The Inpact of Conpu ter-Based Instructional Methods in
General Chenistry"
Bonald W. Collins, Eastern Michigan University
"Computer-Aided Classroom Chemistry Instruction Vim Instantaneous Video Projection of Teletype Output"
V. F. Sliwinski
K. J* Johnson,, Univarsity of Pittsburgh "Pitt's Interactive Graphics and Computer-Gemerated ' Repeatable Examination Systems"
INSTRUCTIONAL PROGRAMS IN CHEMISTRY
Chairman, Harris Burns, Jr*, Randolph-Macon College
Joyce H* Corrington, Xavier University Lee P* Gary, Jr.
L* Chopin Cusachs, Loyola University
"Interfacing Students and Computing Through Undergraduate Chemical Research"
Uon&ld 0* Crain, Oniversity of Kansas
"A CAI Program for Aromatic Organic Syntheses Written in Tiae-Sharing FORTRAN *
Alfred J* Lata, University of Kansas
"An Interactive Tima-Sharing Basic Tutorial Program
Sequence in Introductory Electrochemistry"
ECONOMICS
ECONOMIC AND BUSINESS SIH3 LATION/GAHING
Chairman, Donald Chand, Georgia State University
Donald P* Cole, Drew University J« william Hanlon, Winona State College "Micromod: Description, Use and Evaluation of a
Microeconomics Computer Game"
James D. J. Holmes, St* Andrews Presbyterian College "New Approaches to Business Simulations"
Ray Billingsley
Stanley Wilson, Texas A £ M University
"Computer Simulation of Economic Models for Instructional Usage"
ECONOMICS
Chairman, Martin Solomon, University of Kentucky Fiank J* Bonello
William I* Davisson, University of Notre Dame
"Computer Assisted Instruction in Economics at the University
of Notre Dane"
Frank DePelice, Beliont Abbey College "Integrating Computar Programs in Economics via Time Sharing Terminals"
Richard A* Stanford, Furman University
"Ceteris Paribus Methodology and Computerized Economics- Business Models"
EDUCATION-CAI-CHI
Chairman, Sylvia Chirp, Philadelphia Public Schools Carol A* Cartwright
G* Philip Cartwright, Pennsylvania State University
"An Undergraduate Computer- Assisted Instruction Course in the
Early Identification of Handicapped Children"
Roger H* Geeslin, Univnrsity of Louinville "Preparing Mathematics Teachers to Use the Computer in Secondary Schools*
Joan Straughan
Raymond F. Latta, Wistern Washington State College "Conputer-Nanagnd las tract ioa: A Beginning and a Reality at
Western Washingtoc State College"
SUPPORT OP X MOXf ID U A LIZ ED XISTIUCTIOR
Chairman, Henry T* lippnrt, OSA Medical field Service School
Harold L* Schoen, Virginia Polytechnic Institute "A Coaparison of Types of feedback to Student Responses in a CAI Unit"
Arthur Wagner
Ronald Bleed, Joliet Junior College
"Using a Conputer to Support the Testing Progras in
Audio-Tutorial Biology"
Gail N. Nishinoto John fl. Horowitz Ray E. Burger
Richard P- waiters. University of California at Davis "Initial Development of Individualized Instruction with Conputer Support"
MANAGEMENT OF EXAMINATIONS AND LARGE ENROLMENTS
Chairman, Henry T« Lippert, USA Medical Field Jervice School C« Obert Henderson
Nark Haaaer, Washington State University
"inproving Large Encollsent Undergraduate Instruction with Conputer Generated, Repeatable Tests"
Stanley J* Birkin, University of SoutL Florida "An Analysis of the Use and Effectiveness of EZARINER: A
Cosputerized Question Bank and Ezasination Processing Systee * in College of Businass Courses at the University of South Florida"
fcU ~G« Franke W« D- Dolphin
G« p. Covert, Iowa State University
C. D. Jorgensen, Brighan Young University
NA Con pu ter- Assisted Method for Teaching Large Enrollment
Lecture Sections: The Biology Phase Achievement System (PAS)"
Michael Baldigo, Indiana University School of Business "Operational Aspects of Computer Written and Scorud First Year College Accounting Progress Examinations"
ENGINEERING
ENGINEERING COURSES
Chairman, Rufus F- talker, Jr*, Centenary College of Louisiana
Tadao flurata
Boland Priener, University of Illinois
"On the Use of a Coiputer for Motivating student Projects in Undergraduate Courses on Network Theory"
Arthur Houghton George H* Quentin
Bruce R. Peterson, University of New Mexico "A Course in Conputer Simulation and Analysis for Scientists and Engineers"
177
183
189
195
199
207
217
221
229
235
241
v
2 49
Donald C. Aaoss
John N. Gowdy# clnason Univecalty
"Realization and Cltssrooa Application of a Display- Based Syatea Cor a saall Digital Coaputer"
ENGINE SUING APPLICATIONS
Chairaan, Bernard Rtigaan, Loyola College
Paul T. Borlarty, van York City Coaaunity College "Coaputer Assisted Suaerlcal Control Part Prograaaing"
N. tfaverly Grahaav m
Don S. Haraer, Georjia Institute of Technology
"An On-Line Binicoaputer in the Nuclear Engineering Cltssrooa"
Uichard Schubert
Joseph H. Gill# Nestern Hichigan University
"Coaputer Applications to Kineaatic Synthesis of four Bar
Mechanises"
Hinrich 8. Nartens
Stephen G. Margolis, SUNT# Buffalo
HAn Analog Coaputer Optimized for Undergraduate Instruction"
GEOGaAPHY
GBOGBAPH Y
Chairaan, A. A. J. iioffaan, Texas Christian University
Philip H. Lankford, University of California "Spatial Bodel Builling in the Social Sciences"
Vincent H. Balstroav Middlebury College
"The Coaputer in Uniergraduate Geography at fllddlebury"
Paul E. Lovingood, Jr.
David J. Coven, University of South Carolina
"The Use of Coaputers in Geographic Instruction as a Beans
for Stiaulating Interest in Statistical Bethods"
Nancy B. Hultquist, University of Iova
"Introducing Undergraduate Geographers to Quantitative
Analysis Through a B egionalizatioi Praaevork"
LANGUAGES AND ABT
LANGUAGES AND ART
Chairaan, Haskell Siapson, Haapden-Sydney College
Anna Barie Thanes, Joldea Vest College "CAI and English: A Tentative Helationshi p"
Robert Phillips, BAiai University
"Drilling Spanish Varb Foras on Beaote Teraiaals"
Grace C. Hertlein, Chico State College
"Coaputer-Aided Graphics as an Art Fora for the Artist"
wias allies
MATHEMATICS I
Chairaan, G. P. tfeeg, University of Iova
Thoaas Bailey, The Jhio University
"Use of the Coaputer in Introductory Algebra"
255
265
273
277
285
291
295
299
305
311
317
321
325
Allen D. Ziebur, Stite University of lev fork m A Tiaa-Sharing Coaputer in tka Diffaraatial Equations Course"
(I. M. flcAHistar , floravi.an Collage 329
"Tka Bole of tha Coaputor in Baal Analysis"
(1ATHEI1 AT ICS It
Chairaan, Gar a id L. Engal, Pennsylvania State Univaraity
Arthur E* Falk 335
Bichard Bouchard, Wtatara Bichigan Univaraity "Coaputerizad Halp ia Pindiag Logic Proofs"
Doainic Soda 343
Aaron H. Koastaa
Judith Johnson, Tha Liodenuood Collages "Coaputors, Clay and Calculus"
Everett Hainer, Raapshire College 349
"APL at Haapshire"
Roger B. Kirchner, Car let on Collage 359
"Coaputer Generated Pictures Cor Teaching Calculus"
EdlSICS
QUANTUB PH TSICS
Chairaan, Bayne Lang, flacffurray Collage
Carol Bennett, univarsity of Illinois 369
"coapu ter-Based Education Lessons for Undergraduate Quanta*
Mechanics"
John flerrill, Dartmouth College 375
"Introductory Quantua flachanics and the Coaputer"
COAPUTER GRAPHICS AND PHTSICS
Chairaan, Arthur Lushraann, Dartaouth College
David Grillot 383
JeCCrey D. Ballance
Larry B. Hubble, Origon State University Tie. G. Kelley, Southern Oregon collage "Interactive Classroom Graphics"
Herbert Peckhaa, Gavilan College 397
"Coiputer Graphics in Physics"
Alfred Bork 409
Richard Ballard, University of California at Irvine "Coaputer Graphics ind Physics Teaching"
PHTSICS
Chairaan, Alfred Bork, University of California at Irvine
Harold tfeiastock, Illinois Institute of Technology 417
"Statistical Physics Coaputer Applications"
Charles P- (lunch. University of California at Irvine 427
"An Interactive Coaputer Teaching Dialog for Solving a System of Coupled Oscillators"
W. E. Bron, Indiana Oniversity 433
"Project CAPLIH: Coaputer Aided Physics
Laboratory Instruction for Bon-Science Bajors"
t:
vii
8
IKllk iZlMilS
H£S ART
Chairaan, Joseph Rtban, Qaaais Collago
Betty L. Jeho, University of Daytoa 439
"A Coapu ter- Assisted Instruction Program in Aaa^icaa History , 187 0- 192 1**
Charles a. Dollar, Jklahoaa State University 449
"A Preliminary Sapoct oa Coapu tar- Assisted Learning in Aaerican History Courses at Oklahosa State University"
POLITICAL SCIENCE
Chairaan, Calvin Hiller, Virginia State College
Williaa 0. Coplin 459
Bichael K. O’Loary, Syracuse Univorsity "Educational Uses of PRINCE"
Bruce D. Bowen 463
Wayne K. Davis, The University of Hichigan "VOTES: A social Science Data Analysis Prograa”
Janes E. Harf, Ohio State Univarsity 467
"A Student Handbook of Eapirical Evidence: The
Utilization of CAPE Data in Undergraduate Education"
SOCIAL SCIENCE I
Chairaan, Honald Stiff, Illinois Institute of Technology
Daniel Vandepor taela 477
Honald Stiff, Illinois Institute of Technology
"The Creation and Diffusion of Innovative Uses of the
Computer in Sociology Edncation"
Joseph &• Denk, N . Educational Computing Service 483
" POISSON — A Daughter of Dartaouth*s IMPRESS Has Been Born in the Environment of IBH Tiae-Shar ing"
Thoaas P« Kershner, Union College 489
"Computer Applications for Social Scientists"
SOCIAL SCIENCE II: SlflUUTlON
Chairaan, Jaaes Hogge, George Peabody College
Arthur 0, Croaer 493
John B- Thuraond, Uaiversity of Louisville "Toward the Optiaal Use of Coaputer Simulations in Teaching scientific Besearch Strategy"
John Bartholoaev 495
Judith Johnston
Aaron H« Konstaa, The Lindenwood Colleges
"A serious Gaae as in Introduction to Urban Planning"
Marshall H. Whithed, Teaple University 505
"Political siaulation and the Hini-Coa pu ter* • • A Challenge to the Industry"
srAXtsii£s
STATISTICS I
Chairaan, Williaa G. Bulgren, University of Kansas
Elliot A. Tanis, Hope College 513
"Theory of Probability and Statistics Illustrated by the
Coaputer"
viii
9
Hare S. veins, vaakiagton Stata Daiveraity "PSYSTAT--A Teackiaj Aid Cor Introductory St# .iatica"
Herbert L. Darahea, Hopa Collage
"A Course oa Coaputlng and Statiatica Cor Social Science Studeat a"
STATISTICS II
Chairnan, David G. deinnan, Bolliaa collage
S. c. Uu, California State Polytechnic Collage
"An Altarnatifi Approach in ranching Statiatica! Methoda"
Frederick S. Halley, SONY, Brockport "Individualized laatructioa in Baaic Statiatica: An
Expariaant in Coaputar Managed laatructioa"
Robert Platcker
Clark I. Guilliaee, diaaouri Soatkara State Collage "Through Multiple Bagraaaion aad Thraavay AI0V in Sopkoaora Level Applied Statiatica for tka Behavioral and Natural Sciences: Instructor-Student Daaoaatral.ion of the darchant
Cogito 1016 PBalOTA - 2"
5EeS5Afc
FACULTY TRAINING AND SOPYIAIE EXCHANGE
Chairnan, Judy Edvards, Northwest lagional Education Laboratory
Joseph R. Dank, North Carolina Educational Coaputiag Service "CONDUIT — A Concrata Pipeline for Sof t vare-S tac ved Little People"
Ronald L. Code, Stanford Univaraity
"An Experinent in Coaputer Training for Collage Faculty"
L- D. Kugler
J. N. Snider, Univarsity of Hickigan at Flint
"Friendly Persuasion: Initiating Reluctant Faculty to the
Coaputer in the claasrooa"
SHOESTRING FACILITIES
Chairnan, Herbert Packhan, Gavilan College
0* Tkoaas Bass, Macon Junior College "A Conputerized Physics Laboratory”
Don Leslie Levis, Bae County College
"Heasureaent of an lutoaobile's Fuel Consuaption, Road Horsepower, Maxiaua Speed and Maxiaua Acceleration"
John P. Tucciarone, St. John's University "Infinite Sequences and Series Via the Coaputer"
ix
10
521
525
52 J 533
539
547
555
567
575
577
585
FOREWORD
This proceedings is for the third of a series of conferences on computer uses m un lot gca dua te curricula supported by the National Science Foundation through its Office or :oipj tiny Activities. The 1970 Conference was sponsored by the University of lova and the 1971 Conference by Dartmouth College. The 1972 conference was planned by a national steering cono) ttee consisting of Gerai- L. Engel, Pennsylvania State University (ou leave froe Haapden- Syin?y College), Joh*i W. Haablan, Southern Regional Education Board, Glenn R. Ingraa, Washington State University, Thoaas E. <urt* , Darteouth College, Gerard P. Weeg, University of Iowa and PraJ W. wemgart*»n, Clareaont Colleges*
Eighty-th^ee (B 3) papers wire selected by panels of referees icon the 17J papers sent in cor consideration and are reproduced in the following pages. We are indebted to Jerry Engel for organizing and administering the paper selection process and to uleno Ingram tor preparing the "Call foi Papers."
Computer Science was specifically excluded as an area of interest for the conference. Papers on computer services ara included only if they have novel features or if the services are lnciiental to other topics.
This docuaent was prepared using the ATS ( Ad am istrati ve Terainal Systea) with the IBM Jbd/SO coaputer in the Inforaation Pocessing Systeas Department of the Alanta Pubiic Schools. The text was entered into the coaputer via NOVAR terminals by the Vision Center of Atlanta Public Schools. The splendid cooperation obtained froa Thoaas McConnell and Marion Boyles, aeids of these two departments, respectively, was essential in carrying out this hu;a task* Particular recognition of Linda Reagan of the Vision Center is due tor her constant participation in the typing ot the papers and the corrections, to Edward Peabody who did all of the paste-up work associated with the preparation of tne carneta-ready copy, to Myra Peabodv and her friends tor the aany sours they devoted to proofreading and to Wade Royston, SRE3 Publications Assistant, tor his guidance.
Tnroughout these proceedings you will find several designs created by the students of Grace C. Hcitlein (see her paper p. 317) in her course Coaputer- A^ed Gjraph ±cs as ait Art Fopa at Chico Stita College. They afforl i pleasant break ia the aonotony ot the printed page and we are grateful tor them.
The papers were assuaed to be ready for publication as subaitted and editing was done only m extreme cases. Every atteapt was aade not to introduce errors in spelling, typing, etc. during the copy preparation process. In doing so we have discovered and reaoved soae ot the authors4 preparation errors. We hope that the end result is at least no worse for having passed tnrojgn our hands - indeed we believe that the net result of our efforts is on the laproveaent s ide.
To enhance future coai l n icat ion between the readers and the authors ve have included the telephone number of the author when it was available and a concerted effort was aade to furnish the zip ('ode. Tae reward for our efforts will depend upon how you, the reader, and the conference participants are able to benefit froa these proceedings, the conference presentations, ana what are usually the aost valuable - the mtoraal discussions and personal contacts which are afforded >y such gatherings ot highly motivated persons.
Tne local arrangements for the 1972 conference were made with the assistance of the Department of Continuing Education, Georgia Institute of Technology, under the direction of ^lchiri Wiegand, and its st ff, particularly, bob iierndon and Ken Collins. The chairaan was also assisted by a Local Hosts committee consisting of luell Evans, Emory University, Thoaas McConnell, Atlanta Public Schools, Bob Pearson, University System of Georgia Coaputer Network, Vladimir Slatueck*, Georgia Institute of Technology, Grover Siaaons, Atlanta University Center Corporation, and William Wells, Georgia State University. The extensive effort devoted to the planning and operation of the "Coaputer Pair44 by Bob Pearson and his staff deserves special mention as does also Suzauna Bowaan, the Chairaan* s Secretary, for her dedicated attention to coaau nica ti ons and registration.
Finally, this series of conferences would not have been possible without the unswerving belief that the coaputer can and should be used to iaprove the guality of undergraduate education which is neid by Arthur Melaed and Andrew Molnar of the National Science Foundations Office of Coaputing Activities, their enc our ageaent and their support. Nor would the conferences be possible without the contributions by the many authors, referees and attendees. To these we express our gratitide and hope that theii rewards are aany.
John W. Haablen
1972 Conference Chairman
3EP0BT OR THE I RTEBtf ATIOIAL PAIELS
Villiaa P. Atchison University of Maryland College Park, Maryland 20742
A group of twelve speakers froa other countries have bean invited to taka part in panel discussions at this conference. Each will give a report on soae aspect of the use of coaputara in his country, soae speaking on applications of coaputers in various subjects and others speaking aore directly on coaputer science education at various levels. All acxbers of the group are involve*! in education and the use of coaputers in secondary schools, and aore particularly, all are interested in the training of teachers for secondary schools. At the conference there will be two panel discussions * "Coaputer Applications in the Sciences Abroad," and "The Status of Coaputer Education in Other Countries. w
Poliowing the conference, the group is going to have a workshop to prepare aaterials for a new booklet entitled "Aias and Objectives of Coaputer Studies in General Educatiou" describing a college course tor the training of secondary school teachers of: coaputer education. This work will be an extension of the International Federation for Inf oraai.ion Processing (IPIP) booklet entitled, "Coaputer Education for Teachers in Secondary Schools, An Outline Guide," published by tha IPIP Working Group on Secondary School Education (KG 3.1) in Septeaber 1971. This nex booklet will be the first in a series of booklets to be published jointly by WG 3.1 of IPIP and tha Organization for Econoaic Cooperation and Developaent (OECD). The panel discussions and the work on the new booklet is a joint effort of IPIP and OECD and is sponsored jointly by the National Science Poundation and the U. S. Office of Education. A brief listing of the speakers, along with a coaaent on their reports and background, is given below.
Alfred &££<!§£ froa Vienna, Austria is Head of the Austrian School Coaputer center, lie works on courses for pupils in secondary schools, courses for post secondary vocational training and courses for teachers. The Center also does adain istrative work for the Ministry of Education including the establishment of data banks of teachers of secondary schools and data banks of pupils in one section of Austria. His panel presentation will be on "The lapact of Coaputer Science on the Teaching of Matheaat ics. "
Glen Bonhaa, froa Toronto, Canada, works for the Departaent of Education. He has been a teacher~and is now involved in the developaent of coaputer science ind data processing courses for teachers. He will report on "Confuting in the Shools of Ontario, Canada." He will describe secondary school courses and how they relate to University courses and also report on soae education research projects.
Utje Brondua is froa Copenhagen, Denaark, where he works in the Offices of the Directorate for Vocational Education. He has helped plan the developaent of coaputer education in the Danish educational system. He is in a good position to give the latest news about the state of the art in coapurer education in his country since he recently lectured on this subject in Denaark. The title of his talk is "A Report on Activities in the Field of Coaputer Education in Denaark."
Is. Garcia caaay \ ro froa Madrid, Spain is on the staff of the Coaputing Center at the University of Madrid. He teaches courses in inforaatics and is interested in prograaaing languages and coaputer education at the secondary level. He has been a speaker on coaputer education at aany international conferences and will report to us ou coaputer education in Spain.
