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A study of computer-assisted instructional strategies and learner characteristics Kaufman, David M. 1973

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A STUDY OF COMPUTER-ASSISTED INSTRUCTIONAL STRATEGIES AND LEARNER CHARACTERISTICS  by  DAVID M. KAUFMAN M.Eng., M c G i l l U n i v e r s i t y ,  1970  A DISSERTATION SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF EDUCATION  i n the F a c u l t y ot  Graduate  Studies  We accept t h i s d i s s e r t a t i o n as conforming to the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA October, 1973  In presenting  this thesis i n p a r t i a l fulfilment of the requirements for  an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t freely available for reference  and  study.  I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may by his representatives.  be granted by the Head of my Department or  It i s understood that copying or publication  of this thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission.  Department of  €-t) U C^ATt  The University of B r i t i s h Columbia Vancouver 8, Canada  Date  Oct.  /f/ZJ?  ii  A STUDY OF  COMPUTER-ASSISTED INSTRUCTIONAL  STRATEGIES AND  Supervisor:  Dr.  LEARNER CHARACTERISTICS  David R o b i t a i l l e  ABSTRACT  T h i s study was  undertaken to i n v e s t i g a t e  c o m p u t e r - a s s i s t e d i n s t r u c t i o n as laboratory.  The  d e f i n e d as an for  concept of an  an  of  instructional  instructional logic  a l g o r i t h m f o l l o w e d by  each i n s t r u c t i o n a l u n i t .  the use  the  was  computer program  This step-by-step l o g i c  repeated f o r each i n s t r u c t i o n a l u n i t  but  was  with d i f f e r e n t  content. T h i s procedure p e r m i t t e d the of  the  variable  correctional  of c o r r e c t i o n a l  c o n t r o l l e d manipulation  feedback.  feedback were d e f i n e d by  i n f o r m a t i o n content of  the feedback.  sensitive  feedback,  correctional  correctional that  the  answer was  The learner  .feedback and  no  T h i e e forms of  varying  the  These were response-  response-insensitive  correctional  feedback  (only  incorrect).  i n t e r a c t i o n of c o r r e c t i o n a l  c h a r a c t e r i s t i c s was  feedback with  examined as ' v ^ l l ,  t r a i t s were mathematical a b i l i t y ,  prerequisite  These  selected learner  knowledge  »  iii and  state anxiety.  i t s i n t e r a c t i o n with  The  effect  of c o r r e c t i o n a l feedback  these v a r i a b l e s was  and  examined.  S u b j e c t s of the study were a r e p r e s e n t a t i v e sample o f s i x t y - t h r e e p r e s e r v i c e elementary  s c h o o l t e a c h e r s from  f i v e s e c t i o n s of a mathematics course given i n a l a r g e education f a c u l t y .  These s u b j e c t s were randomly a s s i g n e d to  the three treatment  c o n d i t i o n s , although  CAI  experimental  The  t e s t of mathematical a b i l i t y used was  they s e l e c t e d the  p e r i o d s i n which they would p a r t i c i p a t e . the  Cooperative  S e q u e n t i a l T e s t of E d u c a t i o n a l P r o g r e s s , Mathematics Form 2A  (STEP).  The  s t a t e a n x i e t y instrument  S t a t e - T r a i t Anxiety  Inventory  form used by O ' N e i l  (1972) was  e i g h t e e n item p o s t t e s t was and  (STAI) and  used was  the f i v e iteir short  administered  twice.  c o n s t r u c t e d by the  The  experimenter  the measure of p r e r e q u i s i t e knowledge used was  item p r e l e s s o n with a p o s s i b l e mark of 0,  the  a nine  I or 2 on each  item. The  mathematics l e s s o n was  c a l c u l u s d e a l i n g with the concept was  a topic i n introductory of d e r i v a t i v e .  t r e a t e d from a p h y s i c a l p o i n t of view, u s i n g  o f d i s t a n c e , speed and time concepts.  The  to i l l u s t r a t e  The  topic  concepts  the mathematical  main o b j e c t i v e s were to show that the  d e r i v a t i v e i s a l i m i t and  to show how  to use  this  limit  d e f i n i t i o n to c a l c u l a t e the d e r i v a t i v e of a f u n c t i o n a t a point.  iv  The CAI  l e s s o n was programmed using an author language  developed by the experimenter as a v e h i c l e the  instructional  feedback. advantage  The  l o g i c and v a r y i n g  language i s l i m i t e d  of r e q u i r i n g  essentially  an i n s t r u c t i o n a l d e s i g n e r . language as implemented is  the c o s t ,  the  correctional  i n use but has the no computer  e x p e r i e n c e of  The main l i m i t a t i o n o f the  at the U n i v e r s i t y  which l i m i t e d  f o r implementing  the sample  of B r i t i s h  Columbia  size i n this  experiment. The r e s u l t s  of the study were g e n e r a l l y  i n the  expected d i r e c t i o n but the e f f e c t s were not as pronounced as had been h y p o t h e s i z e d .  The most important f i n d i n g  the  i n proportion of errors  significant difference  main l e s s o n between the r e s p o n s e - i n s e n s i t i v e correctional f i n d i n g was  feedback  ( T 3 ) groups.  learning  w i t h the e f f e c t of l e a r n e r statistically  importance of t h i s  and p r o p o r t i o n of  statistically  other v a r i a b l e s .  as w e l l .  errors  removed. i n predicting  the experiment was mathematical a b i l i t y  in predicting  relationship  t r a i t s and treatment e f f e c t s  The most e f f e c t i v e v a r i a b l e  was  on the  {T^) and no  then i n c r e a s e d by the s i g n i f i c a n t  found between immediate  in  The  was  controlled  and i t s e f f e c t  when t e ^ t i n a the e f f e c t  prerequisite  knowledge was  performance and was  S t a t e a n x i e t y was  performance  of the  a l s c important  statistically  controlled  significant in predicting  V proportion  of e r r o r s but not response l a t e n c y .  significant for posttest The  treatment-by-A-State i n t e r a c t i o n s and f o r response  However, were observed  latency.  three treatment groups d i f f e r e d i n the expected  d i r e c t i o n on most of the important v a r i a b l e s  but the  differences  were not s t a t i s t i c a l l y  significant.  particular,  the A - S t a t e l e v e l s f o r the three groups were  o r d e r e d as expected, but the d i f f e r e n c e s enough to cause the h y p o t h e s i z e d The  In  were not l a r g e  interactions.  r e s u l t s of the study p a r t i a l l y  supported the  h y p o t h e s i s of the important r o l e of c o r r e c t i o n a l  feedback  i n i n s t r u c t i o n and i t s i n t e r a c t i o n with i n d i v i d u a l of  the l e a r n e r . Finally,  and  traits  the v a r i a b l e  of s t a t e  a n x i e t y was examined  i t was found that higher l e v e l s of s t a t e a n x i e t y l e d to  longer response l a t e n c i e s .  Also,  state anxiety  when no c o r r e c t i o n a l feedback was p r o v i d e d  increased  to the students  as w e l l as when the content became more d i f f i c u l t .  This  f i n d i n g confirmed the expected r e l a t i o n s h i p between s t a t e a n x i e t y and task  difficulty.  ACKNOWLEDGEMENT S  I wish t o express my s i n c e r e s t following  thanks  to the  people:  Dr. D a v i d R o b i t a i l l e , f o r h i s p e r s o n a l and p r o f e s s i o n a l guidance and without whom t h i s would not have been  produced.  Dr. Robert Conry, guidance  dissertation  f o r h i s p e r s o n a l and p r o f e s s i o n a l  throughout my d o c t o r a l programme.  Dr. J . S h e r r i l l , Dr. J . Kennedy and Dr.  S.S. Lee,  members o f the d i s s e r t a t i o n committee, f o r t h e i r  extra  efforts  this  i n making i t p o s s i b l e f o r me to complete  d i s s e r t a t i o n on time.  Mrs.  M e l l e t t , from the F a c u l t y o f Graduate  Studies,  f o r her e f f o r t s above and beyond the c a l l of duty. K a t h e r i n e Li-dderdale, f o r her e f f o r t s i n t y p i n g , p r o o f r e a d i n g , e d i t i n g and p r e p a r i n g c o p i e s o f t h i s d i s s e r t a t i o n under g r e a t p r e s s u r e o f time.  B r i n a A r o n o v i t c h , f o r h e l p i n g to prepare the f i r s t d r a f t o f t h i s d i s s e r t a t i o n under g r e a t p r e s s u r e o f time.  Others, Education,  too numerous to mention i n the F a c u l t y  who p r o v i d e d a d v i c e , a s s i s t a n c e and comput  time whenever i t was needed.  P a t r i c i a , f o r understanding difficult  periods.  d u r i n g the more  viii  TABLE OF CONTENTS  Page ACKNOWLEDGEMENTS  :vi  LIST OF TABLES  xi-  LIST OF FIGURES  *ii.„  Chapter I.  THE PROBLEM Overview of the Problem I n t r o d u c t i o n t o CAI O r g a n i z a t i o n a l Scheme f o r CAI D i s c u s s i o n o f the Problem Statement o f the Problem Research Q u e s t i o n s Importance of the Study  II.  . . . .  1 3 7 11 18 19 21  REVIEW OF RELATED LITERATURE AND RESEARCH HYPOTHESES Introduction L i t e r a t u r e on Knowledge of R e s u l t s . . Summary L i t e r a t u r e on S t a t e - T r a i t A n x i e t y . . Summary L i t e r a t u r e on Aptitude-Treatment Interactions . . . . Summary ' L i t e r a t u r e on T u t o r i a l Computer Assisted Instruction . Summary Summary o f Research Hypotheses . . .  . .  .  .  23 23 36 40 44 46 52 52 67 67  ix  Chapter III.  Page METHOD Subjects E x p e r i m e n t a l Procedure Design I n s t r u c t i o n a l Logic f o r Prelesson I n s t r u c t i o n a l L o g i c f o r Main Lesson O p e r a t i o n a l D e f i n i t i o n of Treatments CAI Author Language Instructional Materials Measurement Instruments Posttest Mathematical A b i l i t y T e s t S t a t e - T r a i t A n x i e t y Inventory Prelesson Main Lesson  IV.  • • • • • •  70 71 72 74 77 79 80 80 88 88 90 91 92 93  . . . • • . . . • • • • • • . . . . . .  ANALYSIS AND RESULTS Method o f A n a l y s i s . • • 95 R e s u l t s o f Analysis-Means 97 R e s u l t s of A n a l y s i s - Hypothesis T e s t i n g . . . 100 P o s t t e s t (Y ) 101 Proportion of Errors ) 105 Average Latency (Y3) 107 R e l a t i o n s h i p Between P r o c e s s and Product . . 110 R e s u l t s o f Post hoc A n a l y s i s 115 Summary of S t a t i s t i c a l R e s u l t s 126 ±  V.  DISCUSSION AND CONCLUSIONS Summary of Study -*--Discussion of Findings C o r r e c t i o n a l Feedback 135 A-State Mathematical A b i l i t y P r e r e q u i s i t e Knowledge . . . . 139 R e l a t i o n s h i p Between P r o c e s s and Product • • 140 Post hoc A n a l y s i s R e s u l t s 14 L 3 1  1  3  5  1  3  6  1  3  9  X  Page APPENDICES Appendix A - Users Guide f o r CAI Author Language  156  Appendix B - Users Guide f o r P r e l e s s o n Language  170  Appendix C - CAI P r e l e s s o n L i s t i n g  . . . .  Appendix D - CAI Main Lesson L i s t i n g (versions ]_ > » ) • • • Appendix E - L i s t i n g f o r One CAI Student T  T  T  2  Session  178  1  8  8  3  . .  Appendix F - P o s t t e s t Appendix G - S t a t e - T r a i t A n x i e t y Inventory Appendix H - T a b l e s of C o r r e l a t i o n Coefficients . . . . . . . .  218 227  237 .240  xi  LIST OF TABLES  Table  Page  1.  Experimental  2.  P r e r e q u i s i t e s f o r Main Lesson  3.  I n s t r u c t i o n a l O b j e c t i v e s f o r Main Lesson  4.  P o s t t e s t Data  5.  Item A n a l y s i s I n f o r m a t i o n  6.  A n x i e t y Test Data  92  7.  P r e l e s s o n Data  92  8.  Item A n a l y s i s I n f o r m a t i o n  9.  Main Lesson Data  94  Means of V a r i a b l e s f o r Combined Groups and for T, T, T  99  10.  ±  2  Procedures  71 84 ...  86 88  for Posttest  for Prelesson  . . . .  . . . .  3  89  93  11.  Symbols Used i n S t a t i s t i c a l A n a l y s i s  100  12.  R e s u l t s of R e g r e s s i o n A n a l y s i s f o r P o s t t e s t . .  102  13.  R e s u l t s of R e g r e s s i o n A n a l y s i s f o r P r o p o r t i o n of E r r o r s  105  R e s u l t s of R e g r e s s i o n Latency . . . ,  108  14. 15.  16.  A n a l y s i s f o r Average  R e s u l t s of R e g r e s s i o n A n a l y s i s f o r Five  Hypothesis I l l  Average Number of Responses i n Each Response C l a s s f o r Main Lesson  125  17.  I n t e r c o r r e l a t i o n M a t r i x f o r Combined Groups . .  241  18.  Comparison of S e l e c t e d C o r r e l a t i o n C o e f f i c i e n t s for T , T , T .  242  1  2  3  zii  LIST OF FIGURES  Figure  Page  1.  O r g a n i z a t i o n a l Scheme f o r CAI  8  2.  Prelesson  75  3.  Main Lesson I n s t r u c t i o n a l L o g i c  76  4.  D e t a i l e d View of P r e l e s s o n  83  5.  D e t a i l e d View o f Main Lesson  87  6.  R e g r e s s i o n L i n e s of P o s t t e s t and Main Lesson A-State f o r T , T , T  113  R e g r e s s i o n L i n e s of Main Lesson Latency and A-State f o r T T , T . . .  114  Graph o f E r r o r s on I n s t r u c t i o n a l U n i t s f o r Combined Groups  119  Graph o f E r r o r s on I n s t r u c t i o n a l U n i t s f o r T T , T  120  Graph o f L a t e n c i e s on I n s t r u c t i o n a l U n i t s for T , T , T  123  Graph of A - S t a t e  124  I n s t r u c t i o n a l Logic  1  7.  2  1 ?  8.  9.  l f  10.  2  1  11.  2  3  3  3  2  3  L e v e l s During  Experiment . . . .  CHAPTER I  THE PROBLEM  Overview of the Problem One g o a l of t h i s study  was to develop a methodology  which would demonstrate the power of u t i l i z i n g  a computer  to a s s i s t i n the development o f models f o r i n s t r u c t i o n . T h i s methodology was developed i n the context computer  acting  as p e r s o n a l  By u s i n g the computer  tutor f o r i n d i v i d u a l  T h i s l a b o r a t o r y p e r m i t t e d the  g a t h e r i n g o f r e l i a b l e and v a l i d d a t a under  having  and r e p l i c a b l e  The major goal o f t h i s study methodology to a r e s e a r c h  of c o r r e c t i o n a l Several these  was to apply the  which would make a theory.  problem was examined:  feedback i n the i n s t r u c t i o n a l  First,  A' the r o l e  process.  steps were i n v o l v e d i n the attainment  two g o a l s .  A computer  study  materials  to the students.  to the a r e a o f i n s t r u c t i o n a l  particularly controversial  carefully  c o n d i t i o n s , using  some e d u c a t i o n a l s i g n i f i c a n c e  contribution  students.  i n t h i s manner, a l a b o r a t o r y to study  i n s t r u c t i o n was c r e a t e d .  controlled  of the  of  the methodology was developed.  language was w r i t t e n by the experimenter to  2 implement lessons  a p a r t i c u l a r i n s t r u c t i o n a l l o g i c which p e r m i t t e d  to be programmed f o r the computer  computer u s e r s .  by novice  The language implemented a p a r t i c u l a r l y  f l e x i b l e teaching  l o g i c which was f o l l o w e d  many times d u r i n g  an i n s t r u c t i o n a l s e s s i o n .  step involved dealing  the development  by the computer The second  o f a teaching  unit  with a t o p i c i n elementary c a l c u l u s .  i s presently  (lesson)  This  unit  being used i n an a l t e r e d form as a t u t o r i a l  a i d by c o l l e g e  students i n an i n t r o d u c t o r y  physics  course  (Kalman et. a l . , 1972). The t h i r d organizational using  step c o n s i s t e d  scheme f o r studying  the above methodology.  organizational  of d e v e l o p i n g an the i n s t r u c t i o n a l p r o c e s s  Several  scheme were examined.  variables These  i n the  variables  r e f l e c t e d some u n r e s o l v e d nroblems i n the l i t e r a t u r e on instruction. learning  The e f f e c t of c o r r e c t i o n a l feedback on  was a s s e s s e d by m a n i p u l a t i n g t h i s v a r i a b l e i n a  c o n t r o l l e d experiment. feedback and s e l e c t e d examined.  The i n t e r a c t i o n of c o r r e c t i o n a l l e a r n e r c h a r a c t e r i s t i c s v/as a l s o  The use o f the computer  p e r m i t t e d the v a r i a b l e  of c o r r e c t i o n a l feedback to be examined under conditions  and p r o v i d e d data to c l a r i f y  v a r i a b l e on l e a r n i n g .  controlled  the e f f e c t s of t h i s  3  A l t h o u g h the experiment f o c u s e d on a p a r t i c u l a r aspect of the i n s t r u c t i o n a l p r o c e s s , the methodology that was developed c o u l d be used by others to examine other v a r i a b l e s of i n t e r e s t i n the o r g a n i z a t i o n a l scheme.  I n t r o d u c t i o n to CAI The term c o m p u t e r - a s s i s t e d i n s t r u c t i o n d e s c r i b e s an i n s t r u c t i o n a l  (CAI)  s i t u a t i o n where a student  at a t e r m i n a l connected e l e c t r o n i c a l l y  works  to a computer.  i n s t r u c t i o n a l program i s s t o r e d i n the computer.  An  The  program comprises the complete package of i n f o r m a t i o n , i n s t r u c t i o n s and l o g i c with which the student w i l l during h i s learning session. the i n t e r f a c e between  interact  The t e r m i n a l , which s e r v e s as  the computer  and the student,  usually  c o n s i s t s of a t y p e w r i t e r keyboard and e i t h e r a paper r o l l of T V - l i k e screen, c a l l e d a cathode-ray tube, upon which the communications to and from the computer are d i s p l a y e d . In order to have CAI, the computer must a c t u a l l y  instruct  the student through the program and net j u s t be used as a t o o l to a s s i s t  i n the s o l u t i o n of problems or the r e t r i e v a l  of i n f o r m a t i o n . human-to-computer  By d e f i n i t i o n ,  there must be two-way  communication i n which t h e r e occurs a  stimuxus-response-feedback r e l a t i o n s h i p p r o d u c i n g (Silvern,  1967).  learning  4  Atkinson  (1968a) commented t h a t i n recent years  great number of a r t i c l e s and CAI  has been p u b l i s h e d .  He  a  news r e l e a s e s d e a l i n g with observed  that few  r e p o r t s a r e based on s u b s t a n t i a l e x p e r i e n c e  of such  and  research,  but that the m a j o r i t y c o n s i s t of vague s p e c u l a t i o n s and c o n j e c t u r e s with  little,  i f any,  d a t a or r e a l  to s u b s t a n t i a t e the c l a i m s f o r CAI. that, with few  exceptions,  findings. of m a t u r i t y  He  o f what a p a r t i c u l a r  that CAI  has not reached  Some r e c e n t CAI  work i n the l a s t  i n d i c a t e s that t h i s s i t u a t i o n i s changing  Tobias,  Keats and Hansen, 1972;  an two  (e.g. Judd  O ' N e i l , 1972b;  1973).  Suppes (1966) d i s t i n g u i s h e d t h r e e l e v e l s i n t e r a c t i o n between the student At  the k i n d  t h a t programmed l e a r n i n g has a t t a i n e d as  et a l . , 1973;  CAI  or short statements o f r e s e a r c h  a l s o noted  a r e a of endeavor. years  (1967) noted  a v a i l a b l e i n f o r m a t i o n about  c o n s i s t s o f d e s c r i p t i v e accounts i n s t i t u t i o n i s doing,  Bundy  experience  and  of  the computer program.  the most s u p e r f i c i a l , and a l s o the most economical  level,  are d r i l l - a n d - p r a c t i c e systems.  the student  i s presented  p r a c t i c e , and  d r i l l e d on  respond c o r r e c t l y  At. t h i s  level,  w i t h examples on which he needs those  to which he f a i l s  (Suydam, 1969).  to  I n s t r u c t i o n a l programs  that f a l l under t h i s heading  are merely supplements to  a r e g u l a r c u r r i c u l u m taught by a t e a c h e r . The  next  l e v e l of i n t e r a c t i o n  includes t u t o r i a l  systems which a r e more complex than d r i 1 1 - a n d - p r a c t i c e systems.  The computer-teacher i n i t i a t e s the q u e s t i o n ,  f o r which answers are s t o r e d i n advance and a r e s t r i c t e d k i n d o f d i a l o g u e between the student achieved.  Suppes (1966) c l a i m s t h a t the aim here  individualize many classroom  instruction  and t o f r e e  h i s own i n s t r u c t i o n a l  At the t h i r d and deepest interaction  systems e x i s t  computer w i l l  writing  (Suppes, 1966).  o n l y as rudimentary  prototypes.  can be a c h i e v e d , the  r e q u i r e the c a p a b i l i t y  of interpreting  any  and q u e s t i o n g i v e n by the student, e i t h e r i n or o r a l l y .  A search of the l i t e r a t u r e i n d i c a t e d are three major arguments used i n support are not independent c f one another, indicate  efforts.  a r e systems that a l l o w a complex d i a l o g u e  t h i s l e v e l of i n t e r a c t i o n  response  have  l e v e l o f student-computer  between the student and the computer  Before  i s to  the teacher from  r e s p o n s i b i l i t i e s so that he w i l l  more time to i n d i v i d u a l i z e  Dialogue  and the computer i s  that there o f CAI.  These  but they do serve to  the major views o f CAI which are c u r r e n t l y  prevalent.'  The f i r s t  argument i n support  o f CAI i s that  6 CAI  i s a medium used t o i n d i v i d u a l i z e i n s t r u c t i o n .  Suppes (1966) claimed  that t h i s i s the s i n g l e most  important a p p l i c a t i o n o f CAI. p r i n c i p a l obstacles  He wrote that the  to widespread implementation o f CAI  are not t e c h n o l o g i c a l but p e d a g o g i c a l :  how to devise  means o f i n d i v i d u a l i z i n g i n s t r u c t i o n and how to design a curriculum  that i s s u i t e d to i n d i v i d u a l s i n s t e a d o f  groups. Many r e s e a r c h e r s Seidel,  (Atkinson,  1968b; Bundy, 1967;  1969; Stolurow, 1962) have claimed  a p p l i c a t i o n o f CAI p r o v i d e s to e d u c a t i o n . a laboratory  that a second  the most v a l u a b l e  These w r i t e r s r e f e r t o the use of CAI as f o r research  i n l e a r n i n g and i n s t r u c t i o n .  With the computer, i t i s p o s s i b l e t o be q u i t e about a t e a c h i n g  explicit  method and to reproduce the c o n d i t i o n s  as o f t e n as d e s i r e d . the  contribution  Added t o t h i s i s the c a p a b i l i t y of  computer f o r s t o r i n g and m a n i p u l a t i n g d a t a .  can be used by the r e s e a r c h e r  The d a t a  t o modify the p r e s e n t a t i o n  i n p r o g r e s s and the d a t a can be manipulated l a t e r i n many different  ways t o p r o v i d e  v a r i a b l e s under study.  information  about the i n s t r u c t i o n a l  V a r i a b l e s such as e r r o r s i n l e a r n i n g ,  response l a t e n c y and e f f e c t i v e n e s s of d i a g n o s t i c can be examined i n d e t a i l . (1968c) p r e d i c t e d  Stolurow  materials  (1962) and A t k i n s o n  that the computer w i l l c o n t r i b u t e  to the  emergence of one or more t h e o r i e s o f i n s t r u c t i o n supported by r e l i a b l e and v a l i d d a t a . A t h i r d argument used to support CAI i s that i t i s a medium which can change the r o l e of the teacher and the school environment. extent f o r d i r e c t  Computers have been used to a l i m i t e d  i n s t r u c t i o n i n a few s e l e c t e d s c h o o l s i n  the U n i t e d S t a t e s of America 1970;  Suppes,  1966).  (Atkinson,  Stansfield  1968d;  Pressman,  (1968) c a u t i o n e d that  CAI  i s not ready f o r the s c h o o l s and that the s c h o o l s are not ready f o r CAI.  H i c k s and Hunka (1972) made the f o l l o w i n g  assumptions about  CAI:  Assumption I. C o m p u t e r - a s s i s t e d i n s t r u c t i o n w i l l s u r e l y come i n t o g e n e r a l use i n the s c h o o l s p r o b a b l y w i t h i n the next decade, and p o s s i b l y b e f o r e e i t h e r the s c h o o l s or manufacturers of CAI systems can ensure i t s wise use (1972, p. 69). Assumption I I I . C o m p u t e r - a s s i s t e d i n s t r u c t i o n i s c a p a b l e of becoming a w i d e l y used, v e r s a t i l e and e f f e c t i v e e d u c a t i o n a l t o o l , but i t must overcome many handicaps impeding i t s development (1972, p. 23). 3 e f o r e t h i s a p p l i c a t i o n of CAI becomes widespread, f a c t o r s such as c o s t - e f f e c t i v e n e s s and acceptance of CAT p e r s o n n e l remain to be  Organizational  by  school  solved.  Scheme f o r CAI  T h i s author has proposed an o r g a n i z a t i o n a l scheme i n F i g u r e 1 f o r r e s e a r c h i n t o a p a r t i c u l a r area, o f  CA . T  The  scheme assumes that the important r o l e o f CAI at the  present  time i s that o f an i n s t r u c t i o n a l l a b o r a t o r y ,  a l t h o u g h q u e s t i o n s r e l a t i n g to i n d i v i d u a l i z i n g i n s t r u c t i o n may a l s o a r i s e from the model.  LEARNER  OUTPUT -process v a r i a b l e s -product v a r i a b l e s  -cognitive variables -personality variables -psychomotor v a r i a b l e s  CAI  LESSON  •instructional variables -machine v a r i a b l e s -nature of d i s c i p l i n e  Figure 1 O r g a n i z a t i o n a l Scheme f o r Research Into CAI as an I n s t r u c t i o n a l L a b o r a t o r y  The  organizational  that a l e a r n e r  scheme shown i n F i g u r e 1  suggests  i n t e r a c t s w i t h a CAI l e s s o n and e x h i b i t s  behaviour which i s o b s e r v a b l e and from which one can make inferences  about h i s l e a r n i n g .  u n d e r l y i n g the and  luodel  The b a s i c  assumption  i s that c e r t a i n l e a r n e r  variables  c e r t a i n CAI l e s s o n v a r i a b l e ? w i l l i n t e r a c t to produce  d i f f e r e n t i a l e f f e c t s on the output  variables.  Learner v a r i a b l e s have a l s o been c a l l e d personological be c o n s i d e r e d  variables  learner.  1970) and these  may  as measures o f i n d i v i d u a l student  characteristics. as g e n e r a l  (Bracht,  Cognitive  v a r i a b l e s can be  or s p e c i f i c i n t e l l e c t u a l a b i l i t i e s  considered of the  Examples of c o g n i t i v e v a r i a b l e s a r e IQ,  mathematical a b i l i t y  and p r e r e q u i s i t e knowledge.  P e r s o n a l i t y v a r i a b l e s r e f e r to v a r i a b l e s such as attitudes, anxiety refer  or m o t i v a t i o n .  Psychomotor v a r i a b l e s  to the m a n i p u l a t i v e or m o t o r - s k i l l area,  e.g.,  typing  speed and a c c u r a c y . A CAI  Lesson comprises three  discernible variables.  The i n s t r u c t i o n a l v a r i a b l e s r e f e r to those v a r i a b l e s which c h a r a c t e r i z e  the i n s t r u c t i o n a l s t r a t e g y ,  not the  content, and these can be manipulated by the i n s t r u c t i o n a l programmer.  Examples o f i n s t r u c t i o n a l v a r i a b l e s are  step s i z e , type or frequency of feedback and type of branching.  The machine v a r i a b l e s r e f e r to both  hardware and software v a r i a b l e s which a f f e c t the CAI lesson.  Hardware v a r i a b l e s i n v o l v e  the computer t e r m i n a l  used, t y p i n g  c h a r a c t e r i s t i c s of r a t e f o r example.  Software v a r i a b l e s are c h a r a c t e r i s t i c s o f the CAI author (programming) language used to w r i t e c a p a b i l i t i e s f o r example.  the l e s s o n ,  branching  Rogers (1966) c a u t i o n e d  that  these computer c h a r a c t e r i s t i c s can  impose severe  l i m i t a t i o n s upon both the m a t e r i a l s p r e s e n t e d to the learner  can be  learner  r e q u i r e d and  dimension of the CAI subject  versus highly  the responses which allowed to make.  H i c k s and  structured,  subjects  e a s i l y be handled by  drill-and-practice The  be  and  such as r e a d i n g  and  t u t o r i a l as w e l l as  the  learner  These can be  response l a t e n c y ,  as r e p r e s e n t i n g ( l a t e n c y ) c f the  that  mathematics by  observable  and  from which  considered  the  g i v e an  learning  as e i t h e r  P r o c e s s v a r i a b l e s , such  number or type of e r r o r s made d u r i n g  performance d u r i n g  the  structured  Suppes (1966) remarked  p r o c e s s or product v a r i a b l e s . as the  loosely  output v a r i a b l e s represent  inferred.  final  systems.  b e h a v i o r s e x h i b i t e d by may  The  e x p e r i e n t i a l versus r a t i o n a l ,  v a l u e - l a d e n versus n e u t r a l .  can  the  Hunka (1972) suggested  matter d i s t i n c t i o n s :  well-structured  be  l e s s o n r e f e r s to the nature of  being.taught.  some s u b j e c t  and  which can  learning  i n d i c a t i o n of the  lesson.  These may  e i t h e r accuracy  be  student's  considered  (errors) cr e f f i c i e n c y  student's l e a r n i n g process.  Product  v a r i a b l e s , such as immediate l e a r n i n g , r e t e n t i o n ,  transfer  and  has  a t t i t u d e s , are  the r e s u l t of what the student  gained from the completed CAI  lesson.  11  D i s c u s s i o n of the Problem The present  study made use of the o r g a n i z a t i o n a l  scheme d e s c r i b e d e a r l i e r  to examine the e f f e c t  on the  output v a r i a b l e s of l e a r n e r v a r i a b l e s , CAI l e s s o n v a r i a b l e s and  their interaction.  process  The r e l a t i o n s h i p between the  and product v a r i a b l e s at the output of the model  was a l s o examined. In the CAI l e s s o n component  of the model,  i n s t r u c t i o n a l v a r i a b l e s were under c o n s i d e r a t i o n and three d i f f e r e n t Stolurow  i n s t r u c t i o n a l s t r a t e g i e s were examined.  (1969) e x p l a i n e d  that s t r a t e g y can be thought  of as a set of r u l e s and the f i r s t educational explicit  algorithm  or  to an  so that i t can be programmed f o r Sherman  (1971) p o i n t e d  t h a t most of the time r e q u i r e d to c o n s t r u c t  c o n v e r s a t i o n a l exchanges between student is  of the teacher  t h e o r i s t i s to reduce the s t r a t e g y  implementation by a CAI system. out  task  taken up by two tasks:  l o g i c and programming  designing  and the computer  the i n s t r u c t i o n a l  the c o n v e r s a t i o n a l  network.  He  suggested that by u t i l i z i n g a s p e c i f i c predetermined instructional  s t r a t e g y , which he c a l l e d a template, the  time spent on the second task c o u l d be reduced substantially. which may  The reason f o r t h i s  be compared to a standard  i s that the template, subroutine  or  12 procedure i n computational programs, allows designer  to merely supply  the l e s s o n  the content and not the l o g i c  elements to the CAI l e s s o n .  A l e s s o n c o n s i s t s of a  particular inter-connection  o f one or more o f these  templates.  Two templates were designed and implemented  f o r t h i s study: prelesson. The  one f o r the main l e s s o n and one f o r the  These templates are d i s c u s s e d three  i n Chapter I I I .  i n s t r u c t i o n a l s t r a t e g i e s considered i n  t h i s study were three  v a r i a t i o n s o f the template d e s i g n e d  f o r the main l e s s o n .  The v a r i a b l e which d i s t i n g u i s h e d  these s t r a t e g i e s from one another was the extent of knowledge of r e s u l t s o r , more s p e c i f i c a l l y , feedback given The  the c o r r e c t i o n a l  to the student a f t e r each i n c o r r e c t response.  c o r r e c t i o n a l feedback given  i n the f i r s t i n s t r u c t i o n a l  s t r a t e g y was c h a r a c t e r i z e d as r e s p o n s e - s e n s i t i v e , c o r r e c t i o n a l feedback g i v e n  to the student was  i.e.,  appropriate  to the type of e r r o r that he made i n h i s response. second s t r a t e g y was r e s p o n s e - i n s e n s i t i v e ,  The  i . e . , the  c o r r e c t i o n a l feedback g i v e n c o n s i s t e d of a h i n t which was constant  regardless  that response.  o f the nature o f the e r r o r made on  The f i n a l  strategy  involved  informing  the student whether h i s response was c o r r e c t or not, but  no c o r r e c t i o n a l feedback cr h i n t was g i v e n .  third  strategy  served  The  as a c o n t r o l c o n d i t i o n s i n c e no  13  a s s i s t a n c e was p r o v i d e d to the student when he  responded  incorrectly. Suppes (1966, 1967) concluded c o n f l i c t i n g evidence  that there i s  r e g a r d i n g the e f f e c t s of immediately  i n f o r m i n g the student each time he makes a mistake.  He  s t a t e d that a c e n t r a l weakness of t r a d i t i o n a l p s y c h o l o g i c a l theories of reinforcement  i s t h a t too much o f . t h e theory  has been t e s t e d by experiments  i n which the content of the  i n f o r m a t i o n t r a n s m i t t e d i n the feedback e s s e n t i a l l y very simple. content  of feedback  As a r e s u l t ,  procedure i s the i n f o r m a t i o n  has not been s u f f i c i e n t l y  emphasized  in theoretical discussions. Many i n s t r u c t i o n a l  systems or t h e o r i e s c o n t a i n  knowledge o f r e s u l t s as a major component although the p r e c i s e r o l e s o f t h i s v a r i a b l e are unclear. (1969) and M o r r i l l r e s u l t s appears  (1961) noted  to be e f f e c t i v e  Stolurow  that although knowledge of i n the l e a r n i n g p r o c e s s ,  t h i s problem c o n t a i n s many f a c e t s which need e m p i r i c a l study.  Along  these l i n e s , Gilman  results  suggest  (1967) wrote that h i s  that less elaborate c o r r e c t i o n a l  procedures  a r e as e f f e c t i v e as the more e l a b o r a t e  prompting,  response-contingent  c o r r e c t i o n procedures.  feedback,  He suggested  feedback  and o v e r t -  that h i s r e s u l t s  should  be checked with other s u b j e c t matters and other students to  establish  t h e i r degree o f g e n e r a l i t y .  examined the k n o w l e d g e - o f - r e s u l t s  The p r e s e n t  v a r i a b l e under  study  controlled  c o n d i t i o n s made p o s s i b l e by the use of CAI and p r o v i d e d e m p i r i c a l data to c l a r i f y  the e f f e c t o f t h i s  variable.  Suppes (1967) p o i n t e d out that a troublesome has a r i s e n i n r e c e n t r e s e a r c h .  issue  Should d i f f e r e n t k i n d s o f  r e i n f o r c e m e n t , of which k n o w l e d g e - o f - r e s u l t s may be one k i n d , and d i f f e r e n t  s o r t s o f reinforcement  schedules be  g i v e n to c h i l d r e n with d i f f e r e n t p e r s o n a l i t i e s ? i s s u e r e l a t e s to the problem o f i n d i v i d u a l i z i n g Bracht  (1970) suggested  This instruction.  that i t i s p o s s i b l e that  no s i n g l e i n s t r u c t i o n a l p r o c e s s p r o v i d e s o p t i m a l p o s s i b i l i t i e s f o r a l l students. p o i n t e d out that t o date we s t i l l l e a r n i n g process s u f f i c i e n t l y l e a r n i n g programs.  Bundy  However, Bundy  learning (1967)  do not understand the  to make t r u l y s e l f - a d a p t i v e  (1967) s t a t e d that we might be  a b l e to make s e l f - a d a p t i v e l e a r n i n g programs i n the f u t u r e and the v e h i c l e f o r a c c o m p l i s h i n g CAI,  viewed not as an i n s t r u c t i o n a l  t h i s may w a l l be  t o o l , but as an  instructional laboratory. The p r e s e n t study c o n t r i b u t e d to an understanding of the i n s t r u c t i o n a l process by examining interactions  (ATI).  find significant  a p t i t u d e - treatment  The g o a l of r e s e a r c h on ATI i s to  i n t e r a c t i o n s between  alternative  treatments and i n d i v i d u a l (Bracht,  1970).  c h a r a c t e r i s t i c s of the l e a r n e r  Subsequently,  programs may be developed  alternative  instructional  so that o p t i m a l e d u c a t i o n a l  b e n e f i t s a r e o b t a i n e d when students are a s s i g n e d to the a l t e r n a t i v e programs. Gentile  (1967) emphasized that i f i t i s c l a i m e d  that a d a p t i n g to i n d i v i d u a l d i f f e r e n c e s through CAI would improve some aspect of l e a r n i n g ,  then p a r a m e t r i c s t u d i e s  of v a r i a b l e s c o n s i d e r e d to be important undertaken.  He found that  should be  these p a r a m e t r i c s t u d i e s a r e  s c a r c e because almost a l l of the funds a l l o t t e d  to CAI  p r o j e c t s a r e being spent on the development o f c o u r s e s or equipment to the e x c l u s i o n o f r e s e a r c h on t e a c h i n g - l e a r n i n g v a r i a b l e s , where r e s e a r c h i s needed most. noted that the matter remains  of personality-computer  to be s t u d i e d .  on the i n s t r u c t i o n a l  Dick  (1965)  interaction  T h i s d i s s e r t a t i o n study f o c u s e d  v a r i a b l e s i n the CAI l e s s o n and t h e i r  i n t e r a c t i o n with s e l e c t e d c h a r a c t e r i s t i c s o f i n d i v i d u a l learners. The fell  l e a r n e r c h a r a c t e r i s t i c s examined i n t h i s  study  i n t o two of the three c a t e g o r i e s i n the model,  c o g n i t i v e and p e r s o n a l i t y . not c o n s i d e r e d .  Psychomotor v a r i a b l e s were  The c o g n i t i v e v a r i a b l e s were  mathematical  a b i l i t y and p r e r e q u i s i t e s r e q u i r e d f o r the main l e s s o n . These c o g n i t i v e v a r i a b l e s ranged from g e n e r a l  to s p e c i f i c  i n terms of t h e i r r e l a t i o n s h i p to the content  and s k i l l s  r e q u i r e d f o r the CAI l e s s o n .  The p e r s o n a l i t y v a r i a b l e  under c o n s i d e r a t i o n was a n x i e t y .  O'Neil  e_t al_. (1969a,b;  1972a,b) and S p i e l b e r g e r  (1972) examined the e f f e c t of  anxiety  and found s i g n i f i c a n t e f f e c t s  on  i n a CAI context  student  performance.  They found a d i s o r d i n a l  i n t e r a c t i o n between s t a t e a n x i e t y m a t e r i a l presented pointed  and d i f f i c u l t y  i n the CAI l e s s o n .  O'Neil  o f the  (1972a)  out that some s t u d i e s i n the l i t e r a t u r e have  suggested t h a t the r e l a t i o n s h i p between a n x i e t y and l e a r n i n g i s d i f f e r e n t f o r men and women. not  considered  of students  This  i s s u e was  i n t h i s study but a r e p r e s e n t a t i v e  sample  was employed to i n c r e a s e the g e n e r a l i z a b i l i t y  of the r e s u l t s . The  r e l a t i o n s h i p between the process  v a r i a b l e s i s important. e x i s t s , then p r o c e s s may be u t i l i z e d  and product  I f a well-defined relationship  v a r i a b l e s such as e r r o r s or l a t e n c i e s  to make d e c i s i o n s during  l e a r n i n g i n order  to maximize the product v a r i a b l e s of l e a r n i n g . l a t t e r q u e s t i o n was. a l s o examined i n the p r e s e n t The  questions  under c o n s i d e r a t i o n i n t h i s  appear to be important  theoretical issues.  This study. study  An important  p r a c t i c a l reason e x i s t s as w e l l f o r examining  the  i n s t r u c t i o n a l v a r i a b l e of c o r r e c t i o n a l feedback. i s s u e i s a c o s t - e f f e c t i v e n e s s one. e s t i m a t e d that approximately 100 programming and  Rogers  The  (1968)  hours of a n a l y s i s ,  e d i t i n g e f f o r t s are r e q u i r e d  to produce  programmed i n s t r u c t i o n a l (PI) m a t e r i a l which o c c u p i e s the student f o r one orders  hour.  He  e s t i m a t e d that one  of magnitude separate the CAI  l e s s o n i n terms of the  or  l e s s o n from the  time r e q u i r e d f o r p r o d u c t i o n  a lesson.  A major p o r t i o n of the  developing  a CAI  tutorial  time r e q u i r e d  providing  response-  The  r e q u i r e d becomes more complex and  computer  time, and  response-sensitive  i f this  computer  c o r r e c t i o n a l feedback i s implemented.  c h a r a c t e r i s t i c s has  no e f f e c t on  the model, then the  time, e f f o r t and  Bracht  the  i n the CAI  (1970) a d v i s e d  If t h i s  such as c o s t ,  learner  output v a r i a b l e s i n extra cost  that experimenters  i n mind.  required  l e s s o n are being  b e g i n to f o r m u l a t e hypotheses about ATI factors,  software  execution  i n s t r u c t i o n a l v a r i a b l e or i t s i n t e r a c t i o n with  spent.  of  in  s e n s i t i v e c o r r e c t i o n a l feedback.  cost, increase  PI  l e s s o n i s spent i n a n t i c i p a t i n g  a l l p o s s i b l e student responses and  to i n c l u d e t h i s f e a t u r e  two  The  with  poorly  should  administrative  r e s u l t s of  this  study have c o s t - e f f e c t i v e n e s . s i m p l i c a t i o n s because  the  costs f o r providing from expensive to  the three  types o f feedback range  inexpensive.  Statement of the Problem The  s p e c i f i c tasks proposed f o r t h i s d i s s e r t a t i o n  were: 1.  Development of an o r g a n i z a t i o n a l scheme f o r research  2.  i n t o CAI  Design and  as an  i n s t r u c t i o n a l laboratory.  implementation of an e m p i r i c a l  to examine s e v e r a l v a r i a b l e s i n the scheme.  The  c o r r e c t i o n a l feedback.  i n t e r a c t i o n with the  3.  mathematical  examined.  Development of a CAI  author language  a h i g h degree o f r e s p o n s e - s e n s i t i v e to be served  supplied  to the  student.  as a v e h i c l e f o r the  data regarding  4.  permitting feedback  This  study and  a particular instructional logic,  recorded  Its  l e a r n e r v a r i a b l e s of  p r e r e q u i s i t e knowledge and  a b i l i t y was  organizational  i n s t r u c t i o n a l v a r i a b l e under  c o n s i d e r a t i o n was  anxiety,  study  language implemented  permitting  the s t u d e n t ' s performance tc be  f o r subsequent a n a l y s i s .  Development of a CAI  module d e a l i n g with some  19 elementary c a l c u l u s concepts and  programmed  the above-mentioned author language. included  a CAI  prerequisites  prelesson  dealing  The  with  i d e n t i f i e d f o r the main  using  module  the lesson.  Research Q u e s t i o n s The research  several  terms which were used i n the  q u e s t i o n s are e x p l a i n e d  below. • The  p r o c e s s v a r i a b l e s were p r o p o r t i o n e r r o r s d i v i d e d by The  learning,  as measured by  nature of the was  felt  that  the  of e r r o r s would r e f l e c t  that  two  The  reason f o r  e r r o r s of the  not  same type  computer to produce the c o r r e c t answer instructional unit.  immediately made two  terminate that  i n s t r u c t i o n a l u n i t without being  even though he had  response.  The  use  not  of p r o p o r t i o n  situation.  The  average l a t e n c y  calculating  the average of  the  a l l instructional units.  and  T h e r e f o r e , a student  s i m i l a r e r r o r s i n a row  penalized,  for  immediate  Because of  than t o t a l e r r o r s .  t o t a l e r r o r s was  would cause the  who  was  i n s t r u c t i o n a l l o g i c used i n t h i s study, i t  that p r o p o r t i o n  would end  a posttest.  total  average response  l e a r n i n g product v a r i a b l e  performance b e t t e r using  learning  of e r r o r s , i . e .  t o t a l responses, and  latency.  following  produced the  would seriously correct  of e r r o r s c o r r e c t e d v a r i a b l e was  total It was  obtained  response felt  that  this by  latencies total  latency  on an i n s t r u c t i o n a l u n i t than the l a t e n c y  would b e t t e r  f o r the f i r s t  The reason f o r t h i s i s that effect  of the c o r r e c t i o n a l  reflect  response  total  on that  latency  feedback  performance unit.  r e f l e c t e d the  given during  that  unit. The r e s e a r c h q u e s t i o n s were: 1.  What i s the e f f e c t of c o r r e c t i o n a l learning  2.  on the  feedback  on the  p r o c e s s and product?  What i s the e f f e c t o f c o r r e c t i o n a l learning  feedback  p r o c e s s f o r students with d i f f e r e n t  levels  of a n x i e t y ?  3.  What i s the e f f e c t o f c o r r e c t i o n a l learning  l e v e l s of p r e r e q u i s i t e  feedback  on the  p r o c e s s and product f o r students with  different  5.  skills?  What i s the e f f e c t o f c o r r e c t i o n a l learning  on the  p r o c e s s and product f o r s t u d e n t s with  different  4.  feedback  l e v e l s of mathematical  What i s the r e l a t i o n s h i p variables  ability?  between the l e a r n i n g  and the product v a r i a b l e s ,  of the e f f e c t of che other v a r i a b l e s , prerequisite treatment?  knowledge, mathematical  process  independent i . e . anxiety, a b i l i t y and  Importance of  the  T h i s study was to s e v e r a l The  21  Study important because of i t s  d i f f e r e n t areas of knowledge. use  of CAI  as a l a b o r a t o r y  i n s t r u c t i o n a l p r o c e s s has scheme f o r CAI  as an  developed and  to study  been d i s c u s s e d .  a s p e c t s of the  Some e m p i r i c a l  under c a r e f u l l y c o n t r o l l e d of CAI.  variables  Higgins  evidence was  the  for contributing  to  the  amount o f  The  exists  significance  individualized instruction  i n t e r a c t i o n between the  with the  learner  from e d u c a t o r s .  for  f o r classroom  currently  A pressing to the  and  variables  Reid. 1969). and  their  instructional strategies.  would have i m p l i c a t i o n s  is  study  need of  c o n d i t i o n s of i n s t r u c t i o n and  (Sutter  learner  different  this  f o r subsequent development  to devote more r e s e a r c h a c t i v i t y  examined s e v e r a l  of  lessons.  much a t t e n t i o n  nature of the  information  resolution  theory, p r a c t i c a l s i g n i f i c a n c e  receiving  theoretical  implications  by of  instructional  area of  learning  one  i s s u e has  The  under  (1973) suggested that  feedback s t i m u l u s .  software and  been  provided  controversial  of CAI  has  feedback on  design of e f f e c t i v e i n s t r u c t i o n i s the  i n s t r u c t i o n and  organizational  c o n d i t i o n s made p o s s i b l e  with g r e a t e s t p o t e n t i a l  c o n t a i n e d i n the  An  model are  r e g a r d i n g the e f f e c t s o f c o r r e c t i o n a l  use  the  i n s t r u c t i o n a l laboratory  several  consideration.  the  contribution  for  individualized  the  T h i s study  interaction The  results  instruction  22  since  the presence o f s i g n i f i c a n t d i s o r d i n a l  interactions  makes the assignment of i n d i v i d u a l s to d i f f e r e n t instructional  treatments d e s i r a b l e  optimal learning f o r i n d i v i d u a l The  v a r i a b l e of a n x i e t y  attention required Theory  learners.  i s c u r r e n t l y r e c e i v i n g much  i n the l i t e r a t u r e and e m p i r i c a l  evidence i s  to f u r t h e r develop the S t a t e - T r a i t A n x i e t y  (Spielberger,  1971).  to t h i s a r e a by c l a r i f y i n g on  i n order t o produce  T h i s study a l s o  contributed  some o f the e f f e c t s of a n x i e t y  learning. The  r e l a t i o n s h i p between the p r o c e s s v a r i a b l e s , such  as e r r o r s d u r i n g  learning  product v a r i a b l e s ,  and response l a t e n c y ,  such as immediate l e a r n i n g ,  because o f the p o s s i b i l i t y o f u s i n g variables  and the i s important  the l e a r n i n g p r o c e s s  to o p t i m i z e the l e a r n i n g product f o r i n d i v i d u a l s .  This optimization  could  instructional decisions  be accomplished by b a s i n g on these p r o c e s s v a r i a b l e s  during  learning. An  important  c o n t r i b u t i o n was the development o f a  methodology which implemented the concept of CAI as a laboratory  to 9 t u d y l e a r n i n g and i n s t r u c t i o n ,  The  methodology used i n t h i s study may be u t i l i z e d by o t h e r s or may serve <? s a model f o r other r e s e a r c h e r s t o f o l l o w i n the  development of new methods o f a p p l y i n g  the  s o l u t i o n of e d u c a t i o n a l  problems.  the computer t o  CHAPTER I I  REVIEW OF RELATED LITERATURE AND  RESEARCH HYPOTHESES  Introduc t i o n T h i s chapter c o n t a i n s a survey of the  literature  r e l a t e d to the a r e a s under c o n s i d e r a t i o n i n t h i s The  t o p i c s i n c l u d e d are:  study.  Knowledge-of-Results,  S t a t e - T r a i t A n x i e t y , Aptitude-Treatment I n t e r a c t i o n s and T u t o r i a l  CAI.  L i t e r a t u r e on Knowledge of R e s u l t s Annett  (1964, p.280) d e f i n e d k n o w l e d g e - o f - r e s u l t s  "...  knowledge which an i n d i v i d u a l or group r e c e i v e s  relating  to the outcome of a response  Higgins  or group o f responses.'  (1972) c a t e g o r i z e d feedback  into  three common  forms t h a t p r o v i d e d i f f e r e n t amounts of i n f o r m a t i o n . three forms were k n o w l e d g e - o f - r e s u l t s correct-response  (KCR)  the form  feedback.  c o n t a i n i n g the. l e a s t  i n f o r m a t i o n , i n d i c a t e s o n l y whether a response or i n c o r r e c t .  I f the response  The  (KR), knowledge-of-  and i n s t r u c t i o n a l  Knowledge-of-results,  i s incorrect,  i s correct  knowledge-of-  r e s u l t s does not i n d i c a t e what the c o r r e c t response i s . Knowledge-of-correct-response  as  d i f f e r s from knowledge-of-  r e s u l t s i n that knowledge-of- c o r r e c t - r e s p o n s e always  24 i n d i c a t e s the c o r r e c t response.  I n s t r u c t i o n a l feedback,  the form c o n t a i n i n g the most i n f o r m a t i o n , i n d i c a t e s the c o r r e c t response and p r o v i d e s an e x p l a n a t i o n o f why response i s c o r r e c t .  Higgins  from the r e s e a r c h l i t e r a t u r e to the d e s i g n of e f f e c t i v e  that  (1972) wrote that i t appears that p o t e n t i a l c o n t r i b u t i o n s  i n s t r u c t i o n can be  generated  by r e s e a r c h e f f o r t s c o n t r a s t i n g the e f f e c t s of v a r i o u s combinations of the above forms of feedback. Higgins  (1972) p o i n t e d out that one  factor influencing  the e f f e c t i v e n e s s of feedback i s the nature Specifically, when the  i t appears that feedback i s more e f f e c t i v e  l e a r n e r possesses  a low  r e g a r d to the i n s t r u c t i o n a l Annett in  of the l e a r n e r .  l e v e l of competence with  task.  (1964) observed  that p r o b a b l y  the b i g g e s t i s s u e  the area of feedback i s that of m o t i v a t i o n  information.  He  concluded  the i n f o r m a t i o n content of feedback i s important content  from h i s study  r a t h e r than  However, i n h i s r e c e n t book  of the area that  the m o t i v a t i o n  to l e a r n i n g w h i l e  of feedback i s an important  versus  content  motivation  v a r i a b l e i n performance.  (1969, p.169), Annett  wrote:  . . . to say that k n o w l e d g e - o f - r e s u l t s p r o v i d e s motivation i s misleading. The s o - c a l l e d i n c e n t i v e f u n c t i o n of k n o w l e d g e - o f - r e s u l t s seems to i n v o l v e both p r o v i d i n g the s u b j e c t with a performance standard to aim f o r and i n f o r m a t i o n necessary f o r corrective action.  Annett  (1964) concluded that none of the  generalizations  which have been made i n the past about knowledge-ofresults  can be accepted at f a c e  Annett  (1969) reviewed the p s y c h o l o g i c a l  i n the area of feedback. results  value.  He  literature  concluded that the  role  or consequences i n behaviour seems to have been  underrated.  He  thought of k n o w l e d g e - o f - r e s u l t s as  the  m a n i p u l a t i o n of an e x t e r n a l feedback loop r e l a t i n g certain  of  aspects of a s u b j e c t ' s  Morrill conclusion  performance.  (1961) reached e s s e n t i a l l y  as Annett when he  to  the same  stated:  Because of t h e i r c o n t r o v e r t i b l e r e s u l t s , the above s t u d i e s demonstrate t h a t , although immediate feedback appears to b e ' e f f e c t i v e i n the l e a r n i n g p r o c e s s , t h i s problem c o n t a i n s many f a c e t s which need more e m p i r i c a l , data. Higgins frequently instruction laboratory existing  (1972) p o i n t e d  out  t h a t the r e s e a r c h  most  c i t e d i n d e s c r i b i n g the r o l e of feedback i n has  come from three  sources of e x p e r i m e n t a t i o n :  s t u d i e s of human l e a r n i n g , s t u d i e s  conventional  o r i g i n a l form do not  instructional r e q u i r e overt  materials  employing which i n t h e i r  l e a r n e r response,  and  i n v e s t i g a t i o n s with programmed i n s t r u c t i o n a l  materials.  Most r e s e a r c h  from the f i r s t  very  applicability  t c the d e s i g n  two  sources has  of i n s t r u c t i o n a l  limited  materials  because of the d i f f e r e n c e between the m a t e r i a l s  and  procedures employed i n these s t u d i e s and those used i n s y s t e m a t i c a l l y d e s i g n e d i n s t r u c t i o n , such as i n the present study.  Higgins  (1972) p o i n t e d  out that i n most  laboratory  s t u d i e s o f human l e a r n i n g , the l e a r n e r r e c e i v e s no i n s t r u c t i o n before  being  asked to respond.  He s t a t e d  that  t h i s procedure i s i n e f f e c t i v e i n s t r u c t i o n a l l y when contrasted initial  with procedures i n which the l e a r n e r  i n s t r u c t i o n d e s i g n e d to enable him to respond  correctly.  Higgins  applicability and  as  to i n s t r u c t i o n a l design  the l i m i t e d of laboratory  studies  materials  the s t u d i e s u s i n g programmed i n s t r u c t i o n a l m a t e r i a l s  the b a s i s f o r u s e f u l r e s e a r c h  Obviously, and  (1972) f e e l s that  of i n v e s t i g a t i o n s involving conventional  leaves  receives  up to t h i s p o i n t i n time.  s t u d i e s u t i l i z i n g CAI f a l l  may a c t u a l l y p r o v i d e  stronger  into this  category  evidence due to i n c r e a s e d  c o n t r o l of extraneous v a r i a b l e s . The  v a r i a b l e o f i n s t r u c t i o n a l feedback i s an important  component of most i n s t r u c t i o n a l models (Stolurow, 1971; Merrill,  1971).  Stolurow  (1971) d e f i n e d  three  critical  system f u n c t i o n s i n h i s i n s t r u c t i o n a l approach: a.  The cue f u n c t i o n p r o v i d e d instruction,  by the program of  i . e . the s t i m u l u s  c r i t e r i o n response i s a t t a c h e d ;  to which each  b.  the m o t i v a t i o n f u n c t i o n , i . e . e l i c i t i n g the d e s i r e d performance; and  c.  the feedback  function, i . e . providing  knowledge-of-results. feedback  immediate  K n o w l e d g e - o f - r e s u l t s or  i s d e f i n e d as one o f Stolurow's ten  c r i t i c a l requirements o f a t e a c h i n g machine. . Stolurow d e s c r i b e d h i s c o n c e p t i o n o f k n o w l e d g e - o f - r e s u l t s i n a t e a c h i n g program.  I f the l e a r n e r s e l e c t s the c o r r e c t  a l t e r n a t i v e among a preprogrammed s e t of c h o i c e s , he i s t o l d t h a t he was c o r r e c t and g i v e n a d d i t i o n a l i n f o r m a t i o n . I f he s e l e c t s an i n c o r r e c t a l t e r n a t i v e , he i s t o l d that he is incorrect,  the computer p r o v i d e s c o r r e c t i v e and  supplementary  i n f o r m a t i o n , and he then makes another c h o i c e .  This process continues u n t i l made or u n t i l  the c o r r e c t c h o i c e has been  the computer p r o v i d e s the c o r r e c t  answer.  Feedback implemented by the program i n t h i s way i s thus sensitive  to i n d i v i d u a l d i f f e r e n c e s i n lea.rning.  c l a i m e d that t h i s type o f feedback  Stolurow  i s o f t e n p r e f e r r e d ever  the simple right/wrong feedback when the implementation o f the r e s p e c t i v e f u n c t i o n s takes the same amount o f time. Otherwise, an immediate r i g h t / w r o n g feedback  i s preferred.  T h i s study examined t h i s c l a i m from a c o s t - b e n e f i t i.e.  the c o r r e c t i v e feedback  viewpoint,  f u n c t i o n which p r o v i d e s  i n f o r m a t i o n may be s u p e r i o r t o simple right/wrong  feedback,  28  even when the  former i s more expensive and  difficult  to  implement i f t h i s feedback s i g n i f i c a n t l y improves student learning. G e i s and results  i s the  l i t e r a t u r e on  Chapman (1971) noted that knowledge-ofmost f r e q u e n t l y c i t e d r e i n f o r c e r self-instructional  programmed i n s t r u c t i o n .  systems,  in  the  especially  They found that most s t u d i e s  not  d i r e c t l y aimed at  investigating  are  reinforcers.  q u e s t i o n u s u a l l y being a t t a c h e d i s a  broader one. d u r i n g and  Does feedback i n some way  after  Geis and t h i s a r e a and situations.  The  programmed  The  themselves to  test  investigation  of  the  relationship  so much  unjustified. between  feedback i n programmed i n s t r u c t i o n ,  s c o r e s were higher f o r  no  in  self-instructional  a significant  performance of. g r r d e - s c h o o l g i r l s .  had  literature  that e x t r a p o l a t i o n i s  feedback had  a n x i e t y females who  had  test  Campeau  variable  in  Post-instructional  those h i g h - a n x i e t y g i r l s  had .feedback d u r i n g l e a r n i n g . who  performance  materials d i f f e r  (1968) found that feedback was the  answers  authors c a u t i o n e d that r e s e a r c h u s i n g  from s e l f - i n s c r u c t i o n  a n x i e t y and  affect  Chapman (1971) reviewed the restricted  not  self-instruction?  o t h e r than s e l f - i n s t r u c t i o n a l  In an  whether or  are  who  Low-anxiety female s t u d e n t s  h i g h e r p o s t t e s t s c o r e s than highno  feedback.  No  significant  d i f f e r e n c e s were found between low and high a n x i e t y  students  under feedback c o n d i t i o n s .  similar  Male students  showed no  regularity. Cronbach and  Snow (1969) r e p o r t e d that t h i s  fifth  grade study by Campeau used programmed i n s t r u c t i o n , g i v i n g one  group feedback to a s s i s t  and  the other group no feedback.  was  small  was  performed w i t h i n sexes.  of was  i n the c o r r e c t i o n of The  responses,  number o f s u b j e c t s  (36 boys, 44 g i r l s ) e s p e c i a l l y  s i n c e the a n a l y s i s  Only persons at the extreme  the a n x i e t y d i s t r i b u t i o n were used, the dependent v a r i a b l e a p o s t t e s t score w i t h i n i t i a l  girls  there was  a significant  IQ p a r t i a l l e d out.  i n t e r a c t i o n , with  For  those  high  on t e s t a n x i e t y doing d i s t i n c t l y b e t t e r when g i v e n feedback and d i s t i n c t l y worse than T h i s was  a l s o found  low anxious  on a r e t e n t i o n t e s t .  r e l a t i o n s h i p s were not s i g n i f i c a n t , posttest  there was  inadequate. similar  when g i v e n no  and  For boys, on the  e s s e n t i a l l y no e f f e c t .  girls.  g i r l s are considerably higher that a g i r l ' s  low  Reporting  Campeau's  i n t e s t a n x i e t y and  (1968) i n t e r p r e t a t i o n was  That i s to say,  are  that  i t may  be  score.  that w i t h o l d i n g  feedback i n t e n s i f i e s m o t i v a t i o n by m a i n t a i n i n g incompleteness.  is  toys  I t i s o f t e n found  score matches a boy's h i g h  the  immediate  I t i s u n c e r t a i n that the low anxious  to the low anxious  feedback.  a certain  the no feedback  situation  30  i s more c h a l l e n g i n g and more s t r e s s f u l . one  Alternatively,  c o u l d perhaps say t h a t the p r o v i s i o n of feedback  p r o v i d e s g r e a t e r s t r u c t u r e , l e a v i n g the person much l e s s on h i s own r e s o u r c e s .  The e s s e n t i a l l y n e g a t i v e r e s u l t f o r  boys was not e x p l a i n e d . W i t t r o c k and Twelker  (1964) found an i n t e r e s t i n g  r e l a t i o n s h i p between k n o w l e d g e - o f - r e s u l t s  and r u l e s .  While  r u l e s alone proved most e f f e c t i v e i n teaching s u b j e c t s t o decode c i p h e r e d sentences,  knowledge-of-results  was  e s p e c i a l l y u s e f u l when r u l e s were not s u p p l i e d .  It did  not add to t e a c h i n g e f f e c t i v e n e s s when s u p p l i e d i n c o n j u n c t i o n with r u l e s , that k n o w l e d g e - o f - r e s u l t s  s u p p o r t i n g the authors'  contention  enhances l e a r n i n g , r e t e n t i o n and  t r a n s f e r when the i n f o r m a t i o n i t c o n t a i n s i s not g r e a t l y redundant. G e i s and Chapman (1971) found  conflicting  results  among s t u d i e s that examined v a r i a b l e schedules of reinforcement  and v a r i a b l e d e l a y s i n c o n f i r m a t i o n of  c o r r e c t or i n c o r r e c t responses.  No c o n c l u s i o n s were  reached  about these v a r i a b l e s . Anderson et_ al_.  (1972) used s e v e r a l feedback  arrangements i n v o l v i n g a computer and a program on diagnosing myocardial  infraction.  s e v e r a l groups, they p r e s e n t e d  In on? experiment  the c o r r e c t response  using  (1) o n l y a f t e r a c o r r e c t response (2) o n l y a f t e r a wrong response (3) always  had been e m i t t e d , or  had been e m i t t e d , or  (100 p e r c e n t ) , o r (4) never  (5) a f t e r a c o r r e c t response,  (0 p e r c e n t ) , or  but the s u b j e c t had to  " l o o p " back to the same frame a f t e r the wrong Criterion feedback  t e s t s c o r e s were h i g h e r f o r the 100 percent and the "looped" groups.  significantly group  response.  lower  (0 p e r c e n t ) .  The only group with  t e s t s c o r e s was the no feedback Of i n t e r e s t here  i s the f a c t  that no  s i g n i f i c a n t d i f f e r e n c e was found between the 100 p e r c e n t and the "looped" group, a l t h o u g h  the l a t t e r  underwent much more e l a b o r a t e feedback was no evidence  i n t h i s study that  f u n c t i o n e d as c o r r e c t i v e feedback. knowledge-of-results perform  procedures.  There  knowledge-of-results The group r e c e i v i n g  o n l y when e r r o r s were made d i d not  s i g n i f i c a n t l y b e t t e r on the c r i t e r i o n t e s t than the  other knowledge-of-results  groups.  The knowledge-of-  r e s u l t s - o n l y - w h e n - c o r r e c t group performed as the other groups.  a t the seme l e v e l  The f u n c t i o n o f k n o w l e d g e - o f - r e s u l t s  was not c l a r i f i e d by t h i s experiment. Keats  students  In a r e c e n t CAI study,  and Hansen (1972) examined the e f f e c t s o f c o r r e c t i o n a l  feedback  on l e a r n i n g .  They noted t h a t the p r e c i s e form and  content f o r c o r r e c t i o n a l messages that w i l i maximize l e a r n i n g remains a c l o u d e d i s s u e , a l t h o u g h the requirement f o r  32  c o r r e c t i o n a l feedback to wrong answers i n order to f a c i l i t a t e a c q u i s i t i o n has been w e l l e s t a b l i s h e d .  T h i s study  the e f f e c t s of u s i n g v e r b a l d e f i n i t i o n s and examples as CAI  Students  which was  numerical  c o r r e c t i o n a l feedback i n a program  mathematical p r o o f s . students.  compared  involving  Ss were f o r t y - f i v e n i n t h grade . were o n l y r e q u i r e d to s t a t e the  a p p l i e d to each s t e p Of the p r o o f .  rule  The  feedback chosen f o r a p a r t i c u l a r s t e p v a r i e d a c c o r d i n g to  r u l e s d e r i v e d by l o g i c a l a n a l y s i s c a r r i e d out by  e x p e r i e n c e d mathematics i n s t r u c t o r . reliability  of the instruments  prevented  being drawn about the s i m i l a r i t y scores.  The v e r y  an  low  c o n c l u s i o n s from  i n p o s t t e s t and r e t e n t i o n  However, i n terms of e r r o r s d u r i n g the program,  p r o v i d i n g c o r r e c t i o n a l feedback i n the form of a v e r b a l d e f i n i t i o n was Gilman  more b e n e f i c i a l  to the l e a r n e r .  (1967) i n v e s t i g a t e d the e f f e c t of v a r i o u s  k i n d s of feedback i n a computer a s s i s t e d i n s t r u c t i o n system.  He wrote that ".  feedback other than statements  such as  . . i f t h e r e were no purpose to  to p r o v i d e the student 'you  with  upperclassmen were taught  c h o i c e format.  reinforcement,  are c o r r e c t ' should prove equally-  e f f e c t i v e as c o n f i r m a t i o n of a c o r r e c t answer."  by means of a CAI  (CAI)  t h i r t y general science  self-instructional  University concepts  system, u s i n g a m u l t i p l e  V a r i o u s modes of feedback were used:  no  33  feedback,  " c o r r e c t " or "wrong", feedback  of c o r r e c t  response, feedback a p p r o p r i a t e to the s t u d e n t ' s response, and a combination o f the three l a t t e r modes.  Students  r e p e a t e d items which were missed u n t i l a p e r f e c t run was  obtained.  The  no feedback  ''wrong" group performed  through  group and the " c o r r e c t " or  l e s s w e l l on the program, making a  s i g n i f i c a n t l y g r e a t e r number of responses and r e q u i r i n g  a  g r e a t e r number of i t e r a t i o n s of the program i n order to reach c r i t e r i o n .  On the p o s t t e s t ,  the  combination  feedback  group  others.  T h i s study suggests that more e l a b o r a t e feedback  may  s c o r e d s i g n i f i c a n t l y h i g h e r than d i d the  be more e f f e c t i v e i n changing  Hernandez and Gilman  student behaviour.  (1969) compared the e f f e c t i v e n e s s of  s e v e r a l feedback modes f o r c o r r e c t i n g e r r o r s i n CAI. S e v e n t y - f i v e u n i v e r s i t y upperclassmen thirty  general science concepts.  were taught  The frames were m u l t i p l e  c h o i c e items and f i v e d i f f e r e n t  c o n d i t i o n s were a d m i n i s t e r e d ,  from no feedback  a p p r o p r i a t e to the s t u d e n t ' s  response. factor  The  up to feedback  r e s u l t s i n d i c a t e d that  the most  i n r a t e of e r r o r c o r r e c t i o n i s g u i d i n g the s u b j e c t  to the c o r r e c t response.  The most s i g n i f i c a n t f a c t o r i n  immediate l e a r n i n g i s amount of feedback subject r e c e i v e s . noting  significant  that p r i o r  i n f o r m a t i o n the  The author made an important p o i n t by s t u d i e s i n programmed l e a r n i n g have not  34  been a b l e to compare the e f f e c t i v e n e s s -of the s e v e r a l modes of feedback  in correcting  studies u t i l i z e d S i n c e few  the student e r r o r s because  these  low e r r o r r a t e , l i n e a r type programs.  i n c o r r e c t responses are made by a student i n  t h i s type of l e a r n i n g s i t u a t i o n , l i t t l e c o n c e r n i n g how  feedback  i s presently  can be used to c o r r e c t  known  student  errors. Van Dyke and Newton (1972) examined the e f f e c t of immediate and d e l a y e d knowledge-of-response  i n a CAI  task.  Response d i f f e r e n c e s between the sexes were i n v e s t i g a t e d w e l l as a t t i t u d e s taking that  toward  CAI.  Ss were c o l l e g e  an I n t r o d u c t o r y Psychology  short  effect  course.  as  students  They  concluded  i n t e r v a l s of d e l a y with CAI had no s i g n i f i c a n t  on the l e a r n i n g or t e s t performance  i n d i v i d u a l s used i n t h i s study.  of the  Delay of knowledge-of-  r e s u l t s d i d r e s u l t i n a t t i t u d e d i f f e r e n c e s , and t h i s e f f e c t v a r i e d w i t h the sex of the l e a r n e r . noted that  the e l e v e n item achievement t e s t used  study had a K-R Narva similar CAI  20 r e l i a b i l i t y  c o e f f i c i e n t of  i n the  .44.  (1970) r e p o r t e d a study with c h a r a c t e r i s t i c s  to the p r e s e n t study.  programs, one employing  linear  However, i t should be  i n format.  He  compared two  types of  branching end the othar  He a l s o v a r i e d  the c o r r e c t i o n a l  g i v e n the student i n both types of programs. resporse-sens.it i v e and r e s p o n s e - i n s e n s i t i v e  He  one feedback  used  correctional  35  feedback i n a way s i m i l a r to the present that  the r e s p o n s e - i n s e n s i t i v e  c o r r e c t answer.  tailoring cost.  feedback p r o v i d e d  He used t h i r t y - t w o  f a c t o r i a l design.  study except  The q u e s t i o n  subjects  in a 2 x 2  was r a i s e d about whether  the program to i n d i v i d u a l s t u d e n t s i s worth the  He found that p r e - i n s t r u c t i o n s c o r e s  related  only the  were not  to l a t e r performance but that a p t i t u d e  scores  were s i g n i f i c a n t l y c o r r e l a t e d to p o s t t e s t s c o r e s .  He  a l s o found no s i g n i f i c a n t d i f f e r e n c e s between e i t h e r the two  sequencing programs or between the two types o f feedback.  However, when an a n a l y s i s unadjusted f o r the i n f l u e n c e o f the a p t i t u d e i n favor  score  was performed, a s i g n i f i c a n t  of r e s p o n s e - s e n s i t i v e  Finer grained  difference  feedback was found.  a n a l y s i s o f student behaviour and  k n o w l e d g e - o f - r e s u l t s begin to r e v e a l  specific  conditions  under which k n o w l e d g e - o f - r e s u l t s seems to be a c t i n g as reinforcer.  A few s t u d i e s s c a t t e r e d throughout the  l i t e r a t u r e report  on m a n i p u l a t i o n o f s u b j e c t  v a r i a b l e s and o f kinds  of feedback.  and t e s t  The r e s u l t s of these  s t u d i e s suggest that k n o w l e d g e - o f - r e s u l t s may w e l l be a r e i n f o r c e r when u n c e r t a i n t y  or p r o b a b i l i t y of e m i t t i n g an  i n c o r r e c t response i s h i g h ,  or where c o n f i d e n c e  G e i s ana Chapman (1971) concluded that  i s low.  the weight o f  evidc-nce from g l o b a l s t u d i e s comparing programs with and  36  without feedback  i s that feedback  as measured.by immediate p o s t t e s t scores.  These authors conclude  d i d not enhance l e a r n i n g , s c o r e s or by  retention  that:  . . . one might jump i n t o broader q u e s t i o n s such as how, when and why i n f o r m a t i o n on one's own performance i n a l e a r n i n g s i t u a t i o n becomes r e i n f o r c i n g and c o n t r i b u t e s to more effective learning. Along these l i n e s , concerned  themselves with the e f f e c t  of c o r r e c t i o n a l feedback. above.  s e v e r a l s t u d i e s have r e c e n t l y of d i f f e r e n t  types  These s t u d i e s were r e p o r t e d  The p r e s e n t study examines t h i s q u e s t i o n as w e l l .  Summary The exact r o l e of c o r r e c t i o n a l feedback  on the  l e a r n i n g p r o c e s s and product i s u n c l e a r . Stolurow  (1971), M e r r i l l  (1971) and A n n e t t  have made a s t r o n g case f o r the importance  (1969)  of knowledge-  o f - r e s u l t s i n the i n s t r u c t i o n a l p r o c e s s . Some experimenters have shown that feedback has a p o s i t i v e e f f e c t  correctional  on l e a r n i n g and  e f f e c t depends on the n a t u r e of the l e a r n e r .  that  Campeau  p r o v i d e d some evidence f o r a f e e d b a c k - b y - a n x i e t y on p o s t t e s t Crcnbach  s c o r e s , although t h i s study was  and Snow (1969).  (1967)  interaction  criticised  W i t t r o c k and Twelker  showed that k n o w l e d g e - o f - r e s u l t s enhanced  this  (1964)  learning,  by  37  r e t e n t i o n and t r a n s f e r when the i n f o r m a t i o n i t c o n t a i n e d was not redundant.  Keats and Hansen,(1972) performed a  CAI study which p r o v i d e d some evidence that fewer  errors  were made d u r i n g l e a r n i n g when c o r r e c t i o n a l feedback i n the form of a v e r b a l d e f i n i t i o n was  supplied.  Gilman  (1967) performed a CAI experiment which suggested that more e l a b o r a t e feedback might be more e f f e c t i v e i n changing student behaviour.  Hernandez  and Gilman  (196 9)  found that the most s i g n i f i c a n t f a c t o r i n immediate was  the amount of feedback i n f o r m a t i o n the s u b j e c t  Narva  (1970) c a r r i e d out a CAI experiment which  that a p t i t u d e s c o r e s were r e l a t e d to p o s t t e s t t h a t r e s p o n s e - s e n s i t i v e feedback was  learning received.  showed  s c o r e s and  s u p e r i o r to response-  i n s e n s i t i v e feedback i n terms of p o s t t e s t s c o r e s (unadjusted for  aptitude). D e s p i t e the c o n c l u s i o n of G e i s and Chapman (1971)  t h a t feedback d i d not enhance  l e a r n i n g i n most s t u d i e s  reviewed, there i s enough evidence i n favour o f c o r r e c t i o n a l feedback to q u e s t i o n t h i s c o n c l u s i o n . If is  the i n f o r m a t i o n c o n t e n t o f c o r r e c t i o n a l  feedback  important to l e a r n i n g , then d i f f e r e n c e s i n performance  between the three treatment groups would be expected i n t h i s study.  I t was e x p e c t e d that p r o v i d i n g response-  s e n s i t i v e c o r r e c t i o n a l feedback  (T^) would p r o v i d e more  38  information  to the  student  than p r o v i d i n g  response-  i n s e n s i t i v e c o r r e c t i o n a l feedback  (T )  treatment c o n d i t i o n would then be  less d i f f i c u l t  the T  2  treatment c o n d i t i o n .  Therefore,  that i n terms of p r o p o r t i o n and  immediate l e a r n i n g , T-[  s i g n i f i c a n t l y better  information feedback providing that the i t was  i t was  hypothesized latency  students would perform students.  l e d to the  ( T ) w i l l make the l e s s o n 2  conclusion  that  s t u d e n t ' s response was  correct  information  (T ).  Therefore,  Q  immediate l e a r n i n g , T2  (1972) p o i n t e d  to be more e f f e c t i v e when the  than T^ out  than  than  h y p o t h e s i z e d that i n terms of p r o p o r t i o n  perform s i g n i f i c a n t l y b e t t e r  of e r r o r s ,  s t u d e n t s would  students.  that feedback appears  l e a r n e r possesses a  l e v e l of competence w i t h r e g a r d  to the  low  i n s t r u c t i o n a l task.  the i n s t r u c t i o n a l program i s e f f e c t i v e , then p r o v i d i n g  the student with c o r r e c t i o n a l feedback  (T^ or T )  would  2  a l l o w a l l s t u d e n t s to a t t a i n the o b j e c t i v e s of the However, i f no c o r r e c t i o n a l feedback i s p r o v i d e d l a c k of i n f o r m a t i o n for  providing  correctional  less d i f f i c u l t  no c o r r e c t i o n a l feedback other  Higgins  T-^  than  i n the form of r e s p o n s e - i n s e n s i t i v e  average l a t e n c y and  If  that the  o f e r r o r s , average  than To  S i m i l a r reasoning  and  2  s t u d e n t s who  would render the m a t e r i a l  too  unit.  (T3),  the  difficult  were l a c k i n g the p r e r e q u i s i t e s k i l l s  or  who  had  little  attained ability  the p r e r e q u i s i t e s would be  information their  mathematical a b i l i t y .  own  able  T h e r e f o r e , i t was  would o f t e n be able  for their incorrect  h y p o t h e s i z e d that  of e r r o r s , average l a t e n c y who  are  and  high on p r e r e q u i s i t e  would perform b e t t e r  The an  e r r o r s and  response l a t e n c y  significant  the  may  proportion students ability  in prerequisite  when no c o r r e c t i o n a l feedback  product  between the p r o c e s s and  to maximize immediate  that  product  be  variables.  there would be  l i n e a r r e l a t i o n s h i p between the i . e . proportion  of  be u s e f u l f o r b a s i n g  However, a r e l a t i o n s h i p would have to  othesized  of  immediate  such as p r o p o r t i o n  i n s t r u c t i o n i n order  of e r r o r s and  a  process  average  latency  product v a r i a b l e , i . e . immediate l e a r n i n g ,  the e f f e c t s of treatment and removed.  responses.  immediate l e a r n i n g ,  process v a r i a b l e s  during  Therefore, i t  and  to p r o v i d e  which i n t h i s study was  The  established  of  (Tg).  learning.  variables,  lack  c r i t i c a l c r i t e r i o n of success i s the  learning.  mathematical  i n terms of  than students low  i n s t r u c t i o n a l session,  decisions  had  s k i l l s or mathematical  s k i l l s or mathematical a b i l i t y i s provided  were h i g h on  to compensate f o r the  p r o v i d e d and  explanation  or who  Students who  learner  with  characteristics  40  X  L i t e r a t u r e on S t a t e - T r a i t Spielberger  Anxiety  (1966) p o i n t e d out that s i n c e 1950 over  1,500 s t u d i e s indexed under " a n x i e t y " have been r e p o r t e d in Psychological Abstracts.  D e s p i t e so much e f f o r t  area, attempts to d e f i n e a n x i e t y have met w i t h owing t o widely d i f f e r e n t  i n the  difficulties  conceptions of anxiety.  Szetela  (1970) d e s c r i b e d some of the problems with the a n x i e t y construct.  He mentioned d i f f e r e n c e s i n d e f i n i t i o n ,  l i m i t a t i o n s of paper and p e n c i l t e s t s ,  the u n i d i m e n s i o n a l  versus m u l t i d i m e n s i o n a l q u e s t i o n , and the s t a t e trait  c o n c e p t i o n s of a n x i e t y as u n r e s o l v e d  versus  issues.  O ' N e i l e_t al_. (1969) noted t h a t most s t u d i e s c o n c e r n i n g the e f f e c t s of a n x i e t y on l e a r n i n g have o r i g i n a t e d in a r t i f i c i a l  l a b o r a t o r y s e t t i n g s or i n r e a l i s t i c  controlled natural settings. convenient  either but p o o r l y  CAI systems p r o v i d e a  n e t t i n g i n which i t i s p o s s i b l e to e v a l u a t e the  l e a r n i n g p r o c e s s under c a r e f u l l y c o n t r o l l e d c o n d i t i o n s with m a t e r i a l s that a r e r e l e v a n t t o the l e a r n e r . O ' N e i l e_t a l . (1969) observed  that r e s e a r c h on a n x i e t y  and l e a r n i n g has s u f f e r e d from ambiguity w i t h r e g a r d to .the s t a t u s of a n x i e t y as a t h e o r e t i c a l concept.  Spielberger  (1971, 1972) r e c e n t l y emphasized the need to d i s t i n g u i s h between a n x i e t y c o n c e p t u a l i z e d a.s a t r a n s i t o r y c o n d i t i o n of the organism and as a r e l a t i v e l y  s t a t e or stable  personality  trait.  State  anxiety  (A-State) c o n s i s t s of  f e e l i n g s of apprehension and heightened autonomic nervous system a c t i v i t y time.  that vary i n i n t e n s i t y and f l u c t u a t e over  T r a i t anxiety  differences  ( A - T r a i t ) r e f e r s to i n d i v i d u a l  i n anxiety  proneness, that  i s , to d i f f e r e n t i a l  tendencies among i n d i v i d u a l s ' to respond with d i f f e r e n t l e v e l s of A - S t a t e i n s i t u a t i o n s that threatening.  are p e r c e i v e d  as  Persons h i g h i n A - T r a i t a r e a l s o more  d i s p o s e d to see c e r t a i n types o f s i t u a t i o n s as more dangerous, p a r t i c u l a r l y s i t u a t i o n s that some t h r e a t  to that  i n v o l v e f a i l u r e or  i n d i v i d u a l ' s self-esteem.  F a i l u r e to  make t h i s d i s t i n c t i o n has l e d to the i n a p p r o p r i a t e  use o f  operational  measures of A - S t a t e and A - T r a i t , and t h i s has  contributed  to the i n c o n s i s t e n t  in  i n v e s t i g a t i o n s of a n x i e t y .  and c o n t r a d i c t o r y The most  serious  m e t h o d o l o g i c a l f l a w s a r e the use of A - T r a i t measure t r a n s i t o r y a n x i e t y failing  findings  scales to  and the common p r a c t i c e of  to o b t a i n measures o f A - S t a t e t o c o r r o b o r a t e the  e f f e c t s o f e x p e r i m e n t a l m a n i p u l a t i o n s designed to be stressful  (Spielberger,  1972; O ' N e i l ,  O ' N e i l e_t al_. (1969) p o i n t e d study the e f f e c t s of a n x i e t y learning  i s needed that  between a n x i e t y  1972a).  out that  i n order to  on l e a r n i n g , a theory of  s p e c i f i e s the complex r e l a t i o n s h i p  and behaviour.  A c c o r d i n g to the D r i v e  42 Theory proposed  by Spence and T a y l o r ( S p i e l b e r g e r , 1972)  the performance  of h i g h anxious s t u d e n t s would be  to  that of low anxious s t u d e n t s on complex or  tasks and  s u p e r i o r on easy  tasks.  has.been p r o v i d e d f o r t h i s theory  inferior  difficult  Much e m p i r i c a l  support  ( O ' N e i l , 1969a, 1972a).  O ' N e i l e_t a_l. (1969) i n v e s t i g a t e d the r e l a t i o n s h i p between A - S t a t e and performance  on a CAI  males with extreme scores on the A - T r a i t S t a t e - T r a i t A n x i e t y Inventory.  Difficult  task f o r c o l l e g e s c a l e of the and easy  l e a r n i n g m a t e r i a l s were p r e s e n t e d by an IBM  1500  which a l s o p r e s e n t e d the S t a t e - T r a i t A n x i e t y  The  f i n d i n g s of an e a r l i e r  were c o n f i r m e d i n that  study  system  Inventory  (STAI ) A - S t a t e s c a l e , b e f o r e , d u r i n g and a f t e r task.  CAI  the  learning  (O'Neil e_t al_. ,  1969)  (a) A - S t a t e s c o r e s i n c r e a s e d while  s u b j e c t s worked on d i f f i c u l t m a t e r i a l s and decreased when they responded  to easy m a t e r i a l s ; and  (b) high A - S t a t e  s u b j e c t s made s i g n i f i c a n t l y more e r r o r s on the m a t e r i a l s than low A - S t a t e s u b j e c t s .  While  r e l a t i o n between A - T r a i t and performance, s u b j e c t s responded higher  throughout  l e v e l s of A - S t a t e In  difficult  there was  no  high A - T r a i t  the l e a r n i n g task with  than low A - T r a i t s u b j e c t s .  a l a t e r study, O ' N e i l  (1972aj a g a i n used a CAI  task with c o l l e g e students i n an i n t r o d u c t o r y psychology course.  S u b j e c t s i n the s t r e s s c o n d i t i o n were g i v e n  n e g a t i v e feedback  r e g a r d i n g t h e i r performance  on a CAI  43  learning  task, whereas s u b j e c t s  r e c e i v e d n e u t r a l feedback.  i n the n o n - s t r e s s  condition  Negative feedback about  performance i n the s t r e s s c o n d i t i o n l e d to g r e a t e r increments i n A - S t a t e f o r high A - T r a i t s u b j e c t s low A - T r a i t s u b j e c t s .  initial  than f o r  T h i s d i d not occur i n the non-stress  group.  These r e s u l t s a r e c o n s i s t e n t with S t a t e - T r a i t  Anxiety  theory.  with r e g a r d  T h i s study produced d i f f e r e n t r e s u l t s  to the r e l a t i o n s h i p between A - S t a t e and e r r o r s  because the h i g h A - S t a t e s u b j e c t s made s i g n i f i c a n t l y more e r r o r s than low A - S t a t e s u b j e c t s  on the easy  materials.  T h i s r e s u l t was not c o n s i s t e n t with the p r e d i c t i o n from Drive  Theory. One p o s s i b l e e x p l a n a t i o n  of the i n c o n s i s t e n t  relation  between A - S t a t e and e r r o r s i n O ' N e i l ' s two s t u d i e s i s that the  latter  used males.  study used only female s u b j e c t s O'Neil pointed  out t h a t the l i t e r a t u r e  that r e l a t i o n s h i p between a n x i e t y f o r men and women.  and the former suggests  and l e a r n i n g i s d i f f e r e n t  He noted that sex and a n x i e t y  i n t e r a c t i o n s probably r e f l e c t  specific  situational variables  which i n f l u e n c e l e a r n i n g and which may have d i f f e r e n t i a l s i g n i f i c a n c e f o r men and women. must be e x e r c i s e d  He suggests that  caution  i n making g e n e r a l i z a t i o n s concerning the  r e l a t i o n s h i p between a n x i e t y , Wine's (1971) l e v i e w  sex and l e a r n i n g .  of the t e s t a n x i e t y  literature  has i n d i c a t e d that on d i f f i c u l t s t r e s s i s present, achieve  low a n x i e t y  more than high a n x i e t y  suggested that HA students,  tasks i n which e v a l u a t i v e (LA) students  tend t o  (HA) i n d i v i d u a l s .  Wine  compared to LA, f o c u s a  g r e a t e r p r o p o r t i o n of t h e i r a t t e n t i o n on p e r s o n a l preoccupations Tobias  and l e s s to task r e l e v a n t problems. (1973) wrote that p r e v i o u s CAI r e s e a r c h i n  which s t a t e a n x i e t y was assessed  while  students  were  working on i n s t r u c t i o n a l programs have i n d i c a t e d higher l e v e l s of a n x i e t y f o r c o n s t r u c t i n g responses compared to reading study  the program.  