Jacques Hgbgngt reit is froa Par it- , France. He teaches inforaatics at the Ecole Superior d • Electnici te and at the University of Paris. One of his aain theses is that the ideas of inforaatics should be eajedded in the teaching of aany subjects. He has played a key role in the training of large groups of teachers for secondary schools. The title of his talk is "Teacher Training in Inforaatics in General Secondary Education in France." He ^s selected to be the prograa chairaan for the Second World Conference on Coaputer Edu ation to be held in France in 1975*
jfldfe Kiychber uer of Paris, France will chair the panel discussion on "Coaputer Applications in the Sciences Abroad." He has played an integral role in a nuaber of international seainars and conferences particularly in the area of coaputer education at the secondary level. He has helped to coordinate the international aspects of this conference. Dr. Kirchberger works for the Centre for Educational Research and Innovation of the Organization for Econoaic Cooperation and Developaent (OECD) and is in. a unique position to speak not only of developaents in France, but also of international cooperation.
R. froa Bridges Place, London, United Kingdoa, is i. lecturer in aatheaatics at Chelsea College of Science and Technology, a branch of the University of London. He i.s assisting in the developaent of new science courses which are based on learning and understanding by discovery. Experiaents are siaulated on the coaputer and jiaulation packages are aade available to pupils via interactive terainals. He his a background in physics as well as aatheaatics and is the Director of an associated coaputing project. The title of his talk is "The Developaent of Sianlation Packages for the Teaching of Science. "
&*. Lgvjs is froa Walton, Bletchley, Buckinghaashire United Kingdoa. He is on the faculty of The Open University and is developing curriculaa aaterials for coaputer education. He gave a paper at the Seainar on Coaputer Sciences in Secondary Education held at Savres, Prance, March 9-14, 1970, entitled "Teacher Training and Retraining in Coaputer Sciences.14 The concepts and innovative aethods of The Open University have received auch publicity and vide acclaia. fir. Lovis will give a report based on his own experiences with The Open University.
Xil2 Malpbep g, froa Uppsala, Sweden is with the Departaent of Education and is interested in educational technology as well as coaputer education. He took part in the CEB 1/OECD Conference on Coaputer Sciences in Secondary Education held in Paris, France during Juno 21-25, 1971. He will report on the developacnts in coaputer education in Sweden.
g* Jagg is :roa Bailrigg, Lancaster, United Kingdoa. He is a senior lecturer in the Aatheaatics Departaent of the University of Lancaster, conducting a course in Coapater Oriented Aatheaatics for Students of Biological and Social Sciences, and chairing the Aatheaatics panel in the School of Education. He has spent thirty years as a aatheaatics teacher, having introduced coaputer studies starting in 1957. He was Chairaan of the British Coaputer Society Schools Coaaittee froa 1966 to 1970. The title of his presentation is NSoae Varieties of Approach to the Teaching of Coaputer Studies to Undergraduates."
J. 2*. Tinsley is fraa Manchester, United Kingdoa and is currently Head of the Schools Project of the Rational Coaputer Center. His background is in aatheaatics, and he has been - teacher for a nuaber of years as well as being Head of the Aatheaatics Departaent at St. Edwards School of Oxford. He has been an active aeaber of the British Coaputer Society Schools Coaaittee as veil as an active aeaber of the tFIP wording Group on Seoordary Education (VG 3.1). He will report on "The Present Situation in Collages and Departaents of Education in England and vales concerning the Provision of Courses of Coaputer Studies for Trainee Teachers."
Dt Henk Wolbeps is froa Voorschoten, Netherlands. He is currently Professor of Xnforaation at the Technological University at Delft and has served as Director of the Coaputer Center at Delft. His original training was as an electrical engineer. He has been very active on international coaaittees in coaputer science education and is a aeaber of the EPIP Technical Coaaittee for Coaputer Science Education (TC 1) and the Uorking Group oa Secondary Education (VG 3.1). The title of his talk is "Coaputers in the University Curriculua in the Netherlands."
The workshop on the preparation of the booklet "Aias and Objectives of Coaputer Studies in General Education" will also have five representatives froa the United States assisting. Each of these is well-gualif ied to contribute to this effort on the training of secondary school teachers. They are:
Chairaan of the IFIP Working Group on Secondary Education (VG 3.1) and Director of~the Coaputer Sience Center at the University of Maryland.
Sylvia Char r, a member of VG 3.1 and Director of Instructional Systems for the School District of Philadelphia.
Jgdy ffdwards froa the Northwest Regional Educational Laboratory, Portland, Oregon.
David Ct Johnson froa the Matheaatics Education Departaent of the University of Minnesota.
Thoias Dgye£ froa toe Coaputer Science Departaent at the University of Pittsburgh.
2
THE OSE OP THE COHPUTEH IN AH UN DERG H ADU AT E ECOLOGY COURSE
Joha C. Marshall and Howard D. Dr r Saiat Olaf College Northfield, Minnesota 55057
Thoaas L. Isenhour University of North Carolina Chapel Hill, North Carolina 27514
I fttrgdoct^gn
One of the difficulties encountered in teaching an undergraduate ecology course is finding ways to adequately demonstrate and apply the theory. For example, it is possible to construct aolels of population interactions which deaonstrate how a seif regulating ecological system such as a forest may develop. But to demonstrate the functional dependencies that are important in su:h models is somewhat more difficult. Furthermore, the time interval for developmental change or response to perturbation in natural systems is frequently too long to make significant observations to support all or even significant parts of most theoretical models during a one semester course. This is particularly true in northern latitudes where *he duration of the field worn is limited by the weather. This report concerns our experience with the use of several coiputer programs \v.o supplement a one semester undergraduate couLse in ecology. Testing seems to indicate that the use of tha computer for gaming in the areas of population dynamics and as an aid to the field analysis of community structure has resulted in a significant enrichment in the ecology course. The programs presently in use are part of a large collection of programs, ranging from very simple to quite complex, and designed to encourage undergraduate biology studants to learn to program.
Iha Course Organization
In lecture the course starts with conceptual examination of eco-systems in terms of overall function in relation to structire. This logically leads to a detailed examination of unit parts, populations, and the isolation and discussion of them. Thus, in general, the flow of the course is initially reductionalistic, leading to a focus on the species populations. At this point the detailed study of population dynamics using computer "exper iments" is introduced. Programs illustrating population growth, limited and unlimited, population regulation, competition, predator-prey and a simple acosystem are made available to the students. These programs allow tha student to experiment with parameters and functional relationsips and thereby gain a feeling for the nature of the traditional mathematical models of population dynamics. The programs used quits logically introduce the student to a synthetic approach, culminating in a computer model of a simple ecosystem.
Concurrent with the lecture, the laboratory is centered around a study of community structures using natural ecosystems. Here the computer is used to process data from field collections on a day to day basis, encouraging hypothesis testing and making possible rapid modifications in experimental design, while studies ci natural communities are in progress.
In summary, two general areas of computer application have proven highly significant in an undergraduate ecology course. First, programs simulating population dynamics have allowed the student to examine for himself the effect of certain population parameters over a period of many generations. These simulation 3tudies lead to an experimentation with a systea model, which sharpen concepts in application of theory to management of ecosystems. Secondly, a unified laboratory study of community structure has proven successful using the almost instant data processing of collection data to modify the work as it proceeds. These two points will be discussed in some detail below.
Program
Our experience indicates that generally less than one-fourth of the students who register for undergraduate ecology have had previous computer experience of any kind. This reguires that very explicit input directions be given for each of the programs as no attempt is made in the course to teach programming, tfxile the ecological implications and limitations, of each of the models is discussed in lecture, no attempt is made to explain details of coding. All the programs used are written in FORTRAN and are given the status of system programs while the ecology course is in session.
The use of the simulation programs is timed to correspond with and support the discussion of population dynamics in lecture. Special emphasis is given to the effects of key parameters that can be input to the computer models we have. The student is then asked to game, examining.
14
to his ova rati sf ac t ion , the affect of varying population regulation parameters. All the programs are designed to accept any nuaber of sets of input and to print out, for each set of input, a record of population iensity as a function of tiae or the nuaber of iterations, whichever is appropriate.
The laboratory prograas are Jsed primarily to analyze field data, but are presented in such a vay as to encourage experimeatal design prior to data collection.
orj. Population Dyn aa^cs
The coaputer aodels used in support of lectu r e- d iscussion of population dynamics, listed in their order of presentation to the students are
1. Model of unlimited growth
2. Model of liaited growth
3. Model of self-regulation
4. Model of competition
5. Model of predator-prey
6. Model of a simple ecosystem
1* he first two programs are praLiainary in nature respectively utilizing the relationships
dN
dt
^ = rN
(1)
zr = rN(l-N/K) dt
(2)
Whare N is the population at tiae T, r is the reproduction rate constant and (eguation 2) K is the carrying capacity of the environment. These two aodels demonstrate numerically the explosive prediction of equation (1) and the sigaoid prediction of equation (2).
The third model population model that pressure on the pop following situations:
is based on a treatment by Smith[ 1 1 and quite adequately presents a includes an input parameter (K) , which is indicative of the regulatory ulation. By variation of this parameter the student can demonstrate the
K-0 the population will increase without liait
0<K<1 population will reach eguilibriua without oscillation
1<K<2 population equilibrium will be approached with oscillations of
decreasing magnitude
K>2 the amplitude of the population osdillation will increase
without limit
X ho fourth program presents a aodel of the competition of :lassical description of Sause[2] i. e. which may be stated as follows:
two species based on the
dN
ar s riVKi-MraN2)/Ki
(3)
dN.
dt1 = r2M2(K2-VbNl)/K2
(4)
Where a and b are coefficients that respectively state the effect of species 2 on species 1 and the effect of species 1 on species 2. The values of r, K and N are respectively the reproductive rate constant, the carrying capacity of the environment and the initial population for the two species. The students input wiat they consider appropriate values for the parameters in equations (3) and (4) and the program outputs the population levels for the two populations a r a function of time, tfe have found this to be a very effective way to illustrate clearly this model, which, without illustration is largely concealed by the complexity of the two simultaneous differential equations.
The predator- prey model used is a modification of the treatment presented by Spain[ i ] and well described by him. The student learns a great deal about predator-prey interaction both from consideration of the numerous factors that must be specified on input and the examination of the graphical output of the prograi.
ierJc
*5
It
V
Following experience with the five programs above the student is introduced to a program that attempts to implement many of the ideas he has learned into a model ot a simple ecosystem with three trophic levels. The required input for each trophic level is as follows:
Ei*fits: initial population, probability of "birth", probab
of destructioa by herbivores, optinua space requirements
initial popilation, probability of birth, probabi
probability of eating, probability of being eaten, nua necessary for starvation, optiaua space requirements.
£®£!iil2E®§- initial popJlation, probability of birth, probabi
probability of eating, probability of death by coabat, necessary for starvation, optiaua space regu ireme n ts.
to specify the area in which the system ion and emigration. The probabilities s Le of the aodel and are in terns of the : level. Bach population event is indivi certain type are evaluated as illustrated has a coaputed probability (based on the non-optimum population levels) of 0.5 :e three possible outcomes, no event, one interval. Th? probabilities for each of the three possi cients of a three term binomial expans an be used for a population of any rea ccur within a given population of N in by computing the probability that the event will occur to an individual, between 0 and 1 and sumaing th* normalized coefficient of the binomial e until the summation is equal or greater than the random nuaber. The nu is then taken as one more than the number of normalized binoaial terms s for zero events). A typical output of this program is shown in Table t levels input for this case are plants, 2500, herbivores, 500, and carniv has proven useful as a vehicle for the illustration of modelling. The quite adequately illustrate the nature of a simple ecosystem. Finally, Students have been observed leaning over the printer shouting words of the trophic levels threatened with extinction.
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Labo£atorx
The laboratory approaches the study of community stability and maturity through comparative studies of the structural aspects of ecosystems. The assumption is made that changes in species diversity within selected tropaic levels will reflect decreases in stability and/or maturity due to environmental insults whether natural or man caused.
One ecosystem studied was a local stream in the area of suspected source of pollution. Random samples of benthic invertebrates were collected and catagorized at several locations above and below the suspected pollution source, similar collections were made to compare old fields at different stages of laturity and to measure the extent of injury to a forest which has bean selectively logged.
From the collected data spacies diversity (D) [ 4 ] values were computed based on the Shannon- weaver function from the field of information theory
a
D = "I Pi l°g2 Pi
where is the fraction of the total nuaber of species belonging to the i th species.
The use of responsible for the tedious cal ◦f the studies continually exa sharp contrast calculations w Finally, the av hypotheses tha calculations.
automatic data processing as an integral part of the laboratory has been largely the change of amphasis to quantitative studies of communities. The freedom from culations required when large data collections are analyzed has widened the scope now possible. Almost instant processing of collected data allows students to mine the validity of hypotheses and to revise experiments in progress. This is in to previous procedures where students collected great amounts of data before ere made and frequently found froa the calculations that the data was worthless, ailability of programs for statistical analysis has encouraged students to test t previously could not have been considered because of the time required for
o
ERIC
I
16
MODEL OF A SIMPLE ECOSYSTEM
PLANTS HERBIVORERS CARNIVORES
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TABLE 1
^onci us^on
?
The authors have interpreted the following observations as to sean that coanuter support of the undergraduate ecology course has been a success:
1. laproveaent in test perforaaace in areas relating to population dynaaics 2m k draaatic increase in the nuaber of students electing independent study in ecology
3. Coaputer job log records that indicate that a significant nuaber of students did
aore than the ainiaua required aaount of gaaing 4* Student interest in lab has increased
5. The aaount and quality of student data and the interpretation thereof has iaproved greatl y
6. The student aorale in lab is noticeably better
da are pleased with the present and planning aore extensive coaputer use in the ecology course in the future.
R EP8BENCES
1. Snith , J, N. , I960, IiSi§ IS £121231# Caabridge.
2. Cause, G. F-, 1932. "Eco.lngy of populations," Quart. Review Biol,, 7:27-46.
3* Spain, J. D,, 1970, Soae roaputer ££ogta§§ fi2£ £l2l23l2ll §L£i232£§* Bich, Tech. Univ.
4. Shannon, E. E., and Reaver, H. , 1963. Tfcg flatfceaatiSal 1£§2 £1 2t £2Mtai££ti2fi- University of Illinois Press, Urbana.
i
18
7 fit
Problem:
Develop a graphic using
CONTINUUM by Edwin Young functions, departing from the steriotyped final
presentation
19
QUANTITATIVE ECOLOGY FOB UIDERGBADOATES
Stephen R. Kessell Aaherst College Aaherst, Massachusetts 01002 Telephone: (U3) 542-3125
The past decade has seen a draaatic shift in ecology tovards detailed quantitative techniques, systeas analysis and the aatheaatical aodeling of biotic-abiotic interactions* The holistic approaches of the International Biological Program, the Hubbard Brook Experiaeatal Forest, H. T. Odua's (1971) analog aodels and Margalefas (1960) applications of cybernetics to ecology have becoae faailiar to undergraduates early in their training* A nuaber of texts popular at the undergraduate level, including Eugene Oduaas (1971) fundamentals of Ecology, 8* B. Ford's (1971), Ecological Genetics and several titles in the "Current Concepts in Biology" series (especially Whittakeras (1970) Coaaunities and Bcosvsteas and Boughey#s (1960) Ecology oj Populations) are stressing quantitative techniques~and aethods o. aodeling and siaulation* Yet aany undergraduates - including advanced students conducting serious research - lack the background to critically evaluate these ideas and to incorporate aatheaatical approaches iato their ova work* This paper: will discuss our tvo years1 experiences atteapting to alleviate this problea by teaching quantitative ecology at the level of the introductory ecology course at Aaherst College*
Ecolpqy at Aaherst
Aaherst is a saall, highly selective aenas college firaly devoted to the liberal arts traditions; its student body is outstanding and highly aotivated* Within the liberal arts framework, the student has considerable flexibility in constructing his ovn prograa, allowing a fairly high degree of specialization in aany cases* Although no "ecology11 or "environsental science" aajor is offered, usually from 2 to 5 graduating seniors annually eoter graduate school in ecology* Three alternative aajors are offered to such students: (1) the regular biology aajor with specialization and research iu ecology and population biology, (2) an interdisciplinary "natural sciences" aajor including work in biology and tvo other fields (usually cheaistry, geology or aatheaatics) , and (3) a prograa of "Independent Study," under which all college requireaents are waived and the student conducts course work, independent reading and research under the direction of a tutor* Excluding the senior honors seainars in ecology, three formal courses are offered in the field: Biology 41, Ecology; Biology 26, Diversity in Biological Systeas; and Biology 40, Aquatic Ecosysteas* As all potential ecologists are introduced to the field through the first course, it seeaed the best vehicle to introduce quantitative techniques*
Described as "a study of the relationships of plants and aniaals (including Ban) to each other and to the total environment , " Biology 41 is an elective for sophoaores with a prerequisite of genetics; this is occasionally waived for yell-prepared or highly aotivated students* It is taught by Professor Lincoln Brower, and I take this opportunity to thank hia for his coaplete and extensive cooperation and enco urageaent in aodifying the laboratory portion of his course; I also thank Elizabeth Steele, Acadeaic Coordinator of the Aaherst College Coaputer Center, for her extensive help and cooperation* Scheduled for three hours of lecture and tvo to five hours of laboratory/f ield work a week. Biology 41 often requires extra outside lab work, and deaands competent and well-written lab reports* As it was decided that new aaterial could not be added to the course that necessitated sacrificing aaterial currently included in it, all changes were aade in the laboratory portion of the course*
Computer Facilities
A variety of computational facilities are available to Amherst students* The biology laboratories are equipped with four Wang 360 desk calculators; students have access to several programmable calculators, including a Wang 700 with typewriter output* Four terminals provide APL/360* The acadeaic computer center houses a two-disk, 16K IBB 1130, with high speed reader, line printer and plotter* Although no coaputer science courses are offered, six non-credit FORTRAN lectures are given each semester, while advanced FORTRAN and APL instruction is available on a tutorial basis* No fees of any kind are charged to students for coaputer use*
Teaching Quantitative Ecolog ys Preface
For a nuaber of reasons with which my colleagues may disagree, we feel that the 1 130 is our best available tool for teaching programming and aatheaatical techniques* Although using APL or the der.k computers allows a student to concentrate all of his efforts Oti tt*e prograa at hand, there is an aura of the "magic box" and a frequent feeling that tne machine is aoing something mysterious and incomprehensible - something that only "experts" understand* As the student will
certainly be laced vith a real systea in the near future, we chose to begin with a saall systea the 1130 - and teach the rudiaents of the aonitor and disk operating systea while we teach
FORTRAN and statistics. The results support our choice,
A number of problems confront any effort to teach quantitative techniques within the fraaeworfc of an existing course. The majority of the students have never used a coaputer systea or programing language, although perhaps half of the class has had soae experience with electronic desk calculators. Their level of proficiency in aatheaatics includes a seaester of calculus at best, and virtually none of the students have any background in statistics. A consideration of the work- load is of paraaount iaportance; it is not possible to aerge an ecology course and an introductory statistics/prograaaing course and expect the student to double his conaitaent for single course credit. If we are not to delete a&terial troa an existing course, we aust balance the new aaterial to be added against the extra work and tiae it deaands troa the students; the single solution in reducing this load is to teach both ecology and aatheaatics at the sane tiae. The success in carrying out this strategy will in large part determine the success of the course.
Below is a week by week synopsis of the course's laboratory, in which we shall try to evaluate the good and bad points, the successes and the failures.
Phase 1
Biology 41 originally included 10 laboratory exercises; although aost have been considerably rewritten, they have all been retained, and serve as the core of our quantitative laboratory.
The student starts using mathematics in the first laboratory. It is a field trip to study light relations in a forest community, and the role of light and abiotic agents as limiting factors. Overlooking the Connecticut River, students compare the forests and underjtory vegetation of the flood plain to the lower slopes of the Holyoke Range, and in a successional comaunity of eastern hemlocks (Tsuga canadensis) measure distanczs between an individual tree and its nearest neighbor and the aean diameter of the two trees for 100 such pairs of trees. In the report, they are asked to discuss the role of light as a limiting factor in the community based on their own findings and studies in the current literature (Ovington, 1962), A scatter diagram and least squares fit is required, and while doing the fit by hand, it becomes apparent that there must exist an easier way to conduct the repetitive calculations. "Maybe the computer. . • "
The second lab is the qualitative construction of a food web for a saall pond coaaunity based on samples collected in the field. While they are writing up the report, we begin teaching quantitative ecology in earnest.