He examined t e s t a n x i e t y  i n a CAI  and found no e f f e c t on l e a r n i n g and concluded  that  i f a n x i e t y i s to e x e r c i s e d e b i l i t a t i n g e f f e c t s , more difficult  content  than p r e s e n t l y used i s r e q u i r e d .  (1972) found that r e a l r e d u c t i o n s  i n A-State  were  through i n c r e a s e d use of i n f o r m a t i o n feedback, t h i s r e d u c t i o n d i d not n e c e s s a r i l y r e s u l t  Hensen obtained  although  i n higher  levels  of performance.  Summary The f i n d i n g s from a n x i e t y  s t u d i e s have been  c o n t r a d i c t o r y f o r reasons d e s c r i b e d by S p i e l b e r g e r and  Szetela  Anxiety  (1970).  Inventory  Recent work done with  (1966)  the S t a t e - T r a i t  ( S p i e l b e r g e r e_t al_. , 1970) has shown  promise i n l e a d i n g to b e t t e r understanding  of the e f f e c t s  45  of  a n x i e t y on l e a r n i n g .  some CAI  O'Neil  (1969, 1972a) has done  r e s e a r c h which has produced  D r i v e Theory,  i . e . that the performance  students would be  inferior  on complex or d i f f i c u l t They a l s o found  tasks and  induced i n the s t u d e n t s , p e r c e i v e d as t h r e a t e n i n g .  to suggest  section,  groups i n t h i s study should be ranked  easier  from easy to d i f f i c u l t than T 3 ) .  large d i f f i c u l t y groups.  students  an a n x i e t y by  i n t e r a c t i o n f o r s t r e s s f u l tasks.  As d i s c u s s e d i n the l a s t  T2  anxious  that h i g h e r l e v e l s of A - S t a t e were induced  (1971) a l s o found evidence  difficulty  of h i g h  s u p e r i o r on easy t a s k s .  which meant that the s i t u a t i o n was  difficulty  to support  to that of low anxious  i n s i t u a t i o n s where s t r e s s was  Wine  evidence  the three  i n terms of  (T^ e a s i e r  than  However, i t would appear t h a t  gap would occur between the T  The T-^ or To  treatment  2  T , 2  the  and T 3  treatments would probably be p e r c e i v e d  as r e l a t i v e l y easy i n comparison  to the more d i f f i c u l t T 3  task, where no c o r r e c t i o n a l feedback  i s provided.  The  students have had no experience i n i n t e r a c t i n q with a computer and t h i s f a c t o r  combined with the s t r a n g e content  and s u r r o u n d i n g s would seem to p r o v i d e enough s t r e s s to induce h i g h l e v e l s of a n x i e t y . recent evidence  i t was  high i n A-State w i l l of  e r r o r s and average  Therefore, i n l i n e  with  h y p o t h e s i z e d that students who  are  have a s i g n i f i c a n t l y h i g h e r p r o p o r t i o n l a t e n c y than low A-State  students  46 when no c o r r e c t i o n a l relationship  feedback i s p r o v i d e d  (Tg) and t h i s  would be r e v e r s e d when c o r r e c t i o n a l  feedback  i s provided (To).  Literature  on Aptitude-Treatment  Bracht  (1970) d e s c r i b e d the g o a l of r e s e a r c h on  aptitude-treatment i n t e r a c t i o n s disordinal interactions and  personological  (ATI) as f i n d i n g  between a l t e r n a t i v e  variables,  i n s t r u c t i o n a l programs so that are  Interactions  significant  treatments  i . e . development of a l t e r n a t i v e optimal e d u c a t i o n a l  benefits  o b t a i n e d when s t u d e n t s a r e a s s i g n e d ' d i f f e r e n t l y t o the  a l t e r n a t i v e programs.  The p e r s o n o l o g i c a l  variable  i n ATI  r e s e a r c h was d e f i n e d as any measure of i n d i v i d u a l c h a r a c t e r i s t i c s , e.g. IQ, s c i e n t i f i c  i n t e r e s t or a n x i e t y .  Cronbach and Snow (1969) have w r i t t e n i n the a r e a of ATI.  a major  report  They d e f i n e d " a p t i t u d e " as any  c h a r a c t e r i s t i c o f the i n d i v i d u a l that  increases  (or i m p a i r s )  h i s p r o b a b i l i t y of success i n a g i v e n treatment, and includes the  personality  characteristics.  immediate o b j e c t i v e  specific learner  They agreed +hat  of c u r r e n t ATI work i s to match  i n s t r u c t i o n a l methods or m a t e r i a l s characteristics.  to s e l e c t e d  But more b r o a d l y , they argued  that ATI r e s e a r c h i s concerned with theory to overarch diverse required  ideas such as the branching r u l e s and s t r a t e g i e s i n CA.I.  47 As Bracht interest but  (1970) p o i n t e d  i n the t o p i c o f ATI among e d u c a t i o n a l  very l i t t l e  empirical  support the concept. of r e s e a r c h  studies  treatment t a s k s , variables  out, there i s an i n c r e a s i n g researchers,  evidence has been p r o v i d e d t o  He conducted a s y s t e m a t i c to i n v e s t i g a t e  personological  analysis  the r e l a t i o n s h i p o f  variables  to the occurrence of A T I .  and dependent  He gave a  flowchart  of a procedure f o r t e s t i n g an ATI i n a t r e a t m e n t - b y - l e v e l s factorial  d e s i g n , s i n c e most s t u d i e s  a n a l y s i s of v a r i a n c e .  used t h i s d e s i g n with  He suggested that  powerful than r e g r e s s i o n  analysis  since creating  l e v e l s o f a continuous p e r s o n o l o g i c a l increase  the e r r o r component  t h i s method  variable  i n the a n a l y s i s .  i s less  artificial  tends to Regression  a n a l y s i s , however, was used i n r e l a t i v e l y few ATI s t u d i e s . From h i s a n a l y s i s , B r a c h t  (1970) found d i s o r d i n a l  i n t e r a c t i o n s i n only f i v e of the 103 s t u d i e s . tend to i n d i c a t e that  The r e s u l t s  there i s a r e l a t i o n s h i p between  d i s o r d i n a l i n t e r a c t i o n s and the degree o f c o n t r o l treatment t a s k s o f the experiment.  Controlled  over the  treatment  t a s k s may be a necessary but c e r t a i n l y not a s u f f i c i e n t requirement f o r d i s o r d i n a l i n t e r a c t i o n s . specific abilities,  interests, personality  c l a s s i f i e d as f a c t o r i a l l y  simple.  was c l a s s i f i e d as f a c t o r i a l l y have a s u b s t a n t i a l  loading  Measures of traits  A personological  were variable  complex i f i t was judged to  on many f a c t o r s i n the imaginary  48  \ f a c t o r matrix, e.g.  general a b i l i t y .  Bracht's  (1970)  r e s u l t s l e n d some support to the r e l a t i o n s h i p between ATI and the degree variable,  of f a c t o r i a l  s i m p l i c i t y of the p e r s o n o l o g i c a l  although f a c t o r i a l  sufficient  requirement  simplicity  f o r ATI.  certainly  i s not a  Many experiments  u s i n g IQ  as a v a r i a b l e found no evidence to suggest  that the IQ  score and s i m i l a r measures o f g e n e r a l a b i l i t y . a r e  useful  v a r i a b l e s f o r d i f f e r e n t i a t i n g a l t e r n a t i v e treatments f o r s u b j e c t s i n a homogeneous age group (Bracht, 1970). However, Cronbach and development of a l t e r n a t i v e ability.  They f e e l  synonomous with  i t s u s u a l common sense  the o t h e r treatment o b j e c t i v e s without a priori  treatments  on the b a s i s of genera!  that g e n e r a l a b i l i t y  'ability  s h o u l d be designed  Snow (1969) recommended the  seems to be n e a r l y  to l e a r n ' , when that term i s g i v e n  interpretation.  One  treatment  to r e l y h e a v i l y on g e n e r a l a b i l i t y , should be d e s i g n e d  and  to achieve the same  r e l y i n g on g e n e r a l a b i l i t y .  This  s p e c i f i c a t i o n of treatments had not been done i n  past research.  The  reason f o r a p p l i c a t i o n of a broad,  l o o s e c o n s t r u c t i s that at present there i s no evidence to support a more r e f i n e d Bracht about  one.  (1970) l e a r n e d very l i t t l e  from h i s a n a l y s i s  the r e l a t i o n s h i p between the dependent v a r i a b l e  the o c c u r r e n c e of ATI because the dependent v a r i a b l e  and was  49 most o f t e n e r r o r s  i n l e a r n i n g or p o s t t e s t  (1972) suggested that ATI s t u d i e s  score.  include  as many d i f f e r e n t  c r i t e r i o n measures as p o s s i b l e , e.g. l e a r n i n g retention  tests, transfer  He f e e l s that not  well  the c u r r e n t  tests,  t e s t s , time to completion, e t c . s t a t e of the theory of ATI i s  enough developed to determine the s p e c i f i c dependent  variables  that  should or s h o u l d not be  included.  Bracht found that ATI i s more l i k e l y two  Webb  personological  to occur when  v a r i a b l e s have been i n c l u d e d  experimental design.  One v a r i a b l e  i n the  i s judged to c o r r e l a t e  s u b s t a n t i a l l y with, success i n one treatment and the other judged to c o r r e l a t e s u b s t a n t i a l l y with success i n the second treatment.  The c o r r e l a t i o n between the two  personological  v a r i a b l e s must be moderately low or n o n s i g n i f i c a n t  f o r the  d i s o r d i n a l i n t e r a c t i o n to occur. F i n a l l y , B r a c h t suggested that experimenters should b e g i n to f o r m u l a t e hypotheses about ATI with f a c t o r s , such as c o s t ,  i n mind.  administrative  Hence, even o r d i n a l  i n t e r a c t i o n s may l e a d to d e c i s i o n s  about  differential  assignment to treatments when a d m i n i s t r a t i v e  f a c t o r s are  taken i n t o account. Campeau (1963) found a s i g n i f i c a n t t e s t a n x i e t y feedback i n t e r a c t i o n f o r g i r l s in  the s e c t i o n d e a l i n g  results.  O'Neil  i n a study d e s c r i b e d  by earlier  with l i t e r a t u r e on knowledge-of-  (1972) found A s i g n i f i c a n t State  Anxiety  50 by task d i f f i c u l t y earlier  i n t e r a c t i o n i n another  study d e s c r i b e d  i n the s e c t i o n d e a l i n g with l i t e r a t u r e on a n x i e t y .  Dick and L a t t a  (1970) compared a programmed  i n s t r u c t i o n v e r s i o n with a comparable CAI  v e r s i o n of the  same m a t e r i a l u s i n g grade e i g h t mathematics s t u d e n t s . The  s i x t y - f o u r s t u d e n t s were randomly a s s i g n e d to  programmed i n s t r u c t i o n and CAI significant figures.  The  programs on the t o p i c of  r e s u l t s i n d i c a t e d that the  students using programmed i n s t r u c t i o n  performed  s i g n i f i c a n t l y b e t t e r than those u s i n g CAI. d i f f e r e n c e was  attributed primarily  performance by  the low a b i l i t y  There was  also a s i g n i f i c a n t  This  to the very poor  students i n the CAI  ability  effect.  group.  The p o s t t e s t  and r e t e n t i o n t e s t r e s u l t s , as w e l l as number of e r r o r s in  the a c t u a l l e a r n i n g sequence, i n d i c a t e d that there  a t r a i t - b y - t r e a t m e n t i n t e r a c t i o n which was  was  interpreted  p r i m a r i l y as a very poor performance by low a b i l i t y on CAI,  with almost  ability  students u t i l i z i n g programmed i n s t r u c t i o n a l m a t e r i a l s ,  The c o n j e c t u r e may a r e unable  equal performance by h i g h and  students  be made that the low a b i l i t y  them  students  to cope with the continuous f l o w of i n f o r m a t i o n  as p r e s e n t e d by the cathode-ray • ability  low  tube  (CRT)  without  the  to r e t u r n to the i n f o r m a t i o n p r e v i o u s l y p r o v i d e d  Becker  (1970) wrote that there  o f s t u d i e s that are treatment  e x i s t s a l a r g e number  i n d i r e c t l y relevant  i n t e r a c t i o n research  but  to  aptitude-  that few  s t u d i e s have  been d e s i g n e d to i n v e s t i g a t e i n t e r a c t i o n between and  instruction.  various  abilities  Becker  (1970) d i s c u s s e d  the  aptitude  idea  that  might p l a y an important r o l e i n  d e t e r m i n i n g what method of i n s t r u c t i o n i s p r e s c r i b e d f o r a p a r t i c u l a r l e a r n e r or group o f l e a r n e r s . i n d i v i d u a l s who  are high  m e d i a t o r s than v e r b a l ones. some p o t e n t i a l d i f f i c u l t i e s He  may  be  Becker in  mathematical out  aptitutde-treatment the  s e l e c t i o n of  i n t e r a c t w i t h methods of  be d i f f i c u l t .  In g e n e r a l ,  aptitude  measures  needed that get at s p e c i f i c a s p e c t s of mental  abilities  and  with a c c e p t a b l e  Determining the l e n g t h of the problem. past  should  (1970) p o i n t e d  concluded that  a p t i t u d e measures that w i l l i n s t r u c t i o n may  example,  on mathematical a b i l i t y  p r o f i t more from i n s t r u c t i o n that p r o v i d e s  i n t e r a c t i o n research.  For  The  i t is difficult  achievement  reliability.  treatment p e r i o d i s another  problem e x i s t s of a s s e s s i n g  i n s t r u c t i o n on s u b j e c t s  Finally,  l e v e l s of  the impact  involved i n current  to determine the  research.  type of  ( c r i t e r i o n ) measures from which we  to d e r i v e i n t e r a c t i o n s .  of  are  likely  52  Summary This that  b r i e f review of the ATI  interactions  been r a r e  and  between a p t i t u d e  that  from most ATI  l i t e r a t u r e indicates and  treatment have  more work i s needed.  r e s e a r c h i s not  The  evidence  d e f i n i t i v e enough  to  p r o v i d e guidance f o r i n d i v i d u a l i z i n g i n s t r u c t i o n . This  study has  attempted  e x i s t e n c e of i n t e r a c t i o n s  to p r o v i d e evidence f o r  between c o r r e c t i o n a l  and  a n x i e t y , c o r r e c t i o n a l feedback and  and  c o r r e c t i o n a l feedback and  feedback  prerequisite  skills  mathematical a b i l i t y .  L i t e r a t u r e on T u t o r i a l Computer-Assisted I n s t r u c t i o n The  most r e l e v a n t  CAI  studies  reviewed i n p r e v i o u s s e c t i o n s  of t h i s chapter.  and  gaming, t u t o r i a l  and  practice,  i n s t r u c t i o n and  study i s concerned with CAI the  the  system.  and  modes of  inquiry,  CAI:  simulation  author mode.  system.  The  This  In t h i s racde,  is primarily i t s ultimate  conciotually form w i l l  rather  entered  state  into  of development,  than e m p i r i c a l l y  i n e f f e c t be  the  l o g i c of  i n d e c a i l and  T h i s mbc'e i s i n a p r i m i t i v e  the  examined.  t u t o r i a l mode.  i n s t r u c t i o n must be f o r m a l i z e d  It  Some of  i n s t r u c t i o n a l programmer takes r e s p o n s i b i l i t y f o r  s t u d e n t ' s i n s t r u c t i o n on  the  be  (1968) i d e n t i f i e d s e v e r a l  problem s o l v i n g , d r i l l  (CAI)  have a l r e a d y been  other l i t e r a t u r e i n t h i s a r e a w i l l now Stolurow  the  a theory of  based, teaching.  53 The  theory  w i l l depend f o r development upon s p e c i f i c  d e s i g n e d to generate d a t a on how  to use  studies  different rules  for  i n s t r u c t i n g s t u d e n t s w i t h d i f f e r e n t response h i s t o r i e s  and  unique c h a r a c t e r i s t i c s . Unfortunately,  the above theory  p r o g r e s s e d as w e l l as Stolurow had discussions  of CAI  envisioned.  Most  A few  of the f u n c t i o n s  i n s t r u c t i o n a l block  and  are concerned with d e c i s i o n  i n s t r u c t i o n a l s t r a t e g i e s that p r i m a r i l y  explanation  not  are concerned with computer hardware  software problems. l o g i c s and  development has  involve  i n v o l v e d i n t r a n s f e r r i n g from  to i n s t r u c t i o n a l b l o c k .  Fewer  d i s c u s s i o n s i n v o l v e d e t a i l about the c h a r a c t e r i s t i c s of the  teaching  stimulus  sequence w i t h i n  d i s p l a y , the  information  required  these b l o c k s  i n terms of  student response or the (Glaser,  1971).  The  (1967) and D i c k The  remains to be appropriate matter areas  still  (1965) reached the same  matter of p e r s o n a l i t y - c o m p u t e r i n t e r a c t i o n  studied.  One  program s t r u c t u r e w i l l not  foa. a i l l e v e l s of a b i l i t y (Dick,  1965).  almost a l l f u n i s a l l o t t e d  Gentile to CAI  and  on  teaching  and  various  be  subject  (1967) wrote that  p r o j e c t s are being  cn the development of c o u r s e s or equipment of research  learner  studied.  Gentile conclusion.  feedback  i n t e r a c t i o n of  these v a r i a b l e s with c h a r a c t e r i s t i c s of the remains to be  the  to the  spent  exclusion  l e a r n i n g , v a r i a b l e s , where  54  research  i s needed most.  Sherman (1971) d i s t i n g u i s h e d two a CAI  lesson.  pedagogical  The  task i s one  developing  of d e s i g n i n g  the  exchanges, i . e . the sequence of exchanges that  conversations CAI  first  tasks i n  may  conversations  follow.  The  second task i n  i s that o f programming the  developing conversational  network so that a given computer can p l a y i t s r o l e i n the dialogue.  He proposed r e d u c i n g  second task by  the use  the  time spent  on  of programmed templates.  (1971) d e f i n e d the work "template"  the Sherman  as:  . . . a sequence of i n s t r u c t i o n s to the computer f o r p r o c e s s i n g a p a r t i c u l a r network of c o n v e r s a t i o n a l exchanges and connotes a p a r t i c u l a r p a t t e r n f o r the p r e s e n t a t i o n of q u e s t i o n s , answers and other b a s i c elements of t u t o r i a l conversation. The  p a t t e r n determines only  v e r s a t i o n a l exchanges, not themselves. it  the l o g i c of the con-  the content  of the  conversations  Sherman (1971) developed a template and  to program a d i a l o g u e  used  to teach some c o l l e g e p h y s i c s  concepts. I n v e s t i g a t o r s i n s e v e r a l major CAI c u r r e n t l y conducting  r e s e a r c h and  the a r e a of t u t o r i a l mode CAI. r e p o r t e d by Bande.rsor. et _al, Texas at A u s t i n o.nd Hansen University.  centres  are  development a c t i v i t i e s i n  S e v e r a l CAI  p r o j e c t s were  (1968) at the U n i v e r s i t y of  (1971) at F l o r i d a  State  In a p r o j e c t at the U n i v e r s i t y of Texas at  Austin  (Judd e_t al_. , 1970)  provide  diagnosis  courses.  the p o s t t e s t .  cases program c o n t r o l was i n other  The  CAI  students  achieved  They a l s o found that i n some superior  to l e a r n e r c o n t r o l  cases some form of l e a r n e r c o n t r o l was  Bunderson  (1971) f e l t  so c o m p l i c a t e d  risky.  developed to  demonstrated s u p e r i o r performance to the non-CAI  students on  type,  course was  of d e f i c i e n c i e s i n s k i l l s p r e r e q u i s i t e  to freshman s c i e n c e w e l l and  a CAI  by  Other CAI  superior.  that the r e s u l t s of t h i s study  i n t e r a c t i o n s with p r e t e s t score,  amount o f p r a c t i c e and  t o p i c as  and  are  terminal  to make g e n e r a l i z a t i o n s  programs at Texas are used to  teach  E n g l i s h , Computer Programming, B u s i n e s s Management, Astronomy Mathematics and The  Science,  Arabic Writing  r e s u l t s from these p r o j e c t s are not  p r o j e c t s are regarded as e x p l o r a t o r y information  and  System and conclusive.  i n nature a.nd  methods to ease the problem of  h i g h q u a l i t y i n s t r u c t i o n a l programs; maintenance, and  Chemistry. The provide  designing  the c o s t s of  preparation  r e v i s i o n are the primary v a r i a b l e s .  Minimum l e v e l s of student performance, time to complete and  a t t i t u d e r a t i n g s are used as d e s i g n Several  to study the  recent  criteria.  s t u d i e s have u t i l i z e d  i n s t r u c t i o n a l process.  t u t o r i a l mode CAI  Some of these  (Gilman, 1967;  Keats and Hansen, 1972;  been d e s c r i b e d  i n the e a r l i e r  V^n  Dyke, 1972)  s e c t i o n s of t h i s  Other s t u d i e s i n the areti a r c d e s c r i b e d  studies  below.  chapter.  have  S u t t e r and R e i d  (1969) showed that the e f f e c t i v e n e s s  o f CAI i n t e a c h i n g a course i n problem s o l v i n g i s the same f o r the student working alone with the machine as f o r the student working with a p a r t n e r a t the machine, except when c o n d i t i o n a l upon c e r t a i n p e r s o n a l i t y t r a i t s .  College  s t u d e n t s were used and high t e s t a n x i e t y was a s s o c i a t e d with n e g a t i v e a t t i t u d e s toward CAI i n both the p a i r e d and alone groups.  A significant  i n t e r a c t i o n was o b t a i n e d  between t e s t a n x i e t y and achievement f o r the two groups. Students h i g h i n t e s t a n x i e t y achieved b e t t e r working a l o n e , w h i l e those low i n t e s t a n x i e t y a c h i e v e d b e t t e r working with a partner.  An i n t e r a c t i o n was a l s o found between  sociability  and achievement f o r the two groups. Bunderson and h i s c o l l e a g u e s (Bunderson, developed system.  an imaginary  1971)  s c i e n c e task c a l l e d a Xenograde  The Xenograde system has the h i e r a r c h i c a l s t r u c t u r e  o f concepts  and q u a n t i t a t i v e r u l e s c h a r a c t e r i s t i c o f many  topics i n science education. imaginary  The g r e a t e s t advantage of i t s  c h a r a c t e r has been to enable r e s e a r c h e r s to  c o n c e n t r a t e on d e s i g n v a r i a b l e s - s t r u c t u r e , d i s p l a y , etc.. rather  than s u b j e c t matter  variables.  o f l e a r n i n g have been conducted Olivier  S e v e r a l CAI s t u d i e s  with t h i s  topic.  (1971) compared the performance of students i n  the l e a r n e r c o n t r o l mode with students f o r whom the sequence was c o n t r o l l e d by the program.  He matched students i n both  57  groups and  so the data were not  are s u g g e s t i v e  only.  The  conclusion  small number of e x c e p t i o n a l the  sequence of l e s s o n s  f o r l e a r n i n g new  treated s t a t i s t i c a l l y  students,  i s that except f o r a learner c o n t r o l of  i n a h i e r a r c h y may  material  than a r a t i o n a l l y  c a r e f u l l y designed p r o g r a m - c o n t r o l l e d  but  be  less effective  planned,  sequence.  Bunderson  (1971) wrote that i n subsequent s t u d i e s u s i n g  partially  familiar material  cut.  Merrill  the r e s u l t s were l e s s c l e a r  (1971) i n v e s t i g a t e d the e f f e c t s that  a v a i l a b i l i t y of b e h a v i o u r a l l y  s t a t e d o b j e c t i v e s would have  on  Xenograde s c i e n c e was  the  learning process.  with 130  The  c o l l e g e students.  The  used  r e s u l t s showed that  o b j e c t i v e s s i g n i f i c a n t l y reduced the number of examples required total  to l e a r n the t a s k .  l a t e n c y but  Objectives  d i d reduce t e s t - i t e m response  No  significant  on  the p o s t t e s t s or r e t e n t i o n t e s t s , but  r u l e e f f e c t was  d i d not  d i f f e r e n c e s were found between  found i n favour  reasoning  have o r i e n t i n g and  using  organizing  significant received  test-item-response  f a c t o r scores,  t e s t s as c o v a r i a b l e s .  the r e s u l t s of t h i s study i t was  treatments  Significant ability-by-  treatment i n t e r a c t i o n s were o b t a i n e d  i n d i v i d u a l reasoning  latency.  of the groups which  the r u l e as opposed to examples.  l a t e n c y as c r i t e r i o n and  a  reduce  On  concluded that  plus  the b a s i s  of  objectives  e f f e c t s which d i s p o s e  students  58  to  a t t e n d to, p r o c e s s and  i n accordance Lorber  structure relevant information  with the g i v e n o b j e c t i v e s . (1970) demonstrated that CAI  i s an  effective  means by which to teach the b a s i c elements of t e s t s measurements and p u p i l e v a l u a t i o n of p r o s p e c t i v e school teachers.  and  secondary  H i s r e s u l t s showed that the CAI  group  s c o r e d higher on the p o s t t e s t than the c o n v e n t i o n a l classroom  group and needed l e s s i n s t r u c t i o n a l  A t t i t u d e s towards CAI Tira  were f a v o u r a b l e .  (1970) produced  a CAI program d e a l i n g with  Product-Moment f a c i l y o f c o r r e l a t i o n s . study had f o u r phases:  was  judged  This  (1) d e f i n i t i o n of  (2) design of l e s s o n c o n t e n t , from content,  time.  non-experimental  requirements,  (3) p r o d u c t i o n of CAI  ( 4 ) e v a l u a t i o n of the program.  to be s u c c e s s f u l and  the author  the  The  dialogue  program  recommended that  the e n t e r i n g c h a r a c t e r i s t i c s of the l e a r n e r be  identified  and p a i r e d with a program sequence which would best facilitate CAI  the meaningful  l e a r n i n g of the concepts on  the  course. Ibrahim  (1970) compared CAI  with other  methods i n the t e a c n i n g of the concepts freshman c a l c u l u s .  The  instructional  of l i m i t s i n  other i n s t r u c t i o n a l methods were  (1) t h e . i n s t r u c t o r c e n t r e d or t r a d i t i o n a l approach (2) a combination  of t r a d i t i o n a l and  CAI.  The  and  findings  were that  the CAI  traditionally  students d i d s i g n i f i c a n t l y better  taught s t u d e n t s on immediate  than  achievement  but  no s i g n i f i c a n t d i f f e r e n c e s were found i n r e t e n t i o n , a t t i t u d e s toward CAI and toward mathematics.  CAI  was  as  e f f e c t i v e as other methods i n t e a c h i n g the concepts o f limits. Castleberry  (1970) developed and e v a l u a t e d CAI  programs on s e l e c t e d t o p i c s i n i n t r o d u c t o r y chemistry. drill  These  t o p i c s were a combination of  and s i m u l a t i o n modules designed s o l e l y  supplementary  college  study a i d s .  tutorial  as  The c o n c l u s i o n s were that the  s t u d e n t s a c q u i r e d the b e h a v i o u r a l o b j e c t i v e s of the modules to v a r y i n g degrees.  The modules a l l o w e d f o r a range o f  i n d i v i d u a l d i f f e r e n c e s based on a b i l i t y , p r i o r  learnings  and s e l f - e v a l u a t i o n .  The CAI programs had a s i g n i f i c a n t  e f f e c t on achievement  as measured by the f i n a l  Full  examination.  s c a l e implementation o f a course with these modules  would be  feasible.  C r o p l e y and Gross u n i v e r s i t y s t u d e n t s who  (1970) compared a group o f r e c e i v e d i n s t r u c t i o n i n FORTRAN .  programming v i a CAI through a remote t e r m i n a l connected to a computer more than 400 m i l e s away w i t h a programmed i n s t r u c t i o n group and a c o n v e n t i o n a l l e c t u r e group.  All  t h r e e methods proved  serious  to be e q u a l l y e f f e c t i v e and no  60  n e g a t i v e f e e l i n g s about being r e p o r t e d by the s t u d e n t s .  taught by machines were  CAI compared f a v o u r a b l y with  t r a d i t i o n a l i n s t r u c t i o n as f a r as time was T h e i r f i n d i n g s suggest  concerned.  t h a t CAI i s a r e a l i s t i c and  a c c e p t a b l e a l t e r n a t i v e to t r a d i t i o n a l classroom  procedures  i n appropriate situations. O l d e h o e f t and Conte at Purdue U n i v e r s i t y  (1971) developed  a computer  to teach p o r t i o n s of an  course i n numerical methods.  system  undergraduate  Each i n s t r u c t i o n a l u n i t or  l e s s o n was d i v i d e d i n t o three modes o f i n s t r u c t i o n which a l l o w e d the student  to p r o g r e s s from a c o m p u t e r - c o n t r o l l e d  p r e s e n t a t i o n to a s t u d e n t - c o n t r o l l e d i n v e s t i g a t i o n .  These  were t u t o r i a l mode, problem mode and i n v e s t i g a t i o n mode. The  system was designed as a classroom independent  study, and had been used f o r two semesters  by students i n  p l a c e o f c o n v e n t i o n a l classroom i n s t r u c t i o n . c o n s i s t e d of twenty-five lessons. similar  similar  The program  The t u t o r i a l mode was  t o l i n e a r programmed i n s t r u c t i o n where the student  responded response  course of  to a mixture type items.  of m u l t i p l e c h o i c e and c o n s t r u c t e d The i n s t r u c t i o n a l s t r a t e g y here was  to that developed  by Bork  (1971).  A major f a c t o r  which l i m i t s the o v e r a l l e f f e c t i v e n e s s i s a g e n e r a l l a c k of a n t i c i p a t e d i n c o r r e c t responses  built  into  o v e r a l l i n d i c a t i o n was that the average  the program.  CAI student  The  performed  61  as w e l l as he would have under the c o n v e n t i o n a l system. o v e r a l l a t t i t u d e toward  CAI was f a v o u r a b l e .  F e n i c h e l e_t a l . (1970) developed MIT  to ease  The  the TEACH system  the c o s t and improve the r e s u l t s of  i n s t r u c t i o n i n programming.  at  elementary  To the student, TEACH o f f e r s  l o o s e l y guided e x p e r i e n c e with a c o n v e r s a t i o n a l language which was  d e s i g n e d with t e a c h i n g i n mind.  involvement  i s minimal.  The  Faculty  e v a l u a t i o n of the p r o j e c t  i n d i c a t e d that the t e c h n i c a l aim of completing  the  system  and b r i n g i n g i t i n t o p r o d u c t i o n and smooth o p e r a t i o n has been met. of  No  the e f f i c a c y  the t e a c h i n g method, a l t h o u g h i n t e r v i e w s with the s t u d e n t s  determined The  t e s t s have been made to determine  that  the s t u d e n t s had i n f a c t  l e a r n e d the m a t e r i a l .  authors d i s t i n g u i s h e d between semantic and  errors.  The  t e c h n i c a l i s s u e of e r r o r  and the authors d e s c r i b e d the problem  syntactic  d e t e c t i o n was of semantic  raised  error  d e t e c t i o n as that of i n f o r m i n g a student of what e r r o r has made and o f f e r i n g him time.  The  erroneous or  i n p u t to determine  misunderstanding. by the  s u i t a b l e h e l p at the a p p r o p r i a t e  system mu?t be a b l e to go beyond  whether i t was  he  the r e s u l t  whether i t was  superficially a simple  slip  of some deep c o n c e p t u a l  T h i s task i s p r e s e n t l y being  tackled  experimenters. Bork and  Sherman (1971) and  latei  Kalman, Kaufman and  62  Ladd  (1971) used a t u t o r i a l program to teach the p r o o f of  the c o n s e r v a t i o n of energy to c o l l e g e s t u d e n t s . l e s s o n proved  successful, actively involving  in a t u t o r i a l  l e s s o n and  the  t e a c h i n g the concepts  S e v e r a l problems were noted.  The  difficulty  The  CAI  students  involved.  of u s i n g  standard C a l c u l u s n o t a t i o n on a computer t e r m i n a l and  the  i n a b i l i t y of the computer to r e c o g n i z e a l l c o r r e c t and incorrect  responses  were n o t a b l e  Hansen (1966) reviewed found  CAI  limitations. t u t o r i a l a p p l i c a t i o n s and  that the most c o n s i s t e n t f i n d i n g  i s the marked s a v i n g  in instructional  time with no l o s s i n p o s t - i n s t r u c t i o n  achievement t e s t  performance.  Kromhout, Edwards and  Schwartz (1969) d e s c r i b e d the  use of computers i n p h y s i c s i n s t r u c t i o n .  They p r e s e n t e d  d e s c r i p t i o n of r e p r e s e n t a t i v e CAI p r o j e c t s i n p h y s i c s concluded stage.  that most p r o j e c t s were s t i l l  They a l s o concluded  i n the e a r l y  t h a t the v a r i e d and  uses of the computer were encouraging  and  a  and testing  imaginative  that i n t r o d u c t i o n  of the computer i n t o p h y s i c s i n s t r u c t i o n r e p r e s e n t e d a significant  development.  Atkinson  (1968) d e s c r i b e d a CAI  teach r e a d i n g to f i r s t children.  t u t o r i a l p r o j e c t to  grade c u l t u r a l l y  An experiment was  conducted  disadvantaged which compared a  group to a t r a d i t i o n a l group taught by a teacher  i n the  CAI  63  classroom.  The  two  groups were not s i g n i f i c a n t l y  different  at the s t a r t of the year, but at the end of the year group t h a t r e c e i v e d c o m p u t e r - a s s i s t e d performed  s i g n i f i c a n t l y b e t t e r on almost  achievement t e s t s . of both  reading  He concluded  the r a t e of p r o g r e s s and  completed  d u r i n g the year,  the  instruction  a l l of the r e a d i n g  that from  the  standpoint  the t o t a l number of problems  the computer c u r r i c u l u m  appeared  to be q u i t e r e s p o n s i v e to i n d i v i d u a l d i f f e r e n c e s .  Few  sex d i f f e r e n c e s were found and  that with  CAI,  the r e s u l t s suggest  sex d i f f e r e n c e i s minimized  as the emphasis moves  toward a n a l y s i s and away from r o t e memorization. k i n d of problem on which the g i r l s a c h i e v e d h i g h e r s c o r e s than the boys, word-test e s s e n t i a l l y a memorization  task.  The  significantly  learning, i s  Students,  teachers  parents r e a c t e d f a v o u r a b l y to the i n t r o d u c t i o n of CAI classroom.  one  and to the  V a r i o u s o p t i m i z a t i o n r o u t i n e s were e v a l u a t e d  and A t k i n s o n b e l i e v e s that these e v a l u a t i o n s have other experiments  suggested  and a n a l y s i s which c o u l d l a y the  grcundword f o r a theory of i n s t r u c t i o n  t r u l y u s e f u l to the  educator. C a r t w r i g h t and M i t z e l  (1971) developed  l a b o r a t o r y at P e n n s y l v a n i a S t a t e U n i v e r s i t y IBM  1500  i n s t r u c t i o n a l system.  A CAI  which would p r o v i d e i n t e n s i v e t r a i n i n g  a mobile utilizing  course was in special  CAI an  developed education  64  concepts  to s p a r s e l y p o p u l a t e d c o u n t i e s .  c a l l e d Computer-Assisted  The  Remedial E d u c a t i o n  course  was  (CARE).  Pilot  groups and other f o r m a t i v e e v a l u a t i o n procedures were used to produce free.  a CAI  course which was  i n t e r n a l l y v a l i d and  Summative e v a l u a t i o n s have shown that s t u d e n t s  error who  took the CAI course s c o r e d s i g n i f i c a n t l y higher i n achievement and used about  o n e - t h i r d l e s s time  to cover  the r  same o b j e c t i v e s than students i n s t r u c t e d i n the c o n v e n t i o n a l l e c t u r e - d i s c u s s i o n method. Lower  (1971) r e c e n t l y r e p o r t e d on CAI a c t i v i t i e s at  Simon F r a s e r U n i v e r s i t y reported  (SFU) i n B r i t i s h Columbia.  that more than e i g h t y CAI  He  courses have been  authored at SFU but that most of these have been e x p e r i m e n t a l or e x p l o r a t o r y i n nature.  Only about  ten have a c t u a l l y  r e c e i v e d s u b s t a n t i a l use i n c o n n e c t i o n with r e g u l a r u n i v e r s i t y cr h i g h school c o u r s e s .  Most o f the c o u r s e s  are i n c h e m i s t r y , but t h e r e has been some a u t h o r i n g activity  w i t h i n the areas o f p h y s i c s , mathematics, b i o l o g y  and economics, w h i l e the h i g h school c o u r s e s cover a wider sphere.  He  notes  that s t u d e n t s have p l a y e d an  r o l e i n programming o f the c o u r s e s . is  the i d e a that CAI  i n s t r u c t i o n a l system may  important  An important c o n c l u s i o n  i s o n l y one component of an and  that computer managed i n s t r u c t i o n  be more e f f e c t i v e i n p r a c t i c e .  65  The most s o p h i s t i c a t e d and advanced CAI system i s c u r r e n t l y the PLATO system a t the U n i v e r s i t y of I l l i n o i s (Bitzer, 1970).  1967; B r a u n f i e l d e t a l . , 1962; A l p e r t e t a l . , Hammond  (1972) wrote that the PLATO system i s one  of the most ambitious  time s h a r i n g systems ever  attempted.  Much o f the hardware, a new programming language adapted for  t e a c h i n g , and economical  new techniques f o r l i n k i n g  remote t e r m i n a l s to a c e n t r a l computer were s p e c i f i c a l l y f o r e d u c a t i o n a l use.  designed  The student  terminals  are perhaps the most s o p h i s t i c a t e d and expensive ever developed  devices  f o r communicating with a computer.  a u t h o r i n g new c o u r s e s , a programming language based on E n g l i s h grammar and syntax i s designed teachers with no knowledge o f computers.  For  (Tutor) f o r use by  Some 200 such  t e a c h e r s o f v a r y i n g backgrounds have c r e a t e d courses T u t o r and e a r l i e r v e r s i o n s of PLATO.  with  B i t z e r e_t a l . (1967)  d e s c r i b e d the a p p l i c a t i o n o f the PLATO system t o s c i e n c e education.  Lessons on g e n e t i c s , chemistry,  e n g i n e e r i n g and elementary  physics,  s c h o o l t o p i c s a r e being  B r a u n f i e l d and F o s d i c k  used.  (1962) p o i n t e d out that the  power o f the computer based t e a c h i n g system stems from i t s ability  to pose complex q u e s t i o n s , judge the s t u d e n t s '  answers to these q u e s t i o n s and take an a p p r o p r i a t e course o f a c t i o n on the b a s i s o f student  responses.  The computer a l s o  66  keeps d e t a i l e d and a c c u r a t e r e c o r d s o f student  performance,  which are u s e f u l guides to improving c o u r s e c o n t e n t .  The  authors r e p o r t e d a study u s i n g PLATO to teach nine undergraduate  s t u d e n t s a p o r t i o n of a course i n computer  programming.  The  t e a c h i n g l o g i c was  d e f i n e d and  the  authors p r e s e n t e d t a b l e s to i n d i c a t e the most u s e f u l of d a t a which can be gathered about process. system  instructional  They concluded that the s t u d e n t s found  very easy  distract  to use and  the PLATO  that the system d i d not  the s t u d e n t s ' a t t e n t i o n from  A l p e r t and B i t z e r system,  the  types  the l e s s o n s  themselves,  (1970) r e p o r t e d on the PLATO IV  which i s the l a t e s t v e r s i o n of t h i s system.  They  r e p o r t e d a study i n which a c l a s s of twenty s t u d e n t s i n a m e d i c a l s c i e n c e course was  taught f o r a semester  w i t h the PLATO IV system.  When compared with a c o n t r o l  group i n a n a t i o n a l l y a d m i n i s t e r e d t e s t ,  entirely  the i.tudents taught  with the PLATO IV system were found to have s c o r e d as w e l l i n grade one-third  performance  even though they had r e q u i r e d only  to o n e - h a l f as many student c o n t a c t hours  i n s t r u c t i o n as those taught i n the c o n v e n t i o n a l  of  classroom.  Subsequent measurements extending over a twenty-six week p e r i o d i n d i c a t e d that the PLATO group showed H g r e a t e r r e t e n t i o n over that  interval.  67  B i t z e r et. al. (1967) c l a i m e d t h a t CAI was e f f e c t i v e i n teaching e l e c t r i c a l engineering.  Students  taught by  the i n q u i r y method showed g r e a t e r problem s o l v i n g than those claimed  taught by the t u t o r i a l method.  to have gained some i n s i g h t  process,  thereby  improving  PLATO-CAI system can both b e h a v i o u r a l experiments,  He f u r t h e r  i n t o the l e a r n i n g  the m a t e r i a l p r e s e n t e d  i n q u i r y and t u t o r i a l modes.  ability  He concluded  i n both  that the  teach and e x p l o r e p h y s i c a l and thus he d e s c r i b e d h i s system  as v e r s a t i l e and f l e x i b l e .  Summary The  purpose of t h i s review  of t u t o r i a l CAI was to  p r o v i d e a v a r i e t y o f examples which would demonstrate the p o t e n t i a l c o n t r i b u t i o n o f CAI to e d u c a t i o n . relevant  The s t u d i e s  to the p r e s e n t study were d i s c u s s e d i n e a r l i e r  s e c t i o n s o f the c h a p t e r .  A wide range of a c t i v i t y i s  ongoing i n the a r e a o f t u t o r i a l CAI with r e g a r d to hardware (Hammond, 1972), software i n s t r u c t i o n a l courses Metzel, 1971;  ( F e n i c h e l e t a l . , 1970),  ( B i t z e r e_t a J . , 1967; C a r t w r i g h t and  1971; Lower, 1971), i n s t r u c t i o n a l s t r a t e g i e s  Oldehoeft  (Bork,  and Conte, 1971).  Summary o f Rcser.rch Hypotheses The  r e s e a r c h q u e s t i o n s o f i n t e r e s t were r a i s e d i n  Chapter  1.  hypotheses la.  The q u e s t i o n s can be t r a n s l a t e d i n t o  specific  as f o l l o w s :  In terms of p r o p o r t i o n o f e r r o r s , average  latency  and  with  immediate l e a r n i n g , students p r o v i d e d  r e s p o n s e - s e n s i t i v e c o r r e c t i o n a l feedback perform  (T^) w i l l  s i g n i f i c a n t l y b e t t e r than students p r o v i d e d  with r e s p o n s e - i n s e n s i t i v e c o r r e c t i o n a l feedback ( T 2 ) .  lb.  In terms o f p r o p o r t i o n of e r r o r s , average and  immediate l e a r n i n g ,  students p r o v i d e d with  r e s p o n s e - i n s e n s i t i v e c o r r e c t i o n a l feedback perform  latency  (T ) will 2  s i g n i f i c a n t l y b e t t e r than students p r o v i d e d  with no c o r r e c t i o n a l feedback ( T 3 ) .  2.  Students who a r e h i g h i n A - S t a t e w i l l have a s i g n i f i c a n t l y h i g h e r p r o p o r t i o n o f e r r o r s and average  l a t e n c y than low A - S t a t e  c o r r e c t i o n a l feedback  i s provided  students when no ( T 3 ) and t h i s  r e l a t i o n s h i p w i l l be r e v e r s e d when c o r r e c t i o n a l feedback  3.  i s provided ( T ) 2  In terms of p r o p o r t i o n of e r r o r s , average immediate l e a r n i n g ,  l a t e n c y and  students who a r e h i g h i n  p r e r e q u i s i t e s k i l l s w i l l perform  b e t t e r than  students  low i n p r e r e q u i s i t e s k i l l s when no c o r r e c t i o n a l feedback  i s provided ( T 3 )  69  4.  In terms of p r o p o r t i o n of e r r o r s , average l a t e n c y and immediate  learning,  s t u d e n t s who  are high i n  mathematical a b i l i t y w i l l perform b e t t e r  than  s t u d e n t s low i n mathematical a b i l i t y when no c o r r e c t i o n a l feedback i s p r o v i d e d  5.  There w i l l be a s i g n i f i c a n t  linear  between the p r o c e s s v a r i a b l e s  (T3).  relationship  ( p r o p o r t i o n of e r r o r s  and average l a t e n c y ) and the product v a r i a b l e (immediate l e a r n i n g ) w i t h the e f f e c t s o f treatment and l e a r n e r c h a r a c t e r i s t i c s  (A-State,  s k i l l s , mathematical a b i l i t y ) removed.  prerequisite  CHAPTER I I I  METHOD Subjects The  experimental s u b j e c t s c o n s i s t e d of s i x t y - t h r e e  p r e s e r v i c e elementary  s c h o o l t e a c h e r s i n the F a c u l t y of  E d u c a t i o n at the U n i v e r s i t y of B r i t i s h Columbia. s t u d e n t s were f o l l o w i n g a compulsory t e a c h i n g mathematics and  These  course i n methods of  they were awarded c r e d i t  towards  t h e i r f i n a l c o u r s e grade f o r p a r t i c i p a t i n g i n the A pilot  study c a r r i e d out i n the developmental  of the m a t e r i a l s suggested f o r undergraduate  that the content i s most  s t u d e n t s having some mathematical  s c i e n t i f i c background Students from  experiment.  (Kalman, Kaufman and Smith,  stage suitable or  1972).  the F a c u l t y of E d u c a t i o n were u t i l i z e d i n  t h i s study s i n c e these students had  s t u d i e d the necessary  secondary-school mathematics, but would p r o b a b l y f i n d material f a i r l y d i f f i c u l t .  I t was  assumed that  s t u d e n t s would make more e r r o r s d u r i n g l e a r n i n g .  the  these These  i n c o r r e c t responses would p r o v i d e d a t a f o r e v a l u a t i o n of the e f f e c t s o f c o r r e c t i o n a l feedback and would p r o v i d e a v a l i d  on student  performance  t e s t of the program's t e a c h i n g  effectiveness. 70  71  E x p e r i m e n t a l Procedures The e x p e r i m e n t a l procedure was d i v i d e d i n t o one day periods:  (1) i n i t i a l  l e c t u r e and t e s t i n g session;- (2) task  p e r i o d on CAI computer t e r m i n a l f o l l o w e d  by p o s t t e s t and  debriefing. The procedure i s l i s t e d below i n T a b l e 1.  TABLE 1  EXPERIMENTAL PROCEDURE 1  !  Activity  DAY 1  DAY 2  1. Short l e c t u r e g i v e n to subjects. 2. T e s t s adminis t e r e d to s u b j e c t s .  3. CAI p r e l e s s o n taken by s u b j e c t s. 4. CAI main . l e s s e n taken by s u b j e c t s . 5. P o s c t e s t administered to s u b j e c t s . 6. Short debriefing g i v e n to subjects.  V a r i a b l e s Measured  Approximate Time Required (min.) 15  S t a t e and t r a i t anxiety, mathematical ability.  80  Errors, latencies, o v e r a l l score, state anxiety. Errors, latencies, state anxiety.  30  Immediate learning.  35  -  90  5  72 The  experimental  s u b j e c t s were t e s t e d i n three  separate  groups d u r i n g DAY  arranged  to w r i t e the  1 except  t e s t s at s e p a r a t e  t e s t i n g s e s s i o n s were a l s o u t i l i z e d for  the DAY The  9:00  a.m.  students  f o r s i x students times.  The  to schedule  who DAY  1  students  2 computer s e s s i o n s .  DAY  2 s e s s i o n s were h e l d Monday to F r i d a y at  and 5:00  p.m.  completed these  f o r most students,  although  sixteen  s e s s i o n s on e i t h e r Saturday  Sunday morning or a f t e r n o o n .  The  experimental  or  subjects  d e f i n e d e a r l i e r were run i n groups of three to f i v e persons on IBM  2741  computer t e r m i n a l s i n an i s o l a t e d room above  the Computing Centre  at the U n i v e r s i t y of B r i t i s h  S u b j e c t s from each of the three treatment simultaneously environmental  i n order and  Columbia.  groups worked  to c o n t r o l f o r extraneous  time v a r i a b l e s .  The  CAI  s e s s i o n s were  i n t e r r u p t e d only once when the computer became i n o p e r a t i o n a l f o r f i f t e e n minutes near the s t a r t students were r e q u i r e d to r e s t a r t r e - e n t e r t h e i r responses up  of the p r e l e s s o n . t h e i r CAI  l e s s o n s and  to the p o i n t of the  A few minor d i f f i c u l t i e s were encountered with but by  Four to  interruption. the  terminals  these were e a s i l y remedied by r e p l a c i n g the t y p e - b a l l or t r a n s f e r r i n g the student  to another  terminal.  Design The  s u b j e c t s were randomly a s s i g n e d  to t h r e e  treatment  73  groups and a b a l a n c e d d e s i g n was o b t a i n e d with  twenty-one  students i n each group. Each group r e c e i v e d the same content and i n s t r u c t i o n a l l o g i c f o r the CAI l e s s o n .  The three treatment  d i f f e r e d i n terms o f the i n s t r u c t i o n a l  groups  s t r a t e g y employed  to a c h i e v e the main l e s s o n i n s t r u c t i o n a l o b j e c t i v e s . d i f f e r e n c e was s p e c i f i c a l l y of c o r r e c t i o n a l feedback All  The  i n terms o f the d i f f e r e n t  type  p r o v i d e d to the l e a r n e r .  t h r e e treatment  groups r e c e i v e d i d e n t i c a l  i n f o r m a t i o n r e g a r d i n g the c o r r e c t response  together  with  the e x p l a n a t i o n at some p o i n t d u r i n g the implementation o f the p a r t i c u l a r  i n s t r u c t i o n a l strategy.  v a r i a b l e i n the experiment it  The key  was c o r r e c t i o n a l feedback and  was the i n f o r m a t i o n a l content o f the feedback  being  independent  that was  varied. The  other independent  v a r i a b l e s r e p r e s e n t e d both  c o g n i t i v e and p e r s o n a l i t y c h a r a c t e r i s t i c s of the s t u d e n t s . The c o g n i t i v e v a r i a b l e s d i f f e r e d i n terms of t h e i r r e l a t i o n s h i p of the s p e c i f i c CAI task. mathematical  a b i l i t y and a b i l i t y  These were  to perform  Cronbach and Snow (1969) have suggested  on the p r e l e s s o n .  that the p r e t e s t  score i s an a p t i t u d e and s h o u l d be t r e a t e d along with other aptitudes. The p e r s o n a l i t y v a r i a b l e s were both t r a i t -  and s t a t e -  anxiety.  State-anxiety  was  measured at three  throughout the experiment and at the  T r a i t - a n x i e t y was  measured  beginning. The  dependent or c r i t e r i o n v a r i a b l e s i n t h i s  were p o s t t e s t and  points  score,  proportion  average response l a t e n c y .  p r o c e s s v a r i a b l e s and  of e r r o r s d u r i n g The  latter  the former was  two  study  learning  were  the product  the  variable.  Suppes (1967) c l a i m e d that response l a t e n c i e s are more s e n s i t i v e measures of s k i l l mastery and  depth of  learning  than the response e r r o r s  response  latencies  were examined as  well.  Unanticipated times the  themselves and  student responses and  experimental  The  c o r r e l a t i o n s of  for  r e v e a l s how  s e r v e d as a p r e t e s t  t h i s CAI  of p r e r e q u i s i t e s .  the p r e r e q u i s i t e  concept and  i n s t r u c t i o n i n that concept only respond"correctly. student was  hoc  selected  Prelesson  template used i n the p r e l e s s o n  flowchart  t e s t e d on  of  variables.  I n s t r u c t i o n a l Logic  2.  number  student asked f o r h e l p were r e c o r d e d f o r post  a n a l y s i s , as w e l l as means and  The  the  i s shown i n  tutorial  Figure  lesson  A student was  first  then g i v e n  i f he f a i l e d i n i t i a l l y  After  the  concept was  taught,  again tested,  but  on a d i f f e r e n t example.  to  the As  75 Question i s asked Q±+i  Can ftudent answer on f i r s t  yes  *Mark = 2  Next question 7 i s asked  stry?  no  Assistance i s g i v e n t o student  Student i s asked to answer once a g a i n Qi Question i s asked s i m i l a r to above  * Mark r e f e r s t o the grade a s s i g n e d to the student f o r a p a r t i c u l a r i n s t r u c t i o n a l u n i t , o r item, Q^ .  Figure 2 Prelesson Instructional  logic  Student's answer not recognized NOMATCH  Student i s •)) asked a question  HE1V i s given  37  W  - What i s v a l ue of GX?  T  7  Write "ok"  "Write |"gocd"  Comment  V  Comment  i•  Write "Excellent"  Write other comment  no Comment made  no . \  Comment made  w  *  Write correct answer ' and Comments '  Qj/ C^, Q , Q j ^ f a l l represent d i f f e r e n t i n s t r u c t i o n a l units (IU) i n the lesson. . [i>means the n time through the block. m  +  t h  Figure 3 Main Lesson I n s t r u c t i o n a l Logic  77 shown i n the f l o w c h a r t , a student  r e c e i v e d a mark of 0, 1,  or 2 on each i n s t r u c t i o n a l u n i t , based on h i s p r e v i o u s knowledge and h i s a b i l i t y  to l e a r n the concepts  new  to him.  The p r e l e s s o n had three f u n c t i o n s : (a) to p r o v i d e a measure o f the student's knowledge or ability  to l e a r n t h i s p a r t i c u l a r domain of content i n  t h i s p a r t i c u l a r medium; (b) to ensure that the student  had a t t a i n e d the  p r e r e q u i s i t e s before proceeding  necessary  to the main l e s s o n ; and  (c) to p r o v i d e p r a c t i c e i n working on the CAI t e r m i n a l .  I n s t r u c t i o n a l L o g i c f o r Main Lesson A f l o w c h a r t o f the i n s t r u c t i o n a l three treatment i n Figure 3. be g i v e n .  l o g i c used f o r the  groups on each i n s t r u c t i o n a l u n i t i s shown  An e x p l a n a t i o n o f the f l o w c h a r t  The student  is first  logic will  now  asked a q u e s t i o n by the  computer and he responds e i t h e r by asking f o r h e l p or by attempting  to answer the q u e s t i o n .  I f he types HELP, a h i n t  i s g i v e n and he must respond a g a i n . second time,  the student  i s given the c o r r e c t answer with an  explanation before proceeding The student respond c o r r e c t l y . predetermined occurs,  I f he types HELP a  to the next  instructional  who responds to the o r i g i n a l q u e s t i o n  unit. may  •In other words, h i s answer matches a  c o r r e c t answer keyword.  When t h i s match  the computer types: an a p p r o p r i a t e encouraging  comment  78 such as "good".  The wording of the comment depends on the  value o f a counter, GX, which keeps t r a c k of the number of c o n s e c u t i v e c o r r e c t r e p l i e s up to f o u r i n a row. A f t e r the encouraging  comment, the computer p r o v i d e s the c o r r e c t  answer with an e x p l a n a t i o n b e f o r e p r o c e e d i n g following instructional  unit.  The student may respond question.  incorrectly  to the o r i g i n a l  T h i s means that h i s answer matches a  predetermined branch  to the  i n c o r r e c t answer keyword.  t o another  The computer may  q u e s t i o n f o r r e m e d i a l a s s i s t a n c e or may  p r o v i d e c o r r e c t i o n a l feedback,  depending upon the p r i o r  d e c i s i o n of the i n s t r u c t i o n a l programmer. i n c o r r e c t responses  Making two  of the same type, that i s , f a l l i n g  i n t o the same wrong answer c l a s s twice, causes answer and an e x p l a n a t i o n to be p r o v i d e d b e f o r e to  the f o l l o w i n g i n s t r u c t i o n a l u n i t .  re-initializes  An i n c o r r e c t  response  may not match any o f the c o r r e c t  i n c o r r e c t keywords and h i s response  r e c o g n i z e d by the computer.  will  not be  One or two NOMATCH  cause a comment t o be p r o v i d e d and the student try again.  proceeding  the c o u n t e r , GX, t o z e r o .  The student's response or  the c o r r e c t  A t h i r d NOMATCH response  causes  to p r o v i d e the student with the c o r r e c t  responses i s asked t o  the computer  answer and an  e x p l a n a t i o n b e f o r e proceeding with the subsequent  instructional The  unit.  o p t i o n a l s o e x i s t s f o r b r a n c h i n g to other  i n s t r u c t i o n a l u n i t s i f a c o r r e c t or a p a r t i c u l a r  incorrect  response i s r e c o g n i z e d .  O p e r a t i o n a l D e f i n i t i o n s of The f i r s t  Treatments  treatment group  a c c o r d i n g to the i n s t r u c t i o n a l  (T^) was  instructed  precisely  l o g i c shown i n F i g u r e 3 .  deepest l e v e l o f i n t e r a c t i o n was  The  a t t a i n e d between the  l e a r n e r and the computer through the i n s t r u c t i o n a l program because  the nature o f the s t u d e n t ' s i n c o r r e c t response  used as the c r i t e r i o n f o r p r o v i d i n g c o r r e c t i o n a l feedback.  was  response-sensitive  T h i s feedback was  p r i o r a n a l y s i s o f each q u e s t i o n by the  determined by  instructional  designer. The second treatment group  (T ) received  i n s e n s i t i v e c o r r e c t i o n a l feedback.  2  Each T  p r o v i d e d with a h i n t when he responded h i n t was  0  response-  subject  incorrectly.  was This  predetermined and was p r o v i d e d to each T 2 s u b j e c t  r e g a r d l e s s o f the nature o f h i s i n c c r r e c t response.  An  important c r i t e r i o n f o r choosing the h i n t i n T^ was  that  no  more i n f o r m a t i o n would be p r o v i d e d than c o u l d be o b t a i n e d from a l l the h i n t s f o r the c o r r e s p o n d i n g i n s t r u c t i o n a l u n i t i n T^.  The comment b l o c k s which f o l l o w e d the wrong answers  80  all  contained  i d e n t i c a l comments f o r a p a r t i c u l a r  instructional unit The  third  (see F i g u r e 3 ) .  treatment group  feedback i n f o r m a t i o n .  ( T 3 ) r e c e i v e d no c o r r e c t i o n a l  Each T 3 s u b j e c t was merely  informed  about the i n c o r r e c t n e s s o f h i s response and no remedial i n f o r m a t i o n was p r o v i d e d .  The comment b l o c k s which f o l l o w e d  the wrong answers c o n t a i n e d information t e l l i n g  no h i n t s , but c o n t a i n e d  only  the T^ s u b j e c t t h a t h i s answer was  incorrect. The  reader  can r e f e r  to Appendix D i n order  the t h r e e v e r s i o n s o f the main l e s s o n , T-^, T  2  to compare  and T 3 .  CAI Author Language The by  CAI author,  or programming, language was w r i t t e n  the experimenter i n FORTRAN IV and r e q u i r e s a minimum  amount of computer knowledge and e x p e r i e n c e a  on the p a r t o f  user. A User's Guide f o r the language along w i t h a source  listing  o f the program i s p r o v i d e d  language was m o d i f i e d  i n order  l o g i c f o r the p r e l e s s o n . and  a listing  i n Appendix A.  This  to implement the i n s t r u c t i o n a l  These m o d i f i c a t i o n s a r e d e s c r i b e d  of the m o d i f i e d  source  program i s p r o v i d e d  i n Appendix B.  Instructional Materials The  procedure ui-ed i n d e s i g n i n g  the i n s t r u c t i o n a l  81 m a t e r i a l s was  d e s c r i b e d i n a review of modular  by Goldschmid and Goldschmid c o n s i s t e d of the f o l l o w i n g  (1971).  instruction  The procedure  steps:  1.  I d e n t i f i c a t i o n of the s u b j e c t matter to be taught  2.  D e f i n i t i o n o f a set of o b j e c t i v e s  3.  D e c i d i n g upon the h i e r a r c h y of o b j e c t i v e s which i n • t u r n d e s c r i b e s the sequence  of  instruction  4.  I d e n t i f i c a t i o n of p r e r e q u i s i t e s  5.  Development of a p r e t e s t  6.  P r o v i s i o n of i n s t r u c t i o n a l options  7.  D e s i g n of a p o s t t e s t The  s u b j e c t matter c o n s i s t e d of the concept o f the  d e r i v a t i v e i n elementary c a l c u l u s and the r e l a t i o n s h i p s between the mathematical concepts and o f d i s t a n c e , speed and time.  The  the p h y s i c a l concepts  lesson could  be  c h a r a c t e r i z e d as a mathematical d e r i v a t i o n supplemented n u m e r i c a l problems T h i s t o p i c was  by  which are s o l v e d d u r i n g the l e s s o n .  chosen to s a t i s f y  the requirement f o r a  module to teach t h i s m a t e r i a l to a group of undergraduate s c i e n c e s t u d e n t s at L o y o l a C o l l e g e i n M o n t r e a l , Quebec (Kalman, Kaufman, Smith, 1972). fulfilling  The CAI module i s c u r r e n t l y  t h i s r o l e but i n a d i f f e r e n t form than the one  used i n t h i s experiment. suggested that the i d e a l  Cronbach  and  Snow (1969) have  treatment-set f o r ATI r e s e a r c h i s  likely  to c o n s i s t  in applications  instructional material. this  s u g g e s t i o n was  T a b l e 2.  p r e r e q u i s i t e s f o r the main l e s s o n are  content area performed by of  two  mathematics and  college  science  the  The  prelesson  The  acquired  the  CAI  i n s t r u c t e d and  prelesson  program.  prelesson  i s shown i n F i g u r e  the p r e r e q u i s i t e o b j e c t i v e ,  later retested i n Figure  2.  An  i s g i v e n i n Table  on  item.  If  4.  he  not,  this prerequisite,  A detailed listing  i s given i n Appendix C with  accompanying graphs.  teaching  three years  t e s t of the  proceeded immediately to the f o l l o w i n g  as i n d i c a t e d e a r l i e r  the  d e a l t w i t h these p r e r e q u i s i t e s .  a d e t a i l e d view of the had  been  of  p r e r e q u i s i t e s were  overview of the ccntent of the p r e l e s s o n  I f a subject  had  c o u r s e s f o r at l e a s t  subsequently m o d i f i e d a f t e r a p i l o t  was  given i n  i n v e s t i g a t o r with  i n s t r u c t o r s who  (Kalman, Kaufman, Smith, 1972).  he  in  These were i d e n t i f i e d by a l o g i c a l a n a l y s i s  assistance  and  followed  study. The  the  This  of some r e g u l a r  the  of  2.  Reading a graph  I E v a l u a t i n g the v a l u e of a function at a point Using distance=speed x time to f i n d d i s t a n c e g i v e n speed and time »k  Using DEL(S) n o t a t i o n t o f i n d change IX  C a l c u l a t i n g average speed g i v e n distance, and time sk  Knowledge of the meaning of the term " i n s t a n t a n e o u s speed" F i v e item A - S t a t e instrument i s g i v e n  ,  sJe  C a l c u l a t i n g the s l o p e of a s t r a i g h t l i n e graph Reducing an a l g e b r a i c e x p r e s s i o n such as [(2+x) - 2 ] / C ( 2 + x ) - 2 ] 2  2  I Reducing same a l g e b r a i c e x p r e s s i o n as above but u s i n g DEL(S) i n p l a c e of x Signoff  Figure 4 D e t a i l e d View o f Preleirson  84 TABLE 2  PREREQUISITES FOR  MAIN LESSON  1.  Ability  2.  A b i l i t y to c a l c u l a t e the value of a f u n c t i o n at a p o i n t , g i v e n the e q u a t i o n .  3.  Knowledge of the terms "average speed".  4.  A b i l i t y to c a l c u l a t e d i s t a n c e when g i v e n speed u s i n g the formula, d i s t a n c e = (speed) ( t i m e ) .  5.  Knowledge of the concept  6.  A b i l i t y to apply the n o t a t i o n , DEL(S) and DEL(T) to c a l c u l a t e change.  7.  Knowledge of the d e f i n i t i o n of " s l o p e " .  8.  Ability  9.  A b i l i t y to expand a b i n o m i a l which i s squared and to f a c t o r , i . e . a b i l i t y to reduce a l g e b r a i c e x p r e s s i o n s such as |72 + x ) - 2^] / | 2 + x) - 2J to s i m p l e s t form.  to r e a d a graph,  i . e . t o . f i n d a value a t a p o i n t .  speed" and  "instantaneous  and  of change i n d i s t a n c e or  to c a l c u l a t e the s l o p e of a s t r a i g h t  time,  time.  line.  2  10.  A b i l i t y to perform the above a l g e b r a i c m a n i p u l a t i o n s u s i n g the cumbersome n o t a t i o n used on a computer t e r m i n a l , e.g. ( 2 + DEL(S)) * 2 - 2 * 2 / ( 2 + DEL(S ) ) -  The  o b j e c t i v e s f o r the main l e s s o n were determined  these p r o v i d e d the r a t i o n a l e f o r the l o g i c of the ienson content.  and  iuain  These i n s t r u c t i o n a l o b j e c t i v e s are given  i n Table 3 and a d e t a i l e d view of the content o.~ the mnin l e s s o n i s g i v e n i n F i g u r e ~.  D e t a i l e d l i s t i n g s of the main  2.  85 lesson, versions T  l 3  T  2  and  are p r o v i d e d i n Appendix E.  The f i f t e e n i n s t r u c t i o n a l u n i t s a n a l y z e d i n the study are the i n s t r u c t i o n a l u n i t s w i t h the f o l l o w i n g number i n Appendix E: 23, 24.  1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14,  These u n i t s were the ones g i v e n to a l l s t u d e n t s i n  the experiment.  U n i t s 15, 16 and 17 comprised  s e c t i o n on l i m i t s .  U n i t s 18 to 22 comprised  the o p t i o n a l  the A - S t a t e  s c a l e and U n i t 10 was an e x p o s i t i o n of some content f o l l o w e d by the q u e s t i o n , "Do you understand?" A p o s t t e s t was developed and i s g i v e n i n Appendix F. The items o f the t e s t r e f l e c t e d i m p l i e d by tt-.e i n s t r u c t i o n a l  the s p e c i f i c b e h a v i o u r s  objectives.  86  TABLE 3  INSTRUCTIONAL OBJECTIVES FOR MAIN LESSON  1.  R e c a l l the r e l a t i o n s h i p between the f o l l o w i n g : (a) (b) (c) (d)  slope of secant and average speed s l o p e of tangent and i n s t a n t a n e o u s speed (at a p o i n t ) average speed and i n s t a n t a n e o u s speed s l o p e of tangent and d e r i v a t i v e (at a p o i n t )  2.  C a l c u l a t e average speed from a graph of d i s t a n c e vs. time f o r both l i n e a r and n o n - l i n e a r graph.  3.  C a l c u l a t e i n s t a n t a n e o u s speed from a graph of d i s t a n c e vs. time with tangent to the curve drawn a t a p o i n t on the graph.  4.  C a l c u l a t e simple l i m i t s ,  5.  D e f i n e i n s t a n t a n e o u s speed at any time t as a f u n c t i o n of s and t , i . e . v = l i m i t As At-* 0 At  6.  C a l c u l a t e average speed and i n s t a n t a n e o u s speed a t a p o i n t , g i v e n the e q u a t i o n of s as a f u n c t i o n of t . The student muct use b a s i c p r i n c i p l e s , i . e . l i m i t d e f i n i t i o n .  7.  C a l c u l a t e the d e r i v a t i v e (dy./dx) at a p o i n t g i v e n the e q u a t i o n of y = f ( x ) , from b a s i c p r i n c i p l e s , i . e . l i m i t def i n i t i o n .  e.g. l i m i t (6 + 3/\t) At-* 0  Relationship between slope and average speed of straight, l i n e graph of. S vs.. T... Shown, to. te. constant  X ^  Relationship between slope of secant and average speed f o r non-linear graph of S vs. T. Not constant Relationship between elope of tangent and instantaneous speed at a point Relationship between average speed and instantaneous speed, i . e . , instantaneous speed i s l i m i t of average speed  no no  Examples of f i n d i n g instantaneous speed given non-linear graph of S vs. T with tangent drawn on it.. Can student do. i t ? . . ; X yes—" -• Notation and d e f i n i t i o n of d e r i v a t i v e are given Example of computing average speed from equation of S vs. T at a point Finding instantaneous speed by taking l i m i t of average speed. Can he do i t ?  ino  '\  k  'Has he\ revipwect -nee? [yes  A-State instrument .-. f i v e items  I Another example of computing instantaneous speed from equation of S vs. T. Can he do i t ? 1  ^,£3  Signoff  Figure 5 Detailed View of Main Lesson  •no  Evaluating limits  88  Measurement The  Instruments  a n a l y s i s o f a l l measurement instruments was  performed  u s i n g the PIA and TIA t e s t a n a l y s i s programs  available  i n the F a c u l t y of E d u c a t i o n at the U n i v e r s i t y  of B r i t i s h  Columbia.  Posttest.  The e i g h t e e n - i t e m m u l t i p l e c h o i c e p o s t t e s t  was designed to measure student performance o b j e c t i v e s g i v e n i n T a b l e 2.  on the  T h i s instrument was intended  to serve as a c r i t e r i o n - r e f e r e n c e d t e s t  and a copy i s g i v e n  i n Appendix F. Content  v a l i d i t y was assured f o r t h i s t e s t by  g e n e r a t i n g s p e c i f i c items from  the l i s t  of i n s t r u c t i o n a l  o b j e c t i v e s with due r e g a r d g i v e n to the r e l a t i v e g i v e n to these o b j e c t i v e s i n the main l e s s o n . a n a l y s i s d a t a f o r t h i s instrument  Test  i s g i v e n i n T a b l e s 4 and 5,  TABLE 4  POSTTEST DATA  Sample s i z e Mean Standard D e v i a t i o n  emphasis  63 8. 95 2.89  89 TABLE 5  ITEM ANALYSIS INFORMATION FOR  Item  POSTTEST  P r o p o r t i o n Answering C o r r e c t l y Pooled 2 l T  T  .54 .44 .78 .71 . 94 .40 .49 .40 .84 . 78 .51 .68 . 19 .33 .16 .43 . 08 .25  1 2 3 4* 5 6 7 8 9 10 11 12 13 14 15 16 17 18  .62 .57 .67 .67 . 95 .38 .48 .33 .81 .76 .52 .81 .24 .48 .24 .48 .00 .33  .38 . .24 .86 .76 .90 . .38 ,5.7 .52 .86 . 62 .57 .67 .24 .24 . 14 .48 . 19 .24  (  (Difficulty) T  3  .62 .52 .81 .71 . 95 .43 .43 .33 .86 . 95 .43 .57 . 10 .28 .10 .33 . 05 . 19  *The seventeen s u b j e c t s who answered t h i s item b e f o r e a t y p o g r a p h i c a l e r r o r was c o r r e c t e d on che p o s t t e s t were a s s i g n e d a value of "1" f o r the purpose of u s i n g the item a n a l y s i s program.  The r e s u l t s shown i n T a b l e 5 i n d i c a t e no meaningful individual and  d i f f e r e n c e s between the three groups on the  items, but that c e r t a i n items  should be r e v i s e d .  17 and 18.  tnat there were  The d i f f i c u l t  t?ere too d i f f i c u l t  items were 13, 15,  90 Mathematical  ability  test.  The  Cooperative  Sequential  T e s t of E d u c a t i o n a l P r o g r e s s , Mathematics Form 2A was  administered  experiment.  The  to a l l s u b j e c t s at the b e g i n n i n g o f the norm sample f o r t h i s form of the  c o n s i s t e d of students i n grades ten, e l e v e n and the t e s t was  found  internal  test  twelve  to be of a p p r o p r i a t e d i f f i c u l t y  for students p a r t i c i p a t i n g The  (1957),  level  i n t h i s experiment.  c o n s i s t e n c y c o e f f i c i e n t , K-R  20,  form of the t e s t normed on grade e l e v e n students was to be  .84.  The  concurrent  as the c o r r e l a t i o n r e p o r t e d as grade twelve The  and  validity coefficient  the SCAT-Quantitative  .70 f o r a grade e l e v e n sample and  was  for this reported defined  t e s t and  was  .76 f c r a  sample.  test  c o n s i s t e d of f i f t y  i n seventy minutes. students,  with  and  For  the mean was  the c o e f f i c i e n t  items  and was  the t o t a l sample of  31.1,  administered  sixty-three  the s t a n d a r d d e v i a t i o n was  of i n t e r n a l  c o n s i s t e n c y , K-R  20,  7.6  was  .85. A logical analysis  of the t e s t  t h a t h i g h e r - o r d e r mental p r o c e s s e s ,  items  seems to  such as problem  suggest solving,  were being measured and not o n l y r e c a l l of i n f o r m a t i o n or application  of a l g o r i t h m s .  emphasized i n the p r e l e s s o n .  The  l a t t e r two  processes  were  91 State-Trait Anxiety  Inventory  both A - S t a t e  anxiety inventory.  The S t a t e - T r a i t  (STAI) was  i n order  utilized  and A - T r a i t ( S p i e l b e r g e r e_t al_. , 1970).  twenty-item A - S t a t e were a d m i n i s t e r e d  and A - T r a i t four p o i n t L i k e r t  at the beginning  scale  of the f i v e items with the h i g h e s t  item-remainder  the p r e l e s s o n and  d u r i n g the main l e s s o n .  were a d m i n i s t e r e d  by the computer d u r i n g the CAI  twenty-item A - S t a t e  and evidence  ranging  from  The Table  6.  items  lesson.  i . e . Cronbach's  of c o n s t r u c t v a l i d i t y has been p r o v i d e d  ( S p i e l b e r g e r et a l . , 1970). reliability  These f i v e  during  and A - T r a i t s c a l e s have been  shown to have h i g h value of r e l i a b i l i t y , alpha,  In  ( O ' N e i l , 1972),  c o r r e l a t i o n s i n the STAI normative sample were g i v e n  The  The  scales  of the experiment.  a d d i t i o n , a s h o r t form o f the A - S t a t e consisting  to measure  O'Neil  (1972) r e p o r t e d  (alpha) c o e f f i c i e n t s f o r the f i v e - i t e m s c a l e .83  to .93  i n seventeen a d m i n i s t r a t i o n s .  t e s t s t a t i s t i c s f o r t h i s study  are r e p o r t e d i n  92 TABLE 6  ANXIETY TEST DATA  Test  A - T r a i t (20 items) A - S t a t e (20 items) A - S t a t e p r e t e s t (5 items) A - S t a t e main (5 items)  Prelesson.  Mean  S.D.  41. 9 39.1 9.6 12.0  8.5 9.4 3.8 4.5  Cronbach A l p h a  .88 .89 . 92 . 92  The g r a d i n g scheme used f o r the p r e l e s s o n  was d i s c u s s e d e a r l i e r .  A student r e c e i v e d a grade of 0, 1,  or 2 on a s i n g l e i n s t r u c t i o n a l u n i t and there were nine i n s t r u c t i o n a l u n i t s i n the l e s s o n . The p r e l e s s o n was c o n s i d e r e d as a t e s t o f a s t u d e n t ' s knowledge and a b i l i t y  to l e a r n the p r e r e q u i s i t e s r e q u i r e d  f o r the main l e s s o n as taught by the computer.  The p r e l e s s o n  d a t a a r e g i v e n i n T a b l e s 7 and 8. TABLE 7  PRELESSON DATA  Sample S i z e Mean Standard D e v i a t i o n  63 14, 4 1.84  93 TABLE 8  ITEM ANALYSIS INFORMATION FOR  Mean  Item  *r  Standard D e v i a t i o n  total .35 .32 .52 .17 .22 .29 .34 .73 .71  .48 .42 .27 .29 .38 .27 .44 .64 .81  1.73 1. 78 1. 92 1.90 1.87 1.92 . 1.73 0.68 0. 90  1 2 3 4 5 6 7 8 9  PRELESSON  t o t a l r e p r e s e n t s the c o r r e l a t i o n c o e f f i c i e n t with the t o t a l t e s t s c o r e . T a b l e 7 i n d i c a t e s that the p r e l e s s o n was  of that item  not  difficult  f o r t h i s group s i n c e the mean score f o r the t o t a l group 14.4  on a p o s s i b l e score of 18.  The  o n l y ones which the students found  Main l e s s o n .  s t u d e n t ' s e r r o r s and  subsequent  two  items were the  difficult.  The main l e s s o n was  measure of a student's a b i l i t y The  last  was  c o n s i d e r e d as a  to perform  on a CAI t e r m i n a l .  l a t e n c i e s were r e c o r d e d f o r  analysis.  Each i n s t r u c t i o n a l u n i t was  a l s o c o n s i d e r e d as a  t e s t item with p o s s i b l e s c o r e s of 0 or 1.  The  student  was  94 a s s i g n e d a value c f 0 f o r an item i f the computer  provided  the c o r r e c t answer b e f o r e he answered c o r r e c t l y .  I f the  student  answered c o r r e c t l y b e f o r e being g i v e n the answer,  he was a s s i g n e d a grade of 1 f o r that  item.  A n a l y s i s i n f o r m a t i o n f o r the main l e s s o n regarded a test  i s g i v e n below i n T a b l e  as  9.  TABLE 9  MAIN LESSON DATA  Sample S i z e Number of Items Mean Standard D e v i a t i o n  Table  63 15 10. 9 2.0  9 i n d i c a t e s that the mean score f o r the group  was 10.9 out of a p o s s i b l e 15.  This finding  shows that most  s t u d e n t s were a b l e to produce the c o r r e c t answer b e f o r e the computer d i d so, and the l e s s o n was a r e l a t i v e l y instructor.  effective  CHAPTER IV  ANALYSIS AND  Method of  Analysis  In t h i s study two o f data.  RESULTS  The  first  phases were i n v o l v e d  phase c o n s i s t e d  procedure designed to t e s t the i n Chapter I I .  The  i n the  analysis  of a r e g r e s s i o n  analysis  research  hypotheses  second phase i n v o l v e d  some post  analysis  of the d a t a i n order  to gain a d d i t i o n a l  i n t o the  r e s u l t s o f the f i r s t  phase as w e l l as  several a l t e r n a t i v e questions.  This  as s e p a r a t e l y  f o r the  of l a t e n c i e s and  to examine  second phase  and  Walberg, 1971;  well  Graphs  information.  a n a l y s i s approach employed f o r t h i s  been d e s c r i b e d  Ward, 1963;  of  e r r o r s f o r the main l e s s o n were a l s o  regression  a n a l y s i s has  involved  t o t a l group as  three e x p e r i m e n t a l groups.  examined f o r meaningful The  hoc  insight  the examination o f i n t e r c o r r e l a t i o n s f o r a v a r i e t y measures, which were examined f o r the  stated  by many w r i t e r s  Cohen, 1968; Kaufman and  O v e r a l l and Sweet, 1973).  of this'method o f data a n a l y s i s over the approach have been d i s c u s s e d 95  i n d e t a i l by  (Bottenberg  Spiegal, The  1970;  advantages  c o n v e n t i o n a l ANOVA these  writers.  96  Cronbach and regression i n ATI  Snow (1969) recommended the use  analysis  studies.  this  Separate stepwise u n i v a r i a t e the  i n order to t e s t the f i r s t  three  four  regression criterion  hypotheses i n  study. H y p o t h e s i s 5 was  approach with p o s t t e s t The  the  method f o r t e s t i n g i n t e r a c t i o n terms  a n a l y s e s were performed f o r each of variables  of  proportion  variables  This and  score as  of e r r o r s ,  c h a r a c t e r i s t i c s defined variables.  t e s t e d using a r e g r e s s i o n the  average l a t e n c y  earlier  analysis  dependent  s e r v e d as  variable.  and  learner  independent  technique p e r m i t t e d the  treatment e f f e c t s to be  score and  All British  the other two  between  a n a l y s e s were performed at the U n i v e r s i t y  Columbia Computing Centre.  the BMD02R program  The  (Dixon, 1968).  c o r r e l a t i o n s were c a l c u l a t e d  with  at the  Computing Centre  levels  (p) f o r s i g n i f i c a n c e of the  removed  variables.  regression  were performed u s i n g the MULTIVAR program  using  learner  statistically  ( p a r t i a l l e d ) i n order to t e s t the r e l a t i o n s h i p s posttest  analysis  The the  (Finn,  means and  The  the F - r a t i o s  were  (Dempster, 1969).  hypotheses h a v i n g a s i g n i f i c a n c e l e v e l of used f o r s u b s t a n t i v e d i s c u s s i o n  and  analyses  1968)  and  inter-  STRIP program  (Seagraves, 1971).  l o c a l FPROB program  of  available  probability calculated All  l e s s than .07  i n t e r p r e t a t i o n of  were the  97 results. The  hypotheses given at the end  translated into s t a t i s t i c a l represent  Results  terms.  of Chapter I I I were  The  symbols used to  the v a r i a b l e s i n t h i s study are g i v e n i n T a b l e  of A n a l y s i s  Table  - Means  10 shows the means of the v a r i a b l e s observed  i n the study f o r the t o t a l group and groups taken s e p a r a t e l y .  f o r the  treatment  Although the d i f f e r e n c e between  the means on most of the v a r i a b l e s was s i g n i f i c a n t , a c o n s i s t e n t p a t t e r n was  not  statistically  evident.  The  treatment groups were ranked i n the h y p o t h e s i z e d  order  (T-^>^2i> 3 )  total  T  11.  o n  t l i e  p o s t t e s t scores,  total errors,  r e s p o n s e s , p r o p o r t i o n o f e r r o r s , t o t a l c o r r e c t i n main l e s s o n , number taking o p t i o n a l l i m i t main l e s s o n . with  the T^  The  The  main l e s s o n l a t e n c y v/as the  group having  than the other  two  s e c t i o n , enjoyment and A - S t a t e  a higher  average response  the e x c e p t i o n  the c o r r e c t i o n a l feedback v a r i a b l e had  an e f f e c t  time of the CAI  f o r the mornihg  on  have been o b t a i n e d  p e r i o d of time or w i t h a more d i f f i c u l t The  of l a t e n c y ,  l e a r n i n g i n the e x p e c t e d d i r e c t i o n , but •  t h a t a more d e f i n i t i v e r e s u l t may longer  latency  groups.  r e s u l t s suggest that with  performance and  exception,  (9:00  experimental  lesson.  s e s s i o n was  a.m.), '2' f o r evening  over a  (5:30  coded  '1'  p.m.)  and  '3' f o r the weekend s e s s i o n . three  The means i n d i c a t e that the  treatment groups were w e l l b a l a n c e d i n each  except that the s t u d e n t s i n the t h i r d  treatment group ( T 3 )  attended s l i g h t l y more e x p e r i m e n t a l s e s s i o n s morning and the T the morning.  2  session  group a t t e n d e d the l e a s t  ( 2 ) i n the sessions i n  TABLE 10 MEANS OF VARIABLES FOR COMBINED GROUPS AND FOR T, T T„  Variable  1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.  Posttest Time of Experimental S e s s i o n * T o t a l E r r o r s - main l e s s o n T o t a l Responses - main l e s s o n P r o p o r t i o n of E r r o r s - main l e s s o n T o t a l C o r r e c t - main l e s s o n Do you understand? - main l e s s o n Time to answer (7) above - main l e s s o n Had l i m i t s e c t i o n - main l e s s o n Average F i r s t Latency - main l e s s o n Average T o t a l Latency - main lesson Enjoyment - main lesson P r e l e s s o n Score P r e l e s s o n Correct on f i r s t try Average F i r s t Latency - p r e l e s s o n Average T o t a l Latency - p r e l e s s o n Math A b i l i t y - f i r s t t e s t i n g F u l l A-State - f i r s t t e s t i n g A-Trait - f i r s t testing Short A - S t a t e - f i r s t t e s t i n g A-State - prelesson A - S t a t e - main l e s s o n  Pooled  8.84 1. 76 16.63 27.60 .58 10. 90 .76 83.7 .79 116.4 189. 0 .63. 14.46 6.25 90.3 119.4 31.08 46. 9 41. 8 9.6 4.9 11.9  9. 19 1.86 14. 71 26.48 .53 11. 62 .71 84.0 . 62 118. 0 177. 5 .67 14. 71 6.24 81. 9 108.2 30.86 47.3 41.3 8.8 4. 6 11.2  8. 74 1.81 17. 14 28. 10 .57 10. 71 .76 45.9 .81 123. 7 202.7 . 62 . 14.28 6.10 99. 9 134.0 30.24 46.5 43. 1 10.2 4.7 12.0  8.59 1.62 18.05 28.24 .63 10.38 .81 121. 1 .95 107.4 186. 9 .62 14. 38 6.43 89.2 115.8 32. 14 46.8 41.2 9.8 5.3 12.5  * T h i s i s a nominal v a r i a b l e . I t i s t e c h n i c a l l y i n c o r r e c t to c a l c u l a t e the mean and t h i s value i s merely intended here to serve as a crude shorthand comparison..  100 R e s u l t s o f A n a l y s i s - Hypothesis T e s t i n g TABLE 11 SYMBOLS USED IN STATISTICAL ANALYSIS  V a r i a b l e Represented  Symbol  Posttest  l  Y  Score  P r o p o r t i o n of e r r o r s i n main l e s s o n Y  Average l a t e n c y lesson  3  F i r s t contrast vs. mean of T  i n main  - mean of T^  2  x  X  X  Second c o n t r a s t vs. mean of T^  2  Mathematical a b i l i t y score  3  4  Prelesson A-State i  X  X  Main l e s s o n A - S t a t e  6  Prelesson  score  Prelesson  average  7  a last  score  latency  separate r e g r e s s i o n e q u a t i o n s were d e f i n e d f o r  the a n a l y s i s , one f o r each of the three and  test  score  5  x  Four  - mean of T  equation  dependent measures  to t e s t H y p o t h e s i s 5.  v a r i a b l e s i n these e q u a t i o n s r e f l e c t  The independent  the f a c t o r s which  2  101 t h i s i n v e s t i g a t o r c o n s i d e r e d as important An  o r d e r i n g l o g i c was  in this  study.  d e f i n e d i n t e s t i n g the terms i n the  e q u a t i o n s i n a stepwise manner ( O v e r a l l and S p i e g a l , The  l o g i c used i n v o l v e d e n t e r i n g l e a r n e r  terms f i r s t treatment  1970).  characteristic  i n t o the r e g r e s s i o n e q u a t i o n f o l l o w e d by  terms and  that treatment  then i n t e r a c t i o n terms.  T h i s means  and i n t e r a c t i o n e f f e c t s were t e s t e d with  the e f f e c t of l e a r n e r c h a r a c t e r i s t i c s b e i n g c o n t r o l l e d statistically.  The f o u r e q u a t i o n s and  t a b l e s are g i v e n i n the next  Posttest  T-L  =  section.  (Yi )  Treatment - 2.80 X + 2.32 X  A-State *5  error e  Math Ability X  2  +  .14  X  +  3  Prelesson .26 X, 6  Treatment x Math A b i l i t y • 12 X ^ X ^ — .05 X X^ +  Treatment . 13 X-^X^  +  the c o r r e s p o n d i n g  2  x Prelesson .22 X^X^ +  Treatment .11  X X 1  5  x A-State +  .16  X  2  X  5  102  TABLE 1 2 RESULTS OF REGRESSION ANALYSIS FOR  Source o f Variation  2  Fobs  3  P<  1  6  .  032  1  2.68  .  .  044  1  3.69  . 06  .  000  1  .00  .005  1  .42  .53  .  2  .21  .81  A  5  l X  - ( x  2 1  }  X  l  x  X  2  X  ( 1 3 X x  <x x x  x  x  2  )  92  .001  •  10 -  .020  1  1.68  .20  3  .  019  1  1.59  .21  .  039  2  1.64  .20  .  010  1  .84  .  016  1  .  026  X  6  2  x  6  X  2  3 )  X  .  x x )  6  005  13.  3  , X  X  1  Degrees o f Freedom  166  X  (  2  .  X  X  AR  *3 X  X  X  POSTTEST  6  l  X  s  X  2  X  5  X  5,  X  2  total error  X  5 )  .37  1.34  .25  2  1.09  .34  .053  1  4.44  .04  .027  1  2.26  .14  .  2  3.36  .04  080  .392  11  .608  51  . . .  1  £\R r e p r e s e n t s the increment i n R a l r e a d y e n t e r e d i n the e q u a t i o n .  i  g i v e n p r e v i o u s terms  2  Fobs - R /df-, where d f = number o f degrees o f freedom /i D 2 / J ^ T f o r corresponding term(s) (!- f u l l / t e r r o r ) being t e s t e d j  R  d f f u i i = number of degrees o f freedom f o r f u l l model above 1-R f ll = AR rror above 2  2  u  e  a  s  defined i n table  3 P r o b a b i l i t y of making a Type I e r r o r by r e j e c t i n g n u l l hypothesis, i . e . , claiming s t a t i s t i c a l s i g n i f i c a n c e . 4  I n d i c a t e s ' t h a t the i n d i v i d u a l t e s t e d as a s e t .  terms i n p a r e n t h e s e s are  103 The  r e s u l t s i n T a b l e 12  v a r i a b l e s were s t a t i s t i c a l l y for  v a r i a t i o n i n the  students' variable  i n d i c a t e that significant  i n accounting  subjects'  posttest  scores  mathematical a b i l i t y  ( X 3 ) was  a highly  level  ( X ) was  statistically  5  (p ^*. 06 ) c o n t r o l l i n g f o r the p r e v i o u s  two  have e x i s t e d even a f t e r the  posttest  the was  main l e s s o n . (p<^.04) was  terminal. written  T-L  significant,  l e v e l of  This anxiety  s t u d e n t s completed the main  T h i s was  not  obtained  for posttest  s u r p r i s i n g since  (A-State) 2  scores.  was  (X-^X^).  In t h i s  different for A  examination of t h i s f i n d i n g i s given  are g i v e n  The  immediately at the c o m p l e t i o n of  as compared with T  The  significant  the the  A main l e s s o n A - S t a t e - b y - t r e a t m e n t i n t e r a c t i o n  the e f f e c t of a n x i e t y in  The  variables.  f i n d i n g would seem to i n d i c a t e that a high  l e s s o n on  (Y-^).  (p<.001) i n e x p l a i n i n g p o s t t e s t r e s u l t s .  main l e s s o n A - S t a t e  may  several  case,  subjects  more d e t a i l e d in figure  6.  r e s u l t s f o r the hypotheses s t a t e d i n Chapter below f o r the  Hypothesis l a :  No  III  posttest: s i g n i f i c a n t d i f f e r e n c e was  found  i n immediate l e a r n i n g between s t u d e n t s provided  with  response-sensitive  c o r r e c t i o n a l feedback students p r o v i d e d  ( T ^ ) and  with response-  i n s e n s i t i v e c o r r e c t i o n a l feedback  (T ). 