The opening lecture on programming is given in the regular lecture tiae period (and is the only formal class time sacrificed). It covers a general introduction to the coaputer as a systea - what it is and how it works. Although a number of points are obviously oversimplified, the student learns what a program is, what it means to compile and store a program, what the core storage and disk are, why a user must aake certain specifications to the machine, why a programming language understandable to both machine and user is necessary. •• in short, he has a vague idea of what happens when he pushes the program start button. Pinally, the fora and format of a FORTRAN program is roughly covered, including the distinction aaong arithmetic, specification and control statements. A three hour session is scheduled tor the following evening. Attendance is not required, but next week's laboratory will require a user-written program to solve a portion of the problem; the report is unacceptable without it.
Perfect attendance... During the first session, each student received the Coaputer Center's booklet on FORTRAN programming and the 1130 systea as a re terence/study guide, and the current Newsletter discussing operating procedures (ours is a hands-on systea) , descriptions and documentation of our general purpose subroutines, special packages and disks available, and the like. These materials are designed to coapleaent the class work, and to serve as readable references (unlike some of the foraal user guides) • We now pound FORTRAN for two hours.
We start with the control cards and why they are used. We next review arithmetic statements and simple control statements (IF and GO TO); next come READ and WRITE statements. This leads to the use of FORMAT statenents (I and F only at this stage) . we do* not cover vectors and arrays until the next session - after DO loops. In about an hour, we have the basics to allow us to write siaple programs.
We have found this to be our best tool - siaple programs relevant to the course's lectures and labs. With their notes before them, we pose siaple biological problems and write FORTRAN program solutions on the board. We begin with very simple problems (see Figure 1) and involve
o
ERsLC
1 1
i w i *
22
the whole class (of 15 students) in the solution* The response is slow at first, and then picks up. rfe are certainly aided by the class9 saall size (which is split into two lab groups), our familiarity with the students and their background, and the use of relevant aatenal froi the course. Neai: the end o£ the session, we tackle the least squares fit froi the first lab and write a prograa (using one of the available subroutines) that is five stateaents long and will require five minutes to funch and run. When we look at the output and grapn, aost students are thinking of their tour hours of tediua and are convinced that the task of learning FORTRAN just might be worth it.
By the end of two hours, everyone has handled cards and output, so we head for the coaputer center. Within an hour, everyone has learned to use the keypunches and run a program. The third - and last - formal session is scheduled.
The last group meeting continues the writing of simple programs, and introduces the DO loop; through these programs, we meet the need for vectors, arrays, E formats, computed GO TO*s, and pauses. We end on the vegetation distribution problem shown in Figure 2, and no one has any real difficulty in writing the FORTRAN prograa. This program is very similar to the one required in the next lab exercise.
Lab 3 is a st dy of succession and indicator plants along a transect of a peat bog. The Horizontal sequence of species in space coapares to the vertical sequence in tiae; six indicator plant species are counted in seven plots extending froa the pond edge to the black spruce fpicea Eiriana) forest. In writing up the report, we make a trade-off; the instructions call for a bar graph or frequencies witnin the seven plots. This is written for the students and stored or the class* disk; only an XEQ and 7 date cards are required to produce the graph. In exchange, each student is required to solve fo> the centers of distribution using his own prograa. A slight curve is thrown - the plots are of unequal sizes, so the center coordinates aust be read in as a vector. The author, who serves as laboratory instructor in the course, is available four evenings that week at the coaputer center. By the tiae the lab is due the following week, everyone has his program and results. Each student has taken his own problem and field data, written a successful program and produced the needed answers. "It works. ..»» We are now over the hump.
The time required ot students and instructor alike is obvious. But a week earlier aany of these students had never seen a computer. We (including the students) think it was worth it. The next two labs require no written report and provide both a breather and an or- ctunity to experiment with the computer. The author is available at the computer center iu: evenings, while the center personnel are available full-tiae to assist and teach programaing.
Although these two no-report labs are of no mathematical interest, we include a brief description for continuity. Lab 4 is a one hour flight around the Connecticut River valley, taking the pilot, professor and four students at a tiae. We look at areas already studied, areas about to be studied, the dynamics of a large river system, the geology of the Holyoke Range and the beauty of nature exemplified by New England autumn foliage. Lab 5 follows the same route frofli the ground - the Connecticut River as a system. We stomp around the flood plain, old channels, oxbows, meanders and successional forests. After all, mathematics i*; only a tool for handling this fantastic system.
Phase 2
Lab 6 is formally called ''Modeling of the physical factors limiting eastern healock growth in Pelham, Massachusetts": in one year, it has become known as "The Healock Lab" and has earned a certain degree of infamy. To briefly describe the background, eastern healock (studied in Lab 1) uas an unusual bimodal distribution in southern New England (Kessell and Brower, in press). It is found in the fiats and ravines of saall streams and on the upper slopes of the lower mouutains (below about 2500 feet HSL) , but is uncommon on the intervening slopes. In the first lab, we concluded that sunlight and "other factors" limited growth; the students are now asked to not only determine what these factors are, but to quantify their effects as well, and to produce a mathematical model allowing the prediction of annual growth rates froa env ironaental data alone. Furthermore, they are asked to both qualitatively and quantitatively explain the species' bimodal distribution and the environmental and/or genetic basis for it. They have five weeks in which to complete the lab and write it up.
A field trip to the area under study - two stands, one on an exposed hilltop and one at the stream flats at the base of the hill - shows the students tuc basic differences in flora and the abiotic environment at these extremes where healock predominates. But on the intervening slope, under conditions intermediate to those found where the species thrives, hemlock is below the 1% level. Cores are taken from ten individuals at the two stands with an increment borer, and students measure annual rings for 40 years for each tree. They are provided with the general curve of growth rates as a function of ?ge (Pigure 3), an equation offering a possible approximation of this function, monthly cliaati data for eight variables tor the 40 year
23 ,2
Figure 3
Typical growth curve of an Individual eastern hemlock
Tha solid h na. a tha actual anm>al r*g width.
T ha daahad hna •• an appronmation ot th* tunctior ralating growth rata to aga which may ba wnttan aa
V - a ♦ bX * cK2 whara V ia growth rata and X ia aga
Thi a aquat.on aaaumas a constant anvironmant
Tha abrupt changa to linaanty occurs whan tha traa raachaa canopy atatun
Tha actual growth curia (solid hna) >• cbtamad by adding amoronmantal mdicaa* F0 and Ft> which vary from yaar to yaar. to tha a born aquation, gnmg
V - a • bX Fq ♦ c X*F,
(attar brisking through tha canopy. Fj - 0 and tha aga Junction ia tinaar )
F0 ia utad aa tha dapandant vtnabla in nx>tt ipla rtgraaaiona at growth on climate. tha higher tha correlation. tha ctoaar tha modal appvonmatea tha actual growth curva
Correlations with R- 0 ara common ( aaa tail)
Growth rates - moisture correlations of Tsuge canadensis Ftolham, Massachusetts
i
Mean growth ratda and correlation* to mo.atura ravaal a phynoiog-cai d.morph.am all individuals from tt» hilltop and aoma hemlock* tram tha van«y ara tha low growth, low moatur* typb (caMbd Typa 2). Soma va'lay
Iwnlocli ara tha high growth rat*, high montura morph ( Typa I)
hemlock distribution in southern New England
Tha d<morphiam •■plan* tha spec** unusual d»alribu*K>n.
Ugh growth Typa 1 trait -imittd to ma*< a I tat. ah»la dnn^h
to** ran t Typa 2 hamlocha aa pradominant at mo»a itnc sdbb.
Aopartnfi, nttlhgr morph is a good compatitor under intermediate
condition! . Fm f# >s ticiudtd by tha pines and hardwoods an th« mtarvamng awi-met* atopaa
period, a multiple regression prograa and our best wishes. The author aovos to the computer center to offer suggestions, aid and contort.
It aust be pointed out that the current literature does not answer the questions raised ia the lab. A nuaber ot studies of cliaatic control ot heal'ock growth and distribution (including Avery £tt 1940; Baun, 1950; Olson e t, al, , 1959; Adaas and Loucks, 197H) are furnished to the students7 but these findings are soaewhat inconclusive and occasionally contradict one an* other. Studies of both the distribution of hemlock along eav ironaental gradients (Mhittaker, 1956) and seedling growth under controlled conditions (Olsoa ila.# !>•<:•) suggest ecotypes of the species, but still do not explain the situation the students observe. The student soon realizes that either he is to repeat these earlier attempts, or to find something new not yet ia the literature.
Of course, the latter is the case; this problem has been investigated by tho author for the past two years, and the lab very closely follows ay work - with all the frustration, excitement and dead-ends coaaon to any research problem. And soaehow the students btcoae as excited and involved as we are.
A little thought and tiae i Schaua's Outline in Statistics to be growing season climate aeans (using is a good place to begin. But the cor 1 • c. , tound). Either climate is not the growing season means are not adeq 1966; Kesseli and Brower, l.c.); month througnout the growing season, data - a 12-factor regression is com T lie majority of the multiple H*s are changes in climatic effects for each output.
n the literature and statistical references (we*ve found excellent) snows the students that regressions ot growth on the Fq coaponent as the dependent variable [see Figure 3)) relations are not significant at P 3 .05 (as Avery et . nl. , a signficant factor controlling the annual growth rates, or uate. It turns out that the latter is the cause (Fritts, the effects of a factor differ significantly froa aontb to The regressions are now repeated using individual monthly pleted for each site and each of the eight cliaate factors, highly significant, and the partial r's reveal the monthly factor. The student is now the proud owner of 3U5 pages of
A week or so with t valley to dry hilltop is correlations to wind correlations at the nill correlations are direct the temperature is above and inverse correlation limiting factor. This de than moisture is limi an d more limiting as the correlations to moisture Tne original hypothesis limiting by moisture is
he data gives the basic picture. The environae ntal shown in a nuaber ot ways, including the noted at the more exposed site. Temperature top site, but an optimum temperature of about 10*13 during months when the temperature is below this ra it. In suaaary, at the hilltop site, direct corre s to sunlight during the early spring suggest noist pendence increases into the suaaer. At the valley ting during the ground saturation of early spring; suaaer progresses. A neat package, with one are higher at the wet valley site than at the lore that the lower growth rates on the hilltop are rejected. An alternative explanation is necessary.
gradient froa the wet nuch higher inverse not only gives higher degrees c. is noted; age, and inverse when lations to aoisture ure to be the primary site, light rather aoisture becomes more very bad flaw; the xeric hilltop stand, due to ao^e severe
t this point, the students have us3d only the aean growth rates of t sample! at each site; they are now provided with the individual growth ra correlations for every tree. We suggest that they plot aean growth rates aoisture (expressed as the product of significances P) for the critical Hay- resulting graph (figure 3) shows the responses clustered into two group sampled at the hilltop and some individuals froa the valley exhibit low growt correlations to aoisture, while the remaining individuals froa the valley e rates and high correlations to moisture. The differences are highly signitican both types are sympatric in the valley. Apparently we9ve found a dimorphism morphs physiologically adapted to two different habitats. A aodel built on (with the species excluded on the intervening slope by coapetiti vely better hardwoods) will account for the species9 unusual distribution. He also have au equations (with R = .9) giving a aean error of prediction of annual growth 5%.
he ten individuals tes and aoisture vs correlation to July period. The
s. All individuals h rates and low xhibit high growth
t. Ecotypes?.. • Mo - two specialized
these two aorphs -adapted pines and ltiple regression rates of less than
The lab is a long one, b their work, and hardly gripe ab difficult problem - one in answered a difficult question - are handed in, we discuss (w problem, including morphologica gradient distribution of the in press) • There are no readily students have gone as far as had never seen a FORTRAN progra
ut at its completion the stud out the 20 to 30 page laj which the mathematics alone one wuich had no answers in ith those students who are st 1 differences, sub-specific two aorphs and their roles in available answers to the! anyone has, know it, mod are
ents show an innense satisfaction in reports. They were given a very would take years by hand. They have the literature. After the reports ill interested) other aspects of the hybridization between the norphs, interspecific competition (Kesseli, r questions; at this point, the excited by it. Eight weeks ago they
19
. < >
For the rest of the course, no sore prodding is needed. The students are* familiar with the tools and basic statistics and use thea as needed. Rany are now using APL (at least as a desk calculator) for small jobs, while the desk calculators have becoae "old hat." The following two labs detemine population size, age structure and survivorship curves of sunfish in a saall pond; the place of and need for computing tools and methods is obvious. They're on their own, and really don't need our help.
The final twu labs study density-dependent survivorship a^u interspecific competition in Drosophila. Although it is an excellent opportunity to introduce some new computing tools and procedures, time does net permit too auch sophistication. The Wang 700 is moved to the lab tor 2-way A NO V A 1 s of competing species, and IBR#s analog simulator for the 1130 (C.S.R.P.) is made available. So i±> a little Edmund Scientific analog computer to show basic analog principles. From their data, a variety of methods (each involving different assumption ) for determining saturation densities (K) and alpha and beta coefficients of competition are used, and ve all argue about the validity of the assumptions.
ft strikes ae that we've come a long way in ten weeks.
In Retrospect
Perhaps a third of these students will go on in the field to become professionals. To the nonspecialist, we hope to have given both an appreciation of the field and some understanding of current research being carried out. To the future ecologist, we have tried to give a little firmer foothold than he normally would have received. He is not only aware of the tools and materials available, but is eager to incorporate them into his thinking and future work; he is also eager to point our flaws in the thinking of others, including the autnof's. A small measure of our success has become visible in the students' mathematical sophistication in later courses and independent work. Although obvious time limitations preclude the addition of other interesting material to this couLse, advanced independent reading and research courses are becoming more common, within an interterm project, we are now incorporating the tree climate- growth models into two-axis gradient nomograms (following Whittaker, 1967) using IBR's Numeric Surface Techniques package to solve the orthogonal polynomials, and are attempting discriminant analysis of the major components forming the niche hyper-space of Hutchinson (1966) and Whittaker (1967, 1970). At this moment, three sophomores from the 1972 course are using this technique to determine the differential responses of tour pine species growing in the same community. Recognizing my own prejudice, these students may well have a three year jump on their contemporaries.
Of course, not all we have done is fun and exciting. We have placed a considerable burden of /ork on the students. Those truly excited by the field (and not only those with a professional interest) will take the challenge. Those with a less ec interest may feel overwhelmed or inundated with work, and it is critical that the instructors te prepared to recognize this situation and offer help and encouragement when necessary. The distinction between the student having problems he can best work out for himself and the student about to give up is noi always obvious. We have to recognize that not all students in our course are on their way to a doctorate in biology, nor are all we excited by the subject matter as we are.
A final word: the instructors of such a course must be prepared for a huge work load. Even with only 15 students, three of us were kept on the go for the entire semester. Ptol^tsor Brower taught his course, the author taught the quantitative techniques and programming in the laboratory and computer center, and the computer center people kept the center running smoothly. We think it was worth it.
REFERENCES
Adams, tl. S. and 0. L. Loucks. 1971. Summer air temperatures as a factor affecting net photosynthesis and distribution of eastern hemlock (Tsu^qa canadensis L. (Carriere)) in southern Wisconsin. Am. Midland Naturalist 85: 1-10.
Avery, G. S., H. B. Creighton and C. W. Hock, 1940. Annual rings in hemlocks and their relation to environmental factors. Am. Journal of Botany 27: 825-831.
Bouqncy, A. S. 1968. Ecology of Po Pulations. New York: Hacmillan. 135 pp.
Bran;, E. L. 1950. Deciduous Forests of Eastern North America. Philadelphia: Blakiston. 596 pp.
Ford, E. U. 1971. Ecological Genetics , 3rd edition. London: Chapman and Hall. 410 pp.
Fritzs, h. C. 1966. Growth rings in trees: their correlation with climate. Science 154: 973-979,
Hutchinson, G. E. 1965. 7^e Ecological Theater and the Evolutionary Play, Vow Haven: Tale University Press. 139 pp.
Kessell , s. R. Ecotypic polyaorphisa in the eastern hemlock* Tsuqa canadensis, Submitted to The American Naturalist.
Kessell, s. B. a^d 1. P. Brower , in press. Siaulation of the effects of cliaatic limiting factors. I. Niche variation in the eastern t^mlock, Tsuga canadensis. Ecology.
Margalef, R. 1 96 d. Perspectives jn geological Theory. Chicago: University of Chicago Press. 113
pp.
Oduc, K. p. 1971. Fundaaentals of Ecology, 3rd edition. Philadelphia: Saunders. 574 pp.
Odum, H. T. 1971. Environment, Power and Socket*. New Tork: Wiley. 331 pp.
Olson, J. S. . F. w. Stearns and H. Nienstaedt. 1959. Eastern henlock growth c^jles and early years. Conn. Agr. Exp. Station Circular No. 205.
Ovington, J. D. 1962. Quantitative ecology and the woodland ecosystem concept, ig j. B. Cragg ^ed.) Advances in Ecological Research, Vol. 1, ''p. 103- 192. New York: Academic Press.
Spiegel, M. H. NcGraw Hill.
Whittaker, R, H.
Whittaker, R. H.
Whittaker, R. H.
1961
359
1956.
1967.
1970.
Theo £1 and Problems o£ Sta tistics (Schaun*s outline Series).
pp.
Vegetation of the Great Smoky Hountains. Ecol. Nonog. 26: 1-B0. Gradi, .t analysis of vegetation. Biol. Rev. 42: 207-264. Coaaunities and Ecosystems. New York: Nacaillan. 162 pp.
New York:
DIGITAL AND ANALOG COflPUTING IN GENERAL ANIMAL PHYSIOL OGY
Howard C. Howland Cornell University Ithaca, New York 14850 Telephone: (607) 256-4716
ABSTRACT
Laboratory anl hoaework exercises in analog and digital computing have been introduced into an upper undergraduate course in general animal physiology in order to increase the amount and depth of presentation of quantitative material. The analog coaputer was chosen initially for its physical similarity to aatheaatical flow diagrams of physiological control systems. Subsequently, a saall digital .coaputer was added and used both for numerical simulations of control systems and for solution of booework problens requiring only elementary prograaaing skills. A critical factor in the response of students to these innovations appears to be their prior exposure to applied mathematics in the sciences.
Introduction
General aniaal physiology is a field rich in quantitative topics which deserve, but do not always receive, serious treataent in undergraduate courses. Phenomena surrounding the transmission of the nerve iapulse, osmosis, auscle dynaaics, enzyae kinetics, countercurrent exchange* and, nost generally, homeostatic feedback control systems all require a quantitative presentation if the serious student is to understand themll].
The aathematical background required for a treataent of these topics is primarily algebra, of which our students generally have adequate command, and differential equations, a knowledge of which our students are usually innocent.
Since a majority of biology students lack a formal background in differential equations, and since the great majority of physiological feedback systems studied contain important non- linearities rendering them relatively intractable to formal solution, it seeaed reasonable to turn to the teaching of analog and numerical techniques for obtaining specific solutions of given feedback systems.
In all candor, 1 am not now sure that it is possible to do this successfully entirely within the bounds of a physiology course. But one fact was certain when this endeavor began; naaely, the problem of providing an adequate aathematical background was not being solved elsewhere in our curriculum.
MATHEMATICAL PLOW DIAGRAMS AND ANALOG COMPUTING
A Flow Diagram Notation
It has probably occurred to many persons that analog computer flow diagrams are almost machine independent, and that they are essentially mathematical structures.
This struck me at a moment when 1 was particularly vexed with the ambiguous "arrow" diagrams common in physiology. I mean diagrams which proport to say something about the dynaaics of feedback loops (often labeled with "EXCITATION" and "INHIBITION") but which, in fact, are the mere mental props of their authors, with little meaning for others.
In any event, I sought to replace these with something specific, and I chose a notation similar to that used in analog computing with a few minor changes in convention (Figure 1) £ 2 J. Several lectures were used to introduce this notation to the students and it was then employed to describe models of physioloqical feedback loops. (Figure 2.)
One curious fact emerged immediately from my students1 attempts to understand these diagrams. On the one hand, the diagrams had an intuitive appeal quite apart from their aatheaatical precision, as demonstrated by students9 ability on tests to answer correctly questions concerning the implications of a diagram, without being able to write the equation system that the diagram represented!
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Figure 1.
Operation
A constant
FLOW DIAGRAM ELEMENTS Symbol
Function
(k) — X
X = k
Multiplication by a constant
X = kA
Addition
a — rv_ !=l>~
X = A + B + C
Subtraction
A — B —
X = B - A
Integration
X = Y
+ C (A+B-C) dt
Multiplication
A
B
X = A • B
Division
X = A/B
B
Comparison
A
B
x
X = +1 if A > B X = 0 if A 5 B
"Proportional
Comparison"
A
B
X
X = A-B if A-B > 0
X = 0 if A-B < 0
Figure 2 Flow diagram eleaents. The aajor difference between this notation and sore conventional analog coaputer notation is the representation of inversion, here a dot at the input. Mote that the denominator input in a division operation is denoted by placing it belgw the nunerator input.
ERIC
<*18
2»
6
Figure 2 A flow diagram for a simple model of temperature regulation. Metabolic heat, M, is "produced" vliea the body teaperature, TV falls below a set-point, Tg. Heat is generated in proportion to the difference between the set-point teaperature Ts and the actual body teaperature. Heat is lost froa or gained by the body at a rate, X, which is proportional to the difference between the environaenta 1 teaperature, Te, and the body teaperature T^. The
differential equation for the systen is:
On the other hand, a single, elenentary point continually led students astray. Por a long tine aany students insisted upon seeing the lines of the diagraas as paths through which fluids, horaones, nerve iapulses, what have you, - flowed. It was often a hard fight to convince then that the line siaply represented a particular variable in the systea which could assune a value which night or night not change with tine, depending upon the systea. (Appeals to their intuition to interpret the lines like voltages or p;;essures were futile.)
A second pedagogical difficulty arose when I discovered that there was perhaps good reason for the old, iaprecise diagraas of the physiology cexts--nanely , aany of the systeas which are considered very well understood are, in fact, understood in no dynanic, quantitative way at all. This, of course, is exactly the virtue of a aa thenatical flow diagran, in that it forces one to record in a systeaatic way all of the dynaaic infornation that he possesses about a systea. However, when one is considering a ’classical" physiological feedback systea in an undergraduate course, and the quantitative infornation about it turns out to be precious little, one aay well wonder at the wisdoa of such a treataent.
The ft'cts are, that while the dynaaics of soae physiological systeas are well understood. Others are not, and the physiologist is well advised to choose his exaaples carefully.
Using the Analog Coaputer for fcgfiture Deaonsty ations
Perhaps the aost effective use of the analog coaputer is in lecture deaonstrations. This is because a large nuaber of students can watch the output of the coaputer siaultaneously and the coaputer can be aanipulated by one who is skilled in its operation.
A typical use of the coaputer in this aode would be to deaonstrate a aodel of the feedback loops involved in the generation of the vertebrate respiratory rhythn. (Figure 3.) The systea is of particular interest because one can siaulate sectioning parts of the real physiological systea by perforaing the corresponding "operations" on the aodel systea, and show that the behavior of the systea is analogous to that of thu aniaal.
dQ/dt = k,Z ♦ k3(k2Q-Te) where Z = Ts-k2Q for Ts>k2Q, else Z = 0.
Thermoregulation Model
Body
Q temperature
Heat loss
* — Environmental temperature
19
I
Figure 3.
Respiratory Rhythm Model
Pneumotaxic
Center
Apneusiic
Center
Medullary
Center
Lungs
£iaat§ 2 A aodgl of sespiratorjr r^ythj generation. The node! consists of various qualitative aspects of respiratory rhytha physiology can be demonstrated on the model such as: (a) showinq that the rhythn will persist in absence of vagus inhibition but that the respiration will be deeper and slower; (b) persistence of the rhythn in the absence of feedback froa the pneunotaxic center in the pons but not without vagus feedback; (c) persistence of the rhythn without the pneunotaxic center and the apneustic center. The nodel is based on a sunaarv of facts presented in Comroe (1965)* 1
o
ERIC
3*
20
*
A virtue of the analog computer over the digital coaputer at the current state of the art should be aentioned here- naaely, it provides an econoaic aeans for siaulating in rea 1 tiae relatively rapid physiological processes which would tax any digital aodel written in a higher level langauqe.
AUiioa Computing in the Laboratory
After using the analog coaputer in lecture deaonstrations we were anxious to allow our students in the laboratory portion of the course to have an opportunity to obtain solutions to a siaple equation systea on it. Since our laboratory students already have had soae faailiacity with polygraphs and other electronic equipment it is possible to give then a rough idea about the principles cn which the analog coaputer works without their having had an extensive background in electronics.
This year we hope to supplenent this background by introducing thea to the use of operational aaplifiers as part of the signal processing of physiological data. He hare constructed batteries of ten operational aaplifiers in a convenient plug-board arrangeaent for this purpose (Figure 4).
In our computing exercises we have students obtain specific solution to a thermoregulatory control loop and to a long tern problea in weight regulation which they can then compare to solutions that they obtain on the digital coaputer (to be discussed below).
A major problea in the use of the analog coaputer in the laboratory is the liaited number of students which can aeaningfully work at the coaputer at one tiae. The optinua nuaber would appear to be two students at a tiae and certainly not aore than three. This requires a considerable coaaitnent of laboratory and teaching assistant tiae, as well as a large equipaent investaent [3] •
Piqu£e 4 Ajl operational manifold for signal processing i g, £he phvsi ologicai laboratory. The aaaifold consists of 10 operational aaplifiers and a power supply (Models 105A and 902, Analog Devices Inc.) He have arranged the feaale plugs in such a fashion that connections between aaplifiers can be Bade with components mounted on standard bannana plugs with 3/4" spacing. Bach aaplifier is provided with two negative input points, two output points, one positive input point, three grounding points and a neutral point. Baking eight feaale bannana connectors in all* The aanifold finds use in adding, subtracting, filtering, and integrating physiological wave forms.
DIGITAL COB PUT IMG
Introduction
Instruction in digital confuting is undergoing a rapid change primarily due to the introduction of aini coaputers into aany curricula. In our own course ve purchased a snail digital coaputer in place of a aultiple capacitor delay unit for our analog coaputer. tfe rapidly discovered that the digital coapater offered enoraous educational possibilities as a stand-alone coaputer itself, in aany ways aore powerful than the (Bore expensive) analog coaputer.
Previously, our only access to digital coaputing had been through batch-processed languages available to students only with very long turnaround tines. The aini coaputer afforded us immediate turnaround and meaningful results in the laboratory via its interactive language, FOCAL. Currently there are a wide variety of aini coaputers available, all of which offer interactive FOCAL or BASIC, or both, and hence are suitable for the applications discussed below.
"Stca iqht Li ne" Programming to Solve Quantitative Hoaeworh Problems
One of the first uses we put our coaputer to was to ease the coaputational load of our students in solving quantitative hoaework problems. This was done by teaching then "straight line" programming i.e. progranaing which involved no iteration or logical branches. A student can learn these eleaentary aspects of prograaning within about a half an hour at an interactive terainal. This aaount of computing knowledge greatly increases his or her coaputational skillsf 4 ].
A typical "straight line" prograaning problea is given in Figure 5.
C-FOCAL, 1969
01.10 ASK ?R? , "PRESSURE IN MM HG ",?P?,! 01.20 ASK ?L,VI ?, !
01.30 SET PI=3. 14159 01.40 SET P = P*1333. 22 01.50 SET Q=PI*P*Rt4/(8*L*VI)
01.60 TYPE "FLOW IN CC/SEC" , %12.03, Q,! *G0
R: .08 PRESSURE IN MM HG P:15 L, : 4 VI :.04
FLOW IN CC/SEC 2.011
Figure 5 — A "sinaight line" program in FOCAL (i^e^, a program with no logical branches 0£ iterative loops) . The prograa coaputes the flow of blood, Q, through a hypodermic needle whose length and radius are specified. The pressure drop along the needle and the viscosity of blood are given as input paraaeters. Use of such a prograa completely documents the procedures used in the exercise. Readers unfaailiar with FOCAL aay translate the program into BASIC by substituting LET for SET, INPUT for ASK and PRINT for TTPE. The program is taken froa Howland, (1971).
In learning to write such a prograa a student has:
a. obtained connand of certain functions (like eEE) which he aay not have had before;
b. learned to foraulate the problea in sufficient generality to solve any similar case with different input values;
c. and (assuaing the solution is correct) aade a legible record
of his oethod of solution which he can refer to any tiae in the future or, (if the solution were incorrect) , aade a record of his aethod which can easily be corrected in the future.
I believe that the combination of generality and documentation in such elementary prograaaing shills puts our students veil ahead of even accomplished students who operate with pencil, paper, and a slide rule. One great advantage of the digital computer is its enforced documentation. This is an enormous boon to a teacher who must either wad© through piles of scribbled homework, or take the answers on faith and abandon all hope of correcting his students* mistakes[ 5 ]•
Numerical simulation o£ ph vs iol o q lea l_3*fl tens
With the introduction of a digital computer into the laboratory we began using it along with the analog computer to simulate physiological systems.
To accomplish this we wrote a general purpose, second order Bunge^Kutta routine for solving sets of first order differential eguations. The students were then reguired only to program the differential eguations that the Hunge-Kutta routine would solve.
Figure 6 shows the listing ol the Runge-Kutta routine with eguation subroutine and typical printout. It will be noted that the equation system we have simulated for this example is identical to that given for the analog computer respiratory rhythm model in Pigure 3,
C- FOCAL, 1 969
01.05 E
01.10 T H* "ENTER RUN PARAMETERS"* ! !
01.15 A ?ND* IP* PN* TS* TQ ?* !
01.20 C PLACE INITIALIZATION STATEMENTS HERE
01.22 T !! "SET CONSTANTS"*!!
01.25 F J = 1 * 9 J T "K"* %3* J * " "• A KCJ>;T %5.03* K(J)*!
01.30 T !! "INITIALIZE INTEGRATOR'S'*!!
01.50 F J= 1 *NDl T % 3* J i A ?YCJ> ? !
32.23 S H=(TQ-TS)/CIP*PN)
02.2 4 S TM=TS
02.30 T !! " TIME Y C 1 > Y<2> YC3) PLOT OF YC2) "* ! !
02.31 D 3*35
02.32 F IT=1*PNJ D 3*00
02 • 40 T !!* %6 • 0 5* ?H ?*%4*" NO. )F INTERVALS "*IP*PNiO
03.33 F I = 1 * I P ; S TM = H*( ( IT- 1 ) * I P* I ) + TS * D 4.0
03.35 T %6.03*!*TM;F I=1*NDJT " "*Y(i>
03.36 D 6.0
04.12 F L=1*ND;S 0L(L)=Y(L)1S R<L)=0
04.13 F L=1*2;D 8 . 0 * D 9.0
04.14 F L=l*NDiS Y(L)=0L(L)+R(L)/2
06.10 F L=0*.1*Y<2); T " "
06.20 T "*"
08.05 C PLACE DE EQUATION SYSTEM HERE
08.10 S Z=C+K<2)+K< 3>-( K( 7 > ♦YC 1 )+K( 4>*Y(2>+K( 9 >*Y< 3) )
08. 1 5 S C=. 5*FSGN(Z )♦• 5
08.20 S DC 1 )=C*K( 6)-K< 1 )*Y( 1 )
08.30 S D(2) = C*K(8>-KC 5>*YC 2>
08. 40 S DC 3> = D< 1 >
09.11 F M= 1 * ND* S R(M)=H*DCM) + RCM)
09.20 I CL-D9.3JF M=1*ND?S Y C M ) = Y C M ) ♦ R C M )
09.30 R
figure £A — I second grdey Bunue-Kutta program for systems of first order differential equations. The program is written in FOCAL, The eguations for the differential eguation system are in section 0,0, in this case, the eguations are for the respiratory rhythm model of Pigure 3, The program is sufficiently general that it can be adapted to any eguation system by minor changes in statements 1,25 (setting the number of constants), and 2,3 (output titles) and 6,1 (plotter parameters) •
ENTER RUN PARAMETERS
ND> 3 IP, 2 P N,20 TS> 0 TQ 20
SET CONSTANTS
K l .077 0.077
K 2 .2 0.200
K 3 -2 0.200
K 4.5 0.500
K 5 .2 0.200
K 6 .2 0.200
K 7 .5 0.500
K B .4 0.400
K 9 .5 0.500
INITIALIZE INTEGRATORS
|
1 Y( J) |
0 |
|
2 Y ( J ) |
0 |
|
3 Y < J ) |
0 |
|
TIME |
Y( 1 ) |
YC2) |
Y( 3) |
PLOT OP Y C 2 ) |
|
0.000 |
0.000 |
0.000 |
0.000 |
|
|
1 *000 |
0.193 |
0.362 |
0.193 |
* |
|
2*000 |
0. 371 |
0. 658 |
0.371 |
* |
|
3.000 |
0. 536 |
0.90 1 |
0.536 |
* |
|
4 • 000 |
0. 688 |
1*100 |
0.688 |
* |
|
5 . 000 |
0. 780 |
1.163 |
0. 780 |
* |
|
6 • 000 |
0. 722 |
0.953 |
0. 722 |
* |
|
7.000 |
0. 669 |
0. 780 |
0.669 |
* |
|
8*000 |
0.619 |
0.639 |
0.619 |
* |
|
9.000 |
0.573 |
0.523 |
0.573 |
* |
|
10.000 |
0.531 |
0.429 |
0.531 |
* |
|
1 1 .000 |
0.49 1 |
0.351 |
0.491 |
* |
|
12.000 |
0. 455 |
0.288 |
0.455 |
* |
|
13.000 |
0.421 |
0.236 |
0.421 |
* |
|
14.000 |
0. 390 |
0.193 |
0.390 |
* |
|
15.000 |
0.361 |
0. 158 |
0.361 |
* |
|
16*000 |
0.384 |
0.229 |
0.384 |
* |
|
1 7.000 |
0. 548 |
0.550 |
0.548 |
* |
|
1 8 • 00.0 |
0.700 |
0.812 |
0 . 700 |
* |
|
19.000 |
0.841 |
1 .027 |
0.841 |
* |
|
20.000 |
0.825 |
0.923 |
0.825 |
* |
H 0.50000 NO. OP INTERVALS 40*
^ ifidsi aiik ill ga£ts The lung volune r(2) is also plotted as ■ell as printed. The run paraneters are: HO = nunber of deriuatiTes, IP » nunber of points coaputed betueen each printed point, PH = nunber of points printed, TS * starting tine. TO * quitting tise, H is the step size in tine units. w
*G 1-22
SET CONSTANTS
K
K
K
K
K
K
K
K
K
1 0.077
2 0.200
3 L.200
4 0 0.000
5 0.200
6 0.200
7 0.500
8 0.400
9 0.500
INITIALIZE INTEGRATORS
H
|
1 YC J) |
0 |
||
|
2YC J> |
0 |
||
|
3YC J) |
0 |
||
|
TIME |
YC 1 ) |
Y ( 2 ) |
YC 3) |
|
0 • 000 |
0.000 |
0 . 00 0 |
0 • 000 |
|
1 • 000 |
0. 193 |
0.362 |
0.193 |
|
2.000 |
0. 371 |
0.658 |
0.371 |
|
3.000 |
0.536 |
0.901 |
0.536 |
|
4 • 000 |
0.688 |
1.100 |
0. 688 |
|
5*000 |
0.830 |
1 .263 |
0.8 30 |
|
6.000 |
0.961 |
1 .396 |
0.961 |
|
7.000 |
1 .082 |
1 .506 |
1 .082 |
|
8-000 |
1.194 |
1 .595 |
1 • 194 |
|
9 . 000 |
1.298 |
1 .668 |
1 .298 |
|
1 0.000 |
1 . 395 |
1 • 728 |
1 .395 |
|
1 1 .000 |
1 . 338 |
1.497 |
1 .338 |
|
12-000 |
1 .238 |
1.226 |
1-238 |
|
1 3-000 |
1.147 |
1 .004 |
1-147 |
|
1 4.000 |
1 .062 |
0.823 |
1 .062 |
|
15.000 |
0.983 |
0.674 |
0.983 |
|
1 6.000 |
0.910 |
0.552 |
0.910 |
|
1 7.000 |
0 • 8 A3 |
0.452 |
0.843 |
|
18.000 |
0. 780 |
0.370 |
0. 780 |
|
19.000 |
0. 723 |
0.30 3 |
0.723 |
|
20.000 |
0.669 |
0.248 |
0.669 |
|
0.50000 NO. OF |
INTERVALS |
40* |
PLOT OF Y C 2 >
\
Eiaaie fic — i tas
been set to zero) •
9>£ t&e respiratory tbXikl "lth U* ISflSS AftAi£lU&° e^imjQatgd £. [«] as
Rote the deeper inspiration and longer period.
Vv
36
Id general, one can translate directly from a aatheaatical flow diagraa like that of Figure 3 into the equations of section 8.0 of the second order Runge~Kutta routine of Figure 6a. Our ■ethod is to handle the Miscellaneous algebraic computations first, and then to write equations for each of the integrator inputs in turn[6].
Since FOCAL is an interactive language and space in the mini computer is at a premium we have not tried to write a completely general program (certain aspects of it, like the plotter in section 6.0, Figure 6A, are changed to fit the needs of the particular simulation at hand). We did try to arrange the program so that in each run all of the important parameters of the run are displayed. Again, this is a decided advantage over £Ke analog computer* where a great deal of cfoc umen t a ti on is left to the user.
On the other hand, as noted above, digital simulation in a higher level language is a slow process; a run of 20 points as in Figure 6B or 6C would take approximately 2.5 minutes and cost 21 cents at our Divisional computing facility.
The example of Figure 6 is a qualitative one, designed to illustrate the redundant feedback loops which must exist in the central nervous system to generate the respiratory rhythm. The point of digital simulation in this case is to allow students to obtain a "feel" for the system which they could not otherwise get.
A more complete use of the digital computer is made in the simulation of a system which is quantitatively well described. Such an example is the respiratory model of Grodins, et al. 11954) cited by Rilhorn (1966).
The analog computer program given by Rilhorn shows eight operational amplifiers, two integrators and a multiplier, tie have modified his diagraa into our notation, removing all of the hardware aspects of the analog computer diagraa and also scaling constants. (Figure 7.)
This model has been programmed as a subsection of the Runge-Kutta routine and this section together with a run is shown in Figure 8. The equations are direct translations of Milhorn’s equations (5-10 through 5-12, page 74 of Milhorn, 1966). Our output may be compared directly with that given in Figure 5-42 of Milhorn's treatment. It might be noted that in this simulation we used a smaller step than previously, computing 10 points for every one plotted.
Table 1
Constants and Variables of the Two Compartment Respiratory Chemostat* (After Grodins , ot al. (1954)}
|
Variable or Constant |
Initial Condition or Value |
Physiological Meaning |
|
Y(l) |
.052 |
Alveolar CO., concentration |
|
Y(2) |
.533 |
Tissue CC>2 concentration |
|
KCD |
.00425 |
Slope of C02 dissociation curve (mmllg**1) |
|
K(2) |
.32 |
Intercept of C09 dissociation curve |
|
K(3) |
3.0 |
Alveolar compartment volume (liters) |
|
K(4) |
.01 |
Inspired C0? concentration |
|
K(S) |
760.0 |
Barometric pressure (mmHg) |
|
K(6) |
40 |
Lumped tissue compartment volume (liters) |
|
K(7) |
.263 |
Metabolic C02 production (liters/minute) |
|
K(8) |
471 |
Slope of VR vs Y f 2) curve (liters/minute) |
|
K(9) |
246 |
Intercept of VR vs Y(2) curve (liters/minute) |
|
VR |
5.023 |
Alveolar ventilation rate (liters /minute) |
|
D(l) |
0 |
Time derivative of alveolar CO. concentration |
|
D(2) |
0 |
Time derivative of tissue C02 concentration |
|
Z |
0 |
Non-dimensional normalized response of VR |
*The equation system for this model is given in the flow diagram of
Figure 7 or in the program equations 8.05-8.30 of Figure 8.