2  104  Hypothesis l b :  No  significant difference  i n immediate l e a r n i n g p r o v i d e d with correctional  was  found  between s t u d e n t s  response-insensitive feedback  p r o v i d e d with no  ( T ) and 2  students  correctional  feedback ( T 3 )  H y p o t h e s i s 3:  No  s i g n i f i c a n t i n t e r a c t i o n was  i n terms of immediate l e a r n i n g the T  2  versus T 3 groups  prerequisite Hypothesis 4 :  No  skills.  s i g n i f i c a n t i n t e r a c t i o n was  versus T*  ability.  between  and  i n terms of immediate l e a r n i n g the  found  3  groups  and  found between  mathematical  105 Proportion of Errors (Y ) 2  Y  Treatment = .22 X - .06 X  2  :  A-State + .01 X  -  2  Main  3  5  .03 X  6  2  6  A-State Prelesson - .005 X 4  .Treatment x Math A b i l i t y  Prelesson -  Treatment \. x P r e l e s s o n + .01 X X + .01 X X 1  Math A b i l i t y .004 X  + .000 X X  6  ±  3  + .002 X0X3  Treatment x A - S t a t e Main + .002 X-,X5 - .004 X X 2  5  error + e  TABLE 13 RESULTS OF REGRESSION ANALYSIS FOR PROPORTION OF ERRORS  Source o f Variation 3 6  X x  x X X  A *  4  5 l  x (x  2  x ) X-, x „ x  2  2 3 ( ! 3,X2X ) 1 6 X  X  X  X  3  X  X  x x 2  6  ( 1 6 2 6) 1 5 2 5 ( 1 5, 2 ) X  X  X  X  X  X  X  X  X  X  X  X  5  total error  2  Degrees of Freedom 1 1 1 1 1 1 2 1 1 2 1 1 2 1 1 2  .094 .096 . 008 . 068 .004 .059 . 063 . 006 . 007 .013 .019 . 007 . 026 .000 . 008 . 008 .376 .624  1  12 50  Fobs  P<  7.53 7.69 .64 5.23 .32 4.72 2.02 .48 .56 .52 1.52 .56 1 . 04  .01 .01 .43 .02 .58 .03 . 14 .50 .46 .60 .22 .46 .36  -.64 .32  -  .43 .73  106 I t should be noted that HELP and NOMATCH responses were counted as e r r o r s and responses.  Also,  responses  that were made when a s u b j e c t repeated a s e c t i o n o f the main l e s s o n were i g n o r e d except f o r the l a s t u n i t i n the sequence.  The r e s u l t s of the s t u d e n t s '  performance  on t h i s l a s t  for  times that the student attempted  the two  instructional  i n s t r u c t i o n a l u n i t were combined the u n i t .  The r e s u l t s g i v e n i n Table 13 f o r p r o p o r t i o n of errors  ( Y ) i r i d i c a t e that mathematical a b i l i t y and p r e l e s s o n 2  score were both s t a t i s t i c a l l y  s i g n i f i c a n t a t the .01  The main l e s s o n A - S t a t e l e v e l was  statistically  level.  significant  (p<^.02) i n p r e d i c t i n g p r o p o r t i o n of e r r o r s on the main lesson. A significant the T  2  treatment e f f e c t was found i n comparing  and T^ group means (p<.03) with r e g a r d to p r o p o r t i o n  of e r r o r s .  There were no s i g n i f i c a n t  trait-treatment  interactions. The r e s u l t s of the hypotheses  s t a t e d i n Chapter I I I  are g i v e n below f o r p r o p o r t i o n of e r r o r s : Hypothesis l a :  No  significant  d i f f e r e n c e was  found  i n p r o p o r t i o n of e r r o r s between students p r o v i a e d with responses e n s i t i v e c o r r e c t i o n a l feedback  (Ti)  and s t u d e n t s p r o v i d e d with responsei n s e n s i t i v e c o r r e c t i o n a l feedback  (Tp).  107 Hypothesis l b :  A s i g n i f i c a n t d i f f e r e n c e was found i n p r o p o r t i o n o f e r r o r s between students p r o v i d e d with r e s p o n s e - i n s e n s i t i v e c o r r e c t i o n a l feedback  ( T ) and 2  s t u d e n t s p r o v i d e d with no c o r r e c t i o n a l feedback  H y p o t h e s i s 3:  (T ) 3  A significant  i n t e r a c t i o n was found i n  terms of p r o p o r t i o n of e r r o r s between the T  2  versus  groups and  prerequisite s k i l l s . -  H y p o t h e s i s 4:  No s i g n i f i c a n t in  Average Latency  Y  3  i n t e r a c t i o n was found  terms of p r o p o r t i o n o f e r r o r s  between the T  2  versus  mathematical  ability.  groups and  (Y ) 3  Treatment = 14.92 X - 122.54 X ±  A - S t a t e Main + .50 X + 5  Prelesson Score 9.22 X,  Treatment x Math A b i l i t v + 1.63 X X 3 10 X X X  2  3  + 4.72  3  Prelesson A-State 6.66 X 4  Prelesson Latency + Treatment x Prelesson 6.32 X 1X .o + 4 . 9 6  X do X 0  Treatment x P r e l e s s o n Latency  Treatment x A - S t a t e Main 78 X n X  2  Math A b i l i ty 1.47 X„  X X 2  5  + .24 X X ±  7  - .0.1 X X 2  A  error 7  +  e  108 TABLE 14  RESULTS OF REGRESSION ANALYSIS FOR AVERAGE LATENCY  Source o f Variation  R  2  Degrees of Freedom  1 7 2 7 ( 1 7' 2 7 )  . 156 . 028 .061 . 128 . 001 .006 . 002 . 008 . 003 . 001 . 004 . 009 . 005 . 014 . 006 . 048 . 054 . 007 . 000 . 0C7  2 1 1 2 1 1 2  total error  .461 . 539  15 47  3 6  X X  x  4  7 5 l  X  X X  x (x x > 1 3 xx 2  2  X  X  2  3  ( 1 3» 2 3) 1 6 2 6 ( 1 6' 2 6 ) X  X  X  X  X  X  X  X  X  X  X  X  xx 2 5 (Xix ,x x ) X  5  X  5  X  2  X  X  X  x  5  X  X  X  X  :  i  1  1  1 1 1 1 1 2 1 1 2 1  1  Fobs  13.57 2.30 5. 02  11.14  .09 .52 .18 .35 .26 .09 . 17 .78 .43 .61 .52 4. 18 2.35 .61 . 00 .30  P  < . 001 . 13 . 03 .002 .76 .48 . 68 . 71 .02 .76 .84 .39 .52 .55 .48 .04 . 10 .44  -  .67  109 The  r e s u l t s shown i n T a b l e 14 i n d i c a t e  mathematical  ability  and p r e l e s s o n average statistically  the  (p<^.001), p r e l e s s o n A - S t a t e  (p<-.03)  l a t e n c y (p<^".002) are a l l  significant  i n terms of p r e d i c t i n g  average  main l e s s o n l a t e n c y (Y ). 3 A s i g n i f i c a n t main A - S t a t e - l e v e l - b y - t r e a t m e n t i n t e r a c t i o n was  obtained  treatment  groups.  in figure  8.  (p<-^".04) f o r the T  T^  T h i s f i n d i n g i s examined i n more d e t a i l  The r e s u l t s of the hypotheses are g i v e n below f o r average Hypothesis  and  2  la:  No  response  s t a t e d i n Chapter latency:  s i g n i f i c a n t d i f f e r e n c e was  i n average  III  response  found  l a t e n c y between  students p r o v i d e d with  response-  s e n s i t i v e c o r r e c t i o n a l feedback and s t u d e n t s p r o v i d e d with  response-  i n s e n s i t i v e c o r r e c t i o n a l feedback Hypothesis  lb:  No  s i g n i f i c a n t d i f f e r e n c e was  i n average  response  (T^)  found  l a t e n c y between  students p r o v i d e d with  response-  i n s e n s i t i v e c o r r e c t i o n a l feedback and  (T^)  students p r o v i d e d with  c o r r e c t i o n a l feedback  (T^).  no  (T^)  110 H y p o t h e s i s 2:  A significant interaction was  groups  No  between the T and A - S t a t e .  2  prerequisite  See f i g u r e  No  versus  mathematical  1  7.  latency and  skills.  s i g n i f i c a n t i n t e r a c t i o n was  between the T  3  found  groups  i n terms of average response  Y  T  s i g n i f i c a n t i n t e r a c t i o n was  between the  Relationship  response  versus  i n terms of average response  H y p o t h e s i s 4:  .04)  found i n terms of average  latency  H y p o t h e s i s 3:  (p  versus T  found latency  groups  and  ability.  3etween P r o c e s s and Product  Treatment = -.05 Xi - .03 X Main A - S t a t e .10 X + 5  P r o p o r t i o n of 5.56  2  +  Math A b i l i t y .09 X 3  Prelesson .09 X  +  4  P r e l e s s o n Latency .01 X  Score  7  6  Errors  Prelesson A-State .01 X  Main Latency. .005 Y 3  error e  Ill  TABLE RESULTS OF  REGRESSION ANALYSIS FOR  AR  Source of Variation  ( l, 2, 3, 4, 5, 6, 7 ) X  X  X  X  X  X  X  2 3  Y Y  ( 2, Y  Y 3  )  total error  The errors score  2  HYPOTHESIS 5  Degrees of Freedom  Fobs  .261  7  2.62  .042 .006 .048  1 1 2  3.22 0.46 1.82  .309 .691  9 53  P<  . 07 .46 . 17  r e s u l t s i n T a b l e 15 i n d i c a t e that p r o p o r t i o n  (Y ) 2  was  linearly related  (Y-^) with the  treatment d i f f e r e n c e r e l a t i o n s h i p was posttest  15  (p«^.07) to  e f f e c t of l e a r n e r statistically  of  posttest  characteristics  controlled.  found between average l a t e n c y  and  No (Y ) 2  and  (Y-^ )  H y p o t h e s i s 5:  A  s i g n i f i c a n t 1inear  relationship  (p<^.07) was  found between  immediate  l e a r n i n g and  proportion  errors  with the e f f e c t o f c h a r a c t e r i s t i c s and statistically  of  learner treatment  removed.  112  The graph shown i n f i g u r e 6 i l l u s t r a t e s the d i f f e r e n t i a l e f f e c t of A - S t a t e on p o s t t e s t for  the three treatment groups.  (raw) s c o r e s  An i n c r e a s e i n A - S t a t e  caused a decrement i n p o s t t e s t performance. linear relationship  between p o s t t e s t  was o n l y s t a t i s t i c a l l y group.  However, the  score and A - S t a t e  s i g n i f i c a n t f o r the T^ treatment  The i n t e r a c t i o n between the A - S t a t e and  correctional  feedback was merely o r d i n a l ,  i . e . the  r e g r e s s i o n l i n e s d i d not c r o s s . The graph shown i n f i g u r e 7 i l l u s t r a t e s the r e l a t i o n s h i p between average l a t e n c y i n the main l e s s o n and main A - S t a t e .  F o r the T-^ and T^ treatment groups,  an i n c r e a s e i n A - S t a t e was not s t a t i s t i c a l l y for  the T  3  group  (no c o r r e c t i o n a l  significant.  feedback) an i n c r e a s e  i n A - S t a t e l e v e l l e d to a s i g n i f i c a n t i n c r e a s e i n response latency.  The i n t e r a c t i o n between A - S t a t e and  feedback was merely o r d i n a l , d i d not c r o s s .  correctional  i . e . the r e g r e s s i o n  lines  113  10  T  -t-  10  8  12  A-State  *Tn:  T : 2  T3:  YYT Y^  =9.2 =8.7 =8.6  -  .09 .44 .05  14  (X ) 5  Xc X, X^  Figure 6 R e g r e s s i o n L i n e s of P o s t t e s t (Y-j_) and Main Lesson A - S t a t e (X ) for T T , T 5  l f  2  3  114  150  -+6  10  12  14  A-State ( X J *T :. 2 3 X  T  :  T  :  Y  3  177.5 = 2.02.7 186.9  .68 1.25 5.55  X X X^ 5  5  Figure 7 R e g r e s s i o n l i n e s of Average Main Lesson Latency Main A - S t a t e (X ) f o r the Three Treatment Groups 3  (Y ) an 3  115 Results  o f Post hoc  Analysis  Table.17 i n Appendix H l i s t s  the c o r r e l a t i o n  c o e f f i c i e n t e s t i m a t e s between a l l p a i r s o f v a r i a b l e s observed i n the study f o r the t o t a l subjects.  sample of s i x t y - t h r e e  The reader s h o u l d note that a c o r r e l a t i o n  c o e f f i c i e n t which i s s t a t i s t i c a l l y  s i g n i f i c a n t provides'  a d d i t i o n a l i n s i g h t i n t o the d a t a but does not a l l o w causal  inferences  to be made.  The extremely h i g h c o r r e l a t i o n s  (> .95) o f  of e r r o r s  (4) with t o t a l e r r o r s  responses  (3) suggests that e i t h e r of the l a t t e r  variables  could  place  (2) and with  of p r o p o r t i o n  of errors  prelesson unit could  in results. (.94) between  (15) i n d i c a t e s  latency  f o r thct i n s t r u c t i o n a l  that e i t h e r of these two measures  have been used as independent v a r i a b l e s  Similarly, latency  latency  response of an i n s t r u c t i o n a l u n i t i n the  (14) and t o t a l  experiment.  two  (2 d i v i d e d by 3) w i t h no  The extremely h i g h c o r r e l a t i o n the f i r s t  total  have been used as c r i t e r i o n measures i n  important d i f f e r e n c e s  for  proportion  The t o t a l  latency  i n the  (15) was a c t u a l l y used.  the h i g h c o r r e l a t i o n (.81) between f i r s t  (9) i n the main l e s s o n  and t o t a l l a t e n c y  time  (10)  i n d i c a t e s that e i t h e r v a r i a b l e c o u l d have been used as a criterion variable.  The t o t a l  latency  was a c t u a l l y used.  116 The r e s u l t s i n T a b l e 17 show that mathematical (16)  i s the most important  variable.  This v a r i a b l e  c o r r e l a t e d s i g n i f i c a n t l y with p o s t t e s t latency lesson  i n the p r e l e s s o n  (1), e r r o r s  ability (16) i s  (2,4,5),  (14, 15) and l a t e n c y i n the main  (9, 10). A t one p o i n t  the q u e s t i o n ,  i n the main l e s s o n  "Do you understand?"  the response to t h i s q u e s t i o n question  (7) was s i g n i f i c a n t  the student was asked  The c o r r e l a t i o n between  (6) and time to answer the (-.58) which i n d i c a t e d t h a t  people who answered " y e s " took l e s s time t o respond. A significant main l e s s o n A - S t a t e lesson  c o r r e l a t i o n (-.35) was found between the (21) and the s t u d e n t s '  (11) as measured by a q u e s t i o n  enjoy t h i s method of l e a r n i n g ? "  enjoyment of the  at the end,  'Did you  Lower A - S t a t e l e v e l  was  r e l a t e d to more enjoyment of the CAI e x p e r i e n c e . A p o s i t i v e c o r r e l a t i o n (.33) was found between proportion  of e r r o r s  (4) and whether the s t u d e n t s went  through the o p t i o n a l s e c t i o n on l i m i t s a higher limit  proportion  section during Surprisingly,  trait  anxiety,  Students with  of e r r o r s tended to opt f o r t a k i n g the the main  lesson.  there was no r e l a t i o n s h i p found between  A-Trait  (18) as measured i n the f i r s t  s e s s i o n , and the s t a t e a n x i e t y , prelesson  (8).  A - S t a t e d u r i n g the  (20) or the main l e s s o n  (21).  However,  a  testing  significant A-Trait  linear relationship  (.38) was found between  and the f i v e - i t e m A - S t a t e score  the DAY 1 paper and p e n c i l  (19) measured on  test.  T a b l e 18 i n Appendix H l i s t s a comparison o f c o r r e l a t i o n c o e f f i c i e n t s between s e l e c t e d  variables  t h r e e treatment groups c o n s i d e r e d s e p a r a t e l y . C h i - s q u a r e value i n d i c a t e s  f o r the  The  whether the three c o r r e l a t i o n  c o e f f i c i e n t s are s i g n i f i c a n t l y d i f f e r e n t at t h e " f i v e percent The  level. only s t a t i s t i c a l l y  c o r r e l a t i o n between p o s t t e s t main l e s s o n  correct  s i g n i f i c a n t f i n d i n g was the score and the t o t a l number o f  responses given by the student  being g i v e n the answer by the computer. correlation  A positive  ( > .55) was found f o r the two groups  feedback i n f o r m a t i o n  before  receiving  (T-^ and T ) but no r e l a t i o n s h i p 2  (r = .07) f o r the group r e c e i v i n g  no feedback i n f o r m a t i o n  (T ). 3  The  graph i n f i g u r e 8 i l l u s t r a t e s  the average number  o f e r r o r s made by the t o t a l group on each i n s t r u c t i o n a l unit  i n the main l e s s o n .  made r e l a t i v e l y few e r r o r s  The r e s u l t s i n d i c a t e  d u r i n g the main l e s s o n .  s u b j e c t s averaged more than two e r r o r s i n s t r u c t i o n a l unit  the s t u d e n t s  (9) and on u n i t s  s t u d e n t s averaged almost two e r r o r s .  The  only on one  12, 13 and 14, the This  finding  indicate  118 that  the c o r r e c t i o n a l feedback v a r i a b l e may  not  have been  potent enough to s i g n i f i c a n t l y d i f f e r e n t i a t e between T  1  and  T_ treatment groups. ^  feedback was  The  rarely received  reason f o r t h i s i s that  from more than one  wrong answer c a t e g o r i e s  b e f o r e the  answer to the  Also,  p r o v i d e d the u n i t s 2,  3,  student. correct  4,  5,  6,  the  or  two  computer p r o v i d e d  the  i n some cases many students  response without making an e r r o r , as 10 and  11.  However, a h i g h e r e r r o r  program would have been s e l f - d e f e a t i n g i n terms o f the of e f f i c i e n c y i n learning. the d i f f i c u l t y  l e v e l s of the  evenly d i s t r i b u t e d s i n c e times from easy to The  Another t r e n d  the  was  i n s t r u c t i o n a l u n i t s were not lesson f l u c t u a t e d  9 shows the  treatment groups taken s e p a r a t e l y . u n i t s such as 7,  9 and  was  i n s t r u c t i o n a l unit  several  average number of  12,  the  On  s u p e r i o r i t y of the T^ 9,  r a n k i n g of average number of e r r o r s was 2  T  u  ).  expected i n the  which was  error  as  T h i s f i n d i n g suggests that study may  r a t e of the  three  the more d i f f i c u l t  u n i t where a l l groups averaged more than two  (T^ T  goal  noted i n t h a t  e r r o r s made on each i n s t r u c t i o n a l u n i t f o r the  On  rate  difficult.  graph i n F i g u r e  evident.  in  the  errors,  group only the  hypothesizedthe  results  have been more pronounced i f the  l e s s o n had  been h i g h e r .  119  Graph of E r r o r s on I n s t r u c t i o n a l f o r Combined Groups  Units  120  1  2  3  4  5  6  7  8  9  10  11  12  13  14  Instructional Unit Figure 9 Graph of E r r o r s on I n s t r u c t i o n a l Units for Ti T , T3 2  15  121  The graph i n f i g u r e  1 0 shows the average  total  response l a t e n c y on each i n s t r u c t i o n a l u n i t f o r the t h r e e treatment groups.  A l t h o u g h no obvious trend seemed to  have o c c u r r e d , one  c l e a r f i n d i n g emerged.  the second treatment group on n e a r l y a l l d i f f i c u l t u n i t onward.  latency values.  subjects i n  ( T ) took more time to respond 2  i n s t r u c t i o n a l u n i t s from the seventh  For example, examining  7, 9, 1 2 , 13 and 14,  The  the T  2  instructional  s u b j e c t s had l a r g e r  As noted e a r l i e r ,  units  average  the T 2 group a t t e n d e d  the fewest morning s e s s i o n s and so i t i s p o s s i b l e a f t e r a day of c l a s s e s , a f a t i g u e e f f e c t became  that  predominant  i n the second h a l f of the main l e s s o n . The graph i n f i g u r e 11 shows the A - S t a t e l e v e l s f o r the t h r e e treatment groups at d i f f e r e n t p o i n t s i n time d u r i n g the study.  The graph i l l u s t r a t e s  that on DAY  d u r i n g the p r e l e s s o n , the A - S t a t e l e v e l o f T higher  than that of T^ s u b j e c t s who,  A - S t a t e l e v e l s than the T that the T  2  subjects.  2  s u b j e c t s was  i n turn, had higher T h i s seems to i n d i c a t e  s u b j e c t s were more anxious than the o t h e r s .  However, d u r i n g the main l e s s o n , the r e l a t i v e A - S t a t e were a l l s i g n i f i c a n t l y h i g h e r and was  1 and  as expected  levels  the r a n k i n g i n t h i s case  ( T - ^ 1^ .^T^ ).  A group of f i f t e e n s u b j e c t s reviewed a p o r t i o n of the main l e s s o n and was  p r e s e n t e d with the A - S t a t e instrument  122 twice. the T  Six s u b j e c t s were i n the  group,  five  group and f o u r were i n the T 3 group.  2  A - S t a t e s c o r e of these s t u d e n t s the f i r s t main l e s s o n was  13.1.  were i n  The mean  time through  the .  A f t e r r e v i e w i n g a s e c t i o n of the  l e s s o n and r e p e a t i n g the A - S t a t e q u e s t i o n n a i r e , t h e i r A-State  l e v e l was  14.6.  T h i s i n d i c a t e s that A - S t a t e  level  was  i n c r e a s i n g with time at t h i s stage of the experiment  was  p r o b a b l y q u i t e high when the s t u d e n t s wrote the  posttest.  U n f o r t u n a t e l y , the A - S t a t e l e v e l was  d u r i n g the p o s t t e s t but the f a t i g u e e f f e c t T  2  of  group i n terms of l a t e n c i e s may the r e l a t i v e It  not o b t a i n e d  e v i d e n t f o r the  have caused  order of A - S t a t e f o r the three  i s e v i d e n t that more d i f f i c u l t  a reversal groups.  items would have  i n c r e a s e d the A - S t a t e l e v e l even more and p r o b a b l y would have b e t t e r s e p a r a t e d the three groups i n terms of anxiety.  and  123  \ L  1 2  1 3  1 4  1 5  1 6  1 7  1 8  1 9  ) 10  1 11  1 12  1 ' I 13 14  I n s t r u c t i o n a l Unit Figure  10  Graph of L a t e n c i e s on I n s t r u c t i o n a l U n i t s  1' 15  124  Paper and Pencil Day 1  -  Prelesson Day 2  Main Lesson Day 2  Time o f T e s t i n g  Figure Graph of A - S t a t e  11  L e v e l s During  Experiment  ,125 TABLE 16  AVERAGE NUMBER OF RESPONSES IN EACH RESPONSE CLASS FOR MAIN LESSON  Average  Response Class  T  l  Number of Responses T  2  T  3  0.8  °2.9  2.6  C o r r e c t Answer  11.6  10.6  10. 4  Wrong Answer 1  3.5  3. 9  3.6  Wrong Answer 2  3.2  3.1  3. 9  Wrong Answer 3  1.3  1.5  1. 2  NOMATCH  5.4  5.8  6.3  HELP  The  r e s u l t s shown i n T a b l e 16 i n d i c a t e t h a t the T^  group asked f o r h e l p on the average main l e s s o n . other  •  l e s s than once i n the  T h i s was s i g n i f i c a n t l y fewer  two groups  times than the  (T ,T^). 2  The average number o f c o r r e c t responses made were ranked i n the expected order,  a l t h o u g h the d i f f e r e n c e s  between the three groups were not s i g n i x i c a n t . It i s i n t e r e s t i n g to note that as l e s s c o r r e c t i o n a l feedback was p r o v i d e d unanticipated  from T-^ to T^, the number of  (NOMATCH) responses i n c r e a s e d  slightly.  The  average number of u n a n t i c i p a t e d  responses f o r the  f i f t e e n u n i t main l e s s o n was approximately s i x . a very r e s p e c t a b l e  This i s  f i g u r e i n view o f the f a c t that many o f  the e r r o r s were t y p i n g or n o t a t i o n  errors.  Therefore,  l i m i t a t i o n s o f the CAI author language d i d not s e r i o u s l y hamper the r e c o g n i t i o n of student responses i n t h i s experiment. A f a i r b a l a n c e was a c h i e v e d f o r the wrong answer c l a s s e s except that few responses f e l l class.  i n t o the t h i r d  Some improvement c o u l d be made h e r e . i n  better  a n t i c i p a t i n g student i n c o r r e c t responses.  Summary o f S t a t i s t i c a l The The  regression  Results  a n a l y s i s produced s e v e r a l f i n d i n g s .  r e s u l t s o f the p o s t t e s t  mathematical a b i l i t y  analysis indicate  that  (p<^.001) was s i g n i f i c a n t i n  p r e d i c t i n g immediate l e a r n i n g .  However, when the e f f e c t  of t h i s v a r i a b l e and the other v a r i a b l e s s t a t e d i n H y p o t h e s i s 5 was removed, the p r o p o r t i o n  of e r r o r s f o r  the main l e s s o n was a l s o s i g n i f i c a n t f p ^ . 0 7 ) i n p r e d i c t i n g posttest results. The  expected d i f f e r e n c e between the three  treatment  groups r e c e i v i n g d i f f e r e n t types o f c o r r e c t i o n a l feedback was not observed on the p o s t t e s t . occurred  i n that  An unexpected f i n d i n g  the main l e s s o n A - S t a t e J e v e l was  127 significant and  i n p r e d i c t i n g p o s t t e s t performance  an A - S t a t e - b y - t r e a t m e n t  in predicting posttest The was  e f f e c t of  i n t e r a c t i o n was  state anxiety  a significant  group.  2  Graphical  group compared to a n a l y s i s showed that  but  r e s u l t s of the  o n l y f o r the T  regression  score  significant. (p No  .02)  analysis for  difference i n proportion  significant of e r r o r s .  2  and  T^  observed.  of e r r o r s  A (p03)  treatment groups.  This  i n the e x p e c t e d d i r e c t i o n , i . e . the  a higher  proportion  of e r r o r s than the T  r e s u l t s o:' the r e g r e s s i o n  response l a t e n c y a b i l i t y was  and  i n t e r a c t i o n s were observed.  e x p e c t e d treatment e f f e c t was  d i f f e r e n c e was  The  (p^.Ol)  statistically  the A - S t a t e l e v e l was  f o u n d between the T  group had  were both  proportion  i n p r e d i c t i n g the main l e s s o n p r o p o r t i o n  significant was  Also,  significant The  (p <~\ 01}  occurred  group.  2  of e r r o r s i n d i c a t e d that mathematical a b i l i t y prelesson  (p<".04)  on p o s t t e s t performance  decrement i n p o s t t e s t performance  when A - S t a t e i n c r e a s e d , The  found  scores.  d i f f e r e n t f o r s t u d e n t s i n the T^  s t u d e n t s i n the T  (p<^.06)  significant  2  group.  a n a l y s i s f o r average  i n d i c a t e d t h a t , once a q a i n ,  highly  T^  (p -^. 001) <  performance.  The  A - S t a t e l e v e l that was  the p r e l e s s o n  was  significant  mathematical  in predicting reached  during  i n p r e d i c t i n g response  latency  128 during  the main l e s s o n  (p<.03).  As would be expected, the  p r e l e s s o n average l a t e n c y was s t a t i s t i c a l l y  significant  (p<^.002) i n p r e d i c t i n g the main l e s s o n average The  expected treatment e f f e c t  latency.  was not observed s i n c e no  s i g n i f i c a n t d i f f e r e n c e s were found between the three treatment groups on response l a t e n c y . A-State-by-treatment  However, the expected  i n t e r a c t i o n f o r l a t e n c y was observed  (P<-04). The  e f f e c t o f s t a t e a n x i e t y on response l a t e n c y was  d i f f e r e n t f o r students i n the T 3 group. significant  i n the T 2 group compared to students  Graphical  a n a l y s i s showed t h a t a  i n c r e a s e i n average response l a t e n c y  occurred  with an i n c r e a s e i n s t a t e a n x i e t y f o r the T3 treatment group o n l y . The for  post  hoc a n a l y s i s p r o v i d e d  some u s e f u l  information  i n t e r p r e t a t i o n o f the r e s u l t s and suggested some other  questions.  The t a b l e o f means f u r t h e r i n d i c a t e d that the  T-, group attended group attended longer  the fewest morning s e s s i o n s  the most.  and the T,,  T h i s f i n d i n g suggests that the  l a t e n c i e s may have been due to a f a t i g u e e f f e c t .  T h i s would have been caused by the s l i g h t predominance o f evening s e s s i o n s f o r the T2 group. An  i n t e r e s t i n g f i n d i n g was the s i g n i f i c a n t c o r r e l a t i o n  (r = - .35) between enjoyment o f the main l e s s o n and l e v e l  129 of A - S t a t e .  As might  be expected,  the low A - S t a t e s t u d e n t s  enjoyed t h i s method of l e a r n i n g more than the h i g h A - S t a t e students. The  significant  c o r r e l a t i o n between p r o p o r t i o n of  e r r o r s and whether or not students had section  the o p t i o n a l  limit  (r = . 3 3 ) suggests that s t u d e n t s r e a l i z e d when they  r e q u i r e d e x t r a a s s i s t a n c e and c o n t r o l c o u l d be b u i l t  that,  t h e r e f o r e , more l e a r n e r  i n t o the CAI l e s s o n s .  An examination of the HELP and NOMATCH o p t i o n s showed that the T^ group  asked f o r he.lp s i g n i f i c a n t l y fewer  than the other two  groups  (T , T^). 2  times  This finding again  p r o v i d e s support f o r more l e a r n e r c o n t r o l o f i n s t r u c t i o n . The number o f u n r e c o g n i z e d responses as expected  (T^  T  2  T3).  Therefore, increased information  i n the c o r r e c t i o n a l feedback solution incorrect The  to the problem  (NOMATCH) were ranked  seems to p r o v i d e a p a r t i a l  of a n t i c i p a t i n g a l l p o s s i b l e  responses ta.ble of means showed that the three treatment  groups d i f f e r e d on n e a r l y a l l of the important in  the d i r e c t i o n expected,  but  variables  that the e f f e c t s were not  statistically, significant. The  graphs  of e r r o r s showed that the program had a  low e r r o r r a t e d e s p i t e e f f o r t s by the experimenter u t i l i z e a sample that would f i n d the m a t e r i a l  to  difficult.  130 Only one i n s t r u c t i o n a l u n i t had an average of more than two e r r o r s f o r the t o t a l group. note that a l a r g e d i f f e r e n c e  I t i s i n t e r e s t i n g to  was found i n the expected  d i r e c t i o n i n terms of e r r o r s on t h i s i n s t r u c t i o n a l u n i t among the three groups. The graph of l a t e n c i e s i n d i c a t e d that uneven i n d i f f i c u l t y  and that  the T  2  group  the u n i t s were took  consistently  longer on the i n s t r u c t i o n a l u n i t s i n the second h a l f of the main  lesson. The graph o f A - S t a t e over time i n d i c a t e d  expected p a t t e r n difference  i n anxiety  d i d occur but that  between the t h r e e groups was  as expected. A - S t a t e during  The  not as  that the  pronounced  t o t a l group, however, d i d i n c r e a s e  the main l e s s o n ,  as expected.  the  in  CHAPTER V  SUMMARY, CONCLUSIONS AND RECOMMENDATIONS  Summary o f Study T h i s study was undertaken t o i n v e s t i g a t e  t h e use o f  c o m p u t e r - a s s i s t e d i n s t r u c t i o n as an i n s t r u c t i o n a l laboratory.  The concept o f an i n s t r u c t i o n a l l o g i c was  d e f i n e d as an a l g o r i t h m f o l l o w e d by the computer program for  each i n s t r u c t i o n a l u n i t .  T h i s s t e p - b y - s t e p l o g i c was  repeated f o r each i n s t r u c t i o n a l u n i t  but with d i f f e r e n t  content., T h i s procedure p e r m i t t e d the c o n t r o l l e d of the v a r i a b l e correctional  of c o r r e c t i o n a l  feedback.  manipulation  Three forms of  feedback were d e f i n e d by v a r y i n g the i n f o r m a t i o n  content of the feedback.  These were r e s p o n s e - s e n s i t i v e  c o r r e c t i o n a l feedback, r e s p o n s e - i n s e n s i t i v e  correctional  feedback and no c o r r e c t i o n a l  that  feedback  (only  the answer  was i n c o r r e c t ) . The learner  i n t e r a c t i o n of c o r r e c t i o n a l  feedback with  c h a r a c t e r i s t i c s was examined as y / e l l .  t r a i t s were mathematical a b i l i t y , state anxiety.  prerequisite  The e f f e c t o f c o r r e c t i o n a l  .131  These  selected learner  knowledge and  feedback and i t s  132 i n t e r a c t i o n with these v a r i a b l e s was  examined.  S u b j e c t s o f the study were a r e p r e s e n t a t i v e sample of  s i x t y - t h r e e p r e s e r v i c e elementary  five  s e c t i o n s of a mathematics course g i v e n i n a l a r g e  education f a c u l t y .  These s u b j e c t s were randomly a s s i g n e d  to the three treatment the CAI The  s c h o o l t e a c h e r s from  c o n d i t i o n s , although  they  selected  e x p e r i m e n t a l p e r i o d s i n which they would p a r t i c i p a t e ,  t e s t of mathematical  a b i l i t y used was  the C o o p e r a t i v e  S e q u e n t i a l T e s t o f E d u c a t i o n a l P r o g r e s s , Mathematics Form 2A  (STEP).  The  s t a t e a n x i e t y instrument  S t a t e - T r a i t A n x i e t y Inventory short form used by O ' N e i l The  experimenter used was  and  (STAI) and the f i v e  (1972) was  e i g h t e e n item p o s t t e s t was  used was  administered  c o n s t r u c t e d by  the item twice.  the  the measure of p r e r e q u i s i t e knowledge  a nine item p r e l e s s o n with a p o s s i b l e mark of 0, 1  or•2 on each item. The  mathematics l e s s o n was  c a l c u l u s d e a l i n g with the concept was of  a topic in introductory of d e r i v a t i v e .  t r e a t e d from a p h y s i c a l p o i n t of view, u s i n g d i s t a n c e , speed  concepts.  and time  a point.  topic  concepts  mathematical  The main o b j e c t i v e s were to show t h a t the  d e r i v a t i v e i s a l i m i t and definition  to i l l u s t r a t e the  The  to c a l c u l a t e  to show how  to use  this  limit  the d e r i v a t i v e of a f u n c t i o n at  133 The CAI l e s s o n was programmed u s i n g an author language developed by the experimenter as a v e h i c l e the  instructional  feedback. advantage  l o g i c and v a r y i n g the  f o r implementing  correctional  The language i s l i m i t e d i n use but has the of r e q u i r i n g , e s s e n t i a l l y no computer e x p e r i e n c e  of an i n s t r u c t i o n a l d e s i g n e r . language as implemented Columbia i s the c o s t ,  The main l i m i t a t i o n of the  at the U n i v e r s i t y  of B r i t i s h  which s e v e r e l y l i m i t e d the  sample  s i z e i n t h i s experiment. The r e s u l t s of the study were g e n e r a l l y i n the expected d i r e c t i o n but the e f f e c t s were not as  pronounced  as had been h y p o t h e s i z e d .  The most important f i n d i n g  the  i n p r o p o r t i o n of e r r o r s  significant difference  main l e s s o n between the T of t h i s f i n d i n g relationship of e r r o r s effects  was  2  and T  3  groups.  found between immediate  with the e f f e c t o f l e a r n e r  statistically  learning  other v a r i a b l e s . in predicting as w e l l .  importance  and p r o p o r t i o n  t r a i t s and treatment  removed. i n predicting  i n the experiment was mathematical a b i l i t y statistically  on the  then i n c r e a s e d by the s i g n i f i c a n t  The most e f f e c t i v e v a r i a b l e  was  The  was  controlled  and i t s e f f e c t  when t e s t i n g the e f f e c t of the  Prerequisite  knowledge was a l s o important  performance and was  S t a t e a n x i e t y was  performance  statistically  controlled  significant in predicting  134 response  latency  but not i n p r e d i c t i n g e r r o r s .  Significant  treatment by A - S t a t e i n t e r a c t i o n s were observed f o r p o s t t e s t and f o r response The  latency.  three treatment groups d i f f e r e d i n the expected  d i r e c t i o n on most of the important v a r i a b l e s but  the  differences  were not s t a t i s t i c a l l y  In  particular,  the A - S t a t e l e v e l s f o r the three groups were  significant.  o r d e r e d as expected, but the d i f f e r e n c e s enough to cause The  were not  large  the h y p o t h e s i z e d i n t e r a c t i o n s .  r e s u l t s of the study p a r t i a l l y  supported the  h y p o t h e s i s o f the important r o l e of c o r r e c t i o n a l  feedback  i n i n s t r u c t i o n and i t s i n t e r a c t i o n w i t h i n d i v i d u a l of the  learner. Finally,  the p o s s i b i l i t y of a confounding  became e v i d e n t . possible  in light  A fatigue  e f f e c t f o r the T  2  variable  group  seemed  of the s l i g h t predominance of evening  s e s s i o n s coupled with the l a r g e r response this  traits  latencies for  group. In g e n e r a l , the two  attained.  A methodology was  i n s t r u c t i o n a l laboratory successfully experiment  g o a l s of t h i s p r o j e c t  and  developed f o r CAI  were as an  t h i s methodology was  to perform a c o n t r o l l e d experiment.  p r o v i d e d evidence t h a t  leads to improved  performance  correctional  during learning  used This  feedback compared w i t h  135 feedback t e l l i n g a student merely that h i s response i s incorrect. proportion  A  s i g n i f i c a n t r e l a t i o n s h i p was  of e r r o r s and  posttest  score  that a number of e r r o r s made d u r i n g  found between  which suggests  a lesson i s a  measure that can be used to maximize immediate l e a r n i n g . Finally, and  was  the v a r i a b l e of s t a t e a n x i e t y was  found to n e g a t i v e l y  state anxiety provided  increased  a f f e c t response l a t e n c y .  when no  c o r r e c t i o n a l feedback  to the s t u d e n t s as w e l l as when the  more d i f f i c u l t .  T h i s f i n d i n g confirmed the  r e l a t i o n s h i p between s t a t e a n x i e t y  Discussion  of  and  task  Also, was  content became expected difficulty.  Findings  C o r r e c t i o n a l feedback. v a r i a b l e had  examined  The  c o r r e c t i o n a l feedback  some e f f e c t i n t h i s experiment.  significant difference  (p^.03) i n proportion  observed between the group r e c e i v i n g c o r r e c t i o n a l feedback  ( T ) and  c o r r e c t i o n a l feedback  (T-j).  A of e r r o r s  response-insensitive  the group r e c e i v i n g  2  The  raw  was  means of the  no three  groups on most of the v a r i a b l e s examined i n the  study were  ranked i n the expected order,  However,  the d i f f e r e n c e s were not The  statistically  r e s u l t s suggest that  c o r r e c t i o n a l feedback helpful  i.e. T-^T^^T^.  information  (T?) may  i s provided  the  significant.  response-insensitive  be o p t i m a l  s i n c e some  to the student a f t e r  an  136 i n c o r r e c t response but p r i o r responses  a n a l y s i s of a l l p o s s i b l e  (and keywords) i s not r e q u i r e d .  T h i s form of  c o r r e c t i o n a l feedback r e q u i r e s f a r l e s s time to prepare by  the  i n s t r u c t i o n a l programmer and much l e s s computer  time and  storage  been o b t a i n e d  i s used.  with  More d e f i n i t i v e r e s u l t s may  a l e s s o n having  a higher  e r r o r r a t e , but  t h i s would have been s e l f - d e f e a t i n g s i n c e the program was  to h e l p  the student  succeed.  suggest t h a t i n terms o f u s i n g CAI instructional materials e a s i l y and  cheaply.  feedback can  aim  of  the  These r e s u l t s  i n the s c h o o l s ,  can emulate the  Until effective  have  programmed  strategy quite  response-sensitive  be developed which can be demonstrated to  cause improved performance and the classroom  i s not  l e a r n i n g , the use  justified.  However, u s i n g CAI  i n s t r u c t i o n a l laboratory permits research that c o u l d not be done u s i n g  of CAI as  in an  to be c a r r i e d out  programmed-instructional  materials.  A-State. the  three  As  expected, the r e l a t i v e d i f f i c u l t i e s  treatment c o n d i t i o n s caused  d i f f e r e n c e s i n A - S t a t e l e v e l during these A - S t a t e l e v e l s were not the t h r e e  treatment groups.  the  corresponding lesson.  However',  significantly different for For  a l l groups, the A - S t a t e  l e v e l d i d i n c r e a s e i n the main l e s s o n compared to the t e s t and  prelesson.  of  A l s o , a few  students  written  i n each group  137 repeated a s e c t i o n and were g i v e n the A - S t a t e again.  The mean A - S t a t e  l e v e l f o r these twelve  again increased s u b s t a n t i a l l y suggesting l e v e l s were i n c r e a s i n g towards the end The  hypothesized  that A - S t a t e  of the CAI  criterion  i n c r e a s e i n A - S t a t e f o r the T 3 group (no  response  coupled with a s i g n i f i c a n t  latency.  There was  an  variables.  correctional  increase i n  no s i g n i f i c a n t - r e l a t i o n s h i p  between A - S t a t e and response groups.  session.  f o r p r o p o r t i o n of e r r o r s , but  i n t e r a c t i o n d i d occur f o r the other two  feedback) was  students  A-State-by-correctional-feedback  i n t e r a c t i o n d i d not occur  An  questions  l a t e n c y f o r the T^ and  T h i s f i n d i n g again p r o v i d e d evidence  r e s p o n s e - i n s e n s i t i v e c o r r e c t i o n a l feedback  T^  i n f a v o r of  ( T ) as 2  the  optimal c o n d i t i o n . An unexpected f i n d i n g o c c u r r e d f o r the T  2  group.  i n c r e a s e i n main l e s s o n A - S t a t e f o r t h i s giovp was to a decrease finding  i n p o s t t e s t performance.  is difficult  An  related  Unfortunately,  this  to i n t e r p r e t because the ac tue.l A - S t a t e  l e v e l d u r i n g the w r i t t e n p o s t t e s t was p o s s i b l e that these A - S t a t e  l e v e l s may  not o b t a i n e d . have  It i s  be^n  s u b s t a n t i a l l y d i f f e r e n t from the main l e s s o n s i n c e A - S t a t e a n x i e t y l e v e l s were i n c r e a s i n g towards the end of the main l e s s o n , as p o i n t e d out above. this point f o r this finding  The  e x p l a n a t i o n o f f e r e d at  i s that a f a t i g u e e f f e c t may  have  138 been present  and may have a f f e c t e d the T  2  group.  The  reason f o r t h i s statement i s that s t u d e n t s i n the T group took c o n s i s t e n t l y longer  to respond d u r i n g  h a l f o f the main l e s s o n and were p r o b a b l y most A possible explanation more T  2  2  the second  fatigued.  f o r t h i s i s the f a c t t h a t  slightly  students took the CAI l e s s o n and p o s t t e s t a f t e r  c l a s s e s i n the evening, d e s p i t e e f f o r t s by the experimenter to c o n t r o l f o r t h i s f a c t o r . The main l e s s o n A - S t a t e was s i g n i f i c a n t proportion  o f e r r o r s f o r the t o t a l group.  p r e l e s s o n A - S t a t e was s i g n i f i c a n t the main l e s s o n response l a t e n c y . r e l a t i o n s h i p between a n x i e t y  i n predicting  A l s o , the  (p<.03) i n p r e d i c t i n g Therefore,  the  and performance f o r the whole  group was w e l l e s t a b l i s h e d i n t h i s study.  Surprisingly,  no r e l a t i o n s h i p was found between A - T r a i t and main A-State  lesson  levels.  Tobias  (1973) suggested that i t may be that the  v a r i a b l e of a n x i e t y , limited u t i l i t y  while u s e f u l i n other  areas,  has  i n the a r e a of i n d i v i d u a l i z e d i n s t r u c t i o n .  The reason f o r t h i s statement i s that i n i n d i v i d u a l i z e d i n s t r u c t i o n a l contexts difficulty  i n order  an attempt  to have a high  when i n s t r u c t i o n a l m a t e r i a l s to i n c r e a s e  their d i f f i c u l t y ,  i s made to minimize r a t i o of success.  are experimentally  Even  altered  these a l t e r a t i o n s are o f t e n  139 insufficient sufficient  to both evoke and  to e x e r t  achievement.  maintain l e v e l s of  anxiety  s i g n i f i c a n t d e b i l i t a t i n g e f f e c t s on  T h i s may  e x p l a i n the l a c k of  stronger  f i n d i n g s i n t h i s p a r t i c u l a r study.  Mathematical a b i l i t y . ability  had  the most evident  v a r i a b l e was  The  e f f e c t i n the study.  highly significant  learning, proportion  v a r i a b l e o f mathematical This  i n p r e d i c t i n g immediate  of e r r o r s and  response  latency.  However, the h y p o t h e s i z e d c o r r e c t i o n a l feedback-bymathematical - a b i l i t y  i n t e r a c t i o n was  not  observed f o r  o f the c r i t e r i o n v a r i a b l e s .  T h i s f i n d i n g suggests  mathematical a b i l i t y may  be a u s e f u l v a r i a b l e f o r  individualizing known to be  not  i n s t r u c t i o n and  important  that more s p e c i f i c  to task performance are  P r e r e q u i s i t e knowledge.  The  only.  that  abilities  required.  v a r i a b l e of p r e r e q u i s i t e  knowledge, as measured on the p r e l e s s o n , significant  i n predicting proportion  was  found to  of e r r o r s  be  (p<".01)  T h i s f i n d i n g i s r e a s o n a b l e s i n c e i t would seem that  a good p r e d i c t o r of main l e s s o n performance on a CAI during  any  the main l e s s o n would be  prelesson.  In l i n e with t h i s reasoning,  average response l a t e n c y was predicting  the performance on  significant  the  CAI  prelesson  (p <-•- . 002)  the main l e s s o n average response  lesson  in  latency.  140 The  h y p o t h e s i z e d p r e r e q u i s i t e knowledge-by-  c o r r e c t i o n a l feedback i n t e r a c t i o n was not observed f o r any  of the c r i t e r i o n v a r i a b l e s .  T h i s f i n d i n g seems t o  have been caused by the l a c k of v a r i a n c e scores f o r s u b j e c t s already  i n the experiment.  i n the p r e l e s s o n Most  students  had a t t a i n e d the p r e r e q u i s i t e o b j e c t i v e s and the  prelesson  served merely as a warm-up f o r them,  R e l a t i o n s h i p between p r o c e s s and product. significant  A  l i n e a r r e l a t i o n s h i p ( p ^ . 0 7 ) was observed  between,the p r o c e s s v a r i a b l e the product v a r i a b l e  ( p r o p o r t i o n o f e r r o r s ) and  (immediate l e a r n i n g ) .  No such  r e l a t i o n s h i p was observed between response l a t e n c y and immediate l e a r n i n g . the l i t e r a t u r e  However, there  i s some s u g g e s t i o n i n  (Judd e_t al_. , 1973) t h a t response  may have an e f f e c t on r e t e n t i o n .  The above  latency  significant  r e l a t i o n s h i p was observed a f t e r the e f f e c t of a l l l e a r n e r v a r i a b l e s i n the study and treatment had been removed The  (partialled  out).  f i n d i n g that p r o v i d i n g  response-insensitive  c o r r e c t i o n a l feedback  ( T ) i s better  c o r r e c t i o n a l feedback  ( T ) f o r reducing  and  2  3  than p r o v i d i n g no proportion  that a s i g n i f i c a n t r e l a t i o n s h i p (negative  e x i s t s between p r o p o r t i o n has  important  statistically  correlation)  o f e r r o r s and immediate  implications.  of e r r o r s  The f i n a l goal of the  learning  141 i n s t r u c t i o n i s to maximize the  l e a r n i n g product which i s  what the student takes with him terminal.  The  provided  analysis results.  some u s e f u l i n f o r m a t i o n  r e s u l t s and  The  post hoc  was  strongest  analysis the  The  mathematical  e f f e c t i n t h i s experiment.  It  noted that a s i g n i f i c a n t c o r r e l a t i o n (r = - . 35)  occurred  between main l e s s o n A - S t a t e and  method of l e a r n i n g . tended to enjoy the Two work were:  Students with lower A - S t a t e l e v e l s l e s s o n more.  (1) there  was  o f e r r o r s and  whether or not  l i m i t s , and  o f s t u d e n t s i n each group t h a t had from T^  to T  2  to T^  and  the  (2) the number  limit  the 1^  students  section  group asked f o r  s i g n i f i c a n t l y fewer times than the- other two  These f i n d i n g s suggest that require extra assistance  CAI  a s i g n i f i c a n t c o r r e l a t i o n (r =  chose the o p t i o n a l s e c t i o n on  increased  enjoyment of t h i s  f i n d i n g s that have i m p l i c a t i o n s f o r f u t u r e  between p r o p o r t i o n  help  that  f o r i n t e r p r e t a t i o n of  suggested some f u r t h e r q u e s t i o n s .  the  CAI  least cost.  c o r r e l a t i o n a l a n a l y s i s a l s o i n d i c a t e d that a b i l i t y had  the  c o r r e c t i o n a l feedback i s t h e optimal  to a c h i e v e t h i s g o a l at the  Post hoc  leaves  evidence from t h i s study suggests  response-insensitive condition  when he  groups.  students r e a l i z e when they  and  of i n s t r u c t i o n c o u l d be b u i l t  that more l e a r n e r i n t o CAI  lessons.  control  .33  142 The  only c o r r e l a t i o n a l c o e f f i c i e n t s i g n i f i c a n t l y  d i f f e r e n t f o r the three groups taken s e p a r a t e l y c o r r e l a t i o n between p o s t t e s t correct  was the  score and number o f main  lesson  responses g i v e n by the student b e f o r e the computer  p r o v i d e d the answer.  The c o r r e l a t i o n ( r > .55) f o r the T 1  and  T^ groups suggests that  response themselves d u r i n g on  the p o s t t e s t .  This  feedback i n f o r m a t i o n process.  s t u d e n t s who f i n d the l e s s o n  the c o r r e c t  w i l l perform  r e s u l t suggests that  i s an important p a r t  better  correctional  of t h i s  learning  T h i s f i n d i n g a l s o r a i s e s the q u e s t i o n about the  motivational  properties  of c o r r e c t i o n a l feedback s i n c e no  s i g n i f i c a n t c o r r e l a t i o n was found when c o r r e c t i o n a l  feedback  was not p r o v i d e d ( T 3 ) . The  t a b l e of means i n d i c a t e s that  groups d i f f e r e d on n e a r l y  the three  treatment  a l l of the important v a r i a b l e s i n  the e x p e c t e d d i r e c t i o n , but that e f f e c t s were not statistically posttest  significant.  score,  The v a r i a b l e s r e f e r r e d to a r e  t o t a l e r r o r s , t o t a l responses,  proportion  of e r r o r s , t o t a l c o r r e c t , number of s t u d e n t s t a k i n g limit  s e c t i o n , enjoyment and main l e s s o n A-Sta^e The  graphs of e r r o r s  low e r r o r r a t e d e s p i t e utilize  show that  optional  level.  the program had a  e f f o r t s by the experimenter to  a sample o f s t u d e n t s who would make many e r r o r s .  Only one i n s t r u c t i o n a l u n i t had an average of more tha.n  143 two e r r o r s f o r the t o t a l group. produced  l a r g e d i f f e r e n c e s i n the expected  between the three groups, l e s s o n may have produced difficult  This instructional direction  s u g g e s t i n g that a more d i f f i c u l t more d e f i n i t i v e r e s u l t s .  A more  l e s s o n c o u l d be designed by d e a l i n g with more  c o n t e n t i n each i n s t r u c t i o n a l u n i t this  unit  than was d e a l t with i n  study. The  graph o f l a t e n c i e s shows that the i n s t r u c t i o n a l  u n i t s were uneven i n d i f f i c u l t y and that consistently  the T  2  group took  longer on the u n i t s i n the second h a l f o f the  main l e s s o n , thereby producing a f a t i g u e e f f e c t  that may  have a f f e c t e d the r e s u l t s .  L i m i t a t i o n s of the Study A most apparent  l i m i t a t i o n of t h i s study, and other  s t u d i e s i n the a r e a o f CAI at the present time, i s the c o s t factor.  T h i s f a c t o r was the major c o n s t r a i n t  in limiting  the sample s i z e i n t h i s study to s i x t y - t h r e e s t u d e n t s . U n l e s s an i n s t i t u t i o n i s w i l l i n g to i n v e s t funds  i n this  type o f r e s e a r c h , i t i s p r o b a b l y wiser t o l i m i t CAI r e s e a r c h to i n s t i t u t i o n s h a v i n g the s p e c i a l i z e d hardware and software f a c i l i t i e s r e q u i r e d f o r e f f i c i e n t CAI. The  b i g g e s t d i f f i c u l t y f o r the s t u d e n t s seemed to be  the n o t a t i o n used by the computer. t y p e w r i t e r b a l l was used,  S i n c i a standard  symbols f o r change  ( A ) and a  144 normal d i v i s i o n s i g n c o u l d not be used.  Also, variables  c o u l d not be r a i s e d to a power u s i n g the u s u a l n o t a t i o n . An examination  of the students work sheets i n d i c a t e d that  they o f t e n d i d t h e i r c a l c u l a t i o n s u s i n g t h e i r n o t a t i o n and  then e n t e r e d the answer using the computer's  cumbersome n o t a t i o n .  T h e r e f o r e , the hardware  p r o b a b l y had an e f f e c t  this  s c h o o l t e a c h e r s and  Bork  limitation.  students i n the experiment  elementary  limitations  on the e x p e r i m e n t a l r e s u l t s .  and Sherman (1971) a l s o noted The  own  were p r e s e r v i c e  so the g e n e r a l i z a b i l i t y  of  the r e s u l t s i s l i m i t e d to t h i s or s i m i l a r p o p u l a t i o n s of students.  The c o n t e n t of the CAI  w e l l s t r u c t u r e d mathematical i n the l e s s o n and content may  l e s s o n d e a l t with a  a l g o r i t h m which was  a p p l i e d to c o n c r e t e examples.  act to moderate the e f f e c t s of other  derived Since variables,  the g e n e r a l i z a b i l i t y of the r e s u l t s i s l i m i t e d to m a t e r i a l having  similar  structure.  An obvious the experiment. been observed  l i m i t a t i o n was  The d i f f e r e n c e s that d i d occur may  over a longer p e r i o d of time.  n o v e l t y e f f e c t was the r e s u l t s .  person.  a full  c e r t a i n l y p r e s e n t and may  not have  Also, a have a f f e c t e d  Once a g a i n , t h i s i s a c o s t l i m i t a t i o n of much  of the present CAI develop  the s h o r t term nature of  r e s e a r c h because the time r e q u i r e d to  term CAI  course i s enormous f o r a s i n g l e  145  An  unexpected f a t i g u e e f f e c t seemed to have a f f e c t e d  the r e s u l t s .  T h i s e f f e c t was  not  observed i n the  pilot  group of c o l l e g e students i n M o n t r e a l but  seemed to be  factor  the  i n t h i s study, p a r t i c u l a r l y d u r i n g  Recommendations f o r F u r t h e r  a  posttest.  Research  A l t h o u g h some treatment e f f e c t s were observed i n t h i s study, these were not d e f i n i t i v e due  to the l a c k of  enough d i f f e r e n c e s i n treatment between the T^ groups.  A study s i m i l a r to the p r e s e n t one  should  conducted with a more d i f f i c u l t  l e s s o n and  done by  t r e a t e d i n each  i n c r e a s i n g the m a t e r i a l  and  large T  2  be  t h i s could  be  instructional unit. An  attempt should be made to d e s i g n a longer  study where a student would come more o f t e n to the  term CAI  terminal,  but f o r l e s s time i n order to minimize f a t i g u e  effects.  Possibly  type of  a team e f f o r t would best  facilitate  this  study.  The  organizational  scheme given  many q u e s t i o n s .  The  on r e t e n t i o n and  t r a n s f e r , and  independent v a r i a b l e s may  c r i t e r i o n variables for further Other l e a r n e r motivational  i n Chapter I generates have an e f f e c t  these should a l s o serve studies.  v a r i a b l e s should be examined, such  v a r i a b l e s and  as  verba.l a p t i t u d e .  as  These should  come from an adequate p r i o r c o n c e p t u a l a n a l y s i s of  the  146 treatment.  Other  CAI l e s s o n v a r i a b l e s should be s t u d i e d ,  such as types o f branching  and degree o f l e a r n e r c o n t r o l .  Similar studies u t i l i z i n g p a r t i c u l a r l y elementary  d i f f e r e n t populations,  and secondary  s c h o o l students,  would c e r t a i n l y be d e s i r a b l e as would be s t u d i e s i n a v a r i e t y of s u b j e c t areas.  T h i s would i n c r e a s e the  g e n e r a l i z a b i l i t y o f the r e s u l t s . A CRT ( g r a p h i c s ) t e r m i n a l would p o s s i b l y reduce the fatigue effect  i n further  studies.  An attempt  s h o u l d be  made to assess the e f f e c t s o f a v a r i e t y o f CAI t e r m i n a l types. I t has been noted  that sex may be an important  variable i n anxiety studies.  F u r t h e r s t u d i e s should  to  variable.  look a t the e f f e c t of t h i s  attempt  F i n a l Comment As with many other s t u d i e s , the present weaknesses and produced  one had  some u n a n t i c i p a t e d r e s u l t s .  However, a major goal of the study was a c h i e v e d : demonstration  t h a t CAT i s a powerful  the  and v a l u a b l e means to  examine i n s t r u c t i o n f o r the purpose o f producing a s c i e n t i f i c a l l y - b a s e d theory o f i n s t r u c t i o n . that t h i s study w i l l  I t i s hoped  serve as an example o f the power of the  computer and that o t h e r s w i l l overcoming i t s l i m i t a t i o n s .  accept  the c h a l l e n g e of  BIBLIOGRAPHY  Books Annett, J . Feedback and Human Behaviour. England: Penguin Books, 1969.  Middlesex,  Bunderson, C.V. " I n s t r u c t i o n a l Software E n g i n e e r i n g , " Computers i n Undergraduate Science E d u c a t i o n , Conference Proceedings, ed. Commission on C o l l e g e P h y s i c s (Maryland: C o l l e g e Park, 1971). C a s t l e b e r r y , S.J. 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" D i s t r a c t i o n , Response Mode, A n x i e t y and Achievement i n CAI," J o u r n a l of E d u c a t i o n a l Psychology ( i n p r e s s ) . Presented at annual convention of the American E d u c a t i o n a l Research A s s o c i a t i o n , New O r l e a n s , La., February, 1973. Van  Dyke, B.F., and J.M. Newton. "Computer-Assisted Instruction: Performance and A t t i t u d e s , " The J o u r n a l of E d u c a t i o n a l Research, LXV, 7 (March, 1972), 291-293.  Walberg, H. " G e n e r a l i z e d R e g r e s s i o n Models i n E d u c a t i o n a l Research," American E d u c a t i o n a l Research J o u r n a l , V I I I (1971), 71-91. Wine, J . "Test A n x i e t y and D i r e c t i o n of A t t e n t i o n , " P s y c h o l o g i c a l B u l l e t i n , LXXVI (1971), 92-104. W i t t r o c k , M.C, and P.A. Twelker. 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" C o n t r a s t Coding i n L e a s t Squares R e g r e s s i o n A n a l y s i s . " U n p u b l i s h e d manuscri U n i v e r s i t y of B r i t i s h Columbia, Vancouver, 1973. O l i v e r , W.P.. "Learner and P r o g r a m - C o n t r o l l e d Sequences of Computer-Assisted I n s t r u c t i o n . " Paper p r e s e n t e d at the annual meeting of the American E d u c a t i o n a l Research A s s o c i a t i o n , New York, February, 1971. O ' N e i l , H.F., J r . " A n x i e t y Reduction and ComputerA s s i s t e d L e a r n i n g . " Paper p r e s e n t e d at the American E d u c a t i o n a l Research A s s o c i a t i o n , H o n o l u l u , 1972b. S z e t e l a , W. "The E f f e c t s of Test A n x i e t y and Success F a i l u r e on Mathematics Performance i n Grade E i g h t , " D o c t o r a l D i s s e r t a t i o n , U n i v e r s i t y of G e o r g i a , August, 1970.  155 Tests Educational T e s t i n g Service. 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The U n i v e r s i t y of B r i t i s h Columbia, Vancouver, August, 1971.  APPENDIX A User's Guide f o r CAI Author Language Source L i s t i n g o f Program  T h i s program i s w r i t t e n i n FORTRAN IV and r e q u i r e s a minimum of computer knowledge and experience  on the  p a r t o f the user. Introduction A lesson c o n s i s t s of a s e r i e s of i n s t r u c t i o n a l u n i t s w i t h each u n i t having  the form shown on the next page i n  f i gure 1. These i n s t r u c t i o n a l u n i t s may be p r e s e n t e d student  i n a s e q u e n t i a l manner or i n an order  i n advance by the l e s s o n  to the  determined  designer.  A t y p i c a l l e s s o n c o u l d take the form shown i n f i g u r e 2.  IU 1  7  \  IU 2  7  IU 3  1 IU 4  ) IU. 5  —IK  A  IU 7  Typical  Lesson  Figure 2 User's Guide f o r CAI Author Language  I GX=0 |  Student's answer not recognized NOMATCH  Student i s ^ S ' t ' u d e n t asked a responds, ques'.-.ion  Comment Comncnt  X no Comment made  w  no Comment made  w  to a»o  i ' j ' k ' <V Qj+i' a l l represent d i f f e r e n t units (10) i n the lesson. son. Q  Write c o r r e c t answer | and comments ' , '  Q  Q  ^>means the n  t n  instructional  i  time through the block.  in Co Figure 1 Main Lesson I n s t r u c t i o n a l  logic  Using  the Program Each i n s t r u c t i o n a l u n i t  essentially  (Question) i s coded i n  the same manner as shown below.  CARD 1 Col.  1-2:  Q u e s t i o n number, r i g h t j u s t i f i e d . Must be i n t e g e r number between 1 and 30.  Col.  2:  No. of response c l a s s e s . Maximum i s 4  Col.  4:  No. o f keywords i n response c l a s s 1. Maximum i s 8  Col.  6:  No. o f keywords i n response c l a s s 2. Maximum i s 8  Col.  8:  No. o f keywords i n response c l a s s 3. Maximum i s 8  Col.10:  No. o f keywords i n response c l a s s 4. Maximum i s 8  CARD 2  CARD 3 Col.  1-80: Any comment t h a t the l e s s o n designer wishes to have the computer make t o the student. T h i s comment always b e g i n s the u n i t and w i l l c o n t a i n a q u e s t i o n t o the student. SIX cards maximum. Last c a r d must c o n t a i n a $END i n c o l . 77-80.  CARD 4 Col.  1-80: Any comment that the l e s s o n d e s i g n e r wishes to have the computer make to che student i f the student asks f o r h e l p . THREE cards maximum. L a s t card mu.^ t c o n t a i n a $END i n c o l . 77-80.  160 CARD 5 C o l . 1-10:  The f i r s t keyword accepted as c o r r e c t answer. Should b e g i n i n c o l . 1 and end with a $ s i g n .  Col.11-20:  The second keyword accepted as c o r r e c t answer. Should b e g i n i n c o l . 11 and end with a $ s i g n .  Col.21-30, 31-40, 41-50, 51-60, 61-70, 71-80: Other keywords accepted as c o r r e c t answer. Should b e g i n i n a p p r o p r i a t e column and end with a $ s i g n . The number o f keywords on t h i s c a r d s h o u l d be the same as the number i n d i c a t e d i n c o l . 4 of c a r d 2.  CARD 6 Cel.  1-80:  Any comment t h a t the l e s s o n d e s i g n e r wishes to have the computer make to the student i f ; (1) the student responds c o r r e c t l y , i . e . response wishes a keyword on l a s t c a r d , (2) the student asks f o r h e l p more than once, (3) the student responds more than once to the same wrong answer c l a s s , (4) the s t u d e n t ' s response i s not r e c o g n i z e d more than twice. FIVE cards maximum. L a s t c a r d must c o n t a i n a $END i n c o l . 77-80. T h i s c a r d may a l s o be a GOTO command. See l a s t s e c t i o n .  CARD 7 C o l . 1-10:  F i r s t keyword accepted as wrong answer.' Should b e g i n i n c o l 1 and end with a $ sign.  Col.11-80:  Same as on c a r d 5. Other keywords accepted as wrong answer. Number of keywords on t h i s c a r d should be the same as the number i n d i c a t e d i n c o l . 6 of card 2.  161 CARD 8 C o l . 1-80:  Any comment t h a t the l e s s o n d e s i g n e r wishes to have the computer make to the student i f h i s response matches one o f the keywords g i v e n on c a r d 7. FIVE cards maximum. L a s t c a r d must c o n t a i n a $END i n c o l . 77-80. T h i s c a r d may a l s o be a GOTO command. See l a s t s e c t i o n .  CARD 9  Same form as c a r d 7  CARD 10  Same form as c a r d 8  CARD 11  Same form as c a r d 7  CARD 12  Same form as c a r d 8  The  t o t a l number of keyword cards  ( i . e . cards  5, 7,  9, 11) must be the same as the numbers i n c o l . 2 of c a r d 2. T h i s number i s l i m i t e d t o a minimum of one and a maximum o f four. Note:  In order  to c o n s t r u c t  a l e s s o n having  thirty instructional units, special See  more than  techniques  must be used.  the author f o r d e t a i l s .  GOTC Command B r a n c h i n g to any p o i n t i n the i n s t r u c t i o n a l i s p o s s i b l e by u s i n g a GOTO command. r e p l a c e any comment card  T h i s command may  ( 5 ) such as cards  I f an i n s t r u c t i o n a l u n i t has been presented student, ignored  lesson  6, 8, 10 o r 12. twice  to the  a GOTO command to that i n s t r u c t i o n a l u n i t w i l l be and t h e computer w i l l proceed t o the next  question.  162 A GOTO command must begin i n c o l . 1 and has the form GOTOXX where XX i s the i n s t r u c t i o n a l u n i t justified, class  number, r i g h t -  where the program w i l l branch i f that response  i s chosen by the student.  System Commands The M i c h i g a n T e r m i n a l System use a t the U n i v e r s i t y c r e a t e a desk f i l e e.g. CAI. following  (MTS) i s c u r r e n t l y i n  o f B r i t i s h Columbia.  The user  to s t o r e the i n s t r u c t i o n a l  should  program,  The CAI program may then be run by e n t e r i n g the commands, s t a r t i n g  i n column 1:  $RUN CAI 5=LESSON 9=*MSOURCE  • SAMPLE  oi;fSTiON no. '*•  THTJJ.  i  OuTSTION  ' i n ; .  ! I  ;  • 1 i h 2 2 1 ?; L E T ' S PFVLFV PI'R RAS'lC FACTS. TODAY,WE VI'LL OO MULTIPLICATION WAT I S ' |/ x R ? J'CV? MUCH 15' SEVSfc MULYIPLIFn 8Y EIGHT? i, ' T » ; I ' S - CAM S E V : R I T T : N AS 7 !: • :  :  i  1  per,  .  • i  FIFTY  .MXi  I  .1J:  ,  6 AN P. Px7"f.B. P. MFMPFi; THAT ML.LT I PI- 1/VkTIOtl IS; JUST nrPEATEO ; PPITIOM. !|F VP TAK ' 7 jPfOt'PS. OF' 8' THIJ|PS_OP 8 rPQUPS Or 7 THI TPS,  i?xi--=  r  :  r  . ; ' ; • ' ; jFIFTFFf'$ pO TO •? ' | : , . . . |78*.' ; i i i I i ! :  ;i:o;  : . I !'  :  1  7? M.FA'.'S e w*$  /»wv  7 TF.MS .  THI.VK  OFi  N U L T I P L I C A T I OM  •AoniTioii. IF V.'E TAKE 7 fPOliPS' OF ? t p n r s . i ' o w :?5.i i i i i ! 5 7.$;' \ i • i 58< • :,5.i.$..: ^ 55x.: :  111 ;'T  i: '  1  I  I I  I I 11  II Hi  Ii  r  1  j iI  !  ji-ji  i  1  ; i  1 ii •jT'"' iiii  j j.i.Ll.;!  'I  P.f P A T F P  5.9$.  C  wi  6it$  i' i  11  i- . I • I :  i!  Hi! 11  i: P 111  HAVE.?'  i)8«  1—>-  II!  ii!:! |.i I •Ii 1 !i':iITi i i  AS  MAKY! T H I N G S ' on  :i I i ..!  I!  I  ;; :•;;;<  Mi I t  • ri  164  r3 copt 9  xxxxxxxxxxxxxxxxxixxxxxxxxxxixxxixxxxi.xxxxxxxxxiixxxxxxxxxxxxxxxxx /.xxxxi  S BO. 04991S  OBIVERSITY OF B C COMPUTING CENTRE  IG L404 PRINT=TH t i S T SIGNON WAS:  COPIES=10 13:37:52  unit 1111  LLLLLLLLLL LLLLLLLLLL  ZCCCCCCCC CCCCCCCCCC CC  CC CCCCCCCCCC  ccccccccc  n 44 44 ii 44 ii 14141414!) tit 4Q4441444U44 44 44 44 44 41  NS BH NNH HH Nt'HB BB KK HK HN MB HH SH KB BH MH HH HH HN BB HH HH HH BHNB HH HKB NN HN H KB  HTS(OG073)  PAGES=100  oooooooo  0000000000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  oooooooooo oooooooo  TTTTTTTTTTTT TTTTTTTTTTTV TT TT TT TT TT  TT TT TT TT" TT  _.  i n  1444 41 44 44 44 44 44 44444444441 444444444444 11 41 11 44 11  RRRRRRRRRRB RRRRRRRBR8RB RR BR BB BE RR BB BRRRRRRRRR3R RRRRRRRBRRR BR BR GR BB BR BB BR BB BB BB  SER_"L404"_SIGHED J)H » T _ 15:15:24 ON HOB AOG 27/73 BE -CAI" " " IL15 "-CAI" HiS BEEN CREATED. 08 IB 1ST -CAI 1 C DAVID KAUFMAN PROGRAM FOR MAIN CAI LESSOB 2 C THE KAIiJ PRCGRAh READS THE QUESTION NUMBES [IQ) , HOMBF.R OF RESPONSE 3 C CLASSES(KC) , NUMBER OF KEY WORDS IN EACH CLASS (KTOT),ALL KEYWORDS(KEY) , H C ALL QUESTIONS (Q"I;S) . HELT COMMENTS (QMOD) , COMr, ENTSFOR E..CH i. JESTIOH (TEXT) . 5 C THE MAIN PROGRAM ">!LS6" CO ilTROLS THE" FLU W" O F TK E LESSON" IN A 6 C SEQUENTI'.L Oi> NON-SEQUENTIAL MANNER AS S P Z C I F r E O IN ADVANCE BY THE LESSOR 7 C DESIGNER.THE STATISTICS FOR EACH QUESTION IN THE LESSON,I.E.,NUKE^R 8 (&\ AT THE END C.F T/fE LESSON.?;IIS R ECOR D-K E E P I S F C T I O K PECl'ISES DIS? SPACE 9 *t> OF RESPONSES MADE BY THE STUDENT IN EACH RESPONSE CLASS (I* RES) ARE WRITTEN 10 C _ WHERE THE R ESU LTS_S AY_BE _W R I TT E N. R E S P C 5 E LATENCIES ARE ALSO WRITTEN 11 C FOR KAX::" RESPONSE OH EACH INSTRUCTION AL UNIT. 12 C A LESSON IS LIKITED TO 30 INSTRUCTIONAL U N I T S 13 C 14 C" 15 IH?EGER*2 ANS(£0) .KEY (30,M,3,10) 16 _ IKTEGER QUSS(30,l20),gHOD(30,60),TEXT(je,4,100) ,STHO(30,6),  165  17 18 19 ' 20 21 22. 23 2<t _25 26 27 _2jl 29 30 31 32 33 30 35 36 _37 38 39 HQ 11 42 03 44 45 16 17 18 49 50 51 52 53 54 55 56 57 56 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76  C  C  C C C  C C C  C C  1 COD NT (30) .CLASS (30) DIMENSION NUH (30) , KTOT (30,4),NRES (3, 30, 6) ,BAME (30) , LQ (30) ,LH (30) , IB (30,1) .SEC (30, 10) COMMON TEXT,QUES,QMOD.STNO.IP,IGX.NRES,COUNT,LQ,LH,B 1,ANS,CLASS,KTOT,KEY,SEC,IRES DATA I EN D, IB, IGO/J SEND' , • SiGOTOV DATA NUH(1),NUM(2),NUM(3),NUN(<4),NUH(5),NUM(6),NUM(7),NUH(8), 1NUH(9),NUM(1.9),NUH(11),NUH(12).NUM(13),NUH(14),NUM(1S),NUH(16), 2K0M (17) ,NUM (18) . NUM (19) , NUH ( 2 0 ) / ' 1 «,« 2 «,« 3 1 «, . 3" 5 ".« 6 ',« 7 ',» 8 ',' 9 «.«10 ',«11 «,«12 ', • 13 I ' l l •, • 15 ','16 '.'17 <,*18 ','19 '.^O •/ DATA _HOfl_[2J ) , NUM (22) , NU_M_(23J , MUM t2U_L,_NU_M_(251, NOM (26) . 1 NUM (27) , NUM (2B) ,NUM (29) ,NUM (30)/'21 *,*22 •, ' 23 •, 2«24 ','25 '.'26 •,'27 ','26 ','29 ••,•30 •/ I N I T I A L I Z E COUNTEF.S TO ZERO IGI=0 DO 91 1=1,30 CPU NT (I)=0 ] DO 41 J=1.6 DO 4 2 L=1,3 02 NRES(L,I,J)=0 . _ ._ 41 STKO (I,J) =0 VRITE(6,13) 13 FORMAT (' PLEASE ENTER TOUH FIRST AND LAST NAME') ; 2EAD-1N STUDENT NAME BEAD (9, 11) (NAME (I) , 1=1, 10) 11 FORMAT (10A4) _ DO'33" IH-1,31 L1=1 L2 = 20 ; L3=1 L4=20 BEAD NUMBER OF THE INSTRUCTIONAL UNIT BEING PREPARED READ (5, i;EKD=20) IQ 1 FORMAT (12) READ TH E NO. OF RF.SPONSE CLASHES AND THE SO. OF KEYWORDS IB EACH" RESPONSE CLASS READ(5,2)KC, (KTOT (IQ , J) , J = 1 , KC) CLASS (IQ) = KC . "2 FORMAT (912) BEAD THE QUESTION TO BE PRESENTED TO THE STUDENT 3_READ(5j«) (QUES (IQ. J) , J = L1,L?) 4 FORMAT (20AU ) CHECK FOR THE END OF A COMMENT IF QUES (TO, L2) . EQ. IENDJGO TO 5 _ "CHECK THAT THE INPUT IS CORRECT.IF NOT.GIVE ERROR MESSAGE TO AUTHOR L1=L1+20 L2=L 2*20_ IF(L2.LE.120)GO TO 3 BRITE (6,90) IQ 90 FORMAT (' TOO MAN T C A B DS__ 0_R_ b* O J E N_D IB FIRST PART 'JF Q'JES. BO.'. 113) STOP 5 QUES (IQ.L21 -IB LQ(IQTSL2 BEAD-IN HELP CORKEHT 11 READ (5,4) (QHOD (IQ, J) , J = L3. L4) CHECK TH.'.T INPUT IS CORRECT.IF NOT.GIVE EBROi. RESSAiE ' IP (QMOD ;IQ,L4) . EQ. IEND) GO TO 12 L3=L3*20  O  166  / f  77 78 79 80 81 82. 83 81 85 86 87 86 89 90 91 92 .93 91 95 96 97 98 99 100 101 102 103 V)1 • 05 _106__ 107 108 __109 110 111 112 113 111 115 116' 117  C C C C  C  C  11B  L?_CONTINU_E  119  20 M?OT=IH-1  120  _121 122 123 _120 125 126 127 "128 129 130 131 132 _133 131 135 136  L4=L4*20 IF(L4.LE.60)GO TO 11 VRITE (6,91) IQ 91 FORMAT (' TOO BANT CARDS OR NO J END IN A COBHENT OF QOES. HO.', 113) STOP 12 QBOD (IQ,L4)=IB Ltl(IQ)=L1 DO 66_II=1.KC __ . H1=1 M2 = 20 READ ALL KEYWO R_D S_ IN E A CH RESPONSE C L A.SS ' EEAD(5,6) ( (KEY (IQ, I I , J , K) , K= 1, 10) , J= 1, 8) 6 FOR MAT(80A1) READ COMMENTS TO BE GI'.EN TO STUDENTS FOR EACH RESPONSE CLASS 8 READ(S,4) (TEXT (IQ, I I , J) , J = M1,M2) CHECK FOR A BRANCH TO ANOTHER INSTRUCTIONAL UNIT IFJTEXT (IQ,I_I,_1) .NS.IGOIGO TO 10 CHECK i n AT THE INPUT IS CORRECT.IF NOT,GIVE ERROR MESSAGE TO AUTHOR DO 60 IK=1,30 I F (TEXT (IQ, 11,2) . EQ. NUM (IK) ) GO TO 30 60 CONTINUE WRITE (6.93) I I , I Q 93 FORMKT ( I N C O R R E C T GOTO STATEMENT IN CLASS'. 13. 2X , 1'QUESTION NO. *,I3) STOP 30_ STflO CIQ.II) =IK _ TEXT (IQ, I I . i) =IE TEXT (IQ,II,2)=IB G0_T0_6^ CHECK FOR THE END OF A COMMENT 10 IF (TEXT (IQ, I I , M2) • EQ. IEND) GO TO 9 «1=*1»20 H2=M2*20 CHECK THAT THE INPUT IS CORRECT.IF NOT.GIVE ERROR MESSAGE TO A0T30R IF [US.. LE. 100) GS TO 8 WRITE (6,91) IQ STOP 9 TEXT (IQ,II,B2) = ID ""H(IQ. II) =H2 66 CONTINUE  C  m=^  ;  KEEP COUNT ON THE !.'0. OF THE INSTRUCTIONAL UNIT BEI3G EXECUTED _ >OOK-" (III) =C<Vv.'NT (IH) *1 CALL Q(IN.XOUT) C WRITE RFSPONSE 1ATENCIES ON A F I L E WRIT -J'(i, 105) IN, {SBC (IN.K) , K= 1, IRES) 105 FOP.rATilH ,I5.10F8.1> _GO TO (50,70),II____ '__ 70 IF (COUNT (IOUT) .GE.2) 10UT=IH*1 50 IF (ICOT.GT. MTOT) CO TO 55 IN=ICUT GO TO 13 C WRITE STUDENT NAME ON A F I L E 55 WHITE (1, 102) (NAME (I) , 1-1, 10) _ 102 FOKMA1 (IH . 1C..4J C WRITE TAnLE 0? JI1MEER OF RESIOHSSS IH EACH CLASS WITH HEADINGS OH F I L E WHITE . 100)  137 138 139 100 101 _142 103 100 JOS... 106 107 _10 8 109 150 _151 152 '.53 ".50 155 156 _J57 158 159 _160 161 162 163 " 160 165 166 167 ?68 169 170 171 172 173 170 175 176 177 178 179 180 181 182 183 180 185 186 _10V 188 1B9 190 191 192 _193 190 195 196  C C  100 FORMAT (' QUES',5X. 'CLASSES',IX. "TIMES',51,•HELP•,2X,'CL 1 ', 121,'CL2*,2X,*CL3',2X,'CL4',2X,•KOHATCH'//) DO 103 NQ =1,MTOT KCO=COUNT (NQ) KCL=CLASS (NQ) 103 BRITE (4,101) NQ.KCL.KCO, ( (S3ES (L.NQ.J) ,J=1.6) ,L=1.KC0) 101 FORM AT (4 X, 12.3(91,11), 4 (ix". I1),6X. I 1/(3 IX, 5 (4X, 11) » 61, 11) ) STOP END  SOBR OJDTIN E Q (NQ, IOUT) C THIS SUBROUTINE CONTROLS THE PROCESSING FOR EACH INSTRUCTIONAL UNIT C UNTIL THAT UNIT IS COMPLETED.CONTROL IS THEN RETURNED TO THE MAIN PROGRAM. C__THIS SUBROUTINE GIVES THE APPROPRIATE COMMENT TO THE STUDENT BASKD ON THE C RESPONSE CLASS INTO WHICH FELL HIS RESPONSE. COUNTERS FOR THE NUMBER OF. C ERRORS ON EACH INSTRUCTIONAL UNIT ARE KEPT TRACK OF IN THIS SUBROUTINE.  c  :  INTEGER*2 A NS (80) , KEY (30 , 0 , 8, 10) INTEGER QUES (30, 120) ,QMOD (30,6C) .TEXT (30,1,100) ,STHO (30,6) , 1COUNT (30) ,CLASS (30) DIMENSION K (6) .KTOT (30,4) ,NRES (3,30,6) ,LQ (30) , LM (30) , M (30,1) 1,SEC(30,10) COMMON TEXT , QU ES, QM0D ,_STN0, IP , IGX, NRES, COUNT , LO, LH,B 1, AN S.C LASS, KTOT, KEY",'~SZC.~, I RES C I N I T I A L I Z E COUNTERS TO ZERO " IKES = 0 ~K1 = 0 K2=0 K6=0 DO 77 L=3,5 77 K<L)=0 L2=LQ(NQ) C PRESENT THE QUESTION TO THE STUDENT VRITE (6,1) (QUES (HQ, I) ,7=1,L2) C KEEP A TIBER FOR RESPONSE LATENCY \ 3 CALL TIME (0) C READ-IN STUDENT KESPONSE.FIRST 10 CHARACTERS ARE READ READ (9,2) (ANS (I) ,1=1,10) CALL TISE(2,C.NLAT) IRES=IBES*1 SEC (NQ, IRES) =NLAT/1000. CALL MATCH(KQ,NEXT) C KEEP A COCH1ZP, FOR THE NUMBER OF ERRORS IN EACH FES ?ONL" E CLASS NRES (COUNT (NQ) , NQ, NEXT) = NRES (COUNT (NQ) , NQ,NEXT)_+1 G0~T0 (10,20,30,30.30,98),NEXT " C HKJ.r SECTION 10 K1-K 1 + 1 IF (K1. EQ. 2) GO TO 99 L1 = LH (NQ) VrtlTE ( 6 , J J J Q .^fi.if?.) : GO TO 3 C CORRECT RESPONSE SECTION 20 K2=K2 + 1 12 IOUT=KQ*1 IF(IGX.EQ.O) VRITE(6,21) IF (IGX.EQ. 1) VRITE (6,22) If(IG".EQ.J)WRITE(5,23) 1 (IGX .GE. 3) WRITE (6, 24) IGX=1GX*1 :  •  a 0 D  '  V  .  168  197 198 t99 200 201 _20_2 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 221 225 22C 227 228 229 230" 231 232 233 / 231 • 235 236 237 238 239 240 241 202 243 20* 245 246 2«7 . 218 249 5>50 251 252 253 254 255 256  C  IF (STNO (HQ, NEXT-1) . EQ. 0) GO TO 99 IOUT=STNO(NQ,NEXT-1) IP = 2 RETURN WRONG ANSWER SECTIOH 30 K (NEXT) =K (NEXT) »1 IF (STNO (NO, NEXT-1) . EQ. 0)GO TO 13 IO0T=STNO(NQ,NEXT-1) IP = 2 RETURN 13 IO0T=NQ*1 IP f K (NEXT) . EO. 2) GO TO 99 NN=KEXT-1 HH=M (NQ.NN) WHITE(6.1) (TEXT (NO, NN J) .J=1.BH) GO TO 97 BOBATCH SECTIOH 98 K6=K6+1 IF (K6. EQ. 1) WRITE (6,92) IP(K6.EQ.2) WRITE(6 93) IF (K6. EQ. 3) GO TO 99 97 IGX=0 GO TO 3 99 H1 = B(NQ,1) IOUT=KQ*1 i R I T E ( 6 , 1 ) (TEXT (HQ. I.J) ,J=1.B1) IP=t RETURN 1 FORK AT (/, (IH ,20A4)) 2 FORK AT (80 M ) 21 FORMAT (' OK') 22 FORMAT(• GOOD.') 23 FORR AT ( EXCELLENT!•) 24" FORMAT ( • EXCELLENT! KEEP P? THE GOOD WORK. ') " " 92 FORMAT(• I DON T RECOGNIZE YOUR RESPONSE. TRY AGAIN') 93 FORMAT (• BE CAREFUL.I S T I L L DON«'T READ YOU.ANSWER AGAIH") £110 f  c  r  1  c c c c c c c c  c  " " ~ ~  SOBROUTIKE MATCH(NQ.NEXT) SUBROUTINE TO MATCH STUDENT'S RESPONSE TO KEYWORD THIS SUBROUTINE IS A CHARACTER MATCHING ROUTINE THAT LOOKS FOR A HATCH OF THE STUUENT'T RESPONSE WITH ANY OF THE KEYVORDS,WITH A BLANK RESPONSE OR WITH THE HOED HELP. THIS ROUTINE RETURNS T.iT. VALOB OF THE gESPSSSE CLASS TI'AT THE STUDtiNT HAS HIT WITH HIS RESPONSE TO THE SUBROUTINE Q. INTEGER *k »KS(30),KEr(30,4,8,10),IB,IFIS,I1,I2,I3,I4 INTT^ER QUESOO,120),QSOD(30,60),TEXT'30,4,100),ST.NO(30.6», 1 COUNT (30) .CLASS (30) DIMENSION KTOT (30,H) , NRES (3.30,6) ,LQ (?0) ,LH (30) ,H (3C, 4) 1,SEC(30, 10) COBHOH TEXT.QUES.QKOD.STNO, IP,IGX,NRES, COUNT. LQ, LH, H 1,ANS,CLASS.KTOT,KEY,SEC,TRES DATA IB,IFI.",I1 ,12. 13,I«." •, • S • , • H « , ' E« , ' L • , ' P • / I N I T I A L I Z E COUNTERS KLASS=1 K=1 1=1 LL=1 1=1  169  257  C  258  C H E C K FOR H E L P R E S P O N S E 1 I F ( H N S ( I ) . N E . 1 1 ) GO T O  259  260  3  261  I F J I . L E . 4 0 ) GO  263 260 ..265  C H E C K FOR B L A N K R E S P O N S E I F ( A N S ( I ) . H E . I B ) GO T O 2 2 JO.CONTINUE GO T O 1 0 22 H C H A = 0 D 0_2 0 _ I L=J_._10 h'CHA=NCHA»1 C C H E C K FOR END O F KEYWORD($) I F ( K E Y ( N Q , K L A S S , K , I L ) . E Q . I F I N J G O TO 21 20 CONTINOE 21 HAX=NCHA-1 C C H E C K F O R KEYWORD AND f- NSWER M A T C H 2 I F ( K E Y ( N Q . K L A S S . K . L L ) . E Q . A N S ( L ) ) GO T O 4 21 L=L*1 C _ 0 N L I F I R S T 40 C H A R A C T E R S O F R E S P O N S E ABE CHECKED LL=1 I F ( L . G T . 4 0) GO T O 5 I F ( A N S ( L - 1 ) . EQ. I B ) GQ T O 2 GO T O 24  266  282  1 L=L*1  '  C  _286_ 287 238 289 290 291 292  C  293  IG  1  C  267 268 269 270 _271 272 273 271 275 276 _277 278 279 _280 281  294 _295 ' 296 297 298 299 300 _301 302 303 304 305 306 307  TO  do.. 3 0 _ l = 1., u 0 _  _26.2  _283 284 285  3  I F ( A N S (1*1) . EQ. 12. AND. ANS (1*2) .EQ.I3. AHD. AHS ( 1 * 3 ) . EQ. II) GO TO 1 0 1=1*1  LL=LJ.*1 C H E C K I F A L L L E T T E R S I N R E S 1 O H S E HAVE I F ( L L . I . E . H A X ) G O TO 2 CO TO 12 5 L=1 LL=1 K=K»1 C H E C K T H A T A L L KEYWORDS I N T H A T C L A S S I F ( K . L E . K T O T ( N Q . K L A S S ) ) GO T O 22 L=1 LL=1  _ BEEN  HATCHED  ~  HAVE  ' BEEN" L O O K E D V T  K=1 C  C C  .  KLASS=KLASS*1 _ H A V E A L L R E S P O N S E C L A S S E S B E E N L O O K E D AT I F ( K L A S S . L E . C L A S S ( N Q ) ) G O T O 22 G O _ T O 11 ' N E X T * I S " T H E V A L U E O F T H E R E S P O N S E C L A S S WHERE ST^'DEHT'S R E S P O N S E F E L L . R E T U R N T H I S V A L U E T O S U B R O U T I N E Q •. 1_0_HEXT=1 ; RETURN"" 11 H E X T = 6 RETURN ; 1 2 NF.XT = Ki A S S * 1 RETURN END  '  170  APPENDIX B  User's Guide f o r P r e l e s s o n Author Program Source L i s t i n g o f Program  171  . .Q±.  Question i s asked  Assistance i s given to student  Student i s asked t o answer once a g a i n — — —  1  I i  Question i s j asked s i m i l a r t o above  * Mark r e f e r s t o tne grade a s s i g n e d t o the s t u d e n t f o r a p a r t i c u l a r i n s t r u c t i o n a l u n i t , or item, Q^ .  Figure / Prelesson  Instructional  Logic  172 D e s c r i p t i o n o f CAIPRB, P r e t e s t Program T h i s program i s e s s e n t i a l l y the same as the program for  the main l e s s o n  (CAIPRE).  The s t a t i s t i c s  s e c t i o n has  been removed. M o d i f i c a t i o n s have been made so that the program follows  the l o g i c o f the p r e t e s t  have been taken to i n s u r e through a q u e s t i o n , if  he r e f u s e s  Precautions  that the student cannot "sneak"  i n f a c t , he may be caught i n a loop  to f o l l o w the i n s t r u c t i o n s g i v e n  The l o g i c channelled  - template.  t o him.  i s changed so that a l l NOMATCH answere a r e  to the f i r s t  wrong answer c l a s s .  T h i s means that  comments which the student r e c e i v e s i f h i s answer matches a key if  word i n the f i r s t  wrong answer c l a s s w i l l  a l s o be g i v e n  h i s answer i s not r e c o g n i z e d . The l o g i c used here allows  lessons.  f o r e a s i e r coding o f  I t i s usue*,l to use only  c o r r e c t c l a s s with a l l a c c e p t a b l e  two answer c l a s s e s , a keywords and a wrorig  c l a s s with one keyword i s only r e q u i r e d go to t h i s c l a s s anyway.  See f i g u r e 1.  s i n c e NOMATCH answers  173  (LIST  1  2  CAIPRE C_ DAVID KAOFHAR  - - ---C C  3  i : -' ; ?  / •'  4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20" 21 2i 23 24 2_5 26 27 28 29 30 31 32 33 34  PHOGRAB TO  "  c  PRETEST LESSOH  -  BAIN PROGRAB DETERMINES BRANCHING LOGIC INTEGER+2 ANS (80) , KEY (30,it ,8, 10) INTEGER QOES (30, 120) ,QMOD (30,60) .TEXT (30,fl,100) ,STNO (30,6) , 1 COUNT (30) .CLASS (30) DIMENSION NUK (30) , K T O T (30,4) , NRES (3, 30, 6)., NAME (30) ,LQ (30) ,LB ( 3 0 ) , 1B(30,<!) ,SEC (30, 10) COB HON T E XT_ , Q U E S , Q B 0 D , S T K O , IP, TG X, HR ES, CPU NT. LQ, LB, H 1.ANS, CLASS, KTOT'VKE?; r.TOTTSEC, IRES DATA IEND,IB,IGO/'SEND ,• '.•GOTO'/ DATA NUK(1),NUf;(2),NUK(3),NUM(il),NUM(5),NUr(6),NUM(7),NUB(8), 1HUn(9),MUH(19),HUB(U),NUH(12),MUB(13),NUB(1l»),SUB(15),HDN(16), 2KUK (17) ,NUM (18) .HUM (19) ,NUB ( 2 0 ) / ' 1 ',* 2 •,.' 3 ',• 4 •, 3« 5 ' «_6 L«J _I_ '. ' 8 ', ' 9 ','10 ' ,J 11 '.'12 '.'13 ', 4'1« *15 ','16 ','17 «,«16 '.'19 ','20 '/ DATA HUB (21) , NUH (22) , HUM (23) ,N0fl (2U) ,NU« (25) , HUM (26) , NUK (27) , 1HUB (28) , NUB (29) ,NUfl (30)/' 21 ','22 ','23 '.'2<4 ','25 ', "2'26 ','27 ','28 ','29 ','30 •/ IGX>=0 DO 41 i^iL,_30 . COUNT (I) =0 DO 11 J= 1,6 DO 12 L=1,3 _ 12 HRES (L, I , J) =0 " " ' " " " ~ 11 STHO(I,J)=0 WRITE (_6._1 3 ) _ 13 F0RH"AT("' PLEASE ENTER YOUR FIRST ANu LAST NAME') READ (9, IH) (NAME (I) ,1=1 , 10) 14 FORMAT (10A4) _ DO 33 IH=1,31 """ " " " L1=1 1.2=20 1  t  .  RON  174  35  / '  36 37 38 39 HO 41 42 8.3 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 9J_ 92 .3 94  13=1 t4=20 READ(5.1,END=20)IQ 1 FORMAT (12) READ(S,2)KC, (KTOT (IQ, J) , J= 1, KC) CLASS (IQ) = KC 2 FORMAT (912) 3 READ(5,4) (QOES(IQ,J) ,_ = L1,L2) 4_FORMAT (20AU) _ ___ ._ J. _. IF (QUES (IQ.L2) . EQ. IEND) GO TO 5 L1=L1»20 L2=L2+20 IF (L2.LE. 120) GO TO 3 WHITE (6,90) IQ 90 FORMAT (• TOO MAHI CARDS OR NO_$END IH FIRST PART OF QOES. HO. ', 113) STOP 5 QUES(IQ.L2)= IB LQ (IQ) =L2 11 READ(S,4) (QMOD (IQ, J) , J = L3 ,14) IF (QKOD (IQ.L4) . EQ. IEND) GO TO 12 _ _ _ _ _ _ L3=L3+20 " " " L4=L4*20 I F J L 4 . LE. 60) GO TO 11 WRITE (6,9'. j IQ 91 FORMAT (' TOO -ANY CARDS OR HO SEND IH A COMMENT OF QUES. HO.', 113) STOP ~ 12 QKOD(IQ,L4)=IB __tiQJ_ _ : DO'66 II=1,KC 111 = 1 112 = 20 BEAD(5,6) ( (K EY (IQ^II." 3 . K) . K= 1 , 110) , J= 1 , 8) 6 FORMAT(BOA 1) 8 READ (_ , 4) (T E X TJ1Q, 11,_J_ , J =H1.H2) IF (TEXT (IQ7i'l, 1) . H2. IGOi GO TC 10 DO 60 IK=1,30 _IF (TEXT (IQ, I I , 2) . EQ. HUM (IK) ) GO TO 30 60 CONTINUE WRITE (6.93) I I , IQ 93 FORMAT (• IN CORRECT GOTO STATEMENT IH CL ASS ' , 13 . 21. I'QUESTIOH NO. ',13) STOP _ _ S T N u (lQ.T.I) =IK • TEXT (IQ, IT, 1) =IB TEXT(IQ,II,2)=IB _?_TO 66 10 IF (TEXT (IQ, I I , H2) . EQ. I END) GO TO 9 H1 = ri1+20 H2=K2«20 _ I F ( K 2 . L E . IOC) GO TO U WRITE (6,9 1) IQ S TOP 9 TE.'T(IQ,1-,»2;^IB n(IQ,II)=K2 _6_COHTINUE 33 CONTINUE "~ 20 ETOT=IU-1 IH=1 L  _  t  175  / I  /  95 96 97 98 99 100 101 102 103 101 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 "3 134 135 136 137 138 139 liiO 141 142 1X3 105 146 117 148 149 150 151 15? is: 154  43 COUHT (IN) =COUNT (IN) »1 CALL Q(IN.IOUT) c c c c  c c c c  c  c  WHITE (4, 18) IH. (SEC (IN, J) ,J= 1,1 RES) 18 FORMAT (1H' ,I5,10F8.1) IF (IOUT.GT. HTOT) GO TO 55 IN=IOUT GO TO 4 3 55 CONTINUE STOP END SUBHOUTIKE Q(NQ.IOUT) INTEGER*2 A NS (80) .KEY (30,4,8,10) INTEGER QUES(30,120),QUOD(30,60).TEXT(30,4,100),STHO(30,6), 1COUHT (30) .CLASS (30) DISSENSION K (6) .KTOT (30, 4) , NRES (3 , 30 , 6) » LQ (30) ,LB (30 ) , H (30,4) 1..SEC (30,10) COHHOH TEXT,Q3ES,QHOD,STNO,IP,IGX,HRES,COUNT,LQ,LH,H 1,ANS,CLASS,KTOT,KEY,HTOT,SEC,IRES IRES=0 K1 = 0 K2 = 0 K6 = 0 KAHS=0 DO 77 L=3,5 77 K(L)=0 L2=LQ (NQ) WRITE(6, 1) (OUES (NQ.I) ,I=1,L2) 3 CALL TIHE(O) BEAD(9,2) (Atl-> !I) ,1=1,40) CALL TIME (?,0.N >.T) IRES=IRES*1 SEC (NQ, IRES) = NUT/1000. <Zl>l,L CATCH (NQ, NEXT) HBEJ (COUNT (NQ) , HQ, NEXT) =NRES (C'JUNT (NO) , NQ, NEIT) «1 GO TC (10,20,30,30,30,98),NEXT ~ i d K1=K1*1 I f (CI. EQ. 2) GO TO 99 L4 = LH (NQ) WBITE(6,1) (QKGD (NQ,I) ,1= 1,L4) GO TO 3 20 K2=K2*1 " " 12 IOUT=NQ* 1 I F (IGX. iQ.O) WRVTE (6,21) IF (IGX. EQ. 1) KhITE(6,22) I F ( I G X . EQ.2)WSITE(6,23) i r <iiX.GE.3) WRITE(6,24) IGX=IGX*'< I F (KANS. GE. 1) GO TO 99 I F (STNO (KQ, NEXT-1) . EQ.O) GO TO 99 IOUT=STNO (NQ.NEXT-1) T  - • - •  176  155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 Ifo 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 ?on 209 210 211 212 213 214  RETURN 30 K (NEXT) =K (H EXT) *1 KAHS=KANS* 1 IF(STNO(NQ,NEXT-1).EQ.0)GO TO 13 IOUT=STN0 (NQ,MEXT-1) IP = 2 RETURN 13 I0UT-NQ+1 IF(K(NEXT) . EQ. 2)GO TO 999 BN=N E X T - 1 HH = B (NQ, NH) WRITE [6. 1) [TEXT (HQ.HN.J1 .J=1.HB1 GO TO 97 98 K6=K6*1 IF (K6. EQ. 1) WRITE (6.92) IF (K6. EQ. 2)WRITE(6,93) IF (K6. EQ. 3) GO TO 99 97 IGX=0 GO TO 3 99 H1 = B(NQ,1) I0UT=NQ*1 BRITE(6,1) (TEXT(NQ, I.J) ,J=1,H1) IP=1 RETURN 999 IO0T=NQ+1 RETURN 1 FORHAT (/. (1H .20A4) ) 2 FOR BAT(80A 1) 21 FORHAT (' OK') 22 F C P f l A T C GOOD.') 23 FCKMATC EXCELLENT! •) 24 FORBAT(• EXCELLENT! KEEP UP THE GOOD WORK.') 92 FORMAT (' I DON T RECOGNIZE YOUR RESPONSE. TRY AGAIN *) C  C  93 FORBAT (' BE CAREFUL.I S T I L L DOR'*T READ YOU.ANSWER AGAIH•) END SUBROUTINE BATCH ( NQ,NEXT) SUBROUTINE TO MATCH STUDENT'S RESFONSE TO KEYWORD INTEGER»2 AHS(80),K£Y(30,4,8,10),IB,IFIH,I1,I_,I3,I<i INTEGER QUES(30,120) ,QBOD(3C,60) , T - XT (30,4 , 100) , STHO (_0, 6) , 1CCCNT (30) .CLASS(30) D I M E N S I O N KTOT (30,H),NRES(3,30,6),LQ(3C),LH(3?),fl(30,4j 1 , SEC (30. 10) COMMON TEXT,QUES,CH0D.STN0,IP,IGX,Nfl_2,CC-;.T,LC,Lfl,B 1,A»S,CLASS, K T O T , K E Y , MTOT , S EC , I R SS  DATA IB,IFIN,I1,_2,I3,I«/' ','$'. 'H ",' E ', 'L',':-" / KLJSS=1 K='. I.= 1 _L=1 1=1 1 IF (AHS (I) . HE. 11) Co TO 3 I F ( I N S ( 1 * 1 ) .EQ.I7.-ND.&NS (1*2) .EQ.I3. AND. AHS (I*3).EQ. 14) CO TO 10 3 I= I*i I F ( I . L E . 4 0 ) r,o TO 1 DO 30 1=1,40 IF (ANf (I) . NE. IE) GO TO 22 30 CONTINUE GO TO :0 HCHA=0  215 216 217 218 219 220 221 222 223 221 225 226 227 228 22? 230 231 232 233 231 235 236 237 238 239 200 201 202 203 20 0 205 206 EBP OF  DO 20 1L=1, 10 RCHA=NCHA*1 IF(KEY(NQ,KLASS,K#IL).EQ.IFIN)GO TO 21 20 CONTINUE 21 BAX=NCHA-1 2_IF_(KEY (NQ.KLA_SSjJK._LIO . EQ. ANS (L) ) GO TO 0 20 L=L*1 LL=1 I F {I. GT.10) GO TO 5 _ _ IF (ANS (L- 1) . EQ. IB) GO TO 2 CO TO 20 0 L=L*1 LL=LL*1 I F (LL. LE. HAX) GO TO 2 GO_TO__12 . 5 L=1 LL=1 K=K»1 IF(K.LE.KTOT(NQ,KLASS))GO TO 22 L=1 LL=1 K=1 KLASS=KLASS«1 I F (KLASS. LE.CLASS (NQ) ) GO TO 22 GO TO i 10 NEXT=1 RETURN . 11 EEXT=3 . RETURN 12 NEXT =KLASS* 1 RETURN END 1  FILE  $DES BIBLIO , DOBR. tSIG  178  APPENDIX C  CAI P r e l e s s o n  Listing  ^ M tr g -r  A  179  £ H£FT  ft  180  °i'H F F T  C.  181  182  FBETES • . „ _ ._ 1 1 2 3 3 8 3 3 B I . I'B TOUR PBRSOBAL TDTOR FOR TODAT.LET'S START Bit DOIHO A LESSOH OS. SOBg 4 OF THE THINGSTHAT 'YOU SHOULD"KNOW BEFORE DOING THE MAIN LESSON..... 5 LOOK AT THE GRAPH SHOWN IN SHEET A. 6 WHAT IS THE VALUE OF Y AT THE POINT X=1? ._SE«D 7 BEAD THE VALUE OFF THE GRAPH. SEND 8 10$ 10$ TENS 9 GOTO 3 0 5$ i~5l 20$ T I 2$ 3$ 5$ 81 1 HO. FIHD THE POINT ON THE CURVE WHICH CORRESPONDS TO A VALUE OF X= 1 2 BI DRAWING A VERTICAL LINE UP FROM X=1 UNTIL IT MEETS THE CURVE.TBEH 3 DRAW A HORIZONTAL LINE TO THE LEFT FROM THAT POINT UNTIL IT HEETS THE 4 T-AXIS AT ONE POINT. WHAT IS THE VALUE OF I AT THAT POINT? $EHD 5 10$ LOS 10$ 6 TOU SHOULD USE NUMERALS INSTEAD OP LETTERS TO REPRESENT NUMBERS. 7 TOU ARE CORRECT I F YOU MEANT TO TYPE 10 8 PLEASE ENTER THIS NUMBER AGAIH CORRECTLY. SEHD 9 2 0 2 3 7 ' 1 LOOK AT THE GRAPH IH SHEET A AGAIN. 2 WHAT IS THE VALUE OF i AT THE POIST 1=37 SEND 3 BEAD THE VALUE OFF THE GRAPH. SEHE 4 20$ 20* TWEH$ 5 GOTO 3 6 5$ 15$ 1$ 2$ 3$ «$ OS 7 GOTO 3 8 3 9 2 2 8 0 SUPPOSE THAT TOO ARE TOLD THAT S IS A FUHCTION OF T. _ _ _ T" ' HHAT IS THE VALUE OF S WHEN T=3,IF S AND T A R E RELATED BY THE EQOATIOS 2 S=2T*2 , RTAD THIS AS TWO TIMES (T SQUARED). SEHD 3 SDBSTITUTE THE VALUE CI- T=3 INTO THE EQUATION. SEHC t  183  4 5 6 7 8 3 0 1 2 3 4 5 6 7 8 9 0 J 2 3 * 5 6 7 8 9 0 T  2 3 4 5 6 7 8 9 0 1 2 .* 3 4 5 6  .  18$ EIGHTEEN $ GOTO 5 2$ MS 1 $ 12$ 8$ 9$ 16$ 29$ HO. TOO SHOULD SUBSTITUTE THE VALUE OF T,WHICH IS 3.IHTO THE EQOATIOH AHD OBTAIH S= 2T*2=2 (3) *2 = 2 (9) = ? WMAT IS TBE_¥ALUE OF S HHEH T=3? 4 2 2 7 HOW_SUPPOSE_THAT_WE ABE GIVES THE EQUATIOH S.= 3T*2 .HEAD AS 3 TIRES I SQUARED. WHAT IS THE VALUE OF S WHEN T=2? SUBSTITUTE T H E VALUE OF T=2 INTO THE EQUATIOH. 