Two Compartment Respiratory Chemostat
(After Grodins et.al.)
ai»an* ln^w if horn5 /fqf * » tt*fiAjCii2£l SAglgSil* **>• aodal has b««n foraulatad j, >■ aquations 9i*»n in flxlhora (1946) attar a aodaL of Grodins at al. p9Su> loraal valuas o£ tha variablaa and constants .ca qitra. in Xabla I. Tha aodal par.its xssa.tig.tio. ^o£ tha i.portanca^ ££ nuabar of paraaatars inflnancinq alsaolar vantilation rati. xsportaoca or 1 arqa
O
ERLC
2s . as
Figure £ iMMft-J example shows the veatilatioo rate value within 5 or computed Cor each
08.05 S VR=KC8)*YC2)-KC9)
08.10 S DC ! ) = ( VR* CKC4)-YC 1))*KU0)*(YC2>-CK<1)*KC5)*YC|)+KC2))))/KC3) 08*20 S DC 2)= CKC 7)+KC 10 )*CKC 1 ) *KC 5)*YC 1 ) +KC 2 l-YC2> > > /KC 6>
08.30 S Z = C VR-ZO)/CZI-ZO)
ENTER RUN PARAMETERS
ND> 2 IP#10 PN » 20 TS* 0 TO 20
SET CONSTANTS
ZO# 5-023 ZI 6.106 K 1 4.25E-3 0.004
K 2 .32 0.J20
K 33 3.000
K 40-. 01 0.010
K 5 760 760.00
:< 6 40 40.000
K 7 .263 0-263
K 8 471 471.00
* 9 246 246.00
K 10 6 6.000
INITIALIZE INTEGRATORS
1YCJ) .052 2YCJ) *533
|
TIME |
YC 1 ) |
YC2) |
VR PLOT OF Z |
|
|
0.000 |
0.052 |
0.533 |
||
|
1 .000 |
0.054 |
0.534 |
5.379 * |
|
|
2.000 |
0.054 |
0.534 |
5.640 * |
|
|
3 . 00 0 |
0.054 |
0.535 |
5.806 |
* |
|
4 . 000 |
✓j • 0 5 3 |
0.535 |
5.912 |
* |
|
5.000 |
0.053 |
0.535 |
5.981 |
* |
|
6.000 |
0.053 |
0.535 |
6.025 |
* |
|
7.000 |
0.083 |
0.535 |
6*053 |
* |
|
8*000 |
0. 0C 3 |
0.535 |
6.072 |
* |
|
9 • 000 |
0.053 |
0.535 |
6*084 |
* |
|
10.000 |
0.053 |
0.535 |
6.091 |
* |
|
1 1 .000 |
0.053 |
0.535 |
6*096 |
* |
|
12.000 |
0.053 |
0.535 |
6*100 |
* |
|
1 3.000 |
0.053 |
0.535 |
6. 102 |
* |
|
14.000 |
0.053 |
0.535 |
6. 103 |
* |
|
1 5.000 |
0.053 |
0.535 |
6* 104 |
* |
|
1 6.000 |
0.053 |
0.535 |
6* 104 |
* |
|
1 7.000 |
0.053 |
0.535 |
6.105 |
* |
|
18*000 |
0.053 |
0.535 |
6.105 |
* |
|
19.000 |
0.053 |
0.535 |
6. 105 |
* |
|
20.000 |
0.053 |
0.535 |
6. 105 |
* |
|
0. 10000 |
NO. OF |
INTERVALS |
200* |
utt. focu ijElaiaalatiai si ifei respirator? sAsifflttai isiai stl tiaasa 2- £*•
■o Itol* s response to a step Cros 0 to 1% CO 2 concentration of inspired air* The rises in response to the step input, approaching close to its steady-state 6 aiautes. The prograe as given va a run oa a 4k word coaputer. Ten points were point printed.
O
Such a aodel can be used in the laboratory to study a variety of aspects of the control system. Answers to all of the following questions aay be obtained froa running the aodel with the appropriate values of input constants:
1. How will the rate of alveolar ventilation be affected by:
a.
b.
c.
d-
increased
decreased
decreased
increased
increased
aetabolic CO2 production? cardiac output? baroaetric pressure? inspired CO2 concentration?
gain in the alveolar ventilation feedback loop?
Perhaps it is well to point out that these are indeed theoretics 1 questions, i.e. questions concerning a aodel which aay or aay not accurately airror the behavior of the aniaal. (It would of course be foolish Co be carried away by the siaulation into thinking that aanipulatlng such a aodel was a substitute for aoiaal experiaentat ion. )
DISCUSSION
Difficulties in Prerequisites
One of the aajor probleas I have encountered in atteapting to introduce a quantitative systeas approach into ay physiology course has been a feeling on the part ol many students that they are not really qualified to cope with physical and aatheaatical concepts that the course emphasizes. This is in spite of the fact that all the students are required to take courses in physics and mathematics before registering for general aniaal physiology.
It is not uncoaaon for ae to find, however, that their physics course has oaitted a treatment of one of the classical topics which we need for physiology. Two areas in particular which seen to be getting short shrift in soae physics courses these days are hydrod ynaaics and geometrical optics!
On the aatheaatical side I frequently encounter the following problem: namely, while students are taught in a one year calculus course to differentiate and integrate analytic functions, they do not even know hot to write differential equations, let alone solve them by formal methods. I would, of course, I)e happy if ay students could siaply formulate the equations, because I can show then how to obtain nuaerical solutions to then. But the problem is generally at the initial step of writing equations.
In the face of these prerequisite difficulties, there is strong pressure to liait the discission to qualitative material that is aore easily grasped, and, of course, soae compromise aust Do made if the students are to benefit froa the presentation.
The problem is accentuated by the fact that there are soae students, engineers and aat henat icians interested in physiological systeas, who do follow very well the quantitative approach and are anxious to refine the models to a point well beyond what their classmates can u nder stand[ 7 ].
Our past response to these difficulties has been to attempt to aake the mathematics easier and to teach it along uith the physiology. We have clearly reached a saturation point however, and aore recently we have attempted to shift soae of the burden onto other courses.
We now have a one credit course in interactive computer programming within the Division of Biological Sciences which is in its second year. We will shortly be getting students into the physiology lab who are not only trained in usinq the digital computer, but enthusiastic about its use.
At the saae tiae the Division of Biological Sciences has been instrua3ntal in planning a course in aathenatics for biologists which emphasizes equation systems and aatheaatical models. Students of this course will presumably be more receptive to a systems approach in physiology when they start cosing through.
What About Physics?
The problea with the classical physics prerequisites is a aore difficult one to handle. (Perhaps this would not be true at another institution.) fly own belief is that we aust generate soae good self-study aaterial in bite-sized packages to supplement our students* curriculum. On the one hand it is impossible to take the tiae within a physiology course to teach the fundamentals of, say, geoaetric optics, and even if one had the tiae, most of the students would
41
30
not hold still for it. But on the other hand, it is pointless to try to teach a student about ae eye if he doesn't even know how a lens works, so th^re mat be soae way that a student can fill these lacunae in his background rapidly at a tine when he is notivaited to do so. Hence ny belief that individual self-study naterial affords a solution.
naturally, teachers at different institutions say find a different pattern of deficiencies in prerequisites and different constraints on solutions which attenpt: to renedy then.
SOHfUBY
I have attenpted to show how we have used analog and digital conputation in teaching quantitative systens analysis in general aninal physiology. That approach consists of (1) the enploynent of a nathenatical systens notation sinilar to that connonly used in analog conputation; (2) the physical realizations of such systens on analog conputing equipnent, supplenented by the use of feedback anplifiers in physiological exercises as signal processing equipnent; (3) the use of an interactive digital conputer in the solution of quantitative honework problens in elenentary proqrans with no iteration or logical branching; (4) the use of the digital conputer to obtain nunerxcal solutions to systens of differential equations.
I have discussed the difficulties of such a course which prinarily concern the disparity between the prerequisite knowledge needed and possessed by its students, and I have described soae steps which we have taken and are taking to alleviate these difficulties.
ACKNOWLEDGES BUT
Portions of the equipnent used in the work reported here were supported by Grant GY 6S0S to Cornell University under the Instructional Scientific Equipnent Progran.
NOTES
1. Peter Steward (Stewart, 1970) has eloquently stated the value of quantitative nodels in the physiology curriculua. 1 particular/ endorse his views on the salutory alternative they offer to the "verbal reasoning which has characterized the classical approach."
2. A reasonable source for a "standard" analog conputer notation is that given in Blua (1968).
3* Our laboratory currently has one 15 anplifier analog conputer of type EAI 380 with
repetitive operation feature and X-Y plotter. Zn addition, we have a PDP-8L digital conputer with teletype and A-D, D-A converter.
4. I have written a 30 page booklet on this aspect of prograaaing in FOCAL (Howland 1971) as
well as a FOCAL nanual (Howland 1972a). At the tine they were written, the FOCAL language
appeared to offer the nost conputing power on a snail conputer, and I believe that FOCAL is still superior to nost aini conputer BASICS in power afforded the user.
5. Not all of our students* honework problens are done on the laboratory digital conputer. our students have access to the Division of Biological Sciences* interactive conputing facility which offers FOCAL and BASIC at alternate tines at four terainals on a reservations basis. 1 have described this facility elsewhere (Howland 1972).
6. We have found that Conte*s text on nunerxcal analysis (Conte, 1965) is very useful as a source for algorithns in this area.
7. It should be candidly adnitted that sone of these students are nore knowledgeable in applied nathenatics than their instructor. However, this is a connon situation in physiology which, as one Gernan physiologist observed, "has been getting too difficult for physiologists for the last 150 years." There are a large nunber of problens endenic to the teaching of physiology which sten fron its position as the nost derivative of all sciences. For exanple, teachers of physiology are faced with another enornous expansion of knowledge on the biochenical aspects of their profession.
BIBLIOGRAPHY
(1968). Introduction to Analog Conputation. Harcourt, Brace & world, lac.
31
42
Blue, Joseph j. New York.
/
Coaros# J. H. ( 1 945) • Physiology of inspiration. tsar book Sadical Publishers. Chicago.
Coats, S. o. (1965) • Blaaantary lassrical Analysis. BcGraw-Hill Book Coapaay. law York.
Gcodina# P. S. at al. (1954). tsspiratory iaaponsas to COo Inhalation# k Tbsorstical Study of a lonliasar Biological Bagulator. J. kppl. Physiol. 2- *83.
Howland# H. C. (1972). k TQCkl Priaar# 2nd sd. klgabraic Laaguagss. Ithaca# Ban York.
Howland# H. Cm (1971). Solving Quantitatiws Hoaawork Ptoblaas with POCki. Division of Biological Scisscss Is tsractivs Computing Facility. Corasll Onivsrsity. Ithaca# law York.
Howland# H. C. (1972b). (In prsss) • klgsbraic Language Instruction in ths Biological Scisncss Curriculum at Corasll. dr. Collsgs Scisncs Touching.
flilhorn. H. r. Jr. (1966). Ths kpplicatioa of Control Thsory to Physiological Systeas. tf. B. Saundsrs Co. Philadslphia.
Stsvart# Pstsr a. (1970). Coaputsrs in Undergraduate Physiology Tsaching. la Procssdings of Coafsrsacs on Coaputsrs in ths Undsrgraduats Curricula# Con tar for Confsrsacss and Institutsa# Ths Univarsity of Iowa# Iowa City.
43
COHP UTEBIZED ECOLOGY SIHULATIOI
Ernest (1. Salter Cottey Junior College Cor vonoa Nevada, aissouri
Gerald a. Pitts and Barry L. Batesan University oC southwestern Louisiana Lafayette, Louisiana 70501
Professors in the field of ecology have a difficult time in presenting to the undergraduate student the ideas that make up the concept of genetic-environment interaction which are basic to the study of ecology. At the University of Southwestern Louisiana , Lafayette, Louisiana, and Cottey Junior College for Women, Nevada, Missouri, a simulation model has been developed which allows a student to study such an interaction on a closed population of a single species or to predict the results of such an interaction for various contemplated envionmental changes* The model can b e activated by the professor or the student through one of the eight remote terminals located strategically around the campus (University of Southwestern Louisiana only, Cottey Junior College depends on distributed hard copy). By changing the input of individual factors (individual gene content and dominant and recessive gene factors) and/or environmental factors (population number, number of predators, food supply, water supply, age death chart, and accident ratio) the student can receive direct feedback as to the genetic and environmental results after a selected number of years*
The problem of determining the time (in generations) for a genetic variation to become predominate is dependent on the weight factor which a certain genotype, or group of genotypes, contributes to the survival of the individuals* Since different rates of producing variation occur in nature, seemingly independent of the present, the model permits a variety of environmental factors to interact with the genetic pool of the population on a weighted factor basis* Thus the birth and death of individuals is based on the environment and the genetic make up of the individual.
A genetic examination of the simulation should provide some insight into the working of the model* The input consists of any number of individuals along with their gene patterns, tables for the mating and birth routines and tables for each of the death routines* Death is provided for by predators, lack of food, lack of water, age and accident*
In the sating and birth routines, each sale in the population is given a nusher of chances to sate with a feaale, depending on the population size* For each successful sating, the litter size is conputed fron the genetic characteristics of the parents and a litter size table. The genetic sake up of the newly born individual is deterained by flendelian choice froa the parent genes. After a successful sating, the feaale is tagged to prevent anting again within the saae year.
After aating is coapleted, tho nuaber of predators for two years in the future is conputed. The nuaber of predators is proportional to the nuaber of individuals that they feed on, but the aodel uses a two year delay for the computed nuaber of predators to be engaged in the sodel*
In the predator routine, the individuals die according to the genetic doainant or recessive character of genes which would have an effect on the predator avoidance of the individual* The genetic structure, along with the nusber of predators, deteraines the nuaber of individuals dying by this routine*
The next death routines, lack of food and lack of water will be discussed together because of their siailarity. The current food and water supply are changed according to the present population and a recovery factor based on the previous year's population. This is done in order to reflect the fact of nature that the sore individuals there are the less food and water there exists per individual and the slowness of recovery of the food and water supplies. For the genetic characteristics which effect the ability of an individual to find or utilize food or water supply, a death nuaber is calculated and used to detersine whether the individual sur vi ves.
In the age routine, the death rate is deterained according to the age of the individual and certain genetic qualities. The age table entered previously deteraines the death rate.
The accident routine provides for reaoval of individuals by a raodon, non-geaetic, non- environaen tal basis by a percentage of the individuals in the systea at that aoaent.
a3
xsLHI toe. ...
TABLE I
INTERNAL STATISTICS
|
PERIOD |
YEAR |
NUMBER START |
NUMBER BORN |
NUMBER DIED |
BY PREDATOR |
FOOD |
WATER |
AGE |
ACCIDENT |
|
2 |
1 |
42 |
28 |
19 |
6 |
1 |
5 |
7 |
0 |
|
2 |
2 |
51 |
61 |
26 |
8 |
6 |
5 |
7 |
0 |
|
2 |
3 |
86 |
13 |
16 |
4 |
2 |
5 |
3 |
2 |
|
2 |
4 |
83 |
97 |
46 |
12 |
12 |
7 |
13 |
2 |
|
AGE |
table |
||||||||
|
1 |
2 |
3 |
4 |
5 |
J 6 |
7 |
8 |
9 |
10 |
|
18 |
9 |
11 |
4 |
4 |
0 |
3 |
1 |
1 |
0 |
|
43 |
15 |
7 |
10 |
3 |
4 |
0 |
4 |
0 |
0 |
|
10 |
37 |
12 |
6 |
10 |
3 |
2 |
0 |
3 |
0 |
|
68 |
7 |
30 |
11 |
3 |
9 |
2 |
3 |
0 |
1 |
NUMBER food
6
7
10
16
11
0
0
0
0
1.52
1.53 1.52 1.52
0
0
0
0
0
0
0
0
WATER
SUPPLY
4.52
4.53 4.53 4.55
12 13 14 15
0
0
0
0
0
0
0
0
TABLE II
DOMINANT GENOTYPES PARTS PER TEN THOUSAND
MAU GENE2 GENE3 GENE4
4402 6044 7014
GENE9 GENE10 GENE11
7761 6417 8283
8432
GENE12
5373
GENE5
6865
GENE6
7611
GENE13
7611
GENE7
9029
GENE8
7835
GENE14
7089
GENE15
8582
RECESSIVE GENOTYPE, PARTS PER TEN THOUSAND
F£S -s -s "SB IS IS «8S “»
“ “S -gjj «s «JJ -Bj «•
4&
34
TABLE II (CONTINUED)
|
DOMINANT |
GENOTYPES |
# PARTS |
PER TEN THOUSAND |
||
|
GENE2 |
GENE3 |
GENE4 |
GENE5 GENE6 GENE7 |
GENE8 |
GENE9 |
|
3619 |
4291 |
6268 |
3992 5597 6716 |
5074 |
4962 |
|
GENE10 |
GENE11 |
GENE12 |
GENE13 GENE14 |
GENE15 |
|
|
3768 |
5671 |
3395 |
5149 4776 |
6007 |
|
|
RECESSIVE |
; GENOTYPE |
, PARTS |
PER TEN THOUSAND |
||
|
GENE2 |
GENE3 |
GENE4 |
GENE5 GENE6 GENE7 |
GENE8 |
GENE9 |
|
6380 |
5708 |
3731 |
6007 4402 3283 |
4925 |
5037 |
|
GENE10 |
GENE11 |
GENE12 |
GENE13 GENE14 |
GENE15 |
|
|
6231 |
4328 |
6604 |
4850 5223 |
3992 |
The aodel has peraitted arbitrary selection of e&firoaaent and genetic weight factors. This has allowed the users to ezaaine and re-evaluate the results with the aajor features of interaction presently docuaeated. It also has peraitted the users to Bake predictions of variations likely to be produced if the environeental and genetic factors of the species can be reasonably deteraiaed.
Priaarily, the validation of the prograa was handled by the Biology Departaents of the University of Southwestern Louisiana and Cottey Junior College for Noaea[1,2]. This aodel gives the student a "feel" for the genetic development over a nuaber of years under varying enviroaaestal conditions that could not be obtained through classrooa lecturing or laboratory work. The student has the capability of answering his own guestioas by siaply posing the guestions to the coaputer in the fora of specific input paraaeters aad receiving iaaediate feedback as to the effects.
BEPBBENCES
1. Cordes, Private Coaaunication, University of southwestern Louisiana, Lafayette, Louisiana, Hoveaber 17, 1971.
2. Goering, D. K., Private Coaaunication, Cottey Junior College for Hoaea,
Nevada, Bissouri, Hoveaber 29, 1971.
Problem: Diminishing Polygon Forms
COflPareR BAFRD imqoirt investigations IN biologt
Janes C. Horton, David S. Hinds and nary Ellen Burrows California State College Bakersfield, California 93309 Telephone: (805) 833-2123
All courses in Biology at California State College, Bakersfield, are taught in the inquiry aethod. Students are required to take an elementary course in conputer programing, and this ability is later used for creating aodels, and for analyzing and sumariziag data. He eaploy the conputer in another fashion to overcoae the resistance of students to enploy arithaetic to prove foraalas or to becone faailiar with the workings of a aatheaatical relationship. He have devised several prograas which nay be used by students without any previous knowledge of coaputer equipaent for the specific purpose of extending a foraula into areas not given in the text. The student is able to apply a concept, quantified by the foraula, to various situations of his choosing and thereby validate the expression in each specific case. When groups of students use this technique for a nuaber of different exaaples, a later class discussion can be used to correlate the extension of a foraula over a wide range of situations, verifying its application without a large expenditure of individual effort. In this way, aa thenatical expressions becoae a part of the student's vocabulary because he has used thea extensively rather than accepted then by rote.
As an exaaple, the following foraula for rabbit-fox predation caae anonyaously to the author. It has been used successively in several courses involving predator- prey relationships, in the use of aatheaatical lodeling to predict outcoaes of population interactions, and as an exaaple of population dynaaics.