12$ T- ELS GOTO 5 3$ 6$ 9$ 15$ 2S 27$ 18$ GOTO 5 5 2 3 4 SUPPOSE THAT A CAB IS TRAVELLING AL08G A HIGHWAY AT A SPEED OF 6G BILES PEB HOUB. HOW FAR WILL THE CAR TRAVEL IH 2 HOURS? WHAT WILL T H E DISTAHCE BE I F T H B SPEED IS 60 BILES/BOOB AHD THE~ T I B E I S 2 HOURS? _H>$ ED AHD TWSDRED T-ENS GOTO 7 60S 2S 30S 12$ BO. BEHEHBER THAT DISTAHCE . S P E E D AHD TIHF ARE BELATED BI THE EQUATIOH _  THE CAR PASSES T H E 2 5 0 K I L E  POST.WE U S E T H L SYMBOL  THE CHANGE III D I S _ . \ N C E , T H A T  IS,  9  W H A T ' I S D E L (S)  0 1 2 3  SUBTRACT THE DISTANCE AT T H E 1 0 0 BILE POST F R O B THE DISTAHCE 3 HOURS LATER 15_$ ON- FIFTY$RS0 AHD FS GOTO 9 ~$ 100$ 2505 50$ 350$ 3$ HO. DEL (S) = (FlHAL DISTAHCE) - j I H I T I A t DISTAHCE) " " =250-100=? " ' " WHAT IS D E L ( S ) IH THIS CASE? e ; 2 3 4 SUPPOSE THAT THE _ABE C»R THAT PASSED THE 1?0 BILE POST AT HOOH PASSES THE 400 BLIE : O S T S I I HOURS LATER.  1  $EHD $EH0  _  BE WILL WRITE THIS AS S=VT. THEREFORE, S= (601 (2)=? WHAT IS THE DISTANCE IS TWO HOURS? 6 2 2 4 SUPPOSE ANOTHER CAR IS TRAVELLING ALOHG A HIGHWAY AT A SPEED OF 50~BILES/HOUR. HOW'FAR WILL THE CAR TRAVEL IH 3 HOURS? " ' " "' " WHAT WILL T H E DISTAHCE BE I F THE S P E E D IS 50 BILES/HOUB AHD THE T I B . I S 3 HOURS? 150$ BED AHD FS GOTO 7 50 S 3$ 100$ 200$ GOTO 7 7 2 3 6 ; A CAR P>._3ES T H E V>0 B I L E POST OH A HIGHWAY AT 12 NOOS.'THREE HOUBS LATER,  8  2 3  $EHD SEND  DISTA3CE= (SPEED) (TIBE)  7  S 6 7 8 9 0  S-Ht  IN THIS  D _ L (SI  DEL (S) = ( F I N i L DISTAHCE)  SEHD  DISTAHCE)  CASE?  _» THIS  ~*?HD  TO RECORD  (INITIAL  SEND  _  " ""WHAT IS ! ) E L ( S ?  $EHD  CASE?  DEL (S) = (FIHAL DISTANCE) - (INITIAL DISTAHCE). WHAT IS P E L ( S ) IH THIS CASE?  '  "  •  —  -  SEND  ~ $EHD ••  ;-.J KJ) E  SEND  184  «  5 6  • 7 8 9 0 1 2  3  «5  6  7  e  9 0 1 2  3 4 5  6 7 8 9  0 1 2  3 4 5 6  7 8 9 0  / t l l 3 4 .5 6  7 8 9 0 1 2  .3 4  & 6  7 8 9 0  "•1 •2  •3  300$ GOTO 9  T U B E S HUHSTHREEHUHS  100$  400$  GOTO  500$  4S  9  9 2 2 2 S O P P O S E T H A T A CAB TRAVELS FBOH MONTREAL T O TORONTO,A DISTANCE O F 3 5 0 B I L E S , A N D THE DRIVER STOPS SEVERAL TIMES FOR FOOD AND GAS. WHAT SPEED MUST THE CAR AVERAGE IN ORDER TO MAKE THE TRIP I N 7 H O 0 B S 7 T H E AVERAGE SPEED IS THE SPEED WHICH THE CAR WOULD HAVE TO T R A V E L I N OBDER TO TRAVEL 350 MILES IN SEVEN HOURS WITHOUT STOPPING. SINCE DISTANCE=.SPEED) (TIME) .WHAT IS THIS AVERAGE SPEED? 50$ GOTO11 350$  7$  SEND  SEND SEHD  FOBTY$  4S  11 2 2 4 S O P P O S E T H A T ANOTHER CAR TRAVELLING FROM MONTREAL TO T O R O H T O ( 3 5 0 MILES) ROVES AT 70 MILES/HOUR FOR THE FIRST 3 HOURS AND AT 60 H/HR FOR THE B E X T 4 HOURS. WHAT IS THE SPEED OF THIS CAR EXACTLY 5 0 MINUTES AFTER LEAVING MONTREAL? THE SPEED AT A PARTICULAR TIME IS CALLED T H E INSTANTANEOUS SPEED. THE  SEND  FIFTYS  BO. T H E CAB STOPPED SEVERAL TIMES AND D I D S O T K E E P A C O N S T A N T S P E E D . T H E AVERAGE SPEED IS THE SPEED AT WHICH T H E CAB WOULD H A V E T O T H A V E L IH ORDER TO TRAVEL 3 5 0 MILES IN 7 HOURS. AVERAGE SPEED=DISTANCE/TIHE=350/7=? • B A T IS T H E AVERAGE SPEED? 10 2 2 2 D U R I N G I T S ' JOURNEY.THE SAME CAR PASSED K I N G S T O N , A D I S T A N C E O F 1 6 0 BILES FROM MONTREAL,AFTER 4 HOURS. WHAT SPEED DID THE CAR AVERAGE? D I S T A N C E = (SPEED) (TIME) .WUAT IS THE A V E MAGE S P E E D ? 40$ GOTO11 160$ COT011  SEND  CAR TRAVcLS  AT 70 M I L 2 S / H 0 U R  FOR THE F I 2 S T  3 HOURS. HOW  SEHD  FAST  I S I T MOVING EXACTLY 5 0 MINUTES AFTER LEAVING MONTREAL? 70$ SEVENTY*  SEHD  GOT013 60$  501 3$ 4$ BO. THE SPEED CF THE CAR EXACTLY 5 0 MINUTE-* AFTER LEAVING MONTREAL I S CALLED THE INSTANTANEOUS SPEED AT THAT POINT. THE CAR IS MOVING A T 7 0 :V:!B AT THIS PARTICULAR TIME. WHAT IS THE INSTANTANEOUS SPEED? 12  SEHD  22 C  WHAT IS T H E INSTANTANEOUS SPEED OF T H E C A R EXACTLY 4 HOURS A F T E R L E A V I N G SOSTREAL? T H E CAR IS TRAVELLING AT 6 ? R/KR DURING T H E LAST FOUR HOURS CF T H E T R I P . HOW FAST IS I T GOING 4 HOJRS AFTER LEAVING MONTREAL? 60$ SIXTYS  SEND  1  G0TO13  4$  70S  50$  3$  GOTO13 13 2 2 8  L E T ' S TAKE A SHORT bhEAK FROM THE LESSON.I'D LIKE i 6 KNOW HOW T O O FEEL... . . B I G H T NOW. WHICH OF THE CATEGORIES BELOW DESCRIBE BEST IODB REACTION..NOW. T O T H E STATEMENT I AH TENSE.  SEHD  185  .» •5 •6 .7 •8 •9 •0 1  2 3 « 5 6 7 8 9 0 1  2 3 « S 6 7 8 9 0 •1  2 3 « 5 6 7 8 9 0 1  2 3 « 5 6 7 8 9 0 1  2 3 0 5 6 7 8 9 0 1  2 3  A MOT IT I L L C HODEHATELI SO B SOMEWHAT D VERI BOCH SO SEBD PLEASE AHSWER A,B,C,OR D. ARSWER A,B.C.OR D TO DESCRIBE TOOB BEACTIOH BIGHT BOB TO THE STATEHEHT... SEBD I AH TENSE. BOS IESS GOTO13 VERTS AS BS CS DS SOTS SOBES BODERS GOTO10 in 2 2 8 BHICH CATEGORY BELOW..A.B.C.OB D..BEST DESCRIBES.TOOB BEACTIOH TO THE STATEBENT. I FEEL AT EASE. A HOT AT ALL C BODERATELT SO B SOMEWHAT D VERT KOCH SO AHSWER 1.B.C.OB 0. SEHD PLEASE A,B.C.08 D. SEHD BOS TESS GOT01U AS BS CS DS IOTS SOBES EODEBS VESTS GOTO15 15 2 2 8 I AH RELAXED. _ BOT AT ALL C BODERATELT SO B SOBEWHAT D VERT BOCH SO PLEASE AHSWER A,B.C.OB D. SEBD AHF-EB A,B.C.OR D...TO THE STATEMENT.... I AH BELAXED. SEHD BOS IESS G0TO15 VESTS AS BS CS DS ROTS SOBES rlODEBS GOT016 16 2 2 8 I FEEL CALB. A BOT AT ALL C BODERATELT SO B SOMEWHAT D VERY BOCH SO ANSWER A,B.C. OR D. SEHD AHSWER A,B.C.OR D TO THE STATEBENT... I FEEL CALB. SEHD BOS TESS GOT016 AS BS CS DS IOTS SO-ES BODEBS TESTS GOT017 17 2 2 _ I AM JITTERY. A ROT AT A"LL C BODERATELT SO B SOBEWHAT D VERY BOCH SO ANSWER A.B.C.OR D. SEBD AHSWEB A.B.C.OR D TO THE STATEMENT...I AH JITTERY. SEHD TESS HOS GOT017 AS BS CS DS HOTS SOBES HODS TESTS G0TO18 18 2 6 8 -OW,LET'S GET BACK TO THE LESSON... LOOK AT THE GRAlMI OF S VS. T SHOWN IN SHEET B. WHAT IS THE SLOPE OF THE LINE INDICATED O N T I E GfAPH? SEBD SLOPE IS JUST THfc CHANGE IH S DIVIDED BY THE CHANGE IH T. OSIHG THE NOTATION THAT WE BIFINED EASi LIER , SLOP E = DEL (S)/DEL (T) .  186  4 5 6 7 8 9 0 1 2 3  «5  6 7 8 9 0 1 2 3 4 S 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 •2 •3 •4 -5 •6 .7 •8 •9 0 .1 •2 .3 .4  >i  .6 ;7 .8 .9 •0 M '2  '3  P I C K TWO P O I N T S ON T H E L I N E A N D C A L C U L A T E THE SLOPE. 4 $ FOUR* 20/5$ 40/10$ 60/15$ 80/20$ . GOTO20 20$ 40$ 60$ 80$ 5$ 10$ 15$ 20$ V O . THE SLOPE IS DEFINED AS SLOPE=(CHANGE IN DISTANCE)/(CHARGE I I TIHE) = D E L (S) / D E L (T) . P I C K TWO P O I N T S ON T H E G R A P H . S A Y T = 5 A N D T = 1 0 . T H E N , SLOP E= ( 4 0 - 2 0 ) / ( 1 0 - 5 ) = 2 0 / 5 = ? WHAT I S THE S L O P E ? 19 2 6 8 LOOK A T THE G R A P H O F S VS.T SHOWN I R S H E E T C . WHAT I S T H E S L O P E O F T H E L I N E I N D I C A T E D ON THE G R A P H ? SLOPE I S J U S T T H E C H A N G E I N S D I V I D E D BY T H E C H A N G E I N T. O S I N G O U R N O T A T I O N , S L O P E = D E L ( S ) / D E L ( T ) B E T W E E N TWO P O I N T S CN THE L I K E . CALCULATE THIS SLOPE. 5$ FIVES 10/2$ 20/4$ 30/6$ 40/8$ GOTO20 10$ 20$ 30$ 40$ 2$ 4$ 6$ 8$ GOTO20 20 2 6 2 L E T ' S REVIEW SOME B A S I C A L G E B R A . SAI T H A T YOU A B E G I V 2 N T H E E X P R E S S I O N 3 ( 1 * 1 ) * 2 - 3 (1) *2 / (1 »X) - 1  $END  $ESD  SEHD  SEBD  SESD WHAT L IHF T IE OF T H I NL ?I F Y T H E H O M E R A T O B . E X P A N DIS3 T ( 1H*E X )S *I 2M P I HDE FORM NUMERATOR ASN DETXHHEKNE SSSIIMOP T H E H S I M P L I F Y T H E D E N O M I N A T O R . F I N A L L Y , C A H C E L X FROM BOTH K O M E R A T O S ABD DENOMINATOR. 6*3X$ 6 • 3X$ 3X*6S 3X • 6 $ 3(1*2)$ 3(2*1)$ GOT022 2$ /$ B O . THE N U M E R A T O R B E C O M E S 3 (1 *X) * 2 - 3 ( 1 ) * 2 = 3 (1 * 2 X * T » 2 > - 3 = 6 X * 3 X » 2 = X (6*3X) T H E DENOMINATOR BECOMES ( 1 * X ) - 1 = X THEN, T H E EXPRESSION EQUALS X(6*3X)/X=? WHAT I S T H E F I N A L FORM O F T H E E X P R E S S I O N ? 21 2 5 2 HOW IOU A B E G I V E N AH E X P R E S S I O N (2*X)»2-2»2 / (2*X)-2 WHAT I S T H E S I M P L I F I E D FORM O F T H I S EXPRESSION.' PROCEED EXACTLY AS ABOVE. 4*1$ X*4$ 4 * XS X • 4$ 4 *X$ GOT022 ' 2$ /* GOT022 22 2 5 2 LET'S DC TflE S A M E E X A M P L E A S BEFORE.BUT HOW K E ' L L USE T H E S I B 3 0 L S T H A T H I L L B E U S E D I N THE M A I N LESSON. GIVEN T H E EXPRESSION 3 (1 • OEL (T) ) • '2-3 ( 1 ) » 2 / ( 1 * D E L ( T ) ) - 1 WHAT I S T H E S I M P L I F I E D FORM O F T H I S EXPRESSION? LOOK AT THE P R E V I O U S PROBLEM. THE P R O C E D U R E I S T H E SAME AS iEFOHE E X C E P T THAT V E NOW H A V E "SED DEL (T) I N P L A C E OF X . 6*3DEL* 3DEL(T)*6*6 • DELI 3(2*DEL$ 3(DEL(T)*$ GOT024 1 $ /$ HO. T H E S O L U T I O N I S T H E SAME AS B E F O R E . T H E N U M E(T) R A T•O3RD E L B E(T) COM 3bDEL (1 • DEL 1) * 2= J ("ODE! •=3*6DEL *E 2S -3 = (T)(T) O D)E"2-3 L (T)(»2=DEL (T) ( 6 * 3 D(*E')L •D'vL (Ti )( T ) • 2 ) - 3 THE D E N O M I N A T O R B E C O M E S (1 • DEL (T) ) - 1 = D Z L (T J  SEND  SEHD  SEBD SEBD  SEND SEHD  187  '« '5  '6  '7 '6 '_9_ 10 11 _  13 1% 15 16 ;7 ;8 •9 0 '1 2 3 »  T H E N T H E E X P R E S S I O N B S C O R E S D E I ( T ) (6 + 3DEL ( T ) ) / D E L ( T ) = ? ? ? 23 2 3 2 ROW,TOO A B E G I V E N A S E X P R E S S I O N ( 2 * D E L (T) ) » 2 - 2 * 2 / ( 2 * D E L (T) )-2 BHAT. iS_T..HE—SI?PLIFIED__F0RFL O F THIS__E_.P.BESSIOB7 P B O C E E D E X A C T L Y AS B E F O R E . °° ««DELS II • D E L S DEL(T)»VS GOTO2U _ 2$ /%  SEHD  _S__SD SEBD ;  G0T021 2B 2 2 2 TOO S E E N TO UNDERSTAND T H E CONCEPTS HEEDED TO TAKE T H E HAIB TOO MAT T A K E _ A S H O R T B R E A K OR YOU C A H S T A R T T H E H A I H L E S S O R B I G H T AH A Y . DO YOU WANT T O T A K E A B R E A K ? A H S W E R HO OB TES. BOS NO.S ; TBEH TTPE...SSOURCE LESSOR TES* OKS T H E - T A K E t S H O R T B E S T AHD WHEH T O U ' B E B E A D Y _ T T P E . . . S S O U R C E  r ntE  LESSOB. .  SEHD SEHD  • SEHD LESSOB  SEHD  188  APPENDIX D CAI Main Lesson  Listing  (versions T , T , T ) 2  189  s  t  190 4  5 T H _ £ T  £»n« Us)  2.  !  io-  .—  •  ' *w ?  .  •  _  /  / r  *  /  / /  /  ti  191  SHEET 3  C Aon. J)  192  S H E E T 46fMPH  DI.-MAJ-._-  O F  t/g.  TIMH  D!STAMc_: S  .p  1—  —  \  \  w  --•  — ,i \  1  1  I  J,  Y  K 1__  TIME  T "  =  5 JL33H5  } Y  *•>!-<> ft  194  3  COPT 10.  XXXXXXXXXXXXXXXXXXXXXXXXXXIXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXZZXXZXXXXXXIX)  009919  1,404  OBIVERSITT  PRIBT--TH  ;T S I G B O B  BAS:  COPIES=10  B  C  COMPUTING  CENTRE  HTS (OG073)  PAGES=999  15:15:24  tutti  oooooooo oooooooooo  nnnn nn nn nn nn nn nn  .LLLLLLL .LLLLLLL  OP  4mi4qqtt4itQ.lt 444444444444 44 44 44 44 44  __ nun nnnn  44 44 44 44 44 44 44444444444 444444444444 44 44 44 44 44  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 OOOOOOOOOO OOOOOOOO  RRBRRSRRRRK RRBRRBRRRRRR BB BB BB BB BB BBBBRBBRRRRB BBBBBRRSRRR  CCCCCC  an  BB BB BB BB  CCCCCCC CCCCCC  /  •L404" SIGHED OH _AT  '  I I 1  2 '3 4 5 6 7 8 9 0 . 1 2 3 4 5 6 7 8 9 0  -  • -  16j_>6:19 OB BOH -  •  '  AOG 27/73 "  •  -  --  1  4 6 2 2 3 LET'S STUD! THE HOTIOH OF A BOAT AS IT LEAVES A DOCK. SOPPOSE THAT IT'S MOVING AT A CONSTANT SPEED OF 10 MILES/HOUR. WHAT IS THE DISTANCE S OF THE BOAT FROM THE DOCK AT A N Y TIMs T? HEHEBBER THAT DISTANCE (S PEED) (TIME).WRITE AN EQUATION FOR S IN TERMS OF T. 10TS 10*T$ 10 TIMES $10XT$ S=10TS S=T10J T10S T»10S THE EQOATION WHICH DESCRIBES TEE MOTION 0P_THE„'OA'T_JS_ S=10T. THIS IS SIB PL I THE FAMILIAR DfSTANCE= "(SPEED)'(TIME") EQUATION, WITH SPEED V BEING CONSTANT \7 10 MILES/HOU".. 10-3/T S T=10/S $ ' THIS IS THE EQUATION RELATING DISTANCE, SPEED, AND TIME. NOW RF» '.RANGE IT TO GET DISTANCE S ALONE OH THE LEFT HAND SIDE. 10 S T S THIS I S FART OF THE ANSWER. REMEMBER THAT DISTAPC3= (StTED) (TIME) AND TOO HAVE ONLY LOO.-.ED AT ONE OF THESE QUA1IITIES. TRY AGAIN. S S DISS 10SS THE DISTAfCE ^ GIVEN BY S.NOW,WHAT IS TUZ EQUATION IC? S IN TERMS OF T7 2 3  SEHD SEBD  fEBD SEBD SBSD SEBD  195  M  1  e u  2 3 4 5 6. 7  L O O K A T SHEET 1 THAT WAS GIVEN T O TOU.THE GRAPH INDICATES HOB F A R THIS BOAT IS FROM THE COCK AT ANY TIHE. WHAT IS THE SLOPE OF THIS STRAIGHT LINE REPRESENTING THE B O A T ' S B O T I O H I H A TIME INTERVAL T = 2 TO T = 6 HOURS? T O U _NEED__Tp__OBTAIN THE CHANGE__IN DISTANCE AND THE CHANGE IH TIHE BETWEEN THESE TWO P O I N T S IN ORDER TO C A L C U L A T E THE S L O P E . GO AHEAD...  8  10S  SI 0 1  T H E SLOPE IS THE CHANGE IN D I S T A N C E DIVIDED BY T H E CHANGE I H T I H E . WE WRITE THIS AS S LOPE= D E L ( S ) / D E L (T) WHICH IS EQUAL T O < 6 0 - 2 0 ) / ( 6 - 2 ) = 1 0 HILES/HOUR.  2  1_1_Q$  10/4$  .__1_$  4/40$  2/20$  6/60J$_  e/_B0S  SEBD  6-2/60-20S6-2) / (60-S  ALMOST RIGHT.YOU'VE CALCULATED THE CHANGE IN D I S T A N C E AND THE CHARGE IB T I H E CORRECTLY BUT YOU'VE DIVIDED THEM I N C O R R E C T L Y . T H E SLOPE IS THE CHANGE IN D I S T A N C E DIVIDED BY CHANGE IH T I B E . T B T A G A I H .  6  60S  7 8 9 0  TOO'BE ON T H E RIGHT TRACK SINCE YOU'RE DIVIDING DISTANCE B Y TIHE, BUT YOU'RE ONLY L O O K I N G AT ONE END OF THE INTERVAL FROM T = 2 TO T = 6. L O O K AT BOTH ENDS OF THE" INTERVAL AND D 1 V I D E T H E CHANGE IH DISTANCE 8 1 THE CHANGE IH TIHE.  1  80/8$  2 3 4  T O O ' R E PARTLT RIGHT SINCE YOU'RE DIVIDING DISTANCE BY TIHE,BUT TOO'BE ONLY LOOKING AT ONE POINT OH THE LIRE.LOOK AT THE CHiSGE IB DISTANCE AND DIVIDE BT THE CHANGE IN TIHE FROH T = 2 T O T = 6 .  S 6  20$  SZIE  S/T$  """ SEHC  3 4 5 8 4 2  WHAT IS THE SLOPE O F THE LINE IN THE TIHE INTERVAL T = 1 TO T « 8 HOURS? T O U HEED TO OBTAIN THE CHANGE It." D I S T A N C E AND T H E CHANGE I H TIHE BETWEEN" THESE TWO P O I N T S IN ORDER TO C A L C U L A T E THE 3 L O P E . GO AHEAD...  0  10$  $  SEBD  20/2$  7 8 9 1 2 . 3 4  SEHD  0 - 2 0 ) / ( 6 - $60-20/6-2$  3 * S_  60/6$  SEHD  10/" $  .1$  SEHD  0 - 0 0) / ( 8 - $ 8 0 - 4 0 / 8 - 4 SCONSTA N T $  T H E SLOPE IS CONSTANT AT 10 HILES/l-ODR. THIS I S " ALWAYS THE CASE WHEN T H E GRAPH O P THE M O T I O N IS A STRAIGHT LINE.THE GRAPH IS JUST A PICTURE OF THE E Q U A T I O N OF MOTION S=10T,AND_SO THE SLOPE O F T H E LIBE_ IS" THE SPEED O F THE BOAT. ' " " S E 1/10$  SEBD  4/40J  2/20$  6/60$  8/80$  H  D  8-4/80-10$8-4) / (80-$  _ 7 8  ALMOST RIGHT.YOU'VE CALCULATED THE CHANGE I N D I S T A N C E AND THE CHANGE IB TIME C O R R E C T L Y , E U T YOU 'VE~ D I VICED" T H E M I N C O R R E C T L Y . THE SLOPE IS THE (CHANGE I N D I S T A N C E ) / ( C H A N G E I N TIME). TBI AGAIB.  9  80$  0 1 2 •3  lOU'RE ON THE RIGHT TRACK S I N C E YOU'RE DIVIDING D I S T A N C E BY TIME B O T YOU'VE ONLY L O O K E D A T O N E E N D OF THE I N T E R V A L FROM T = 4 T O T = 8 . L O O K AT BOTHENDp O F THE INTERVAL AND DIVIDE THE CHANGE IS DISTANCE BT'T'HE CHANGE I * T I M E .  •4  60/6$  5 « •7 9 0 •1 '2  T O O ' R E PARTLT RIGHT SIKCE YOU'RE DIVIDING DISTANCE BY TIME,BUT Y O U ' V E ONLY LOOKED A T ONE TOINT ON THE LINE.LOOK AT C H A N G E IH"DISIANCE AHD D I V I D E E I i'HE CHANGE IN TIME FROH T = 4 T O 1 = 8 . SEHC 1 4 1 1 3 2 SHEET 2 ILLUSTRATES THE HOTION O F A SECOND SOAT COMPUTE T H E AVERAGE SfE::D C F T H t B O A T I N THE INTERVAL FROH T = 2 T O T = 6 BBS. SEHC PROCEED EXACTLY AS BEFORE. " " " ' " $ i  *3  2S  8  -  80/8$  10$  4$  _  $EBD  _  $EBC  20/2$  —  M  8/4S  (9-1) / (6-S9-1/6-2$  _4 '5 •6 |7 •8 •9  T H E AVERAGE SrESr- I S SIMPLY THE CHANGE I H DISTANCE DIVIDED t i T ti £ CHANGE" IK TIME. T H I S i s ' G I V E N BY V- DEL (S» /DEL ,T) = ( 9 - 1 ) / ( 6 - 2 ) = 8/1 = 2 MILES'HCUR 9/6$ 1/2 f 1.5$ .5$ ALMOST HlGhT S I N C E YG'J HAVE DIVIDED" D I S T A N C E BY TIML EUT'YOtT" HAVE' CilLY CONSIDERED OKI; t'»D OF T h 2 INVEHVAI FROM T = 2 TO T = 6 .  «0  CALCULATE  T H E CHANGE  I H DISTANCE  AND D I V I D E  BY T H E C H A N G E  IH TIKE  . SEHl  196  11 12 13 m 15 Ijj 17 8 i_ 0  T O GET AVERAGE SPEED. 9$ IS 6$ HO. THIS IS THE VALUE Of A COORDIHATE AT O H E E H D O F T H E INTERVAL. T H E AVERAGE SPEED IS GIVEN BY CHANGE IH DISTAHCE, D E L (S) , DIVIDED BY CHANGE I H TIME, DEL (T) .FROM P TO Q.CALCULATE SHIS FR0_K_THE_ JJHAP_H. 8$ 4S HBOHG. YOU'VE CALCULATED THE CHANGE OH OHLY OHE AXIS OF T H E GRAPH.THE AVERAGE SPEED 1 3 THE CHANGE IH DISTANCE DIVIDED BY THE CHARGE I H TIME FROM T=2 TO T « 6 . CALCULATE THIS FBOM THE GRAPH...  1  2  3 jl 5 6 7 8 9 O  i  2 3 4 5 6 7 8 9 0  SEHt  o ii a 3 2 • LOOK AT SHEET 3,WHICH IS JUST THE GRAPH I H SHEET 2 KITH T H . E E POIHTS P,Q, AHD R IHDICATED OH I T . WHAT I S THE SLOPE OF THE LINE SEGMENT JOIHIHG THE POIHTS P AHD Q ? SENG TOO NEED TO KNOW THE CHANGE IH DISTANCE AND THE CHANGE IN T I H E BETWEEH P AHD C I " ORDER TO CALCULATE THE SLOPE OF THE LINE SEGHEHT. GO AHEAD... SEHC 2$ 8_*$ ) /__{(>_I9-1/6-2$ T H E SLOPE OP THE LINE SEGHEHT JOINING P AHD Q IS GIVEN BY CHANGE IN DISTAHCE DIVIDED BY CHARGE IN TIME, WHICH IS DEL (S)/DEL (T) = 8 / 1 = 2 H/HR. THIS IS_THE SAME AS TF1E AVERAGE SPEED OF THE BOAT BETWEEH P AHD Q. _ SEND 9/6$ " 1/2S 1.5J .5$ ALMOST RIGHT SINCE YOU'VE DIVIDED DISTANCE BY TIME.BUT Y O U HAVE OHLI __HSI0ERED_ONE__ENp_OF_rHE_ INTERVAL_FROK_ P_TO____CALCDLATJ_ TJ_E_ CHAKGE IN DISTAHCE AHD DIVIDE BY THE CHANGE IN TIME FROM P TO Q TO G E T ' T H E SLOPE. SEHD 9S 1S 6$ RO. THIS IS THE VALUE OF A COORDINATE AT OVt END OF THE INTERVAL. THE SLOPE OF THE LINE JOINING F AND Q IS GIVEN BY CHANGE IH DISTAXCE, D E L (S) .DIVIDED BY CHANGE IH TIME, DEL (T) .FROM P TO ..CALCULATE THIS FROM THE GRAPH. SEHC  3 4 5 6 7 8 9 0 1  1  SENI  5  2  2 3 1 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0  SEN.  8  $  US  HO. TOO'VE CALCULATED THE CHARGE OH OHLI ONE A.IS OF THE GRAPH.THE SLOPE OF THE LINE JOINING P AHD Q IS GIVEN BY CHANGE IN DISTANCE,DEL(S), _ DIVIDED BT CHARGE IN TIME, DEL (T) , FROM P TO Q. CALCULATE THIS FROH T E E GRAPH... 6  ;  SEHD ;  4 8 5 2 1 L E T ' S TAKE A SMALLER SIZE INTERVAL THAH BEFORE OH THE GRAPH I H SHEET 3. WHAT I S THE AVERAGE SPEED O F THE BOAT IH T _ £ INTERVAL T « 2 TO T=4 HOURS? PROCEED EXACTLY AS BEFORE. " " 1.5$ 3/2$ 1*1/2$ 11/2$ 1 1/2$ 4-1/4-2$ (4-1)/(4-$H1L$ TH_E_AVER-GE_SPEED IS jr=DEL ( S ) / J 3 E L (T) = (4- 1) / (4-2) = 1. 5 H/HR. THE SLOPE OP THE LINE SEGMENT JOINING P AND 5 IS rt THE SAME AS T H E AVERAGE ?PEED OVER THIS INTERVAL. NOTICE THAT THE AVERAGE SPEED IS NO LONGER COHSTAHT! I I F THE GRAt-_ IS HOT A STRAIGHT LINE.THE SLOi.'E IS NO LOHGEP COHSTAHT. I S V4$ 1/2$ .5$ 1H1S ALMOST RIGHT SIKCF. TOU HAVE DTVIDED DISTANCJBY TIM E. BUT_IOJ_ _AVE OHLY CONSIDEBEJ ONE END OF THE "INTERVAL. " CALCULATE" THE CHANGE IN DISTAHCE AHD DIVIDE BT THE CHASGE IN TIKE FtiOB T = 2 TO T=H.  SEND $EHD  T  3$  2$  SEND  SEBD  HROHG. YOU'VE CALCULATED THE ChAHGE ON OHLY CHE AXIS OP TKE GRAPH. THE SLOPE OF TH? L I ! _ JOINING P AND R IS GIVEN BY CHANGE "J DISTANCE, DEL (S) ,DIVIDED_3Y CHANGE I!_ TIME. DEL ( T ) FROM r__0_R. • CALCULATE THIS FROft THE GRAPH... " SEHD 4$ BO. THIS tS ?BI VALUE OF A COORDINATE AT ONE EN ^ O" THE INTERVAL.THE SLOPE OF THE LINE JOINING P AND S IS GIVEN BY CHANGK IN DISTAHC?,bEL (S>, OIVIDED BY CtiANGE IN TIME, DEL (T) , FROM P TO R. CALCULATE ThI3 FROM THE GRAPH... SEHD -  197  t 2  3 » 5 6 7 8 J| 0 1  2 3 4 S> 6 7 8 9 0 J| 2 3 «| 5 6 7 8 9 0 1 2 3. 4 5 6  7 8 9  7 4 3 2 3 5  WHAT HAPPENS TO THE SPEED AS WE H A K E THE TIHE INTERVAL SBALLER AHD SMALLER.LET'S CONTINUE WHAT WE DID WITH SHEET 3 BT CONSTRUCTING A TABLE. LENGTH OF I N T E R V A L ( H R S ) • * 4 2 1 .5 .25 0 SLOPE__OF__LINE (BILES/HR).** 2 1.5 1 . 2 5 1. 12 1.06 ? AVERAGE S P E E D (BILES/HR) *• 2 1.5 1 . 2 5 1. 12 1.06 ? WHAT I S THE L I M I T OF AVERAGE SPEED AS THE INTERVAL SHRINKS TO SIZE 0 7 . SEND STUDT_THE TABLE CAREFULLY AND NOTE WHAT HAPPENS TO SLOPE AND AVERAGE SPEED AS THE LENGTH OF THE TIHE INTERVAL SHRINKS FROH DEL(T)=4,DOWN TO 0 . SEND 1S 1.00$ mis THE LIHI_T__OF_AVERAGE_.SP.EED _AS _T_HE_INTERVAL APP_R0ACHES_ZER0_IS 1 H/HR. ' H E SEE THAT AS THE~ INTERVAL K E E P S GETTING SMALLER, I T SHRINKS TO A POIHT A T T=2,AS SHOWS OS S H E E T 3 . T H E SPEED AT T = 2 IS JUST THE SLOPE OF THE LIRE L WHICH TOUCHES THE CURVE AT ONLT ONE POIHT P. THIS LINE IS_ _ CALLED THE TANGENT TO THE CURVE A T POIHT P. SEBD 2S TWOS BO. THIS IS THE 7 A L U E OF AVERAGE SPEED FROM T = 2 TO T ° 4 . LENGTH »* .5 .25 .15 .10 0 SLOPE •» 1.12 1 . 0 6 1.04 1 . 0 2 ? AVERAGE SPEED** 1.12 1 . 0 6 1.04 1 . 0 2 7 _ WHAT I S THE L I B I T OF AVERAGE SPEED AS THE INTERVAL SHBIRKS TO SIZE 0 ? ~ SEBD OS OS ZEROS HO.THE LEHGTH OF THE IBTERVAL TENDS TO 0 BUT AVERAGE SPEED DOES ROT. LEHGTfl ** .5 .25 .15 .10 0 SLOPS *• 1.12 1 . 0 6 1.04 1 . 0 2 7 AVER/iGE SPEED** 1.12 1 . 0 6 1.04 1.02 7 BHAT IS* THE L I B I T OF AVERAGE SPEED AS THE INTERVAL SHBIKKS TO ~SIZ_ 0 7 ' SEBD 1.03$ 1.01$ DEFIHEDS HO LIHITS HOLIBITS HO.J-ET'S TAKE A CLOSER LOOK AT THE INTERVAL AS WE SHRINK I T TO SIZE 0 . LENGTH *• .5 .25 .15 .10 0 SLOPE *• 1.12 1 . 0 6 1.04 1 . 0 2 7 AVERAGE SPEED** _ 1. 1 2 1 . 0 6 1.04 1 . 0 2 7 _ WHAT IS"THE L I B I T OF AVERAGE SPEED AS THE INTERVAL SHRI-kS TO SIZE 0 ? SEND 8 4 4 2 3 5  WHAT I S THE INSTANTAHEOUS SPEED OF THE BOAT AT T H E TIHE,T=2 HOURS? THIS I S THE SPEED AT THE INSTANT O F TIHE T = 2 HRS. STU.I THE TABLE ABOVE *__J____ * _ S H E E T 3._ THEN TRY TO ANSWER...  SEHD  _1_"L_  o"  1 $  1 • 2 3 4 5 .6 7 8 9 0 1  THE SPEED AT TI!.S T = 2 HOURS IS DEFINED AS THE LIBIT OF THE AVERAGE SPEED_ AS THE T I B E INTERVAL ABOUT T = 2 SHRINKS TO Z E R O . T H E SHORTER THE TIHE INTERVAL USED.'THE CLOSER T H E AVERAGE S PE EC I S TO T H E ACTUAL SP~EED AT T D A T I N S T A N T . T H E ACTUAL SPEED AT THAT INSTAuT I S JUST T H E SLOPE O F THE TANGENT TO THE CURVE. SEHC 2"$ ' " " rwo$ WRONG.THIS I S THE VALUE OF AVERAGE SPEED F50B T = 2 TO T=6. THE_I N b TAN TANEOUS_ JSP E _ D _ I S D E F I » E 0 AS THE VJ L U _ 0 F _ A VE KAGE SPE E D W _ E H THE T I B E INTERVAL HAS SHRUNK TO ZERO. LOOK AT THE TABLE ARC TRY AGAIN... $EHI OS 0$ ?_ROS BRONG. THE LENGTH OF THE_ T I B - INTERVAL STARTING AT T=2 IS O.BUT THE SPEED__  •2  I S HOT  i.oos  EQUAL  TO  'OSES'"  IBIS  0."  "  3 i4  THE INSTANTANEOUS S P E E O IS DEFINED AS THE VALUE 01' AVERAGE SPEED WHEN THE TIHE INTERVAL :'AS SHRUNK TO Z E R O . LOOK AT T H E TABLE AND TRY AGAIN...  '5  1.03$  '6 17 18  THE INSTANTANEOUS TJIETIHJE JENTERVAL  •9  10  9 4 6 2 7 3  1.01$  SO  LIB IT $  N 0 LIB IT $  SPEED I S DEFINED Ab THE VAL!:E O F .'.VERAGE SPEED WHEH KAS_SHRU__; TO Z E R O . LOOK AT T 3 E T A B L E AND TRY AGAIN.., ~~  '  SEND  UNCEY-NED'S'  "  LOOK AT SHEET 4 VHICH IS THE GRAPH OF THE HOTIOH OF A FEATHER DROPPED  SEHI  1.98  •1 12 •3 •4 15 l_ •7 •8 '9 0 1 2 3 4 5 6 7 8  - BOfl A TOWER. S R E P R E S E N T S T H E D I S T A N C E O F T H E F E A T H E R FROH THE G R O U N D . • R H A T I S T H E SPEED OF T H E F E A T H E R AT T = 2 S E C ? REHEHBER T H E R E L A T I O N S H I P B E T W E E N S P E E D AND S L O P E ARD THEN FIND THE INSTANTANEOUS S P E E D AT T = 2 S E C . FROH T H E GRAPH. -0 S -FOUR $ - FOURS -4MIS IS-4 S — 4 S THE__AC_TUAL _.S PEED _AT_T=2_ S EC. I S -4 F E E T / S E C . T H I S I S T H E S L O P E O F THE L I N E WHICH T O U C H E S T H E C U R V E AT O N L Y O N E P O I N T P. T H E S L O P E I S N E G A T I V E S I N C E THE D I S T A N C E S I S G E T T I N G S M A L L E R A S T H E TIHE T I H C R E A S E S . T H I S _ H E A N S T H A T D E L (S) K I L L B E N E G A T I V E . _ ._ . _ 0 S FOURS TOU'RE A L M O S T R I G H T . T H E C H A N G E I H D I S T A H C E D E L ( S ) I S G I V E R BT ( F I R A L _ J ) 1 S T A NCE)j__(TNITI AL_ D I S T A N C E S I N C E PI S TANCE I S GE T T I H G S H A L L E B A S TIHE G E T S B I G G E R , D E L ( S ) W I L L BE N E G A T I V E . TRY AGAIN. " 6S 2S 3$ TWOS IS 3.5S -3S H0,_THE S L O P E O F T H E L I N E - R I C H T O U C H E S T H E C U R V E AT P O I N T P REPRESENTS _ THE I H S T A H T A N E O U S S P E E D O F T H E F E A T H E R AT T = 2 . THINK A B O U T I T AND T R T A G A I N OR P L E A S E T Y P E REVIEW I F TOU T T P E . . . R E V I E W . W E W I L L R E P E A T T H E L A S T S E C T I O H AGAIH FROH SHEET 2 .  9 0  REVS GOTO 4  j  2 3 4 5 6 7 1 •9 0 1 2  3 4 5 6 7  8 , 9. 0 1 2! .3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 C  9 0  BOS  io  2  .  7  SZBl SEHt  SEHC  SEHI  SEBD  DORS  ;  3  T H I S ACTUAL SPEED I S CALLED T H E INSTANTANEOUS S P E E D OF THE F E A T H E R AT T=2 S E C . T H E I H S T A H T A N E O U S SPEED I S T H E SLOPE OF THE STRAIGHT LINE . H I C H T O U C H E S THS C U H V E ' I N SHEET 4 AT T H E P O I N T " P. T H I S L I N E I S C A L L E D T H E T A H G E N T TO THE C U R V E AT P O I N T P . DO T O U U N D E R S T A N D ? WE'VE D E V E L O P E D T H E I D E A OF S L O P E R E P R E S E N T I N G S P E E D . THE S L O P E O F A LIRE J O I N I N G TWO P O I N T S Oi! T H E CUR'/E I S A V E R A G E S P E E D . T H E S L O P E O F A LIRE T O U C H I N G T H E C U R V E AT O N E P O I N T I S I N S T A N T A N E O U S SPEED.IS IT CLEAR? TESS CKS BITS LITTLES S_DF.ES THINK S GUESSS THE I N S T A N T A N E O U S SPEED' I S WRITTEN AS V= L I M I T ( D E L (SJ / D E L ( T ) ) A S DEL(T) A P P R O A C H E S 0 . T H I S I S A B B R E V I A T E D BY W R I T I N G ;  SEND ' SEBD  V = DS/DT = L I M I T (DEL (S) / DEL (T) ) AS DEL.T) T E N D S T O 0 .  DS/DT I S C A L L E D T H E D E R I V A T I V E S F S WITH R E S P E C T T O T AND R E P R E S E N T S THE S L O P E O F A L I R E T O U C H I N G T H E C U R V E O F S V S . T AT O H L Y ORE P O I N T . BOS DO NS HOTS THEN" B E A D i f " A G A I H AHD A S K FOR H E L P .  SEBD SEND  11 4 Jl 4 4 4 ROW L E T ' S F I N D T H E " I N S T A N T A N E O U S " S P E E D " BT U S I N G T H E E Q U A T I O N " OF H P T I O H . S H E E 1 5 I L L U S T R ' T E S T H E GRA.H OF T H E E Q U A T I O N O F M O T I O N , S»3T»2 F I R S T LOOK A T T H E T I M E I N T E R V A L B E G I N N I N G AT T = 1 S E C . WHAT I S THF, D S T A N C E S A T I H E B E G~I H H I MG O F T H I S T I R E I N T E R V A L ? SEHD O S E T B _ E O U A T I . N OF M O T I O N . SEHD 3__S THREES S= 33 3(1)*2$ "THE D I - T A - . E S I S E A S I L Y O B T A I N E D FROH THE E Q U A T I O H OF H O T I O N . " S = 3 T * 2 = 3 ( 1 ) *2=3. BE ARE S I H P L Y CJk L C UJ. A T I d G T H E _ D I S T A H C E A T 0 1 g P O I N T . SEND SS DISTS" " 3T*2S S=3T*2S RO. THIS R E P R E S E N T S T H E D I S T A N C E AT ANT T I K E T, WE W I S H TO C A L C U L A T E THE D I S T A H C E AT A S I S G 1 . S P O I N T T - 1 . O S E THE E Q U A T I O N OF M O T I O N S = 3 T * 2 T O E V A L U A T E S A T THE PCIfcT T = 1 . . . S E N D TS 1$ C-L(T)S 1*DEL(T)$ WRONG. YOU'RE L O O K I N G ^ A T T H E T I H E I N S T E A D O F C A I C U L - T I - - T h - D l - T A H C E AT A . PARTICOIAR TIME IHS.AUT. O S E T E E E Q U A T T O S OF M O T I O N S = 3 T « 2 T O E V A L U A T E S AT T H E P O I H T T = 1 . . . SEHD 0$ OS _ IN FIN I T Y $ DNDEFIHEDS O S E T H E E Q U A T I O N O F iiOTION S = 3 T * 2 T O E V A L U A T E S A T T H E P O I H T 1=1... SEHD  12 4 1 1 1 2  199  1 2 3 * 5 (j 7 8 9. 0 1  THE LENGTH OF THE TIME INTERVAL INDICATED ON THE GRAPH IS DEL ( T ) . WHICH OF THE FOLLOWING REPRESENTS THE DISTANCE AT THE END OF THE TIHE INTERVAL,THAT IS, AT TIHE T=1 »DEL ( T ) ? PLEASE ANSWER A,B,C,D,OR E. A 3(DEL(T))»2 B 3 (1 + DEL (I) ) *2 C 3(1»DEL(T)) D 3T*2 E NONE OF THE ABOVE OSE THE EQUATION OF ROTIOS. BS THE TIHE AT THE END OF THE TIHE INTERVAL IS T=1*DEL(T). THEN THE . DISTANCE AT THIS VALUE OF TIHE IS GIVEN BI S = 3T»2= 3 (1 *DEL (T) ) *2 WHICH IS ALSO EQUAL TO 3*6DEL (T) • 3DEL (T) »2  3 • _ 6 7 8 9  THIS IS THE DISTANCE FROH THE ORIGIN AT A POINT T=DEL(T). IT IS HOT THE DISTANCE AT THE EHD OF THE INTERVAL WHICH STABTS AT T=1. T B I AGAIN. send CS BBOHG. THE DISTANCE I S GIVEN BI S=3T*2. IOU HAVE CHOSEN THE DISTANCE AT THE END OF THE INTERVAL FOR AH EQUATION OF HOTION S = 3T=3(1*DEL <T)) . T B I AGAIN. SEHD DS ES BBONG. THE DISTANCE IS GIVEB BI S=3T*2 AND TBE TIHE AT THE EBP OF THE TIHE INTEBVAL IS T = 1 * D E L ( T ) . TBI AGAIN. SEBD 13 4 8 3 3 4 HE WOULD LIKE TO FIND THE AVERAGE SPEED IN THIS TIHE INTERVAL FHOS T=1 TO T=1•DEL(T).THE CHANGE IN DISTANCE,DEL(S),IS GIVEN BY (DISTANCE AT END OF INTERVAL)-(DISTANCE AT START OF INTERVAL). _ THEM " DEL (S) (3 + 6 DEL (T) + 3DEL (T) *2) -3 • WHAT IS THE S I H P L I F I E d FOHH i)EL (T) DEL (T) )-1 OF DEL (S)/DEL (T) ? SEND DO SOKE ALGEDRA TO SIMPLIFY THIS EXPRESSION. SEND SODELS 6 • 3DELS 6« 3DELS 6 ODELS 3(2»DELS 3 (2 • DES 3DEL (T) »6$3 (DEL (T) •$ DEL(S) /DEL (T) = (5DEJ. (T) O C E L (T) »2)/DEL (T)--60DEL (TI SINCE DEL (T) CANCELS IN BOTH NUMERATOR AND DENOHINATOR. THIS IS TBE AVERAGE SPEED I I THE INTERVAL. SEND /DELS DEL (TJ $ DELT$ IOT QUITE. SIMPLIFY THE NUMERATOR AND THEH CANCEL DEL (T) FROM BOTH NUMERATOR AND DENOHINATOR. GO AHEAD... SEBD 3*6DET$_ 3»6S 3 • 6$ _ ' BO. THE •3'" IN~THE "FIRST PART OF THE HUHERATOP CANCELS WITH THE"" •3"' IB THE SECOND PART OF THE DENOMINATOR.THEN YOU CAB CANCEL DEL ( T ) FROM BOTH NUHERATOR AND DENOMINATOR. TRY AGAIN... SEND 6»DEL$ 3VDELS 3+3DELS 3(1*DEL$ BOT QUITE. YOU SLIPPED UP WHEN YOU EXPANDED 3 (1 * D E L ( T ) ) * 2 . T H E NUMERATOR SHOULD BE 3 ( l*2DEL (T) «DEL(T) *2)-3 = 6* DEL (T j O P E L (T) » 2 . THEN S i H P L T F I T H E iXPRESSION. GO AHEAD.".". " S~EHT 14 3 2 7 3 RECALLING THAT INSTANTANEOUS SPEED IS THE LIMIT OF AVERAGE SP2ED A- TBE TIHE INTERVAL SHRINKS TO ZERO,THAT IS,AS D E L ( T ) APPROACHES ZERO. WHAT IS THE INSTANTANEOUS SPEED AT TIME T= 1 S E C ? SEHC FIND "THE LIMIT OP DEL (SJ/DEL (r> "«S "DEL (T) APPROACHES 01 ' SEBD 6S SIXS GOT018 3$ 0$ n$' 2$ 95 DELS" THE LIMIT AS DEL (T) TENDS TO 0 IS THE VALUE OF b* DEI- (T) WHEN D E L ( T ) = 0 . YOU SECM TO B E UNCLEAR ABOUT WORKING OUT LIMITS.YOL' SHOULD CO_SOME WORK OH LIMITS FOB A FEW MINUTTS BEFORE GOING ON WITH THE MAIN LESSON. ." PLEASE E::T-R TKH BOF.D.-. LIMIT ,OR TBI AGAIN I F .CU !(ISU. SEBI LIMITS SOS DONS  2  0  J 2 3 « 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9. 0 1 2 3 4 •5 6 7 '8 •9 0 1 2 3 _4 15 16 17 18 19 SO  u BBONG.  : IN TIHE  SEHD SEND . SEBD  200  >1 !2 •3 »4 SS Ui •7 !B JS SO ii •2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 • 9 0 1  2 3 4 5 6 7 8 / 9 0 1 2 3 4 5 6 7 8 9  .e 1 2 3 4 5 6 1 8 9 0  G0T015 15 2 M  LET S=3T«7. WHEH T=2.IT IS EAST TO SEE THAT S=13. BOT HOB DOES S BEHAVE WHEN T IS CLOSE TO 2? EXAMINE THE TABLE GIVEN BELOW. I 2.S 2.7 2.J 2.01 2.001 2._000j S=3T*7 14.5 13.6 13.3 13.03 13.003 13.0003 I S S CLOSE TO 13 WHEN T IS CLOSE TO 2? SEBD D.OES._S..SEEM TO B E GETTING CLOSER TO 13 AS T GETS CLOSES TO 27TES OB 80? SEBC TES$ OK$ THINKS SURES BE SAT THAT IF S=3T+7,THSN S APPROACHES 13 AS T APPROACHES 2 AND WRITE LIMIT (3T*7) AS T APPROACHES 2 . 1 S EQUAL TO 13. SEBD BOS DONS HOTS NOS LOOK AT THE TABLE CLOSELT AND ANSWER AGAIN OB ASK FOB HELP. SEBD 16 , 4 4 3 3 1 THE LIMIT OF S AS T TENDS TO A PARTICOLAR VALUE SEEMS TO BE SIMPLT THE VALUE OF S AT _THAT__VALUE OF T. THIS IS GENERALLY TRUE EXCEPT ONLT ORDER CERTAIN CON DITIONS, WHICH YO'J WILL LEARN ABOUT LATER IN YOUR CALCULUS COURSE. WHAT IS THE LIMIT OF S=20-6T AS T APPROACHES 3? SEHD FIND TBE VALUE OF S AT THE POINT T=3. SEBD 2 $ ~" TWOS ' 20-6 (3) S 20-18$ - - TBE LIMIT OF 20-6T AS T APPROACHES 3 IS 2. AS WE KAK2 THE VALUE OF T CLOSER AND CLOSER TO 3,TH:~ V.1LUE OF S GETS CLOSER AND CLOSER TO 2, SEBD 20$ TWENTYS 20$ BO. THIS IS THE LIMIT OF 20-6T WHEN T=0 SINCE 20-6(0)=20. FIF0_T_HE LIMIT WHEN T=3. GO AHEAD... _ SEBD. 6$ 6(3) 19$ * BO. YOU'VE ONLY LOOKED AT THE SECOND PART OF THE EXPRESSIOE 20-6T. SUBTRACT THE VALUE OF 6? FROM 20 TO GET THE ANSWER GO AHEAD... SEBD 14$ WRONG.THIS IS THE LIMIT OF 20-6T WHEB T= 1 SINCE 2U-6(1) = 14. FIBD THE LIMIT OF 20-6T WHEH _T = 3. SEBD 17 4 4 2 1 2 FIHD T H E_L I MIT 0 F_DE L (S ) /DEL (T)= 6 • 3 D EL (T) AS DEL (T) APPROACHES ZERO. $EHD FIBD THE VALUE OF 6*3DEL(T) AT DEL(T)=0. SEHD 6 $ SIXS 6.S 6*3 (0) S AS DEL (T) GETS CLOSER AND CLOSER TO 0,THE 7ALUE OP 6«3DEL(T) GETS CLOSER ABD CLOSER TO 6.THE LIMIT OF 6*3DEL(T) AS DEL (T) APPROACHES 0 I S 6. SEND 3$ THREFS BO. THIS IS THE LIHIT OF 6*DEL (T) AS DEL (T) APPROACHES - 1 , SINCE 6*3(-1)=3. FIND THE LIMIT AS DEL (T) TENDS TO 0. GO AHEAD... $EBD 6*3i WRONG. YOU SHOULD SIMPLIFY THE EXPRESSIOH. PIBP THE VALUE OF 6 + 3DEL(T) WHEN DEL(T)=0.~ GO AHEAD... "' " $ E i ^ 9S SINE$ BO. THIS I S THE LIMIT OF 643DEL (T) AS DEL (?) TESDS TO 1. FIHD THE VALUE OF~6*3DEL (T) WHEN DEL(T)=6. CO AHEAD... SEBD ;  18 2_2 8 LET'S TAKE A SHORT BTEAK "ROM 1 HE LESSON.I'D LIKE TO KNOW HOS TOU FEEL... ..BIGHT NOW. W H I C H O" J-H" CATEGORIES BELOW DESCRIBE BEST TOUR REACTION..HOB.. TO TH E ST A TEME N V. _.. . - ._. . . I AH TENS E. A HOT AT ALL C HODER AT FLY SO B SOHEWHAT D VERY RUCR SO PLEASE ANSWI.R A.B.C.OR D. ' SEHD ANSWER" A. B.C OR D TO DESCRIBE YOL'P !;EAC:iOB" ?ICHT NOW TO THE ST AT EM EN T i i . . I AH TENSE. SEBD BOS YESS  201  1 2 3 » 5 6 7 8 9. 0 1 2 3 «  5  6 7 ft 9 0 1 2 3 _ 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 :0 :1 2 :3 :4 •5 :6 !7 :'4  :9 10 !t_ 12 " 13 14 15 16 17 18 19 10  G0T018 AS BS CS DS ROTS SORES BOOEBS VESTS G0T019 19 2 2 8 WHICH CATEGORT BELOW..A.B.C.OB P..BEST DESCRIBES TOOB BEACTIOH TO THE STATEMENT. I FEEL AT EASE. A BOT AT ALL C HODEBATELT SO B_SOMEWHAT D.VEBT HUCH SO _ AHSWER A,B.C.OB D. SEHD PLEASE A,B,C.OB D. SEBD BOS TESS G0TO19 AS BS CS DS ROTS SOBES HODEBS VESTS GOT020 :  25  2 2 8  ;  I AM BBLAZED. A BOT AT ALL C BODERATELT SO B SOMEWHAT D VERT MUCH SO PLEASE AHSWER A.B.C.OR D. ABSWEB A, B.C.OB D...TO THE STATEMENT. ... I AB RELAIED. BOS IESS GOT020 IS BS CS DS BOTS SOBES G0T021 21 2 2 8 I FEEL CALB. A HOT AT ALL C HODEBATELT SO B SOMEWHAT D VERT MUCH SO AHSWER A,B.C. OR D. ARSWEB A,C.C.OB D TO THE STATEBEHT... I TE'_L CALB. BOS TESS G0T021 AS BS CS DS ROTS SOBES G0TO22  SEBD SEBD  _ HODEBS  TEBTS  SEHD SEBD BODEBS  VERTS  22  2 2 8  . I IE J I T T E R T . HO. AT "ALL C BODF^ATELT SO SOMEWHAT D VERV MUCH SO ___!___ A.B.C.OR ?. SEHD ARSWEB - , _ , C . J _ D TO THE STATEMEHT...I AB JITTE_T. SEHD IESS HOi GOT022 ; AS BS CS DS ROTS SOBES ROD'S VESTS GOT023 23 4 1 2 2 4 LEt'S.THT ONCE BORE TO FIND THE IHSTAHTANEOUS SPEED DSIHG THE 3QUA7I0N OF fiOTIOH, S = T*2. FIRST, WHILH OF THE FOLLOWING IS THE AVERAGE SPEE" BETWEEH T=2 AND " T=2 + EEL (T) ? ANSWER A.B.C.D.OR E. " A <2*DEL <T, > - i B (2* DEL (T) ) * 2 - 2 * 2 C_(2*'_ ELJT) ) * 2 - 2 * 2 / ( 2 * D E L ( T ) ) - 2 D (2* DEL (T) ) * ? . - V - L l\, *2 / DEL (T) E HONE C P THE"ABOVE * . . . SEHC DO SOBE AI-GE3F.A TO GET DgL(S) AHD DEL ( T ) BEFOBL FIHDliJG AVERAGE SPEED IR THISIH1ERVAL. SCHC CS THE AVERAGE SPEED IS SiMPLT DEL ( S ) / D E L ( T ) IH THE IHTERVAL,WHICH I S GIVEH BT .'2 + DEL {T) ) » 2 - 2 « 2 / (2 + DEL CH ) - 2 . SEN! A B  202  AS BS •0. THIS REPRESENTS DISTANCE.THE DISTANCE AT T=2 IS S=T»2=2»2=« AND THE DISTANCE AT T= 2*DEL (T) IS S= (2*DEL (T) ) *2. YOO HOST DIVIDE DEL (S) BI D E L ( T ) . YOO SHOULD REPEAT THE HATERIAL DEALING WITH SHEET 5 TO BECOHE CLEAR ABOUT THIS. EITH EB TYPE ...REVIEW .OR ANSWER A GAIN. DS ES BO. THE AVERAGE SPEED IS DEL (S)/DEL (T) IN THE INTERVAL. DEL(S)=FINAL DISTANCE-INITIAL DISTANCE^ (2* DEL (T) ) «2-2*2 AHD DEL (T) =FIHAL TIMS-INITIAL TIB E= {2* DEL (T) ) - 2. SIHPLIFY DEL (S) AND DEL (T) AND DIVIDE THE."!.YOU SHOULD REPEAT THE HATERIAL DEALING WITH SHEET 5 TO BE CLEAR ABOUT THIS. TYPE...REVIEW .OH TRT AGAIH. BEVS HOS DORS OKS GOTOII  ;  SEBD _ SEHD  H 3 5 3 2 BHAT IS THE IHSTANTAHEOUS SPEED AT T=»2? SEHD BEBEHBEH THE RELATIOHSHIP BETWEEN AVERAGE SPEED AHD INSTANTANEOUS SPEED •j AND THEN GO AHEAD... SEBD •I as <t.S FOURS J THE AVERAGE S P E E D I S DEL ( S ) / D E L (T) « (2 + DEL (T) ) *2-2»2 / 2*DEL(T)-2 _ _ •I S I M P L I F Y I N G THE NUMERATOR i N D DENOMINATOR G I V E S •'; DEL (S) /DEL (T) = 4 DEL (T) + DEL (T) *2 / DEL (T) NCW CANCEL DEL (T) FROM HUHERATOR AND DENOMINATOR A_ D_W_E_E N D_U P WITH U*OSL ( T ) . THE L I B I T OF •»• DEL (T) AS DEL (T) TEHUS TO ZERO IS U. WHICH IS THE IHST. SPEED SEHD 0/0$ 0 $ ZEROS OS 0/0$ JTOO DIDB'T SIMPLIFT THE NUMERATOR AND- DENOMINATOR FIRST IH EEL (S)/DEL (T) BEFORE FINDING THE LIMIT. DO THI- AHD THEN CANCEL DEL (T) FROM BOTIi NUMERATOR AHD DENOMINATOR BEhORE FIHDING THE LI3IT OF D E L ( S ) / D E L ( T ) . GO AHEAD AND TRY AGAIN. $EBD 2 $ 1 $ DEL$ TOU SEEH TO HAVE SLIPPED UP IN YOUR CALCULATIONS. SIHPLIFTIhG THE HUBEBATOR OF DEL (S)/DEL (T) GIVES (4 • 1 DEL (T) • DEL (T) *2)-« = <i E E L (T) *DEL (T) »2 SIHPLIFYING THE DENOMINATOR GIVES DEL(T).CANCEL CEL(T) FROH NUBERATOR AHD DEHOBINATOB. THEN FIND THE LIMIT OF THE R EBA INING EIPRESSIOR. SEHD _/_$ •$ BOT QUITE. YOU RAVEH'T REDUCED THE EXPRESSION TO SIMPLEST FORM. TOO SHOULD SIMPLIFY THE NUMERATOR AND DENOMINATOR AND CANCEL _DEL_[T_ FROK_BOTH_0F_ THESE. THEN FIND THE LIMIT OF THE REMAINING EXPRESSION SEND 25 " " 2 2 2 CONGRATULATIONS! TOU HAVE COMPLETED A CAI LESSON. I HOPE THAT I ' . » 0 ENJOYED OUR CONVERSATION AS MUCH AS I DID AND THAT Y07 LEARNED SC"-THING TOO. DID TOU EM JOT THIS METHOD OF LEARNING;' ANSWER YES OR HO. SBHE ASSWES YES OR NO. SEHD TESS HCS I F TCI WISH TO HAKE ART COMMENTS ABOUT THE LESSOS,ASK TH. INSTRUCTOR TO PROVIDE YOU WITH A COMMENT 5H-_T. GOOD-BYE FOE HOW... SEHD BATBES CONS PLEASE AHSWER YES OB HO. SEND FILE  T2 » 8 2 2 3 l E T ' S STUD: THE KOTION OF A BOAT AS IT LEAVES A DO SUPPOSE THAT IT'S HOVIHG AT A COHSTAHT SPEED OF 10 BILES/HOUR.  203  WHAT I S THE D I S T A N C E S OF THE BOAT FBOH THE DOCK AT ANT T I H E T ? REHEHBER THAT D I S T A N C E (SPEED) ( T I H E ) . B B I T E AN EQUATION FOB S I N TEBHS O F T. S 10T$ S=T10S T10S T»10S 10TS 10*T$ 10 T I H E S S10XTS S=10T. T H E EQUATION WHICH D E S C R I B E S THE HOTION OF THE BOAT I S DISTANCE- (SPEED) ( T I H E ) EQUATION, WITH T H I S I S S I M P L Y THE F A M I L I A R S P E E D V B E I N G CONSTANT AT 10 HILES/HOUR. l"0*S/T S T=10/S $ • 0. D I S T A N C E (SPEED) ( T I H E ) . THE S P E E D I S 1 0 R I L E S PEB HOUB AHD THE T I H E _IS__T, WBITE AN EQUATION FOB S I H TERHS OF T...GO AHEAD 10 S T $ • 0. D I S T A N C E (SPEED) (TIME) . THE S P E E D I S 10 R I L E S PEB HOUB A I D THE T I H E IS T. WRITE AN EQUATION FOR_ S I N TERHS OF T. . . GO AHEAD S S DISS 10SS 10. D I S T A N C E (SPEED) ( T I M E ) . THE S P E E D I S 1 0 R I L E S PEB HOUB AND T H E T I H E _IS_T. WBITE AN EQUATION FOB S I N TERHS OF T...GO AHEAD 2 3  SEND SEND  3  SEHD  3  SEHD  3  SEHD  3  4 4 LOOK  8  4  SEID  2  AT SHEET 1 THAT WAS G I V E N TO TOU.THE GRAPH I N D I C A T E S BOH FAR T H I S BOAT I S FROM THE DOCK AT ANT T I M E . HEAT I S THE S L O P E OF T H I S S T R A I G H T L I K E R E P R E S E N T I N G THE BOAT«S BOTIOH I N A T I M E I N T E R V A L T=2 TO T=6 HOURS? ~X"OD "REED TO O B T A I N THE CHANGE I N DISTANCE AND THE CHANGE I H T I R E BETWEEN THESE TWO P 0 I 2 T S I N ORDER TO C A L C U L A T E THE S L O P E . GO AHEAD... _10$ __<! $ 0-20) / (6 - J 6 0-2 O/bj-2 $ THE S L O P E I S THE CHANGE I N ~ D I S T A N C E D I V I D E D B I THE CHANGE I I T I M E . B E B I I T Z T H I S AS SLOPE= DEL ( S ) / D E L (T) WHICH I S EQUAL TO _ ( 6 0 - ? 0 ) /J.6-2) = 1 0 _ H I L E S / H 0 0 a .  _  SEID SEID  SEBD  1/10$ .1$ 4/40S 2/20S 6/60S 8/80S " 6-2/6C-2CS6-2)/(60-$ HBOBG. THE S L O P E OF THE STRAIGHT L I N E I S THE CHANGE I N D I S T A N C E D I V I D E D BT THE CHANGE I N T I M E BETWEEN THESE TWO P O I N T S . NOW, GO AHEAD AND SORK OUT THE S L O P E . . . SEBD 60S 60/63 201 20/2S _WBOHG._THE S L O P E OF TBE STRAIGHT L I N E I S TBE CHAHGE I H D I S T A H ^ E D I V I D E D B I THE CHANGE I N T I M E BETWEEN THESE TWO P O I N T S . HOW, GO AHEAD AND WORK OUT THE S L O P E . . . SEBD 80/8$  S/T S  B B O H G . THE S L O P E OF THE STRAIGHT L I N E I S THE CHANGE I S D I S T A N C E D I V I D E D B T T H E CHANGE I N T I M E BETWEEl' THESE TWO P O I N T S . NOW, GO AHEAD AND WORK OUT TBE S L O P E . . . 3 4  5  8  4  SEHD  2  BHAT I S THE S L O P E OF THE L I N E I N THE T I H E I N T E R V A L T-4 TO T = 8 HOURS? TOU NEED TO OBTft"iH THE CHANGE I N DISTANCE AND THE CHANGE I N T I M E BETWEEN T H E S E TWO P O I N T S I * ORDER TO C A L C U L A T E THE S L O P E . GO AHEAD... _10$ 40/4$ 0-40) / ( 8 - $ 8 0 - 4 0 / 8 - 4 SCONSTANTS THE S L O P E I S CONSTANT AT 10 H I L E S / H O U R . T H I S I S ALWAYS THE CASE WHEN THE GE".PH OF THE MOTION IS A STRAIGHT L I N E . T H E GRAPH I S J U S T A P I C T U R E OF THE EQUATION OF MOT10H S=10T,AND SO THE S L O F E OF THE L I ? ' I S THE S P E E D OF THE BOAT. 2/20$ 6/60$ 8/80$ 8-4/80-40S8-4)/ 1/10$ .1$ 4/<4CS T H A T I S I N C O R R E C T . S L O P E I S CHANGE I N D I S T A N C E D I V I D E D 3Y CHANGE I H V I M E BETWEEN THESE TWO P O I N T S . NOW,GO ABEAD AND C A L C U L A T E T H I S S L O P E . . . 4$ 80$ 80/81 40$ THAT I S INC0RRECT_» '"T.0v_K IS CHANGE I H D I S T A N C E D I V I D E D BY CHANGE I H T I H E BETWEEN THESE TWO P O I N T S . NOW, GO AHEAD AN D~ C A L C U L A T E T H I S S L O P E . . .  $EHD $EBD  -  60/6$  4  SEBD TEND  20/2$  THAT I S I N C O R R E C T . S L O P E I S CHANGE I H D I S T A N C E D I V I D E D B I CHANGE I H _ T I 5 E ISZTWEEN THEST TWO P O I N T S . NOW,GO AHEAD AND C A L C L A T E T E I S S L O P E . . . 4 4  SEND .80-$  4  3  2  SEHD  204  SHEET 2 I L L U S T R A T E S THE flOTIOH OF A SECOND BOAT COMPUTE THE AVERAGE SPEED OF THE BOAT I N THE I N T E R V A L FBOS PROCEED EXACTLY AS BEFORE. 2$ 8/4$ (9-1)/(6-S9-1/6-2S TBE AVERAGE SPEED I S S I M P L Y THE CHANGE IN D I S T A N C E D I V I D E D CHANGE IN T I M E . T H I S I S G I V E N BY V = DEL ( S ) / D E L (T) = (9-1)/(6-2)--8/4 = 2 HILES/HOUB 9/6S 1/2$ 1.5$ .5$ JB.RONG. .THE AVERAGE SPEED I S THE CHANGE IN D I S T A N C E D I V I D E D III TIHE FROM T=2 TO T=6. C A L C U L A T E T H I S FROM THE GRAPH... 9$ 1$ 6$ BBONG. THE AVERAGE SPEED I S THE CHANGE I N D I S T A H d E P I V I D E D IH TIHE FBOH T=2 TO T=6. C A L C U L A T E T H I S FROH THE GRAPH...  es  T-2 TO T»6 Bt  BBS.  THE SEHD  Bt THE  CHANGE SEBD  BY THE  CBABGE SEBD  is  WRONG. THE AVERAGE SPEED I S THE CHANGE IH D I S T A N C E D I V I D E D BI THE CHAHGE IB TIHE FBOH T=2 TO T=6. C A L C U L A T E T H I S FBOH THE GBAPH... 1 4 4 3 2 LOOK AT SHEET 3.WHICH I S J U S T THE GRAPH I H SHEET 2 WITH THBEE P O I N T S P,Q, AND R I N D I C A T E D ON I T . _BHAT I S THE S L O P E OF THE L I N E SEGMENT J O I N I N G THE P O I E T S P AND C ? YOU HEED TO KNOW THE CHANGE I N DISTANCE AND THE CHANGE IN T I M E BETWEEH t ABD 0 I N ORDER TO C A L C U L A T E THE SLOPE OF THE L I N E SEGMENT. GO AHEAD.. _2_S 8/4 $ (9-1) / . 6 - _ - _ / _ ? > THE S L O P E OP THE L I N E SEGMENT J O I N I N G P AND Q I S GIVEN 3T CHAHGE I H D I S T A N C E D I V I D E D BY CHANGE I N T I M E , WHICH I S DEL ( S ) / D E L (T) = 8/1 = 2 .1/HB. J T H I S J S THE SAME AS THE A V E R S E SPEED OF THE BOAT BETWEEN P AND Q. 9/6$ 1/2$ 1.5$ .5$ HBOBG. THE SLOPE OF THE STRAIGHT L I N E J O I N I N G P AND Q I S G I V E N B I CHANGE "CH D I S T A N C E , DELJJJ_,Q1JIDED BY CHANGE I N T I M E , ftEL (T) , FBOH P TO Q. C A L C U L A T E T H I S FROM THE GRAPH... 9$ 1$ 6$ BBONG. THE SLOPE OF THE STRAIGHT L I N E J O I N I N G P AND Q I S G I V E H B t CHAHGE IB D I S T A N C E , D E L (S) . D I V I D E D BY CHAHGE I B T I H E , DEL (T) ,FBOH P TO Q. C A L C U L A T E T H I S FBOH THE GRAPH... 8$ 1$ WROBG. THE SLOPE OF THE STRAIGHT L I N E J O I N I N G P AND Q I S G I V E H Bi' CHANGE I B D I S T A N C E , D E L ( S ) , D I V I D E D BY CHANGE I N T I M E , D L L ( T ) , F R O H P TO Q. JCALCJUL ATE_. THIS FP.OM THE GRAPH... 6  '  "  " "•  '""  ir  THE  $  GRAPH  IS  1/4S  NOT  A  STRAIGHT  1/2$  HO. T B E ' A V E R A G E S P E E D I<IB T I H E F R O H T=2 TO T=4.  