Xj_ = x0 + (Ax0 - Bx0y0)t
VI = y0 + fCVoxo - “Vo)*
Verbally the foraula states that the nuaber of rabbits present at a given tine (xl) is equal to the nuaber of rabbits found initially (xo) plus rabbit natality (Axq) less those rabbits preyed upon by foxes (Bxoyo) • Sinilarly the foxes present at the sane tiae (y i ) are equal to the initial nuaber of foxes (yo) plus fox increases resultinq froa reproducing parents existing on rabbits (CyQXo) ainus those dying of starvation (Dyo). The foraula is siaple enough to be readily understood by cost students and is still capable of considerable aanageaent. The original values in the foraula of A, B, C, D are 4, 2, 3, 1 respectively, xo vas 6000, yo was 2530 and t was 0.01 with a printout every 12 cycles. The expression obviously is curvilinear so an ipproxiaation of the curve was obtained by re-establishing new values of x-j and y ^ at unit intervals of tiae (0.01) and printing each twelfth approxiaat ion. (For convenience in our prograa every tenth value was printed.) It is possible of course to consider each unit tiae interval as a generation, but we found it aore convenient to regard each tenth interval as a generation tiae. (A copy of a publication given to the senior author included the above inforaation as well as a progna for calculation, for printout and for a display of the output as a graph. Unfortunately, the copy contained neither author nor publication source. Hence we are unable to express proper credit, but it probably should be attributed to L. B. Slobodkin.)
Printouts of tenth intervals were plotted against population size by the student. Two data cards were supplied, one for the constants A# B, C, D and one for initial population size. Once tha prograa was operational, duplicate decks of cards were provided to groups of 2 or J students. Local stored prograas would be better but in the absence of easy access to this aethod, card decks were nuabared to prevent ais-operation due to shuffling. Individual student groups were identified by separate job cards and they punched their own data cards. Persons without experience at the keypunch aachines asked their colleagues to illustrate bow these night be used, and all students had an opportunity to punch their own cards.
Our first use of this particular problea in an envir onaental population biology course required that students apply tae foraula expression using different population sizes. Fixed data cards for the constants were used and students were allowed to vary population sizes between one and ten thousand. The figures they selected were individual and each group plotted their printouts. Coaparisons were aide in a discussion session. After an early and initial variation, tha students were surprised to find that curves for all populations were reaarkably parallel. Froa this they reasoned (with help) that the relationship dictated by internal constants forced a pattern of fluctuation which was not overcoae by population size. -This indeed, was the first point we wished to sake. It is our opinion that the students were aore aware of this condition by being forced to discover it for theaselves, than if we had told then this was so.
48
The second step was which would be stable over curves fro* their graphs paralleled those generated recognize that population but regain in soie kind of
to xsK the students to predict those levels of fox-rabbit populations tins. The students connonly selected an intersection of foz-rabbit aid then placed these values in their progi^m. Again the curves in the first output and the students were once lore forced to interactions dictated that these situations would not beco*e static a variable balance.
The third step was to allow students to change the internal constants at will. In this case various proposals suggested the direction of the change e.g., suppose something increased or decreased the rabbit birth rate (A), somehow success of fox predation varied (B) , the fox natality or bir.th mortality changed (C) or fox nutrient requirements were altered (D) • In groups, students were asked to generate reasons for changes in a constant and then to create a series of curves by plotting tie resultant populations against the original (Table 1). Groups increased or decreased a particular constant so that all variations aight be explored. These comparisons provided insight of how minor changes could result in drastically altered population patterns. Students speculated an situations which night bring about changes in constants and in a fourth step, to predict the consequences of this change. A further condition was established in which students were asked to predict the conditions required for stasis. The output allowed verification of each student prediction and although none resulted in the static condition, the students were aware of the Multiplicity of factors influencing any population level.
y Proa these kinds of inputs, further discussion led the students into exchanges concerning dynamic balances, population interaction, the cyclical nature of population variability, and the difficulty of estimating correct constants, without the stimulus of a progra* which they could manipulate, the students would invariably have reiterated the formula and would have known little of its operation. The problem selected was almost juvenile in its simplicity and yet the individual flexibility to predict, to Manipulate the variables and constants, and to plot the outcome produced in the stidents an unusually wide recognition of the forces implicit in population interactions.
A similar project involved the Hardy- Weinberg formula in a genetics course. This formula which is an expansion of a simple binomial predicts gene frequency in a randomly mating population where gene changes do not take place, where the population remains constant, and immigration or emigration does not occur. The Kar dy-Weinber g equation is:
(p + q)2 = 1
where p, q are frequencies of two alleles of one gene and where p ♦* q - 1. The formula is widely used in all genetics courses and without exception, the students memorize the formula, and apply it in situations without, perhaps, fully understanding its import. Using the same idea as mentioned above, a program was concocted to provide the arithmetic machinery and printout with the data cards being the only variable to be punched by students. At first students were asked to verify that the formula does indeed predict gene frequency over long periods of time (50-100 generations) using individually selected gene frequencies and population sizes. Perhaps this exercise was redundant in that students invariably received printouts with the same gene fre- quency for the lengthy period and it is suggested that a shorter period of time might be more profitable.
Once the students were convinced that these predictions were true, variations were introduced. Gene freguency for each generation was changed to simulate the process of gene mutation and the resulting changes in gene frequency were plotted. Selections for or against certiin gene combinations were programmed and shifts of gene frequency were again plotted. The influence of migrants entering the population with different gene frequencies was included and lastly, gene drift was introduced using a random number generator and was used with different gene frequencies. In each cise, the students selected constants which were in the usual range encountered and were required to plot the effects of these gene changes over a period of 50-100 generations.
In a large sense, much of a genetics or population dynamics course can be built around the programming. From those cases where population geae pools were constant, (egual to conditions encountered on a small island* students were asked to illustrate the "founder principle" and to relate its effects upon ensuing generations. Natural selection and evolution of traits were included in this particular discussion and the students became aware that a gene pool consists of a large number of individuals and breeding randomly. The next variation introduced was mutation and students were able to plot changes in population size (in terms of gene frequency) as a consequence of forward and back mutation rates. Because of the ability to see the effects ot mutations over a large number of generations immediately, the students were aware of the slow rate of gene freguency change under normal rate conditions ( 1 0“ 4 to 10”® /generation) . Students would not normally be exposed to thisvisible evidence since they are reluctant at least, to
3S
T
Table 1. An example of printout resulting from changes in the variables B and C in the fox-rabbit predation formula. Only the maxima, minima and amplitude from each situation are given. The figures represent the change in each population from original value:.' of 6000 rabbits (x0) and 2500 foxes (y0) . The two curves are not superimposed and the time lag is that of the fox curve behind (in response to) the rabbit curve.
Maximum Minimum Rabbit Maximum Minimum Fox Time
Rabbit Rabbit Amplitude Fox Fox Amplitude Lag
A B C D
4 2 13 6.186 1.168 5.019 3.759 0.892 2.867 0.320 (original)
" 3 " " 7.720 ' 0.773 6.947 3.042 0.421 2.621 0.290
4 " ” 9.827 0.445 9.382 2.819 0.200 2.619 0.260
" 5 " " 12.164 0.243 11.291 2.716 0.098 2.618 0.240
" 6 " " 14.634 0.129 14.505 2.658 0.049 2.610 0.220
4213 6.186 1.168 5.019 3.759 0.892 2.867 0.320 (original)
" " 2 " 6.046 0.124 5.992 6.756 0.248 6.508 0.240
" " 3 " 6.020 0.018 6.003 9.557 0.072 9.485 0.190
" " 4 " 6.010 0.003 6.008 12.171 0.021 12.150 0.160
M " 5 " 6.005 0.000 6.005 14.645 0.006 14.639 0.140
TABLE 1.
3*50
carry oat 100 separate arithmetic binomial expansions involving a slightly different gene frequency change ia aach expansion. in tha next example where aalactioa against or for a specific genotype occurred, students were able to see immediately tha affects of selection. Populations, in terns of gtae frequency, decreased or increased aarkedly illustrating the principles so often iterated to undergraduate students and so least often understood. , The additional coaplicating factor of iaaigrants and emigrants in the population was also illustrated graphically, partirulary when they were allowed to vary the auaber of nigrants per population cycle.
Once these ideas were wall in hand, the value of the coaputer was; reinforced when students were able to put together two or three of these separate changes to gene frequency ia the population. Nutation under conditions of specific selection for the autant, nigrants with seiected-for or selected-against characteristics, closed populations with selection against the recessive, and the eaergeoca of doainant foras served to illustrate aore dramatically to studentn the changes in population than lectures ever could have done. The full iaplications of this type of prograaaing in tie teaching of genetics courses has not yet been explored, but the possibilities seen endless. Costs per student in terns of conputer tine were approximately SO. 16 per prograa and each student (working in groups) ran 2-3 programs.
luaerous other axanplen ia quantitative biology are susceptible to iaaediate application of this node of conputer inguiry. Be have initiated exaaples of lung-gill-oxygen exchange, muscle- bone- leverage principles, diffusion over cell gradients, and the integration of taxonoaic siaiiarities in prograas which allow students to explore the variabilities allowel in a aatheaatical aodel of a syntem, and to relate these studies to physiologic, anatoaic, and thought problems. Be feel confident that these prograas which provide students with an opportunity to explore the parameters dictating a dynamic balance or organisnal capability will play an iaportant part in enticing student involvenent and elucidating hither-to obscure relationships. Be feel that an iaportant portion of the educative process is in the incorporation of a working relationship of predictive foraula into the students personal body of knowledge. In aost cases thesa relationships can be displayed most econonically through the use of coaputer prograns. In the conparison of 100 generations of fruit flies versus 100 generations of coaputer printout there is little doubt of econoay. Sinila^v that these relationships should becone a working part of the student's vocabulary there is liVcle doubt. Be suggest thin method as worthy of exper iaentation by other institutions and intend to eaploy it further in our inguiry investigations.
51
40
COMPUTER ASSISTED ALGORITHM LEARNING IN ACCOUNTING
William F. Bentz The University of Kansas Lawrence, Kansas 66044 Telephone: (9 13) 864-4665
Introduction
The purpose of this paper is to present several hypotheses about the potential advantage ot learning accounting methods with the aid of computers. A synthesis of relevant learning theory principles forms the conceptual foundation for these hypotheses, and several examples serve to illustrate computer assisted instruction* The focus is only on those accounting methods which can be characterized by computer algorithms* Due to space limitations, many other equally important aspects of accounting instruction cannot be considered here.
Background
While many innovative applications of computer technology have been developed tor accounting instruction purposes, almost no attention has been given to learning theory concepts implicit in these applications. The development of computer assisted instructional (CAI) [1] materials for accounting is apt to be both haphazard and inefficient until a conceptual model of the relevant learning processes has been developed. More precisely, we must have a conceptual model of learning processes in mind in order to
(1) set specific instructional objectives that serve to guide the educational pr ocess[ 2 ] ;
(2) formulate hypotheses, based on learning theories developed in other contexts, about the expected contributions of alternative instructional aethods to the set of instructional objectives;
(4) efficiently select CAI materials, based on their hypothesized benefits as indicated by theories of learning, for turther development and experimental testing; and even to
'5) investigate successful applications of CAI to identify the important elements of these applications and to determine the nature of the success achieved.
In addition to having a weak conceptual foundation , many educators adopt such a limited view of CAI that its development may be unnecessarily constrained. In accounting, the dominant view of the computer is that it is a giant calculator. Thus, computers are viewed as a particular type of instrument which serves one function - calculating [3]. A more inclusive view is that computers are valuable teaching aids that can facilitate the learning process in many ways, in addition to performing purely calculating f unct ion s[ 4 ]. The instrument view of coaputers tends to limit their use to beginning courses, while a broader perspective is more likely to result in the development of CAI materials at all levels of instruction.
The Structure of Accounting
The superstructure of accounting has been studied by several researchers, including Tjiri [16], Mattessich [18] and Sterling [23]. These efforts involve attempts to describe accounting, as practiced today, in as compact a manner as is possible. There are at least two practical benefits of such efforts. First, by capturing the essential structure of accounting in a tew axioms or laws, one can better communicate the essential characteristics of accounting to those outside the discipline; and, secondly, one can more efficiently describe accounting to prospective accountants.
However, at another level of abstraction, the structure of accounting can be viewed in a less formal, and more limited way. The subject ot accounting is frequently explained by first partitioning it into topical areas which are deemed to have a structure ot their own. For example, depreciation accounting, accounting for leases, accounting for pension plans and many other topics are discussed somewhat independently, in spite of the common superstructure which describes all of financial accounting.
, 41
Bf shifting our focus from the superstructure of accounting to a lower level of abstraction, accounting can be viewe! as a collection of algorithms which relate to particular topic areas. "An algorithi is a procedure for solving a problem." [15, p. 1] In sore torwai terms, an algorithi is something that can be carried out on an idealized machine, called a Turing machine. Although the properties of Turinq machines have been more precisely defined, let it suffice to note that a Turing machine can do anything a o tored-prog ran computer can do [15, p. 170]. Therefore, for our purposes those procedures that can be performed by a stored- program computer are called algorithms.
l!l£ jnce o£ Algorithms ifl &c£Ountjjig
flany accounting techniques can be characterized as algorithms; thus, the learning of accounting techniques involves the learning of algorithms. Typically, the student reads through a demonstration problem and notes the sequence of steps used therein. Then, the student works several problems, mimicking the sequence of operations that are executed in the demonstration problem. The sequence of operations (an algorithm) necessary to solve an examplar of a class ot problems becomes apparent to the student during the process ot examining the demonstration problem, or while working the homework problems. If the method is understood, it is understood is a technique which is applicable to problems other than the particular one at hand. Thus, the student who understands the method can apply it to a new problem with little difficulty, while the student who rotely learns a sequence of operations to solve problem X may have difficulty solving problem Y, even though X and Y arc of the same class of problems. Although other types of learning may take place while one works problems, the learning ot accounting algorithms, and the practice involved in applying them to specific situations, are the major functions served by procedura 1- ty pe homework problems.
There are two additional reasons for focusing on accounting algorithms, in auditing, the professional accountant is faced with the problem of evaluating the system of internal controls tha; assures the quality of the accounting data on which an opinion must be rendered. Because many accounting records and recording processes are being automated, modeling or flowcharting the processing system is of utmost importance on almost every audit. Part of what is being modeled or tlowcharted is the algorithm that represents the method by which a machine transforms inputs into output. Therefore, the auditor must be prepared to deal with algorithms in their general form, not with a particular solution method for test problem X. Precisely because the clerical procedures performed inside the machine cannot be observed, the modeling ot these unobservable algorithms is more important than ever before.
The construction aud testing of algorithms is an equally important function ot the auditor's counterpart, the management consultant. In designing a new system, or in revising an existing system, the management consultant must specify how activities are to be accomplished. At some stage in the design process, a designer must specify the detailed procedures to be executed by the system. This specification is, in essence, an algorithm even though the system being designed may not be an automated system. Thus, for management consultants, the spec: f icat ion of accounting algorithms is an integral part of the system iesign process.
L£d£ning flegoun t^ng Algofi t hms
Now that the importance of looking at the algorithmic nature of accounting methods has been discussed, we can focus on three approaches to learning accounting methods: (1) The traditional problem-solving approach, (2) reception learning of generalized algorithms, and (3) discovery learning of generalized algorithms.
I &e tltiitiorial method. In treahman through junior level courses, the instruction sequence usually includes the presentation of some concepts, propositions, and background information. This material is followed by tne working of accounting problems which serve to clarity and illustrate the concepts presented and the accounting methods involved. As mentioned in the previous section problems involving a sequence of operations t^nd to be solved in one of two general ways. First, if a demonstration problem is presented, the student tends to examine the demonstration problem and then attempts to work a problem, or he attempts to work a homework problem using a demonstration problem as a guide. In either case, the learner is actively attempting to discover for himself the sequence of arithmetic operations involved in the accounting method. Understanding of the method can be regarded as complete when the student can apply the method to similar problems (application), or even to novel situations which have not been related to the technique before (problem-solving learning as described by Ausubel[4]).
Several criticisms of the "problem" method of learning implicit algorithms are in order. First, since the student never sees the algorithm in its general form, he may stumble through several problems before understanding the methodology embodied in the indisclosed algorithm. Second, the slower learner may not receive sufficient feedback from a tew homework assignments
to fully qr-isp the method. Third, the learning of a method by working problems may only result in pre-verbal un:l°r stan d iny which cannot be retained as long as a verbally created description. Fourth, even it a student learns a method by working proolems and can verbalize that understanding, he may have difficulty remembering the more important features of the method unless ho has the opportunity to work with an abstract model ot the method. Further, the more general and clearly defint?d algorithms should be more easily remembered than a collection of loss genoiai methods which are not clearly di f f erentia ble[ u , Chapter 5]. Fifth, there is a tendency to teach business terminology and business practices by introducing them in assignment problems. While learning about business practice is important, the super imposing of concept learning, prospoui t ion learning and problem-solving may only confuse the student and impede the learning of accounting algorithms.
learning of genera li zed algorithms. A second way of learninq accounting methods i\ to encounter them in complete form, and then to apply the method, or algorithm, to particular problems. The sequence of instruction would include a presentation of concepts, propositions and hackqround information, as before, followed by a presentation of the accounting algorithm in general form. After the algorithm is studied, it is applied to a series of problems which serve to clarify the students* understanding of the algorithm, as well as demonstrating the range of applications associated with the algorithm being studied. Each student’s understanding of the algorithm is tested in the same manner as described above
Algorithms can be presented for reception learning by means of several different devices. Flowcharts, decision tables and computer programs coded in procedure-oriented languages can he used to describe almost any accounting procedure. As computer courses become required, these tools become more and more familiar to all business students, so their classroom use is feasible in many schools.
Note that these two methods of learning are very different. In the first case, the algorithm must be inferred from an example, or from the feedback provided while the student is attempting to solve problems "cor rect ly. " In the second method, the studen : learns the algorithm by reception, rather than by discovery. The algorithm is presented in its final fora, so the student noed not discover it foL himself.
There are severcil criticisms of the reception learninq method, as there were of the traditional method. First, students may apply the algorithm to speciric problems in a rather mechanical manner, which may not require them to think about the method itself. Second, even when students think about the algorithm as a generalized technique, they may attain only a pceverbal understanding of the algorithm. Preverbal understanding is only an intermediate phase of the learning process and does not represent a terminal learninq objective. Third, the act applying a specified algorithm to a set of problems may lack the motivational qualities ot a problem or puzzle, that must be solved.
Presenting accounting methods as algorithms does have several advantages which alleviate the limitations of the traditional method mentioned above. First, by focusing on the algorithm itself, the instructor is telling the student what is important, in the process of solving individual problems without knowing that a qeneral solution method exists, a student may not be able to separate the important features of a homework problem from the trivial. Secondly, by working with a defined algorithm, rather than attempting to discover the algorithm, a student may be able to learn more about its structure and essential features because it has been fully specified for him, in general form.
Another important reason for present algorithms is probably clear to most readers. Sono ideas are simply vague and somewhat ill-delined until expressed in equation fora, or as algorithms. For example, the time value of money is a concept which is readily accepted by students on an intuitive level when first e/plained. After a careful and tedious presentation of present value concepts, many students can handle straight-forward interest problems with the use ot interest tables, but only the students with some mathematical sophistication seem to grasp the process of discounting a series of payments to determine their present \alue. The ability to work iwth symbols and equations seems to be necessary if a student is to understand interest prob leras.
In summary, presenting accounting methods to students in the form of algorithms has certain advantages over the more traditional problem solving approach. Specifically, it is hypothesized that understanding is more nearly complete and retention is greater when students study and apply explicity algorithms, rather than discovering accounting methods by solving problems. This hypothesis is based on Ausubel's theory of the learning and retention of meaningful mate r ia 1.
However, there are some disadvantages associated with reception learning. The ways in which CAI can be expected to alleviate these disadvantages are discussed next.
Computer assisted discovery learning of acco^rntrnu algorithms. An alternative to reception learning is the discovery learning of accounting algorithms. In contrast to solving a sequence of problems, the assignment is to construct a general algorithm which then can be used to solve a whole class of accounting problems. Text material, illustrative problems and handouts can be used to specify the accounting method, but the student is forcc?d to generalize the method so that an algorithm can be formulated. The algorithm can be characterized by flow charts, decision tables, or an operational program coded in a language such as BA.SFT, FOPTHAN, or COBOL,
What are the potential benefits of having students reconstruct accounting algorithms by writing computer programs? First, consider the potential motivational benefits. In the process of writing a program, t.he student receives a lot of feedback which tends to support continued work on the problem (a h y pot hes 15 ) • The feedback is in the form of error listings from the computer and the computed answers to a test problem. Tf a student gets an incorrect answer, he has a clear signal that his algorithm contains souie errors. Discussion with the other students that congregate at the computer center and comments by the instructor also serve as valuable feedback. Incidentally, it is relatively easy to follow the logic of a student's program when the procedure being programmed is a familiar one and when a list of suggested variable names has been provided as part ot the assignment.
Second, people tend to think about incomplete tasks more than they do about completed tasks[4, o. 490 ]• Therefore, it is hypothesized that working on on"' computer program for N days may maintain more concentrated student attention than working and completing several different problems over the same time period. Another motivational aspect is the greater opportunity tor satisfying ego- f u If ill i ng needs when the student must construct an algorithm which is not presented to him in completed form. Constructing the algorithm is satisfying in itself, and learning computer skills is satisfying to many students because ot the career opportunities associated with a knowledge of computers.
One linal motivational benefit, is the opportunity to complete satisfactorily a task before submitting it tor final approval. Some students find it very frustrating to spend hours working complex accounting problems, Lo achieve only partial success. With programs, it enough lead time is provided, diligent students have the opportunity to write satistactory programs.
The potential cognitive learning benefits of the process ot constructing accounting algorithms are dependent on the claim that the student will thoroughly uniorstand an accounting procedu* it he has written a computer program for it. Further, it is hypothesized that understanding an algorithm is a higher level of abstraction than can be achieved by most students in the process of solving particular problems. To th'J extent that these claims are true, a s t u* nt's knowledge of the accounting procedure that he programm ?d should be integrated into his cognitive structure as a generalized method which is clearly differentiable from other accounting methods.
There are several conditions which can be expected to facilitate greater cognitive learning behavior. First, t.lic construction of an algorithm requires more active participation in the learning process than does the learning of an algorithm presented in the final form (reception learning). Some students will critically evaluate new ideas to "make sense" out of them while wonting at the task of incorporating them into cognitive structure. However, all too many students are passive listeners when propositions or problem solving methods are presented to them in final form. Therefore, to the extent that more active learning can be induced by requiring students to construct algorithms, it is hypothesized that greater learning is to be expected. Experience indicates that most students do need some inducement to become actively involved in the learning process.
Second, the benefits of massed learning, as opposed to distributed learning, are related to the learning of algor it h ms[ 5 ]. In this case, the alternative learning methods being compared are the learning of accounting methods by solving individual problems as opposed to constructing algorithms for subsequent application. In solving a sequence of problems, usually of increasing difficulty and complexity, the student encounters two problems: forgetting between problem- solving sessions, and the warm-up required to recall the methods and settle into the new problem. It seems plausible that iiorgetting can be a factor since most undergraduate students take rive or six different courses each semester, plus working and being involved in other activities. Further, since accounting problems usually represent complex tasks, substantial warm-up and reorienting ot one's thinking may be required each time a new accounting problem is encountered. Under these conditions, massed learning can be more efficient than learning distributed over a number of sessions.
Therefore, to the extent that there is a sizeable threshold of effort required to discover and fully grasp accounting algorithms, the massed learnirq that is usually associated with the writing of a computer program may be more efficient the. the solving ot a series of individual problems over time. Because of the difficulties created by forgetting between problem-solving sessions, and t.he warm-up required to settle into a new problem, it is being hypothesized that
o
AH
w
the benefits of massed learning are applicable to the construction of computer programs, thus improving learning.
Greater lateral transferability of knowledge Should also be facilitated by having students write programs. Gagne[12, p. 235] theorizes that applying one's knowledge in a number or different contexts increases transferability, although we know little about the precise factors which are involved. A student can use his own program, or a previously written program, to solve a variety of problems, thus emphasizing the generality of the techniques without increasing the busywork that is usually associated with working a large nuoioer of problems. Thus, a student can be encourayet] to generalize his conception of a technique.
12[iS 2l Computer Assisted Instruction
Process cost account ing, the allocation of service department costs among reciprocally dependent service departments and operating departments, the allocation of profits among reciprocally owned cor po ra t ions, corporate budgeting models, and the financial accounting methods which involve present value calculations are all complex topics which involve algorithms. For process costing, students can be given a set of program speci f ica t ions in order to write programs which accept standardized inputs, and generate the required cost reports. Students can also be asked to specify how the input data is to be collected, and how cost reports are to be designed and distributed within a fictional company.
.Service department cost allocation techniques, profit distribution techniques, and corporate budgeting models all involve using matrix operations to solve systems of simultaneous linear equations. Their common structure becomes quite apparent to students when they program these techniques. Similarly, the common structure of lease contracts, pension plans, bonds, and long-term investments becomes apparent to students who have constructed an algorithm to rind the present value of a single payment or of a series of payments. Moreover, students seem to understand the present value techniques much better after having written such a program.
SUMMARY
In this paper, several learning theory concepts have been related to algorithm learning in accounting. An examination of the relevant learning theory concepts leads to the hypothesis that appropriate CAI techniques will facilitate the learning of accounting algorithms.
FOOTNOTES
1. No distinction is made between computer assisted instruction (CAI) and computer extended instruction (CBI) here.
2. The importance of setting measurable objectives in education is well accepted as is demonstrated by the comments of Church man[ 6 and 7], Goldi aaon d[ 1 3 ], Ilommof 14 ], SvansflO], Gagne[12], and Ausubel[4].
3. The instrument view of computing is found in Anderson[3], Beams[5], Mastro[17], Mecimore[ 1 9 ], Penick[20]. Person[2 1], CorcoranfH], and even
the committee reports of the AAA[ 1 ] and the AICPA[2].
4. See Cowie and Fremgr en[ 9 ] , Frank[11], Prater[22], and parts ot[ 1 ].
5. For a discussion of massed learning of low-level capabilities, see Stanley Stevens[24, pp. 636-40 ], and Robert S. Woodworth and Harold Sch olsber g[ 26 , pn. 766-94 ].
REFERENCES
1. American Accounting Association Committee (1964) on Courses and Curricula — Electronic Data Processing. "Electronic Data Processing in Accounting Education," The Accounting Review, Vol. XL, No. 2 (April, 1965), pp. 4l2-2tt.
2. American Institute of Certified Public Accountants, Report of the Commit tee on
Education and Experience Requirements for CPAs. New Yorx: American Institute
of Certified Public Accountants, Inc., 1969.
3. Anderson, John J. "Integrated Instruction in Computers and Accounting,” The Accounting Review, Vol. XLII, No. 3 (July, 1967), np. 563-66.
56
45
4. Ausubel, David p. and Ployd G. Robinson. School Learning: An In t roduc t ion to
fidugatiogaJL Psychology. New York: Holt, Rinehart and~Winston, Inc., 1969.
5. Beasa, Floyd A. 11 EDP and the Elementary Accounting Course, •• The Accounting
Review, Vol. XLIV, No. 4 (October, 1969), pp. 832- 36.
6. Churchman, C» West. The Systems A pproach . New York: Dell Publishing Conpany,
1968.
7. Churchman, C. West. "On the Design of Educational Systems." Working Paper No.
86. Center for Research in Management Science, University of California,
Berkeley, 1964. (Mimeographed)
8. Corcoran, A. Wayne. "Computers Versus Mathematics,*4 The Accounting Review, Vol.
XLIV, No. 2 (April, 1969), pp. 359-74.
9. Cowie, James B. and James ft. Freragren. "Computers Versus Mathematics: Round
2," The Accounting Review, Vol. XLV, No. 1 (January, 1970), pp. 27-37.
10. Evans, James.. "Behavioral Objectives Are No Damn Good," in Aerospace Education
Foundation, Technology and Innovation in Education. New York: Frederick A.
Praeger, Publishers, 1968.
11. Frank, Werner. "A Computer Application in Process Cost Accounting,” The
Accounting Review, Vol. XL, No. 4 (October, 1965), pp. 854-62.
12. Gagne, Robert fl* The Conditions o£ Lea£ning. New York: Holt, Rinehart and Winston, Inc#, 1965.
13. Goldiamond, Israel. "Motivation-- Some Ways and deans," in Aerospace Education
Foundation, Technology and Innovation in Edu cation. New York: Frederick A.
Praeger, Publishers, 1968.
14. Homme, Lloyd. "A Behavioral Technology Exists-~Here and Now," in Aerospace
Education Foundation, Technology and Innovation in Education. New York: Frederick A. Praeger, Publishers, 1968.
15. Hull, T. E. In troduct ion to Computing. Englewood clitfs, N. J.: Prentice- Hall, Inc.., 1966.
16. Ijiri, Yuji. "Axioms and Structures of Conventional Accounting Measurement,”
The Accounting Rev iew. Vol. XL, No. 1 (January, 1966), pp. 36-53.
17. Mastro, Anthony J. "EDP in One Elementary Course," Tne Accounting Review, Vol. XLII, No. 2 (April, 1967), pp. 371-74.
18. Mattessich, Richard. Accounting and Analytical Methods. Homewood, Illinois: Richard D. Irwin, Inc., 1964.
19. ttecimore, Cbarles D. "Integrating EDP into the Elementary Accounting Course," The Accounting Review, Vol. XLIV, No. 4 (October, 1969) , pp. 837-39.
20. Penick, Jack G. ”ADP Equipment as an Accounting Teaching Tool,” The Accounting E«view, Vol. XLI, No. 3 (July, 1966) pp. 549-51.
21. Person, Samuel. "The Integrated Use of Data Processing Equipment in Teaching Accounting Subjects," The Accounting Review, Vol. XXXIX, No. 2 (April, 1964), pp. 473-75.
22. Prater, George I. "Time-Sharing Computers in Accounting Education," The
Accounting Review. Vol. XLI, No. 4 (October, 1966), pp. 619-25.
23. Sterling, Robert R. "An Explication and Analysis of the Structure of
Accounting.” Working Papers No. 22 and 23 (Part Two) . Lawrence, Kansas: The
School of Business, The University of Kansas, 1969.
24. Stevens, Stanley S. Handbook of Mental B-^XCnol oqy. New York: John Wiley
6 Sons, Inc., 1951.
25. Williamson, J. Peter. "The Time-Shar ir.g Computer in the Business School
Curriculum,” Paper presented at the Kiewit Conference, Dartmouth College, Hanover, New Hampshire, June, 1971.
26. Woodworth, Robert S. and Harold Scholsberg. Experimental Psychology. Now
York: Holt, Rinehart and Winston, 1965.
U£
THE BUSINESS CORE INTEGNATOi AT INDIANA UNIVERSITY
Thoaas L. Guthrie Indiana Univeraity Fort Nayne, Indiana 46805 Tale phone: (219) 483-8121
In the acadeaic year 1966-69, faculty at the School of Buaineas, Indiana Univeraity, Blooaington Caapus, began exper iaentation with a thoroughly reviaed undergraduate curriculua which included what has been called the four course integrative core. The core is taken by firat seaester Junior class standing business students who aeet specific prerequisites. The core consists of three principles courses in the functional areas of finance, aarketing and production and a new course, Siaulation of Business Enterprise. The conception and developaeat of the core . by the faculty, spearheaded by Dr. williaa B. Panacher, reached such a stage of aaturity by the acadeaic year 1970*71 that the Aaerican Association of Collegiate Schools of Business awarded Indiana University School of Business the prestigious western Electric Fnndvs award for educational innovation in higher education for its outstanding undergraduate core prograa. The purpose of this paper is to describe the objectives of the integrative core, deaonstrate the procedures involved, and relate the experiences and reactions to date, with priaary eaphasis being given to the unigue part that the Siaulation courae plays ia the core.
Objective
Given the overall objective of the Business school to graduate students capable of contributing to society in general and the business coaaanity in particular, the iaaediate objectives of the four-course integrative core are:
1. to provide the junior year business student with a rigorous and integrative education in the functional areas of business.
2. to provide a simulated business experience that will cause students to begin to think like businessaen, to identify theaselves with business and to increase their enthusiasa for a business career.
3. to provide for the student a snail group ataosphere facilitating the change froa a passive educational experience to one of involveaent and action.
4. to provide the student the further advantage of snail size classes and a closer student faculty relationship in at least one of the four core courses (4) .
Prerequisites to the core, in addition to Junior class standing, include the following:
Principles of Econoaics.
Econonic Statistics. •• 3
Pinite Hatheaatics . . . 3
Calculus ..3
Introductory Psychology. 3
Principles of Sociology. 3
Hinageaent Accounting. ••••• 6
Legal Environaent of Business 3
These prerequisites, which are strictly enforced, provide the student with a higher level of coape tency and consistency than had been required heretofore, tbus allowing a aore rigorous treataent of subject aatter in the basic functional areas of business.
lagleaentation overview
The siaulation course is paraaount in aeeting the objective to integrate the students' initial work in business decision-aaking. A coaputerized business siaulation gaae is utilized in the course which is, of course, nothing new, since auaerous business courses use coaputerized qaaes of one type or another. What is unigue is the relative iaportance of the gaae in the
58
47
course. Iq lost busiaess courses gases are used as sidelights to demonstrate principles or to reinforce desired learning patterns. In the Indiana Simulation course the game is literally the course, and sidelight assignments are made in conjunction with the other three courses.
To administer the game, the students are divided into teams of 4 to 8 people, each, which comprise individual companies for gaming purposes* This is, again, not unique, bat what is unique is that (1) individual team members attend the same section of all four core courses and (2) all four core courses must be taken concurrently.
By utilizing the team approach and the business simulation game as a central classroom activity, demanding the knowledge, analytical tools and methods taught in the other three courses, integration is achieved in several ways:
First, as a result of each team being in the sane section of finance, marketing and production, each student is a member for the entire semester of a small management group which is responsible as a group for several assignments* The management group is bound together by common goals, especially with respect to the Simulation course. This, in effect, provides every student with 3 to 7 counselors, tutors and friends, business and social. The advantages of this type of atmosphere should be self-evident in these days when many universities and programs are being charged with interest only in bigness and its often alleged counterpart, anonymity.
Second, principles being taught in marketing, production and finance are reinforced through specific related assignments made in conjunction with the Simulation course. Such assignments seem far more relevant and urgent to the student than the typical potpourri of problems at the end of the chapter in textbooks.
Third, the integration and assimilation by each student of knowledge in marketing, production, and finance into a management philosophy is fostered. Since each team is required in the Simulation course to make several marketing, production and financial decisions over an extended period of simulated time, it must do so from
delicate quality c
Fourth, integration is achieved not only with respect to the student, but the faculty, also. For the integrative core to be successful, there must be serious planning and coordination of individual course topics, assignments and examinations. As a result, duplication of subject matter is eliminated and more importantly, gaps are closed. Overloads are coordinated. By precept and example, faculty show their acknowledgement of and respect for all functional areas, regardless of their specialities, and particular research interests.
Implementation Details
The implementation details of the integrative core will be discussed primarily from the point of view of the Simulation course. As a matter of review, a business simulation or game may be defined as a sequential decision-making exercise structured around a model of business operation, in which participants assume the role of managing the simulated operations[ 2 ]• Business simulations abound today, but few are both sufficiently complex and comprehensive to provide the basis for a one semester, three credit hour course. One that does meet both criteria is INTOP (International Operations Simulation of the University of Chicago) developed by thorelli and Graves[ 6, 7 , 8 ]. Of course, the purpose of this paper is not to report about INTOP; however, the reader must have some conception of the character of INTOP, if he is to appreciate the role that the Simulation course is capable of performing in the integrative core. The "typical" business simulation can he represented in a 1000-2000 card FOBTRAN program. The INTOP model is represented in approximately 9000 FORTRAN cards* If one makes the dangerous assumption that there is a direct relationship between the number of cards and game complexity and comprehensiveness (and realism) , INTOP and the few models like it are in a separate league* INT0P is not a program to be "dumped-on" the small departmental computer one day and processed the next day. INTOP is international in scope and allows fundamental decision-making in all functional areas of business except production balancisq and raw materials purchasing. Environmental parameters may be changed so as to emulate segments of recent international economic activity* Typical computer output in the form of financial statements, marketing reports and ancillary data is shown in Illustration 1.
Procedurally, the Simulation course meets i;i 75 minute sessions twice a week for 15 weeks. Individual sections are limited to nine teams. The first few class sessions are used to explain the purposes and mechanics of the course and then the course is divided into two separate, but related parts, occupying the two weekly class sessions. (
One session can be described as open company meetings; that is, teams (companies) are in open session analyzing operations and results, formulating plans and otherwise getting ready tor their new round of nanagemant decisions which are made on a weekly basis (and represent one
an interrelated
effectively. The learning of that
48
59
ILLUSTRATION 1. SAMPLE INTOP C*JTPUT. COMPANY 1
INCOME STATEMENT
STANDaRO SALES CONSUMER INTRA-COMPANY INDUSTRIAL LESS-COST OF GOOOS GROSS MARGIN DELUXE SALES CONSUMER INTRA-COMPANY I NOUS TRIAL LESS-COST OF GOOOS GROSS MARGIN TOTAL GROSS MARGIN operating EXPENSES CONNER. ANO AOMIN. ADVERTISING SHIPPING INVENTORY SALES EXPEDITING METHODS IMPROVEMENT DEPRECIATION ANO FIXED NET OPERATING FXPENSE NET EARNINGS FROM OPER. TOTAL NET OPER . EARNINGS
NON-OPERATING INCOME
INTEREST INTERCO. LOANS L I CENSE S-X LIC6NSFS-Y MISC. INTERFST TOTAL NON-OPER. INCOME NON-OPFRATING FxPENSE MARKET RESFARCH LICENSFS-X LICENSES-Y
R ANO 0 NFW PROOllC T X R ANO 0 NFw PRliDllCT Y TOTAL INTERFST TOTAL NON-OPER. EXPENSE GROSS EARNINGS LESS-TAXES
LESS-CAPITAL TRANS. TAX NET EARNINGS LESS-OI VIOENOS TO RETAlNEO EARNINGS
BALANCE SHEET AREA 1
ASSETS CASH
A/R FIRST QUARTER A/R SECOND QUARTER INVENTORY STANOARO X 260630
OELUXE X 0
STANOARO Y I910IB
OELUXE V 66fc9B2
TOTAL
SECUR I T! ES
TOTAL CURRENT ASSETS
NET PLANT ANO EQUIP*
INVESTMENT INTERCOMP.
SUBSIDIARY CONTROL
TOTAL ASSETS
LIABILITIES
A/P PfRST QUARTER A/P SECOND MARTEN SUPPLIER CREOIT AREA BANK LOANS TOTAL CURRENT LIABILITY
LOANS PAYABLE
TOTAL LIABILITIES
STOCKHOLDER EQUITY
CONNON STOCK AT PAR PAiO IN CAPITAL RETAlNEO EARNINGS HONE OFFICE CONTROL
TOTAL EOUITV
TOTAL LIAB. ANO EQUITY
INTflP - UNIVFRSITY UF CHICAGO
|
area |
I |
AREA |
2 |
AREA |
3 HOMfc |
|
|
DUCT * |
PRODUCT Y |
PRODUCT X |
PRODUCT Y |
PkiJOnCT x |
PRODUCT Y |
|
|
726000 |
1 131661 |
49132ft |
1 2 AftAft 0 |
313791 |
0 |
|
|
0 |
0 |
n |
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0 |
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|
|
22754.6 |
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1 3 A 309 |
297072 |
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357018 |
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300276 |
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|
|
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|
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|
|
10000 |
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5000 |
ftOOO |
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|
|
215000 |
190000 |
100000 |
146000 |
0 |
0 |
|
|
A 36861 |
A29063 |
220795 |
317173 |
79862 |
0 |
|
|
63592 |
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136223 |
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22041 3 |
-0 220413 |
PERIOD 6
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|
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||||
|
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|
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|
1000 |
1000 |
0 |
127M) |
14760 |
|
|
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100 0 |
n |
12760 |
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|
|
72000 |
72000 |
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|
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|
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|
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\ 71000 |
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|
44 2.372 |
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22041 3 |
-|6«?5»> |
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|
|
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|
|
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|
|
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1 6428*1 |
- \ 6H'6() |
6 12680 |
|
|
0 |
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||||
|
212M9 |
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1 64289 |
- ) SM/6h |
632680 |
|
|
AREA 2 |
AREA 3 |
home office |
CONSOLIDATED |
||
|
12757 |
260351 |
106257 |
110793 |
490156 |
|
|
1115737 |
476189 |
143379 |
1735305 |
||
|
0 |
521942 |
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||
|
116060 |
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||||
|
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||||
|
17018 |
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||||
|
353492 |
0 |
||||
|
1117431 |
406570 |
0 |
1604002 |
||
|
100000 |
100000 |
0 |
750000 |
950000 |
|
|
2345925 |
1045053 |
375152 |
060793 |
5426923 |
|
|
5160000 |
5000000 |
0 |
10160000 |
||
|
0 |
0 |
||||
|
1 1095000 |
|||||
|
7505925 |
6045053 |
375152 |
12755793 |
16586923 |
|
|
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||
|
0 |
1378 49 |
0 |
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||
|
0 |
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|
|
0 |
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0 |
0 |
||
|
705401 |
614947 |
66124 |
0 |
1466472 |
|
|
3300000 |
3300000 |
||||
|
785401 |
614947 |
66124 |
3300000 |
4766472 |
|
|
10000000 |
10000000 |
||||
|
0 |
0 |
||||
|
395524 |
705106 |
184028 |
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020451 |
|
|
6325000 |
5445000 |
125000 |
|||
|
6720524 |
6230 1Q6 |
309020 |
9456793 |
10020461 |
|
|
7506925 |
6045053 |
375152 |
12756793 |
165H6923 |
O
ERIC
6*
ILLUSTRATION t, CONTlNUCO. COMPANY 1
INTOP - UNIVERSITY OF CHICAGO
PERIOD 6
ANCILLARY OATA
STANOARO SALFS UNITS CONSUMER
intra-company
industrial
AREA 1
PRODUCT X PRODUCT V
AREA 2
PRODUCT X PROOUCT V
28000
8000
0
OELUXE * SALES UNITS
CONSUMER 0
INTRA-COMPANY 0
I NOUS TRIAL 0
NFG, COST ANALYSIS
PLIU STANOARO COST 117351
UNITS 18000
OELUXE COST 0
UNITS 0
PL ( ? I STANOARO COST 1*3280
UNITS 20000
OELUXE COST 0
UNITS 0
PL I 3) STANOARO COST 0
UNITS 0
OELUXE COST 0
UNITS 0
STANOARO GRAOE 0
OEUIXE GRA06 0
INTRA-CD* purchases
STANOARO COST 0
UNITS 0
DELUXE COST 0
UNITS 0
INOUS TRIAL PURCHASES
STANOARO COST 0
UNITS 0
OELUXE COST 0
UNITS 0
ENOlNG INVENTORY
STANOARO UNI TS 38000
GRAOF 0
OELUXE UNITS 0
GRAOF 0
NO* REG* SALES OFFICES l
max* Grade of imprivhmfni o
10859
0
0
0
0
0
0
0
66*982
32000
0
0
0
0
0
0
0
0
0
1
1 11*1 0
32000
1
158*9
0
0
106071 1 3000 0 0 0 0 0 0 0 0 0 0 0 0
179
0
0
0
20808
0
0
0
0
353*92
21000
0
0
0
0
0
0
0
0
0
1
1 192 0
21000
1
AREA
PROOUCT X
8965
0
0
0
0
0
0
0
0
0
0
0
o
0
0
0
0
0
8000
0
0
8000
0
0
0
PROOUC T Y
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
market RESEARCH 1 area 1
PROOUCT x
PRICES POSTEO THIS ORT. STO. OH.
COMPANY NUMRER 1 26 -o
COMPANY NUMBER 2 12 -O
COMPANY NUMBER ) ft -O
COMPANY NUMBER * -6 -o
COMPANY NUMBER 5 f* -O
COMPANY NUMBER 6 60 -0
COMPANY NUMBER 7 30 -O
COMPANY NUMBER • 20 «0
COMPANY NUMBER 9 2J-0
GRAOES MEG. EOR NEXT ORT.
COMPANY NUMBER 1 0 -O
COMPANY NUMBER 2 01
COMPANY NUMBER 3 0-0
COMPANY NUMBER * -0 -0
COMPANY NUMBER 5 *01
company number t o -o
COMPANY NUMBER 7 01
COMPANY NUMBER 6 -0-0
COMPANY NUMBER 9 01
AREA 2
AREA 1
|
PROOUCT |
Y |
PROOUCT |
X |
PROOUCT |
Y |
PROOUCT |
X |
PROOUCT |
V |
|
TO. |
DEI. |
STD. |
DEL. |
STD. |
DEL. |
STD. |
DEL. |
STD. |
DEL. |
|
60 |
-0 |
It |
-0 |
60 |
-0 |
35 |
-0 |
-0 |
-0 |
|
34 |
-0 |
2B |
-0 |
50 |
-0 |
-0 |
-0 |
*0 |
-o |
|
-0 |
-0 |
M |
-0 |
60 |
-0 |
37 |
-0 |
-0 |
-0 |
|
33 |
65 |
-0 |
-0 |
80 |
-0 |
-0 |
-0 |
-0 |
-0 |
|
44 |
37 |
-0 |
-0 |
-0 |
-D |
-0 |
-0 |
-0 |
-o |
|
70 |
•5 |
-0 |
-0 |
75 |
09 |
-0 |
-0 |
-0 |
-o |
|
65 |
-0 |
15 |
-0 |
37 |
B2 |
-0 |
-0 |
-0 |
-0 |
|
•5 |
-0 |
22 |
60 |
B5 |
-0 |
-0 |
-0 |
-0 |
*0 |
|
52 |
-o |
10 |
-0 |
5* |
-0 |
-0 |
-0 |
-0 |
-0 |
|
-0 |
I |
0 |
-0 |
-0 |
I |
-0 |
-0 |
-0 |
-0 |
0
1
0
0
1
1
0
-0
2
I
1
-0
-0
-o
-0
-0
-0
-0
-0
-0
2
1
-0
-0
-0
-0
1
2
-0
-0
-0
0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
0
-0
-0
-0
-i>
-0
-0
NOTE. -0 OENOTES NO PRODUCTION. 0 OENOTES THAT ZERO* IS THE GRAOE BEING MANUFACTURED
-0
-0
-0
-0
-o
-0
-0
-0
0
ERIC
G±
(LUSTRATION t. CONTINUED.
|
COMPANY |
1 |
INTOP |
- UNIVERSITY OF |
CHICAGO |
PEKluO 6 |
|||||||||
|
MAR RE 1 |
research |
2 |
. AREA |
l |
AREA |
2 |
AREA |
3 |
||||||
|
PROOUCT |
X |
PROOUCT |
Y |
PRD0OC1 |
X |
PROOUCT |
Y |
PROOUCT |
X |
PRODUCT |
Y |
|||
|
SALES THIS OUAATCAIOOO) |
STD. |
on. |
STD. 1 |
DEL. |
STO. |
DEL. |
SID. |
DEL. |
SID. |
DEL. |
STO. |
DEL. |
||
|
COMPANY |
NUMBER |
1 |
20.0 |
0.0 |
10.9 |
0.0 |
15.8 |
0.0 |
20. B |
D.O |
9.0 |
D.O |
0.0 |
0.0 |
|
COMPANY |
NUMBER |
2 |
10.6 |
0.0 |
22.2 |
0.0 |
1 7.0 |
0.0 |
28. 0 |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
|
company |
NUMBER |
3 |
17.1 |
0.0 |
0.0 |
0.0 |
16.7 |
0.0 |
20.0 |
0.0 |
7.1 |
0.0 |
0.0 |
0.0 |
|
company |
NUMBER |
4 |
0.0 |
0.0 |
7.0 |
37.5 |
0.0 |
0.0 |
19.9 |
0.0 |
0.0 |
D.O |
0.0 |
0.0 |
|
company |
NUMBER |
5 |
34.9 |
0.0 |
35.7 |
24.4 |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
|
company |
number |
6 |
.9 |
0.0 |
6.7 |
6.0 |
0.0 |
0.0 |
4.6 |
6.5 |
0.0 |
0.0 |
0.0 |
0.0 |
|
Company |
number |
7 |
IS. 9 |
0.0 |
12.3 |
0.0 |
7.6 |
0.0 |
22.9 |
5.4 |
0.0 |
0.0 |
0.0 |
0.0 |
|
COMPANY |
number |
B |
1.3 |
0.0 |
5.4 |
0.0 |
18.2 |
0.0 |
R.2 |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
|
COMPANY |
number |
9 |
35.9 |
D.O |
28. 5 |
0.0 |
U.9 |
0.0 |
26.0 |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
|
TOTAL SALES ( 000 ) |
144.6 |
0.0 |
137.3 |
67.8 |
90.2 |
0.0 |
150.3 |
11.9 |
16.1 |
0.0 |
0.0 |
0.0 |
quarter of business operations) • The role of the instructor is to visit each team and, aided by managerial accounting data and statistics (to be explained later) froii all previous quarters of company operations, to prod and question each regarding analyses, strategies, tactics and specific decisions for reacting previously established company objectives. The instructor, of coarse, aids companies having specific questions and/or any difficulties with analyses they should be able to do at any given tine during the semester. The open class session also provides a convenient tiae for companies to negotiate all types of inter-coapan y deals including industrial product sales, product licensing, leasing of facilities and services, etc. INTOP has sufficient flexibility to accoaaodate practically any intercompany transaction imaginable.
The other weekly session is aore traditional, being devoted to instruction. The subject Batter includes planning, controlling and the decision-making process. Considerable tiae is devoted to bringing the functional areas of aanageaent into focus, and integrating then with the operational decision- making taught in aarketing, production and finance. A skeletal course outline is shown in Illustraiton 2. The topical presentation order in Welsch[9] is extremely complementary to the developaent of the lecture schedule and the sioulation.
The first two to three weeks of the course are involved with explanation of the INTOP environment, learning of the specific rales and development of philosophy, objectives and organizational structure by each conpany. The fourth week the first round of decisions is due and then one round of decisions is due each week thereafter until a total of 12 quarters (J years) of operations have been simulated. (Actually only 10 sets of decisions are completed;; the first set of decisions is for three quarters of operations. It takes two quarters to build production facilities and one quarter to aanufacture products, so product aarket interaction is not begun until the fourth quarter.)
Coanenciog with the first lecture on planning and control, a second conputer program is processed with INTOP. The introduction of this sunaary analysis[5] is unique to ganing and has so enhanced the course that it warrants specific discussion. The program is run in conjunction with the INTOP program and subsequent to it; saaple output is shown in Illustration 3. The instructor gets a copy of the suamary analysis for all teams and each teaa receives a copy pertaining to its operations, linus the sumaary rankings; these are on the instructor's copy only. The program solves two problems. First, in order for companies to make the aost intelligible, rational, objective INTOP decisions, it is necessary for them to generate a aass of aanagerial accounting data, in addition to the ancillary data that is a part of the regular IMTOP output. The generation of these data required students to engage in busy work that (1) did not enhance their learning and (2), in fact, limited even further the amount of tine available for true decision-making. In addition, the logical argument was forwarded that in the "real" world, managerial data would be systeaatically provided on a timely basis by the accounting department of the company. Note the wealth of detailed sales, production, inventory, financial and cost accounting inforaation arranged by geographical area in the sumaary analysis. This type of information measurably enhances managerial decison- making. The second problea was concerned with the systematic and periodic analysis of each teal's progress and problems. The aaount of INTOP output generated weekly by a nine team section of Simulation of Business is voluminous. In order for the instructor to provide a meaningful critique for each team during the open session, the analysis of the output by hand was jast too burdensome. The output format of the summary analysis is so arranged that the instructor can easily trace performance of a teaa in any particular aspect of the simulation by just reading across the appropriate page and line(s). Teams are required to submit forecasts by geographical area of sales, cash, production costs and BOI (return on investaent). The weekly forecasts, first described as a written assignment for week five in Illustration 2, are required for every quarter of simulated operations. Any resulting high forecast errors tend to flag, automatically, problems that a team is having with particular aspects of the simulation. Armed with summary statistics, forecast errors, relative rankings and a complete historical summary of each company's operations, the instructor efficiently prepares for his conference with each team during the open session. Problea areas are quickly uncovered so that therapy aay begin.
A secondary benefit resulting from requiring each team to make quarterly forecasts should be aentioned. The benefit is tiat guessing is practically eliminated. If a particular forecast of a team is in serious error, the first thing the instructor asks the team during the open session is to review with him the particular analysis that produced the forecast. Having none
ILLUSTRATIO:; 2.
Business Simulation Course I.VTOP Related Lecture Schedule
!-'cck
1-2
3
4
5
6
7
8
9
10
11
12
13
14-15
Topics
Business Philosophy and Objectives
Organizational Structure
development of Specific Coals and Strategies
Sales Planning and Control; Forecasting
Production and Inventory Planning
Planning Expenses-*?!anuf acturing Overhead, Distribution and Administrative Expenses
Planning and Controlling Cash, Dividend Policy
Planning and Controlling Capital Expenditures
Development of the Annual Profit Plan
Cos t -Volume-Prof it Analysis
Variance Analysis
Demand Analysis and Price Setting
Company Audits
Assignment
Company Philosophy and Objectives
Company Organizational Chart and Individual Job Descriptions
Company Goals and Strategies
Forecast of Sales, Variable Costs, Net Darnings , Cash and KOI for each Quarter of Operations
Formal Proposal for a Major Capital Expenditure
Annual Profit Plan for Next Year of Operations
Cos t-Volune-Prof it Analysis Supporting an INTOP Decision
Variance Analysis of One Marketing Area
Demand Analysis for One Product in One Market Area
Oral Presentation of Audits
proves to be very embarrassing* Also, in order to do an acceptable job of forecasting, teaas ■ust engage in a systematic analysis of the variables that impact on the particular variable to be forecast*
The topics covered in wmeks six through twelve are traditional and should need no farther explanation here* Of course, the point to reiterate is that each, of these topics is suppieaentary to the simulation and is presented as just another aid to improve the decision- making that each company is required to do*
The topic of demand analysis in week thirteen does warrant specific discussion* 1 think many business students, as a result of their classroom training, are convinced that the concept of a demand curve is one of those theoretical constructs which does not really have any practical value in aiding business decision-making* By week thirteen teams have generated sufficient data to plot a demand curve which is very aesthetically appealing in terms of fit* It is a real joy to watch students rediscover (or discover) one of the basic principles of economics and to determine that the principle is applicable to the simulated world in which they have been operating (which by this time in the semester is as real to the students as if they were running 6(1 or IBS).
The last topic, company audits, also deserves comment* At the completion of three years of simulated operations, each company's records are turned over to an auditor (which is, in reality, one of the other companies) • Records include, in addition to the standard financial reports produced as part of the INTOP output, reguired charts, graphs and brief narratives of salient discussion points covered prior to each decision* The auditing company is asked to do a complete audit in terms of management, finance, production, etc*, culminating in a 15-20 minute oral presentation* Given the benefit of hindsight and a semester's practice at decision-making, an auditing team quickly flags the "boners'* and the quality decision-making of the audited company* To insure that students never forget for a moment the need to plan for the future, each auditing team is asked to make a minimum of three specific major recommendations to the future management of the audited company*
£££&as
The team being the basic decison unit (rather than the individual) is reinforced in the grading schema for the Simulation course; overall team performance accounts for 40 percent of the course grade* The paramount danger here, as with most simulations, is to reward intuitive behavior too generously* The rewards should go to the teams mastering sound management principles, prescribed analyses, etc* But, on the other hand, those teams that practice these principles and analyses and combine them with intuition, yielding a superior strategy, should also be rewarded* I will not argue further as to whether it is "how you play the game** or "whether you win or lose" that is important in terms of learning* Personally, 1 mix the two in equal proportion* One-half of the 40 percent is based upon INTOP written assignments - development of team philosophy, objectives, strategies, goals, analyses, sound forecasting methods, etc* Each visitation during the open session has been institutionalized via a simple summary performance sheet on which the instructor evaluates the quality of decision-making
during the last quarter of operations* The other one-half of the team grade is based upon team
performance vis-a-vis other teams* This is a particularly difficult grade to quantify because (1) it is fraught with all the perils that real companies have in quantitatively measuring performance and (2) the instructor needs to maintain consistency from one semester to the next* For example, does one utilize return on sales, return on investment or return on total assets as the quantitative measure of performance[ 1 )? Also, how does one guard agaiast the possibility of the "last place" team this semester being "better" than the "first place" team the semester before? If the same aggregate profit potential were generated each semester by the simulated environment, then objective measures of level of performance could be ascertained after a couple semesters* In INTOP, the economic environment is changed every semester to (1) prevent previous class notes on INTOP being of any value and (2) to emulate a recent period of economic activity to gain even more realism* Each environment has a different aggregate profit potential that is
really not measurable, a priori. In an attempt to negate some of these problems, I use the
following grading procedure for~this portion of team performance:
1. Rank teams according to the sum of their retained earnings and paid in capital as of period 12* This is a measure of each team's leadership position in the industry, based upon results to date*
2* Bank teams according to their average return on capital over quarters 4-12* This is a measure of each team's efficiency in utilization of capital, regardless of source or how much they use*
3* Bank teams in their average plant and equipment investment over quarters 8-11* This is a measure of each team's potential ability to do competitive battle in the future*
4* Take the 80th percentile team (iu terms of number of teams particpating) and assign the team with that ranking a 100 percent rating* Calculate the
64
H LUST RAT If IN 3. SAMPlF INTDP ANALYSIS REPORT - I MO I A NA UNIVERSITY STHOPI HE BUSINESS - COMPANY 2. r
PTR 1 UTR ? OTR 3
********* AR£A 1 (US)
EC ON
index x
SALES X STP-ORD
consumer
pricf
OTHER PRICF T I ! T A L FORECAST PC T ERROR SALES X t'LX-GRD CONSUMER PRICE FORECAST PC T ERROR
For FAC.M A UP 1 T 1 ( iNA L OUARTt0 OF S I M ( i L A T E 0 (IP E P A T I PN S ANOTHER COLUMN (IF PAT A IS APOFP TO THE RIGHT HAI\lu
si of of this repupt. note
THE FASF WITH WHICH THE PWllGRFSS HE THE COMPANY MAY RF FOLLOWED.
prupuct y = pad j us
PRUPl'CT Y = VACUUM CLFANERS
|
OTR 4 |
OTR 5 |
|
] .06 |
1 .07 |
|
0 |
n |
|
1 ft?n 3 |
1 ft 98 5 |
|
?4 |
2 5 |
|
n |
0 |
|
n |
0 |
|
1 h?o 3 |
1 ft9ft5 |
|
1 6000 |
] soon |
|
13.77 |
1 3 . 2 3 |
OTR 6
I .0?
0
1 057? •*? 6000 I ft 5 7 2 1 ft 5 7? I o ooo -1? .7P I
642ft
^5
l*non
- 5 9 . P 4
EC On I NO EX Y
sales Y STP-GRI) CONSUMER PRICF FURECAST PC T EPROR
AOVFPT I S INC
PRoour.i x
PRODUCT Y
SALES OFFICES C AND A COSTS
X actual
X OPTIMAL
Y ACTUAL
Y OPTIMAL
AVG COG SOLO X STO OR 0
X olx-grd
Y STO-GRO
MFTHOUS I \* PRI IVFM FNT PRODUCT X PRODUCT '
|
.03 |
.97 |
• q 1 |
|
n |
0 |
n |
|
3i noo* |
30 50 P |
2 P90P |
|
43 |
45 |
4 4 |
|
2 9000 |
2 900 0 |
20500 |
|
6.90 |
5 . ?0 |
P . 1 6 |
|
?]ono |
? 1 non |
? 1 non |
|
31 000 |
3onnn |
2 0 00 0 |
|
0 |
n |
2 |
|
3 .30 |
3 .30 |
3 .30 |
|
? .P6 |
2 .8 5 |
2 • P 5 |
|
4 .00 |
4 |