3$ BO. THE IH TIHE _«$ BO. THE I B TIHE 7  LINE,THE  .5$  SLOPE  SEHD  SEBD SEBD  SEBD  SEBD  SEBD  SEBD  """  4 8 5 2 1 L E T ' S TAKE A SMALLER S I Z E I N T E R V A L THAN BEFORE OS T..E GRAPH I N SHEET 3. WHAT I S THE AV EnAGE SPEED OF-THE BOAT I N THE I N T E R V A L 1 = 2 TO T=4 HOURS? PBOCEED EXACTLY AS BEFORE. 1.5$ 3/2$ 1*1/2$ 11/2$ 1 1/2$ 4-1/1-2$ (1-1)/(1-$HAL$ THE AVERAGE SPEED I S V = DSL ( S ) / D E L (T) = (4-1) / .4-2) = 1. 5 M/HR. TBE S L O t E OF THE L I N E SEGMENT .JOINING P AND a I S AGAIN THE SASE AS T H E AVERAGE SPEED OVER T H I S I N T E R V A L . liOTICE T H A T T H E AVERA2K SPEED I S NO L O N G E R C O N S T A N T ! ! J  SEHD SEBD  IS  NO  LONGER  COBSTAfiT.  SEHD $EBD  $EBD  1HI$  T H E C H A N G E I N D I S T A N C E D I V I D E D BY C A L C U L A T E T H I S FROM T H E G P A P H . . .  THE  CHANGE  2$ AVERAGE S P E E D I S THE CHANGE I N D I S T AN "t" D I V I D E D BY THE FROH T=2 TO T=4. C A L C U L A T E T H I S FROM THE GRAPH...  CHANGE  AVERAGE SPEED I S THE CHANGE I H D I S T A N C E T I V I D E D BY THE CHANGE FROM T=2 TO T=4. C A L C U L A T E T H I S FROM THE GRAPH...  SEBD SEBD SEBD  205  • 3 2 3 5 BBAT HAPPEHS TO THE SPEED AS BE HAKE THE T I H E I N T E R V A L S H A L L E R AND S H A L L E R . L E T ' S CONTINUE WHAT HE DID WITH SHEET 3 B I CONSTBUCTING A T A B L E . LENGTH OF I N T E R V A L (HRS)»* 0 2 1 .25 0 .5 1.06 S L O P E OF L I N E ( B I L E S / H R ) * * 2 1.5 1.25 1.12 AVER AG E__S PEED ( B I L E S / H R ) «» 2 1.5 1.25 1.06 1.12 ? BHAT I S THE L I B I T OF AVERAGE SPEED AS THE INTERVAL SHRINKS TO S I Z E 0 ? SEHD STUDY THE T A B L E C A R E F U L L Y AND ROTE WHAT HAPPENS TO SLOPE AND AVERAGE S P E E D _ A S THE LENGTH OF THE T I H E I N T E R V A L SHRINKS FROH DEL (T) = 1.DOWN TO 6. SEND IS I.OOS 1HIJ THE L I B I T OF AVERAGE SPEED AS THE I N T E R V A L APPROACHES ZEBO I S 1 H/HR. BE S E E TH AT. AS TH E...INTERVA L K EEP S_G E T T I N G SB ALL E R_I T_S H RIN KS_ TO_A • POINT AT T=2,AS SHOWN ON SHEET 3.THE SPEED AT T = 2" I S JOST THE S L O P E OF THE L I N E L WHICH TOUCHES THE CURVE AT ONLY ONE POIHT P. T H I S L I R E I S _ C A L L E D THE TANGENT TO THE CURVE AT_POIHT P. SEBD 2S " " TWOS • 0 . L E T ' S TAKE A C L O S E S LOOK AT THE I K T E R V A L AS HE SHRIHK IT TO S I Z E 0. LEHGTH *« .5 .25 . 15 . 10 0 SLOPE ** 1.12 1.06 1.00 1.02 ? AVERAGE S P E E D * * 1.12 1.06 1.00 1.02 T _HHAT_ I S THE L I B I T OF AVERAGE SPEED AS THE I H T E B V A L SHRINKS TO S I Z E 0 ? _ _ SEND OS OS ZEROS l O . L E T ' S TAKE A CLOSER LOOK AT THE I H T E R V A L AS WE SHBIRK IT TO _ I Z E 0 . LES G_TH ** .5 .25 . 15 . 10 0 SLOPE *• 1.12 1.06 1.00 1.02 ? AVEB1GE S P E E D * * 1.12 1.06 1.00 1.02 ? JTHAT I S THE L I B I T OF AVERAGE SPEED AS THE I H T E R V A L SHBIHKS TO S I Z E 0 ? SEHD 1.03$ 1.01$ DEFINED$ HO L I B I T S N O L I H I T S HO.LET'S TAKE A CLOSER LOOK AT THE I N T E R V A L AS WE SHRINK I T TO S I Z E 0 . LEHGTH »» .5 .25 .15 .10 0 SLOPE ** 1.12 1.06 1.00 1.02 ? AVERAGE S P E E D * • 1.12 1.06 1.00 1.02 ? BBAT I S THE L I BIT OF A VERAG E SP EEP AS T H E I NT EBV A L S H S I H K S TO S I Z E_ 07 SEHD 8 19 2 3 5 BHAT I S THE IHSTAHTANEOUS S P E E D OF THE BOAT AT THE T I H E , T = 2 HOURS? SEBD T H I S I S THE SPEED AT THE INSTANT OF T I B E T=2 HRS. STUDY THE T A B L E ABOVE AS WELL AS SHEET 3. THEN TRY TO ANSWER... SEND 1 $ 1.00$ ONES IBIS THE SPEED AT T I B E T=2 HOURS I S D E F I N E D AS THE L I B I T 0 1 THE AVERAGE S P E E D AS THE T I B E I N T E R V A L ABOUT T= 2 S H R I N K S TO ZERO.-iiS SHORTER THE T I H E I N T E R V A L USED,THE CLOSER THE AVERAGE SPEED I S TO THE ACTUAL SPEED AT THAT INSTANT. THE ACTUAL SPEED AT THAT IHSTAHT I S J U S T THE SLOPE SEND OF TFic TAKGE..T TO THE CURVE. _2$ _TWOS_ _ _ _ _ _ _ INCORRECT. THE SPEED AT T=2 I S THE L I B I T O T ' t H E AVERAGE S P E E D THAT «E O B T A I i E D AS WE SHRANK THE I N T E R V A L S T A R T I H G AT 1 = 2 DOWN TO S I Z E ZERO SEND WHAT I S T H I S VALUE OF S P E E D ? 0$ 0$ ZEROS INCORRECT. THE SPEED A r T=2 I S THE L I M I T OF THE AVERAGE S P E E D THAT VE _OBTAIHED AS WE SHRANK THE I N T E R V A L S T A R T I N G AT T=2 DOWN TO S I Z E ZERO. WHAT I S T H I S ' VALUE OF S P E E D ? ~~ " * SEND 1.03$ 1.01$ S.0 L I r t . T S H O L I B I T $ UNDEFINED:. IHCORRFCT. THE S P a ? D a t 7=2 I S THE L I B I T OF THE AVERAGE S P E E D THAT WE OBTAIH-D AS WE SHRANK THE I H T E R V A L S T A R T I N G AT T=2" DOWN TO S I Z E ZERO. BHAT I S T H I S VALUE OF S P E E D ? SEND 9 0 6 2 7 3 LOOK AT SHEET 0 WHICH I S THE GRAPH OF THE HOTIOH OF A FEATHER DROPPED FROH A TOWER. S P.EPRESENTS THE DISTANCE OF THE FEATHER FROM THE GROUND.  1  206  I • I I !  WHAT I S THE SPEED OF THE FEATHER AT T=2 S E C ? BEHEHBER THE R E L A T I O N S H I P BETWEEN SPEED AND SLOPE AND THEM FIND THE INSTANTANEOUS SPEED AT T=2 S E C FROH THE GRAPH. -1 S -FOURS - FOURS -IBIS IS-U S =-« S THE ACTUAL SPEED AT T=2 S E C . I S -« F E E T / S E C T H I S I S THE S L O P E OF THE L I NE W_H I CH TOUCHES _TH E _CUR.V_E_A.T_ON L Y_0 N E POINT P.THE S LOPE I S BEGAT-VE S I N C E THE DISTANCE S I S GETTING SHALLER I S THE T I B E T I N C R E A S E S . TBIS BEANS THAT D E L ( S ) WILL BE N E G A T I V E . _J $ . FOURS HO. F I N D THE INSTANTANEOUS SPEED OF THE FEATHER AT T=2 S E C . BT F I N D I N G TBE SLOPE OF THE L I N E WHICH TOUCHES THE CURVE AT THE POINT P. GO AHEAD... 6$ 2.S 3$ TWO$_ 1$ __ 3.5$ _3S_ 1 0 . F I N D THE IHSTAHTANEOUS f PEED OP THE PEATHER AT T=2 S E C . BT F I N D I N G THE S L O P E OF THE L I K E WHICH TOUCHES THE CURVE AT THE POIHT P. GO ABEAD... REVS HOS. DOHS GOTO a  SEND SEBD  SEND ' SEBD SEHD  10  2 7 3 TBIS ACTUAL SPEED I S C A L L E D THE INSTANTANEOUS SPEED OF THE FEATHER AT T=2 S E C . THE INSTANTANEOUS SPEED I S THE SLOPE OF THE S T R A I G H T L I N E WHICH TOUCHES THE CURVE IN SHEET M AT THE POINT P. THIS L I N E IS C A L L E D "TBE 'TANGENT TO THE CURVE AT POINT P. DO YOU U N D E R S T A N D BE * VE DEVELOPED THE IDEA OF SLOPE REPRESENTING SPEED.TH? SLOPE CF A LINE J O I N I N G TWO POINTS ON THE CUIiVE I S AVERAGE SPEED.THE S L O P E OF A L I N E TOUCHING THE CURVE AT ONE POINT I S INSTANTANEOUS S P E E D . I S I T CLEAR ? TESS 0K$ BITS LITTLES SURES THINKS GUESSS _THE INSTANTANEOUS SPEED TS S R I T T E H AS V = L I B I T (DEL ( S ) / D E L (T ) ) AS D E L ( T ) APPROACHES 0. T H I S I S A B B R E V I A T E D BY WRITING V=DS/DT = L I B I T (DEL ( S ) / D E L (T) ) AS DEL (T) TENDS TO 0. DS/DT I S C A L L E D THE D E R I V A T I V E S F S WITH RESPECT TO T AND REPRESEHTS THE S L O P E OF A L I N E TOUCHING THE CURVE OF S VS.' T AT ONLY ONE P O I H T . BOS DONS HOTS TBEH_REap_IT AGAIH AND ASK FOR HELP. ~ii  ""'  "  - -  .  M U M HOW L E T ' S F I N D THE INSTANTANEOUS SPEED BY USIHG__ THE EQUATION OF BOTIOH. SHEET 5 I L L U S T R A T E S THE GRAPH OF THE" EQUATION OF BOTl"OH„ S=3T»2 F I R S T LOOK AT THE T I B E I N T E R V A L BEGINNING AT T=* 1 SEC. WHAT I S THE DISTAHCE S AT "!:E BEGINNING OF T H I S T I H E I H T E R V A L ? OSE THE EQUATION OF BOTIOH. 3 $ THREES S=3$ 3(1)«2S THE DIST.'HC" S S _ E A S I \ Y OBTAINED FROH THE EQUATIOH OF BOTIOH. S-3T*2=3"("ljV2-3. BE ABB S I R P L J C A L C U L A T I N G THE DISTAHCE AT OSE P C I H T . _SS _ DISTS 3T*2$ S=3T*2$ NO. USE THE EQUATION OF BOTION, S=3T*2 AND EVALUATE S AT THE POINT T » 1 IH OBDT;R TO OBTAIN THE DISTANCE S AT T=1. GO AHEAD... TS 1 J_ DEL (T) $ 1*DEL$ 1 0 . USE THE -QUATIO. OF BOTJON, S = 3 T " AND EVALUATE S J T TH- POINT ?=• I S ORDER TO OBTAIN THE D I S T A N C E S AT T=1. GO AHEAD... _0$ 0$ I N F I N I T Y I UNDEFINED* HO. USE THE EQUATION OF BOTION, S=3T*2 AND EVALOATF S "7 T n t POVHT T=1 IH ORDER TO OBTAIN TH- D I S T A N C E S AT T=1. GO AHEAD., , 12 • 1 1 1 1 2 THE LENGTH OF THE T I B ? T u T E i i V A L I N D I C A T E D ON T h E GRAt'H I S DEL (T) . WHICH OF THE FOLLOWING REPRESENTS THF. DISTANCE AT THE YHO It THE TIBF. I N T E R V A L , T H A T I S , AT T I B E T=1«D2L(T)? F - E A S - ANSWER A , B, C, D, OR E. A 3(DEL(T))*2 * 3 (1 • DEL (T) ) »2 C 3(1*DEL(T)» 1 3T»2  SEBD SEHD  SEHP SEND  SEHD SEHD  T  SEBD SEBD SEBD SEND  207  E BONE OF THE ABOVE OSB THE EQUATION OF H 0 T I 0 N .  SEND SEBD  BS  T B E T I H E AT THE END OF THE T I H E I N T E R V A L I S T=1*CEL ( T ) . T B E B T B E D I S T A N C E AT T H I S VALUE OF T I H E I S G I V E N B I S=3T»2=3 (1 • DEL (T))»2 WHICH I S ALSO EQUAL TO 3 * 6 D E I (T) * 3 C E L (T) »2 IS BBONG.THE EQUATION OF MOTION I S S = 3 T » 2 . THE T I H E I N T E R V A L OF LENGTH .BEGINS.AT T=1. . F I N D THE VALUE OF T AT THE END OF THE I N T E R V A L AND S U B S T I T U T E T H I S VALUE INTO THE EQUATION OF HOTION TO GET S...  cs  SEBD  DEL(T)  BBONG.THE EQUATION OF HOTION I S S = 3 T « 2 . THE T I H E I N T E R V A L OP LENGTH DEL (T) BEGINS AT T = l . F I N D THE VALUE OF T AT THE END OF TEE I N T E R V A L AND S U B S T I T U T E T H I S VALUE INTO THE EQUATION OF HOTION TO GET S... _D$ ES HBOBG.THE EQUATIOH OF HOTION I S S = 3 T » 2 . THE T I H E I N T E R V A L OF LENGTH D E L (T) B E G I N S AT T = 1 . F I N D THE VALUE OF T AT THE END OF T E E I N T E R V A L AND S O B S T I T U T E T H I S VALUE INTO THE EQUATION OF HOTION TO GET S... 13 4  I • . f 1 , r  r »  i  t »  / i I  I I t I t i . * I  8  3  3  SEBD  SEHD  SEBD  4  _SE_WOULD L I K E TO F I N D THE AVERAGE SPEED I N T H I S T I H E I N T E R V A L FBOH T* TO T = 1 * D E L ( T ) . T H E CHANGE I N D I S T A N C E , D E L ( S ) , I S GIVEN BY ( D I S T A N C E AT END OF I N T E R V A L ) - ( D I S T A N C E AT START O f I N T E R V A L ) . TBEB DEL (S) (3 + 6DE L (T) + 3 DEL jT) »2)-3 _ WHAT I S T E E S I H P L I F I E D FORH DEL (T) (1 • DEL (T) ) — 1 OF DEL ( S ) / D E L (T) ? SEND D 0 _ S 0 B E ALGEBRA TO S I H P L I F Y T H I S E X P R E S S I O N . SEND 6 * 3 i > E L S ~ 6 • 3 D E L S 6* 3DELS 6 *3DELS 3 { 2 * D E L S 3 (2 • DES 3DEL (T) *6S3 (DEL (T) •$ DEL (S) /DEL (T) - (6DEL (T) * 3 DEL (T' *2) /DEL (T) = 6* 3D EL (T) S I N C E DEL (T) C A N C E L S I B BOTH NUMERATOR AND DENOHINATOR. T H I S I S THE AVERAGE S P E E D I B THE I N T E R V A L . SEBD /DELS DEL(T)S DELTS _W80NG. S I H P L I F Y THE NUMERATOR B I REMOVING THE BRACKETS AND C O L L E C T I N G • L I K E * TERMS.THEN CANCEL DEL (T) FROM BOTH NUMERATOR AND DENOHINATOR. CHECK YOUR ALGEBRA AND TRY A G A I N . . . SEBD 3*6DET$ 3*6$ 3 • 6$ WRONG. S I M P L I F Y THE NUMERATOR B I REMOVING THE BRACKETS AND C O L L E C T I N G • L I K E ' TERHS.THEN CANCEL DEL (T) FROH BOTH NUMERATOR AND CENOHIKATCK. CHECK YOUR ALGEBRA AND TRY A G A I N . . . SEND 6*DELS" 3+DFLS 3+3DELS 3(1*DEL$ WRONG. S I M P L I F Y TKiJ NUMERATOR BY REMOVING THE BRACKETS Ai»D C O L L E C T I F " ' L I K E * TERMS.THEN CANCEL DEL (T) FROM BOTH NUMERATOR AND DENOMINATOR. CHECK YOUS ALGEBRA AND TRY A G A I N . . . SEND 14 3 2.7 3 _ _ R E C A L L I N G THAT INSTANTANEOUS" SPEED" IS"" THE L I M I T CF AVERAGE S P E E D AS T B E T I H E I N T E R V A L SHRINKS TO ZERO,THAT I S , A S D E L ( T ) APPROACHES Z E E O . WHAT I S THE INSTANTAll EOIJS S P E E T T I M E T=1 SE-". ? SEHD F I B D THE L I M I T O F DEL (S) / D L L (T) AS DEL (T) APPROACHES 0. "SEND 6S SIXS G0"0'"3 • 3$ OS 0$ 2S 9$ DELS THE L I M I T A3 DEL (T, TENDS TO 0 I S THE VALUE OF 6 * D E L ( T ) THEN D E L ( T ) = 0. I O U SEEM TO BE UNCLEAR ABOUT WORKING OUT L I M I T S . 1 0 U SHOULD SOSE WORK OH L I M I T S FOR A FEW MINUTES BEFORE GOING ON WITH TH : MAIN L E S S O N . SEHD P L E A S E EIITE.' THE "OB D.. . L I M I T ,0R TRY A G A I N I F YOU WISH. JLIMITS _0J DONS GOT015" 15 2 M 1  208  LET S = 3 T * 7 . WHEN T = 2 , I T I S E A S T T O S E E T H A T S = 1 3 . B O T HOH D O E S D E B A T E WHEN T I S C L O S E T O 2 7 E X A M I N E T H E T A B L E G I V E N B E L O W . T 2.5 2.2 2.1 2.01 2.001 2.0001 S-3T*7 11.5 13.6 13.3 13.03 13.003 13.0003 I S S C L O S E TO 13 WHEN T I S C L O S E T O 2 ? D O E S S S E E K T O B E GETTING_.C_L0SER T O 13 AS T G E T S C L O S E R T O 2 7 I E S OR NO? IESS OK$ THINKS SUHES I E S A I T H A T I F S = 3 T * 7 , T H E N S A P P R O A C H E S 1 3 AS T A P P R O A C H E S 2 AHD W H I T E L I B I T ( 3 T * 7 ) AS T A P P R O A C H E S 2 , I S EQUAL TO 13. BOS DONS HOTS NOJ L O O K A T T H E T A B L E C L O S E L Y AND AHSWER A G A I H OR A S K FOR H E L P . 16 4 4 3 3 1 T H E L I B I T O F S AS T T E N D S T O A P A R T I C U L A R V A L U E S E E H S T O B E S I H P L T THE_ V A L U E O F S AT T H A T V A L U E O F T . T H I S I S G E N E R A L L Y T R U E E X C E P T O H L I O R D E R C E R T A I H C O H D I T I O N S , W H I C H YOO W I L L L E A R H A B O U T L A T E R I N YOUR CALCULUS COURSE. WHAT I S T H E L I B I T O F S = 2 0 - 6 T AS T A P P R O A C H E S 3 ? F I N D T H E V A L U E OF S AT THE__PPINT T = 3 . 2 S TWOS 20-6(3)$ 20-18$ T H E L I B I T O F 2 0 - 6 T AS T A P P R O A C H E S 3 I S 2 . AS WE B A K E T H E V A L U E O F T CLOS_ER_AHD C L O S E R T O 3 , T H E V A L U E O F S G E T S C L O S E R AHD C L O S E R T O 2 . 20$ TWENTY$ 20$ B O . F I B D T H E V A L U E O P S AT T H E P O I H T T » 3 . . . 6 $ 6 (3) 18$ B O . F I B D T H E V A L U E 0 ? S AT T H E P O I H T TO... 1«S BO. F I N D T H E V A L U E _ O F _ S _ A T T H E P O I H T T « 3 . „ . _ _ S  ' I »_ I I » I » | i I I » I I  5  > 1  17  SEBD SEHD  SEBD SEBD  SEHD $EHD  SEBD SEBD SEHD SEHD  4 4 2 1 2 TJ H P T H E L I B I T _ 0 F D E L ( S \ / P E L (T) = 6 * 3 D E L ( T ) AS S E L ( T ) A P P R O A C H E S Z E R O . SEND F I N D T H E V A L U E OF 6 + 3 P E L (T) A T D E L ( T ) = 0 . SEND 6 S SIX$ 6.S 6*3 (0) S _AS D E L ( T ) G E T S C L O S E R AHD C L O S E R TO O . T H E V A L U E O F 6 * 3 D S L ( T ) G E T S C L O S E R A H D C L O S E R T O 6 . T H E L I B I T O F 6 » 3 D E L (T) AS D E L (T) A P P R O A C H E S 0 I S 6. $EHD 3$ THREE$ HO. F I N D T H E V A L U E O F 6 * 3 P E L (T) A T D E I ( T ) = 0 . . . $END 6*3$ HO. F I B D T H E V A L U E O F 6 + 3 D E L (T) A T D E L ( T ) = 0 . . . SEBD ?$ NINES "80. F I S S THE VALUE 6F~6*3D-L(T) AT~DEL(T)=0.". . SEND 18 2 2 8 L E T ' S T A K E A SHORT B R E A K F R O i l THE L E S S O N . I ' D L I K E TO KNOW HOW YOU F E E L . . . . . B I G H T ! V . WHICH O F THE C A T E G O R I E S BELOW D E S C R I B E B E S T YOUR B E A C T I O H . . N O V . . TO THE _ T / . T E i : : : r . . . . . . . . i AH T E N S E . _ _ _ _ _ _ A NOT AT A L L " ' C HODERATELY SO " " B SOMEWHAT D VERY BOCH SO P L E A S E ANSWER A . B , C , O R P. SEHD ABSWE'I A . B . J . O H D T O D E S C R I B E -OUR R E A C T I O N R I G H T HOW T O T H E S T A T E H E H T . . . I AH T E R S E . SEHD _EOS JESV GOT018 '~ " AS DS CS DS HOTS SOBES HOD E S S VESTS GOT019 19 2 2 8 W B I C B C A T E G O R Y iSPLOW.. A , B . C . OR P.. B E S T D E S C R I B E S TOUR R E A C T I O B TO T H E S T A T E B E 5 T . I" F E E L AT E A S E . A HOT AT A L L C BODERATELT SO B SOMEWHAT P V E R Y HUCH SO AHSWER A , B . C . O R D. SEND n  :  209  I i >  SEHD PLEASE A,B.C.OS 0. BOS IESS GOTO19 BODIES VESTS CS SOBES At BS OS •OTS GOTO20 20 ; 2 2 8 I A8 B E L A Z E D . A_HOT AT A L L C MODERATELY SO . B SOMEWHAT D VEST BUCH SO SEBD P L E A S E ANSWER A,B.C.OB D. SEHD A B S 8 E B A.B.C.OR D.... TO TBE S T A T E M E N T . . . . ! AB B E L A I E E . BOS IESS GOT020 BODEBS TEBTS SOBES • OTS as BS CS D$ GOT021 21 2 2 8 I FEEL CALB. A HOT AT A L L C MODERATELY SO B SOMEWHAT D VERT HOCH SO SEBD " ANSWER" A,B.C. OR J . SEBD I FEEL CALM. ANSWER A,B.C.OB D TO THE STATEHEHT.. • OS TESS G0T021 ?EBTJ SOBES BODEBS AS BS CS DS • OTS G0TO22 22 2 2 8 I AB J I T T E R T . MODERATELY SO BOT AT A L L VERT MUCH 3 0 SOMEWHAT SEHD _ABSWER A,B.C.OR D. SEND ANSWER A.B.C.OB D TO THE STATEMENT. .1 AM J I T T E R T . TESS BOS G0TO22 SOBES VESTS BS CS OS HOTS BODS AS GOT023 23 «t 1 2 2 1 LET'S TRT ONCE MORE TO F I N D T H E INSTAHTANEOOS SPEED USING THE EQUATION OF HOTION, S = T*2. F I R S T , W H I C H OF THE FOLLOWING TS THE AVER? GE StZIO BETWEES. 1*2 AND T=-'~ D * L ( T ) ? ANSWER A-B.C,D.OR E.~ A  (2*DEL.T.)*2  B  ( 2 * EEL (T) ) * 2 - 2 * 2  C__(2 + D E L ( T ) ) * 2 - 2 * 2 /___(2_3EL ,T) ) - 2 D J 2 - DEL (T) ) « 2 - C S i . (T) *2 / DSL (T) E HONE o r THE" ABOVE - - - - - -DO SOME ALGEBRA TO GET DEL (S. ..HD DEL (T) BEF'.RE F I 3 D I N G AVERAGE SPEED I B _TBIS INTEBVAL. CS TE',2 AVERAGE S P E E D I S SIMPLY D E I ( S ) / D E L (T) I N THE INTERVAL,WHICH I S _G I VE H_B I_ (2 • D E L_( T) ) • 2 - 2 * 2 / _ ( 2 « D E L (T) ) - 2. AS " BS BBOHG. LOOK AT AH I N T E R V A L S T A R T I N G AT T = 2 AND ENDING AT T = 2 * D B L . T . . THE AVERAGE SPEED I S G I V E N BY DEL ( S ) / D E L ( T ) I N T H I S I N T E R V A L YOU SHOULD REPEAT THE M A T E R I A L DE is L I N G 'i-ITS SHEET 5 TO BECOBE CLEAR AEOUT T H I S . _ E I T H E R T Y P E ...REVIEW .OR ANSWER AG AIW. "DS " ES " " " "'""" " KRONG. LOOK AT AN I N T E R V A L S T A R T I N G AT T=2 AND ENDING AT T = 2 * D E L ( T ) . TBE AVERAGE S P E E D I S G I V E U BY D E L ( S ) / D E L ( T ) I N T H I S I N T E R V A L  SEND  ,  SEBD  SEBD  SEHD  210  TOO SHOULD REPEAT THE H A T E R I A L DEALING NITH SHEET CLEAR ABOUT T H I S . EITHER T T P E . . . R E V I E R ,0R ANSWER A G A I N . REVS ROS DORS OKS • GOTO11  5 TO BECOHE SEBD  __J  4 3 5 3 2 BHAT IS THE INSTANTANEOUS S P E E D AT T = 2 ? SEBD Jt.EHEBBER THE R E L A T I O N S H I P BETWEEN AVERAGE SPEED AND INSTANTANEOUS SPEED ABD THEN GO AHEAD... SEBD 4 S 4.$' FOURS THE AVERAGE SPEED I S DEL (S )/DEL (T) = (2»DEL ( T H »2- 2»2 / 2 + D E H T 1 - 2 S I M P L I F Y I N G THE NUMERATOR AHD DENOMINATOR G I V E S DEL(S)/D£L (T) = 4D£L (T) * t _ L (T) *2 / DEL (T) NOW CANCEL DEL (T) _FBOn BDMEBATOR AND DENOMINATOR AND WE END DP WITH 4 * D E L ( T ) . THE L I M I T OF 4 • DEL (T) AS DEL (T) TENDS TO ZERO I S 4, WHICH I S THE I N S T . S P E E D SEBD 0/OS OS ZEROS 0$ 0/OS BO.SIMPLIFY__THE_BUH_ERATOR AND_DENOMINATOR^F__pELJS1/_DEL (T1.THEN C A N C E L DEL (T) FROM NUMERATOR AND DENOMINATOR. THEN F I N E THE L I M I T OF THE B E H A I N I N G E X P R E S S I O N AS D E L ( T ) TENDS TO 0...GO ABEAD AND BE C A R E F U L . . . SEBD _2_S 1 $ DELS _ B O . S I M P L I F Y THE NUMERATOR AND DENOMINATOR OF DEL (S) /DEL (T) . THEN C A S C E L DEL (T) FROM NUMERATOR AND DENOMINATOR. THEN F I N D THE L I M I T OF T i i g B E H A I N I N G E X P R E S S I O N AS DEL (T) TENDS TO 0...GO AHEAD AND BE C A R E F U L . . . SEBD  /$  •*  B O . S I M P L I F Y THE NUMERATOR AND DENOMINATOR OF DEL ( S ) / D E L ( T ) . T H E N CANCEL D _ L ( T ) FROM NUMERATOR AND DENOMINATOR. THEN F I N D THE L I M I T OF THE B E R A l a I N G E X P R E S S I O N AS D E L ( T ) TENDS TO 0...GO AHEAD AND BE C A R E F U L . . . 25 2 2 2 _ CONGRATULATIONS! TOU HAVE COMPLETED A C A I L E S S O N . I UOPE THAT TOU ENJOYED OUR CONVERSATION AS MUCH AS I DID AND THAT YOU LEAPNED SOMETHING TOO. DID YOU ENJOY T!IIS METHOD O F _ L E A B H I N G ? AHSWER YES OR NO. — AHSWER TES OR NO. TESS NOS TO HAKE ANY COMMENTS ABOUT THE LESSON,ASK THE IHSTBDCTOR TO I F TOO WISH P R O V I D E TOU WITH A COMMENT S H E E T . GOOD-BTE FOR HOW... BATSES DOHS P L E A S E AHSWER TES OR HO.  SEHD  SEHD SEHD SEBD SEHD  FILE  t_3  . • • • 1 ' 4 8 2 2 3 L E T ' S ST"DT T E E MOTION OF A BOAT AS I T L E A V E S A DOCK. S U P P O S E THAT I T ' S MOVING AT A CONSTANT SPEED CF 10 MILES/HODS. BHAT I S THE D I S T A N C E S OF THE BOAT FRO_ THE DOCK AT ANY T I M E T ? S2HD 8 EH EMBER THAT DISTANCE= (SPEED) ( T I M E ) . W R I T E AN EQUATION FOR S I N T-RBS OF T. SEND 10TS " 10*TS '.0 TIMES S I C . T J S=10TS S=T10S T10» T*10S THE EQUATION WHICH D E S C R I B E S THE MOTION OF THE BOAT I S 3=10T. T H I S I S S I M P L Y Trig H . i i i i . r . D I S T A N C E ^ (SPEED) ( T I B E ) EQUATION, WITH S P E E D V l E I N G "CONSTANT A . ' " l b "MILES/HOUR. SEBD 10=S/T $ T=10/S _ T O o P _ R E S . ONSE I S HOT THE CORRECT ORE. TRT AGAIN... ..SEND fO S T $ TOUR ABSWER I S INCORRECT. T H I N K ABOUT THE PROBLEB AHD T B I A G A I B . . . ?*.ND SS DISS 10SS  211  THINK  ABOUT  2 I M  ) 2  T H E PROBLEM  AGAIN  A N D T B I TO F I N D  T H E RIGBT  ANSWER.  GO  AHEAD..  SEHD  LOOK A T S H E E T 1 T H A T B A S G I V E N T O I O U . T H E G H A P H I N D I C A T E S HOB F A R T H I S BOAT I S F R O H T H E DOCK A T A N . T I H E . B H A T I S TH E_S LO P E_ 0 F._T H I S . S T B A I G H T _ L I N E_R EP R E S E N T I N G T H E B O A T ' S B O T I O H I H A T I H E I N T E R V A L T = 2 TO T = 6 H O U R S ? SEBD I O O N E E D T O O B T A I N T H E C H A N G E I N D I S T A N C E AND T H E C H A N G E I H T I H E B E T V E E B _ T H E S E TWO P O I N T S I N O R D E R T O C A L C U L A T E T H E S L O P E . GO A H E A D . . . SEHD 10S 40/4S 0-20)/(6-J60-20/6-2S T H E S L O P E I S T H E CHANGE I N D I S T A N C E D I V I D E D B I T H E CHANGE I B T I H E . B E W R I T E T H I S AS S L O P E = D S L IS)/DEL(T1 W H I C H I S E Q U A L TO ' ( 6 0 - 2 0 ) / ( 6 - 2 ) =10 H I L E S / H O U B . ' SEHD 1/10S .1$ U/UOS 2/20S 6/60S 8/80S 6-2/60-20S6-2)/(60-S SEND _THAT'_S HOT T H E ANSWER I ' H L O O K I N G F O B . THINK ABOOT IT AHD T B I AGAIH... 60S 60/6S 20$ 20/2$ HO. T H I N K A B O U T I T A H D T B I A G A I H . . . SEBD 80/8$ S/T$ 10. CHECK I O U R WORK AHD T R Y A G A I H . SEHD  3 4 5 8 4 2  BBAT I S THE S L O P E OF T H E L I N E IN T H E TIHE I N T E R V A L T » 4 TO T = 8 H O U R S ? SEHD TOO HEED TO O B T A I N T H E C H A N G E I N D I S T A N C E AND T H E C S A S G E IH TIHE B E T W E E B SEHD T H E S E TWO P O I N T S I N O R D E R T 0 _ C A L C U L A T E _ _ T H E S L 0 P E . GO A H E A D . . . 10$ 40/US 0 - 4 0 ) / (8-$"80~-40/8-4$C6HS~TAHTS THE S L O P E IS C O N S T A N T AT 1 0 H I L E S / H O U R . T H I S I S ALWAYS T H E C A S E WHEN J t H E G R A I H OF T H E B O T I O N I S A S T R H G H T L I N E . T H E GRAPH IS J U S T A P I C T U R E OP T H E E Q U A T I O N OF H . Y I O H S = 1 0 T , A H D SO T H E S L O P E OF T H E LINE I S THE S P E E D OF T H E B O A T . SEND 1/10S _J$ 4/10$ 2/20S 6/60$ 8/80$ 3 - 4 / 8 0 - 4 0 $ 8 - 4 ) / (8 0 - $_ THAT'S HOT T H E ANSWER I ' H L O O K I N G F O B . T H I N ? A B O U T IT AHD T E Y A G A I N . . . SEND 80S 80/8$ 40$ 4S SEHD JtO. T H A T J S I N C O R R E C T . . . TRT A G A I H . . . 60/6$ 20/2$ TOOB RESPONSE IS INCORRECT. TRT TO ANSWER AGAIH... SEND  - 4 4 4 4 3 2 SHEET 2 I L L U S T R A T E S THE HOT ION OF A SECOND BOAT _CGrtPUTE THE AVERAGE S P E E D OF THE BOAT I H THE I U T E R V A L FBOH T = 2 TO T = 6 B B S . S E H D PROCEED EXACTLY AS BEFORE. SEND 2$ 8/4S (9-1)/(6-$9-1/6-2$ THE AVERAGE S P E E D I S SIMPLY T H E CHANGE I H DISTAHCE CHANGE IN T I B E . T H I S I S G I V E N BY  V = --_ ( J ) / D E L ( T ) = ( 9 - 1 ) / ( 6 - 2 ) =8/4 = 2 9/6S  1/2$  BO.  CHECK  9$  1.5$  BT T B E  $EHt>  MLSS/HCUu  .5$  SEHD  YOUR WORK AND TRT A G A I H . . . 1$  6S  TOOB BE.POHSF. I S I N C O R R E C T . 8$  DIVIDED  T"Y TO ANSWER A G A I N . . .  SEND  4$"  VOUB AKSWEB I S I N C O R R E C T .  iHIHK  4 4 4 3 2 LOOK A T S B E E T 3.WHICH I S J U S T P,Q, A N D R I N D I C A T E D ON I T .  ABOUT THE PROBLEB AND T B I A G A I N . . .  T H E GRAPH  I H SHEET  2 31--  TH-EE  POIHTS  BHAT IT- THE SLOPE OF THE L I N E SEGMENT J O I N I N G THE POINTS P AND Q? , . 0 0 NEED TO ».NO'J THE CHANGE I N D I S T A N C E AND THE CHANGE I N T I B S BETWEEN _P A N D Q I N ORDER TO C A L C U L A T E T H . S L O P E OF T l i t L I N P.5EGBENT GO AHEAD.. 2$  '  " "f'.'4$  ' "'" ' » 9 - l ) / . 6 - « 9 - 1 / 6 - 2 S  "  "  SEHD  """  T H E S L O P E OF THE L I N E SEGMENT J O I N I N G P AND Q I S G I V E N BT CHANGE I H D I S T A H C E D I V I D E D BY CHARGE I H T I M E . WHICH I S DEL ( S ) / D E L (T) = 3 / 4 = 2 H/HB.  SEND SEND  212  T H I S I S THE SAME I S THE AVERAGE SPEED OP THE BOAT BETWEEN P ABD Q. 9/6$ V2$ 1.5$ .5$ THAT'S BOT THE ANSWER I ' f l LOOKING FOB. T B I B K ABOUT I T ABD T B I A G A I N . . . 9S IS 6S BO. T B I AGAIB _8 S 4$_ TOUB ABSWER I S I N C O R R E C T . THINK ABOOT THE PROBLEM ABD TRT A G A I N . . . 6 __4 . 8 3. .1 . .. L E T ' S T A K E A S M A L L E R S I Z E I N T E R V A L THAN BEFORE ON THE GRAPH I H SHEET 3. BBAT I S THE AVERAGE S P E E D O F T H E BOAT I N THE I N T E R V A L T=2 TO T»4 HOURS? PBOCEED E X A C T L I _ A S _ B E F O R E . _ . 1.5S 3/2$ 1»l/2$ 11/2$ 1 1/2S 4-1/4-2$ (4-1) / ( U - S H A L S THE AVERAGE S P E E D I S V = D E L ( S ) / D E L (T) » («-1) / ( 1 - 2 ) = 1. 5 S/HR. _THE_.SLOPE O F T H E L I N E SEGMENT J O I N I N G P AND R I S AGAIN T H E SAME AS THE AVERAGE S P E E D OVER T H I S I N T E R V A L . H O T I C E THAT T H E AVERAGE S P E E D I S NO LONGER C O H S T A N T M I F THE GRAPH I S HOT A STRAIGHT L I N E . T H E S L O P S I S NO LONGER COHSTAHT. 1 S 4/4$ 1/2S .5$ 1MIS BBONG. T B I A G A I H . . . _3S 2$ _ _ • _ T H I N K ABOUT THE PROBLEM AGAIN AND T B I TO F I H D THE EIGHT ARSWEB. GO AHEAD..  SEBO SEBD SEBD SEBD  2  «s  TOUB B E S P O H S E I S I H COB SECT. T R I TO ANSWER A G A I H . . . 7 4 3 2 3 5 J R B A T HAPPENS TO T H E S P E E D AS WE BAKE THE T I M E I B T E B V A L SMALLER ABD S M A L L E R . L E T ' S CONTINUE WHAT WE D I D WITH SHEET 3 B I CONSTRUCTING A T A B L E . LENGTH OF I N T E R V A L ( H R S ) » • 4 2 1 .5 .25 0 S L O P E O F L I N K ( M I L E S / H R J «« 2 1_. 5 1.25 '.12 1 _06 7 AVERAGE S P E E D (M1LES/KR) ** 2 1.5 1.25 '.12 1.06 ? HEAT I S THE L I M I T OF AVERAGE SPEED AS THE I N T E R V A L SHRINKS TO S I Z E 0 ? _STUDI THE T A B L E C A R E F U L L Y AND NOTE WHAT HAPPENS TO SLOPE AND AVERAGE S P E E D AS TriE LENGTH OP THE T I M E I N T E R V A L S H R I N K S FROM DEL (T 1 =4 , DOWl! TO 0. IS I.OOS 1HI$ T H E L I B I T OF AVERAGE S P E E D AS THE I N T E R V A L APPROACHES ZERO I S 1 H/HR. HE S E E T H A T AS T H E I N T E R V A L K E E P S G E T T I N G S M A L L E R . I T S H R I N K S T O A P O I N T AT T=2.AS SHOWN ON S H E E T 3 . T H E S P E E D AT T=2 I S J U S T T H E S L O P E OF _THE L I H E L WHICH T O U C H E S T H E C U R V E AT O N L Y O N E P O I N T P. T H I S L I B E I S C 1 L L Z D T H E T A N G E N T T O T H E C U R V E A T P O I N T P. 2$ TWOS  TOUR ANSWE'J I S INCORRECT. TV.INK ABOUT T H E PROBLEM OS THAT'S  OS HOT T I E  "ZEHOS ANSWER I'M  LOOKING  FOR.  THINK  AND T R Y A G A I H . . .  ABOUT  IT  ARD  TRY  AGAIH...  SEHD SEND  SEND SEHD SEHD SEBD _  SEHD SEBD  SEBD  SEBD SEHD  1.03$ DEFINEDS NO L I M I T S N O L I M I T S IOUB~ B E P L Y I S NOT C O B K K C T . RECONSIDER YOUR AaSBzR AND T B I A G A I H . . . SEHD 8 4 4 2 3 5 BRAT I S '.HE INSTANTANEOUS S P E E D OF THE BOAT «T THE T I H E , T = 2 HOURS? SEND T H I S I S VHE S P E E D AT THE IHSTAIiT OF T I M E T=2 HRS. STUDY THE T A B L E .'.BOVE A S C E L L I S S H E E T 3. THEN TRY TO ANS3PR... _ _ • SEBD 1 $ 1.00$ CNE$ 1M$ " THE S P E E D AT T I M E T=2 HOURS I S DEFINED AS THE L I M I T OF THE AVERAGE S P E E D AS THE T I H E I t t T T P V A L ABOUT T=2 S H R I N K S TO ZERO.THE SHCRTEP THE T I R E I N T E R V A L USED,THE CLOSER THE AVERAGE S P E E D I S TO THF H-ITUM. SPEED AT THAT I N S T A N T . Tii£ ACTUAL S P E E D AT THAT INSTANT I S J U M THE S L O P E JOF THE TAI.GENT l O THE CURVE. SEBD 2$" " " TViS 80- T H I N K ABOUT I T AND VRY A G A I N . . . SEBD  os  os  zer.^s  213  TOUB BESPONSE I S INCORRECT. TRT TO ANSWER A G A I N . . . SEND 1.03S 1.01$ NO L I M I T S N O L I H I T S UHDEFINEDS BBONG. T B I AGAIN SEBD 9 4 6 2 7 3 IQOK AT SHEET 4 WHICH I S THE GRAPH OP THE HOTION OP A FEATHER CROPPED r B O B A TOWER. S REPRESENTS THE DISTANCE OF THE FEATHER FROH THE GBOOHD. HHAT I S THE SPEED OF THE FEATHER AT T=2 S E C . ? SEBD _BEHEHBEB THE R E L A T I O N S H I P BETWEEN SPEED AND S L O P E ABD THEN P I B D THE INSTANTANEOUS - SPEED AT T=2 S E C . FROH THE GRAPH. SEBD -4 S -FOURS - POURS -4HIS IS-4 S =-4 $ TBE ACTUA L__SFEED_AT_T= 2__S E C . I S -4 FE E T / S E C . _ T H I S I S T HE _SLOPE _OP THE L I N E WHICH TOUCHES THE CURVE AT ONLY ONE POINT P.THE S L O P E I S B E G A T I V E S I N C E THE D I S T A N C E S I S GETTING S H A L L E R AS THE T I H E T I N C R E A S E S . _TBIS._HEANS THAT DEL (S) WILL BE N E G A T I V E . SEND 4 S FOURS TOUR ANSWER I S INCORRECT. THINK ABOUT THE P R 0 3 L E H AND TRT A G A I B . . . SEBD 6$ 2$ 3S TWO$_ 1$ 3.5$ -3$ THINK ABOUT I T AND TRY A G A I N OR P L E A S E T Y P E REVIEW I P TOO TIPE...REVIEW.WE B I L L REPEAT THE L A S T SECTION AGAIB FBOH SHEET 2. SEBD _BET$_ NOS DOBS __ __ _ GOTO 4 ~ " . 10 2 7 3 . THIS ACTUAL S P E E D I S C A L L E D THE INSTANTANEOUS SPEED OF THE FEATHEB I T T«2 S E C . THE INSTANTANEOUS SPEED I S THE S L O P E OF THE S T R A I G H T L I N E B B I C H TOUCHES THE CURVE I N SHEET 4 AT THE POINT P. T H I S L I N E I S C A L L E D "THE" TANGENT TO THE CURVE AT POINT P. DO YOU UNDERSTAND? SEND B E ' V E DEVELOPED THE I D E A OF SLOPE R E P R E S E N T I N G S P E E D . T I E S L O P E OF A L I B E J O I N I N G TWO POINTS ON THE CURVE I S AVERAGE SPEED.THE S L O J E OP A LINE TOUCHING THE CURVE AT ONE POINT I S INSTANTANEOUS S P E E D . I S I T CLEAR ? SEND TESS OK$ BITS LITTLES SURES THINK $ GUESSS _THE__INSTANTANEOUS S P E E D I S WRITTEN AS V = L I H I T (DEL ( S ) / D E L (T) ) AS DEL (T) "APPROACHES 0. T H I S I S A B B R E V I A T E D BY WRITING V=DS/DT = L I H I T (DSL ( S ) / D E L (T\) AS C E L ( T ) TENDS TO 0. DS/DT IS C A L L E D THE D E R I V A T I V E SF S WITH RESPECT TO T AND R E P R E S E N T S THE S L O P E OF A L I N E TOUCHING THE CURVE OF S V S . T AT ONLY ONE P O I N T . SEND •OS DONS NOTS THEN READ I T AGAIN AND ASK FOR H E L P . SEBD 11 4 4 4 4 4 BOW L E T ' S F I N D THE INSTANTANEOUS SPEED BY DSING THE EQUATION OF HOTION. SHEET 5 I L L U S T R A T E S THE GRAPH OF THE EQUATION OF H O x I C N , £> = 3I-»2 F I R S T LOCK AT THE T I H E I N T E R V A L BEGINNING AT T- I S 3 C . WHAT_IS THE D I S T A N C E S AT THE B E G I N N I N G OF T H I S T I H E I N T E R V A L ? StND_ OSE THE EQUATION OF HOTION. .$£HD 3 S THREES S = 3$ 3 (1) «2S THE D I S T A N C E S I S E A S I L Y OBTAIHLD FROH THE ECUATION OF HOTIOH. S=3T*2 = 3 (1) »2 = 3. BE ARE S I H P L Y C A L C U L A T I N G THE DISTAilCH AT OKE P O I N T . SEBD _SS DISTS 3T*2$ S=3T*2$ _ I O 0 B REPLY I S NOT CORRECT. RECONSIDER YOUR ANSWER AND T K T A G a i H . . . SEND TS 1$ t>Et.(Tl' 1»DEL(T)$ TBAT'S NOT THE A N E V R I'H LOOKING FOR. THINK ABOUT I T AND TRT A G A I N . . . SEHD 0$ OS I N F I N I T Y S UNDEFINEDS BO. V R I AGAIN SEBD 12 4 1 1 1 2 •» THE LEHGTH OF THE T I H E I N T E R V A L I N D I C A T E D ON THE GRAPH IS D c L ( T ) . •HICH OP THE FOLLOWING REPRESENTS THE D I S T A N C E AT THE EBD OF THE  214  TIBE  IHTERVAL.THAT IS,AT T I B E T=1»DEL(T)7 P L E A S E ANSWER A.B.C.D.OR B. A 3(DEL(T))*2 B 3 (1+DEL (T) ) »2 C 3(1*DEL(T)) D 3T*2 E BOBE OF THE ABOVE OSE T B E EQOATIOH OF BOTIOH.  SEHD SEHD  T B E T I H E I T THE END OF THE T I B E I N T E R V A L I S T = 1 * D E L ( T ) . THEH THE D I S T A H C E AT T H I S VALUE OF T I B E I S G I V E N BY S = 3T«2=3 (1 *DEL (T) ) *2 WHICH I S ALSO EQUAL TO 3+6DEL (T) • 3DEL (T) *2  SEBD  __i  AS  TOOB A B S B E B I S I H C O B B E C T . THINK ABOUT THE PROBLEB AND T B I A G A I B .  SEBD  CS  THINK ABOUT THE PROBLEB AGAIN AND T B I TO F I B D T H - BIGHT ANSWER. GO AHEAD.. DS ES I O 0 B _ H E P L T _ I S _HOT COBBECT. BECOHSIDEB IOUR AHSWEB AHD T H I A G A I H . . .  SEND SEBD  13  4 8 3 3 1: B E WOOL D L I K E T O F l N D_T HE AVER A G_E_ SPE E D I H T H I S T I HE I N T E R V A L FBOH T=1 T O T * 1 + D E L ( T ) . T H E CHANGE I H D I S T A N C E , DEL (S) , I S GIVEN BY ( D I S T A N C E AT END OF I N T E R V A L ) - (DISTANCE AT START OF I N T E R V A L ) . THEN  DEL (S_  ( 3 * 6 D E L (T) + 3 DEL (T) * 2 ) - 3  _  WHAT I S THE S I M P L I F I E D FORH DEL (T) (1 + D E L ( T ) ) - 1 OF DEL ( S ) / D E L (T) ? SEHD DO SOB- ALGEBRA TO S I H P L I F Y T H I S E X P R E S S I O N . _SZND_ 6*3DELS 6 • 3 D E L S 6+ 3 DELS 6 ODELS 3(2*DILS 3 (2 • DES 3DEL (T) * 6 $ 3 (CEL (T) • $ DEL (S) /DEL (T) = (6 DEL (T) O D E L (T) * 2 ) / D E L ( T ) = 6 * 3 D E L ( T ) S I H C E DEL (T) C A N C E L S IK BOTH KOHERATOR AND DE-OHIBATOR. T H I S I S T B E AVERAGE S P E E D ~ I H THE I N T E R V A L . ""' SEND /DELS DEL (T) S DELTS »Q. CHECK YOUR WORK AND TRT AGAIN SEHD 3*6DET$ 3*6$ 3 • 6S BO. THAT I S I N C O R R E C T . . . TRT A G A I N . . . SEHD _6»DELS 3*DEL$ _*3DEL$ 3(1*DEL$ HO. CHECK TOUR WORK AND TRT A G A I N . . . SEBD 14 3 2 7 3 R E C A L L I N G THAT INSTANTANEOUS SPEED I S THE L I B I T OF AVERAGE S P E E D AS THE T I R E I N T E R V A L S H R I N K S TO ZERO,THAT I S , A S D E L ( T ) APPROACHES ZERO. S THE INSTANTANEOUS S P E E D AT T I B E T=1 S E C ? SEHD _R_AT F I N D THE L I B I T OF DEL ( S ) / D E L (T) AS DEL (T) APPROACHES 0. SEND 6S SIXS GOT018 3$ 0$ OS 2S 9S DELS TOO S.-."! TO 2?. UNCLEAR ABOUT WORKING OUT L I H I T . S . i C u SHOULD DO SOME WORK O B _ L I H I T S FOR A FEW BTNUTES BEFORE GOING ON WITH THE BAIN L E S S O R . P L E A S E EHTER THE WORD. . . L I B I T ,OR TRY AGAIH I F 1 0 0 WISH. SEBD LIMITS -OS DOHS GOTO15 15 7 4 4 L E T S = 3 T * 7 . WHEN T = 2 . I T I S FAST TO S E E THAT S=13. BUT HOW DOES S BEHAVE WHEN T I S C L O S E TO 2 ? EXAfiIHE THE T A B L E G I V E N BELOW. T 2.5 2.2 ".I 2.01 2.C01 _.00G\ S-3T + 7 14.5 I'.o iJ. 3 13.03 13.003 13.0003 I S S C I O - E TO 13 WHEN t i S CLOSE TO 2 ? SEND SEND DOES S SEEN TO BS G E T T I N G CLOSER TO 1 j AS T GETS CLOMPS TO 2 ? T E S OR HO? _T_3$ OKS THINKS SURF.S t _ S A I THAT I F S= 7, THEN S APPROACHES 13 A S T .-."PSOACHES 2 AND WHITE " SEBD L I M I T ( 3 T * 7 ) AS T APPROACHES 2 , I S EQUAL TO 1 3 . BOS DOHS HOTS HO S 1  215  LOOK  AT THE T A B L E C L O S E L Y AND  ANSHER  AGAIH OR  $EHD  ASK FOR H E L P .  16  4  4  3  3  1  T H E L I B I T OF S AS T TENDS TO A PARTICtJLAH V A L U E SEEHS TO B E S I H P L I T H E V A L U E OF S AT THAT VALUE OF T. T H I S I S G E R E R A L L Y TRUE E I C E P T O N L I ORDER C E R T A I N C O N D I T I O N S , - HICH YOU. 8 ILL_L_EARN _AB.OUT_LAT.ER_I H_TO_UR C A L C U L U S COURSE. WHAT I S THE L I M I T OF S=20-6T AS T APPROACHES 3 ? F I N D THE VALUE OF S AT THE POINT T=3. _2..$ __TWO$ 20-6(3)$ 20-18$ T H E L I B I T OP 2 0 - 6 T AS T APPROACHES 3 I S 2. AS HE BAKE THE VALOE OP T CLOSER AND CLOSER TO 3,THE VALUE OF S GETS CLOSER AND CLOSER TO 2. 20$ TW.S N T TS 20$ „ ; • 0 . T H I N K ABOUT I T AND TRY A G A I N . . . 6 S 6 (3) 18S I O 0 B _ B E P L T I S _ H O T CORRECT._ R E C O B S I D E B TOUB AHSWE8 AHD T B I A G A I H .  $EHD SEHD  SEHD SEHD SEHD  14S  T O O B BESPOHSE I S I H C O B R E C T . 17 4  4  2  1  T R T T O AHSWER A G A I H . . .  SEBD  2  F I B D T B E L I B I T OF DEL ( S ) / D E L (TJ =6• 3DEL (T) _F_IBD THE VALUE OF 6 * 3 D E L ( T ) AT D E L ( T ) = 0 . 6 S' " SII$ 6.$ 6 + 3 (0) $ AS D E L ( T ) GETS CLOSER AND CLOSER TO 0,THE ABD CLOSER TO 6.THE L I B I T OF 6»3DEL(T) AS 3$ THREES SOUR AHSRER I S IHCORRECT. THINK ABOUT THE J6*3$ __ -BONG. T B I A G A I N . 9$ HIRES • O . T H I N K ABOUT I T AHD TRT A G A I H .  AS DEL (T) APPROACHES _  ZEBO.  SEBD SEBD  V A L U E OF 6 + 3 D E L ( T ) GETS C L O S E B DEL (T) APPROACHES 0 I S 6.  SEHD  PROBLEB AHD T B I A G A I H . . .  seir SEBD SEHD  16  2 2 6 L E T ' S TAKE A SHORT BREAK FROH THE L E S S O R . I ' D L I K E TO KNOW HOW TOU F E E L . . . • •BIGHT HOW'. WHICH OF THE CATEGORIES BELOW D E S C R I B E BEST TOUR B E A C T I O H . .HOW. . TO THE STATEBENT I AH T E N S E . A HOT AT A L L C BODERATELT SO VERY HDCH SO B SOMEWHAT P L E A S E AHSWER A,B.C.OB D. SEND AHSWER A,B.C.OR D TO D E S C R I B E TOUB R E A C T I O N 3IGHT HOW TO T B E S T A T ^ f l S - T . . . "SEND" I AH T E N S E . •OS TESS G0T018 AS G0T019 19 2 2 8  i:  cs  DS  HOTS  S0^»$  nODERS  VERTS  WHICH C.'TEGORT EELOW..A,B.C .OR P..BEST D E S C R I B E S TC.OR H E A C T I 0 3 TO THE S T A T E B E N T . I F E E L AT E A S E . C -ODERATELY _C A NOT AT A L L SEND AHSWER A , B . C . O P D. B SOBEWHAT D VERT MUCH SO SEHD P L E A S E A.B.C.OR D. •OS IESS GOTO19 AS GOT020 20 2 2 8  BS  c:  DS  I A- RELAXED. A HOT AT A L L C MODERATELY 30 B SOBEWHAT D VEST MUCH SO  HOTS  SOBES  HODEBS  VERTS  216  P L E A S E ANSWER A,B,C,OB D. AHSBEB A,B,C.OB D...TO THE STATEHEHT... . I AH RELAXED. •OS IESS 6OTO20 AS BS CS DS »OTS SOBES  SEBD SEBD BODEBS  VESTS  GQTQ21  21 2 2 8  I PEEL CALB. HOT AT A L L C BODEBATELT SO SOBEHHAT D VERT HUCH SO ANSWER A.B.C. OB D. ABSHEK A,B.C.OB D TO THE STATEMENT.. IESS •os _G OT02J_ BS AS os cs GOT022 1 B  I  PEEL  SEBD SEBD  CAEH.  • OTS  SOBES  BODEBS  VESTS  _22_  2 2 8  I AH J I T T E B T . HOT AT ALL _ C_ BODEBATELT SO SOBEWHAT D TEST BUCH SO ANSWER A,B.C.OR D. ANSWER A.B.C.OR D TO THE S T A T E H E H T . . . I AB J I T T E R T . TESS BOS G0TO22 "EBIS BODS AS BS CS _DS :_»OTS SOBES GOT023 23 8 1 2 2 0 L E T ' S TRT ONCE BORE TO F I N D T E E INSTANTANEOUS SPEED USING THE EQUATION OF HOTION, S=T*2. F I R S T , W H I C H OF THE FOLLOWING I S THE AVERAGE SPEED BETHEES T ° 2 ABD T-""2*DEL (T) ? ANSWEB A,B,C,D,OR E. A (2*DEL(T))*2 " B (2 + DEL (T) ) * 2 - 2 * 2 " " " " C (2*DEL(T))*2-2*2 / t2*DEL(T))-2 D ( 2 • DEL (T) ) *2-DEL (T) »2 / DEL (T) E BOHE OF THE ABOVE DO SOBE ALGEBRA TO GET D E L ( S ) AND DEL (T) BEFORE FINDING AVERAGE S P E E D I B THIS IBTERVAL. A B  _cs_  T B E AVERAGE S P E E D I S S I H P L T DHL ( S ) / D E L ( T ) I N THE INTERVAL,WHICH I S GIVEH BT ( 2 * D E L (T) ) * 2 - 2 * 2 / (? + DEL (T) ) - 2 . AS BS  SEHD JtEBD  SEBD SEBD SEHD  WRONG... TOO S B C f L D B F P E A T T B E H A T E B I A L CiiALi-G CLEAR ABOUT T H I S . _ ""EITHEBTYPE . . . B E V I E W ,0B AHS.WEB A G A I H . DS. ES WRONG  -'ITH  SHEET _  5 TO _ _  BECOBE _  100 SHOULD REPEAT THE H A T E R I A L DEALING B I T B SHEET 5 TO BECOBE CLEAR ABOUT T H I S . E I T H E R T Y P E ...REVIEW ,0R iNS«EB A C i l H . . REVS BOS DOSS OKS ~ ~~ " G0T011 21 * 3 5 3 "2 BHAT I S THE INSTANTANEOUS S P E E D AT T = 2 ? _6EHEHBER THE R E L A T I O N S "'IP BETWEEN AVERAGE S P E E D ABD IBSTABTANEOUS S P E ' D • AliD THEN GO A"EAD... " « S «.$ FOURS THE AVERAGE S P E E D I S ""EL ( S ) / D E L (T) = (2*DEL (T) ) »2-2*2 / 2->0EL(T)-2  SEBD  SEHD • SEHD SEHD  217  1 S I H P L I F T I N G THE NUMERATOR AND DENOHINATOR G I V E S DEL (S) / D E L (T) = UDEL (T) + DEL (T) »2 / DEL (T) NOW CANCEL DEL (T) \ FBOH NUMERATOR AND DENOHINATOR AND WE END UP WITH 1*DEL ( T ) . THE L I B I T OF <**DEL(T) AS DEL (T) TENDS TO ZERO I S a,WHICH I S THE U S T . SPEED SEHD 0/0$ 0$ ZEROS OS O/OS SEBD BO. CHEC K_ Y0UR WORK AND___HY_AGAIN 2 S I S DELS SEBD THAT'S HOT THE ANSWER I'H LOOKING FOB. THINK ABOUT I T AHD T B I A G A I H . . .  vs_  •s  IOUB ANSWER I S INCOBRECT. T H I N K ABOOT THE PROBLEM AHD T B I A G A I H . . . 25 2 2 2 COBGBATOLATIONS! YOU HAVE COMPLETED A C A I L E S S O H . I HOPE THAT YOU ENJOYED OUR CONVERSATION AS MUCH AS I DID AND THAT TOD L E A B B E D SOHETHIBG TOO. _ D I D YOU ENJOY T H I S METHOD O F _ L E A B N I N G ? . ANSWER YES OR NO. ANSWER I E S OR HO. TESS HQS I F TOO WISH TO HAKE ANY COHHENTS ABOUT THE LESSON,ASK T H E IHSTBUCTOB TO P B O V I D E TOU WITH A COHHENT S H E E T . GOOD-BYE FOB BOW... J_ATBE$ _ DONS . ... P L E A S E ANSWER YES OB HO. FILE  SEBD  SEHD SEBD SEBD SEHD  218  APPENDIX  E  L i s t i n g f o r One CAI Student S e s s i o n  (T )  «source #$RUN  pre  CAIPRE.0  fEXECUTION PLEASE  4-0ATAPREUAST+1)  S-PRETES  tSEGINS  ENTER  YOUR  FIRST  AND  LAST  9-»MS0URCE*  NAME ••  •  H I . I'M YOUR P E R S O N A L T U T O R F O R T O D A Y . L E T ' S S T A R T BY D O I N G A L E S S O N O F T H E T H I N G S T H A T YOU S H O U L D KNOW BEFORE D O I N G T H E M A I N L E S S O N L O O K A T T H E G R A P H SHOWN I N S H E E T A . WHAT I S T H E V A L U E O F Y AT T H E P O I N T X - 1 7 %  ON  SOME  10 OK S U P P O S E T H A T YOU A R E T O L D T H A T S I S A F U N C T I O N WHAT I S T H E V A L U E O F S WHEN T « 3 , I F S AND T S » 2 W ,READ T H I S AS TWO T I M E S  OF T. A R E R E L A T E D BY ( T SQUARED).  THE  EQUATION  18 GOOD. SUPPOSE PER  THAT  A  CAR  IS TRAVELLING  ALONG  A  HIGHWAY  AT  A  SPEEO  OF  60  MILES  HOUR.  12 0  HOW  FAR  WILL  THE  CAR  TRAVEL  IN 2  HOURS?  EXCELLENT: A CAR P A S S E S T H E 1 0 0 M I L E P O S T ON A H I G H W A Y A T 1 2 N O O N . T H R E E H O U R S L".TER, T H E C A R P A S S E S T H E 2 5 0 M I L E P O S T . W E U S E T H E S Y M B O L D E L ( S ) TO RCTRORD T H E C H AN L- E I N DL S T A N C E , T H A T I S , D E L ( S ) » { F I N A L D I S T A N C E ) - ( I N I T I A L D I S T A N C E ) WHAT I S D T L ( S ) I N T H I S C A S E ?  150  •  .  220  EXCELLENT!  K E E P UP THE  GOOD WORK.  —  S U P P O S E THAT A CAR T R A V E L S FROH MONTREAL T O T O R O N T O , A D I S T A N C E OF J 5 0 M I L E S , A i J D TriE D K I V t K S T O P S S E V E R A L T I M E S FOR FOOD AND G A S . WHAT S P E E D MUST T H E CAR A V E R A G E IN ORDER TO MAKE THE T R I P IN 7 HOURS? 50 E X C E L L E N T ! K E E P UP T H E GOOD WORK. S U P P O S E T H A T A N J T H t R CAR T R A V E L L I N G FROM MONTREAL TO T O R O N T O C 3 5 0 M I L E S ) MOVES AT 70 f-lI L E S / r l O U R FOR T H E F I R S T 5 HOURS AND AT CO M / H R FOR T H E NEXT <t H O U R S . WHAT IS THE S P E E D OF T H I S CAR E X A C T L Y aO M I N U T E S AFTER LEAVING MONTREAL? T H E S P E E D AT A P A R T I C U L A R T I M E I S C A L L E D THE I N S T A N T A N E O U S S P E E D . 70 t X L E L L t N T ! K E E P U P T H E GOOD WORK. LET'S T A K E A SHORT BREaK FROM T H E L E S S O N . I ' D L I K E TO KNOW HOW YOU F E E L . . . . . R I G H T NOW. WHICH O F T H E C A T E G O R I E S BELOW D E S C R I B E B E S T YOUR R E A C T I O N . . N O W . . TO T H E S T A T E M E N T I AM T E N S E . A NOT AT A L L C M O D E R A T E L Y SO B SOMEWHAT 0 VERY MUCH SO PLEASE ANSWER A , B , C , O R D.  c  WHICH  a  CATEGORY B E L O W . . A , B , C , O R D..BEST DESCRIBES I FEEL AT EASE. A NOT A T A L L C M O D E R A T E L Y SO B SOMEWHAT D V E R Y MUCH S O I AM R E L A X E D . A NOT AT A L L C MODERATELY SO B SOMEWHAT D V E R Y MUCH SO P L E A S E ANSWER A , 8 , C , 0 R  YOUR R E A C T I O N  ANSWER  -  TO THE  STATEMENT  A,B,C,OR D.  - .-.  D.  d A B  I FEEL C A L M . NOT AT A L L C M O D E R A T E L Y SO SOMEWHAT D V E R Y MUCH S O ANSWER A , B , C , OR D.  A B  I AH J I T T E R Y . NOT A T A L L C MODERATELY SO SOMEWHAT D V E R Y MUCH S O ANSWER A , B , C , O R 0.  "  "  d  a  "  "  -  NOW,LLT'S G E T BACK T O T H E L E S S O N . . . AT T H E GRAPH OF S V S . T SHOWN IN S H E E T 8 , WHAT If. T H E S L O P E O F T H E L I N E I N D I C A T E D :iN T H E GRAPH?  LOOK  k E X C E L L E N T I K E E P UP T r i t  LET'S WHAT -3x  GOOO WORK.  R E V I E W SOME B A S I C A L G E B R A . SAY T H A T YOU A R E G I V E N V H E }(l+X)-2-i(l)*2 / (1*X)-1 IS T H E S I M P L I F I E D FORM OF T H I S E X P R E S S I O N ?  BECOMES 3 < 1 + X? « 2 - 3 C1) * 2 » 3 C 1 + 2 X + X - < i «cX+3X«2«X(6-3X) THE DFNUMIMATOR BECOMES ( 1 * X ) - 1 = X T H E N , T H E EXPRESSION EOUALS X ( 6 + 3 X ) / X » ? WHAT I S T H E F I N A L FORM OF T H E E X P R E S S I O N ? NO.  THE  J(2*X>  OK  NUMERATOR  EXPRESSION "  )-?  " - - - - -  -  221  NOW  YOU ARE GIVEN AN EXPRESSION ( _ * X ) « 2 - 2 « 2 / ( 2 * X ) - 2 IS THE SIMPLIFIED FORM OF THIS EXPRESSION?  WHAT X*k  GOOD. LET'S DO THE SAME EXAMPLE AS BEFORE,BUT WILL BE USED IN THE MAIN LESSON.  NOW  WE'LL USE THE SYMBOLS THAT  GIVEN THE EXPRESSION 3 ( 1 * D E L ( T ) ) » 2 - 3 ( 1 ) * 2 / (1*DEL(T))-1 WHAT IS THE SIMPLIFIED FORM OF THIS EXPRESSION? }(2*del(t)) EXCELltNTI YOU SEEM TO UNDERSTAND THE CONCEPTS NEEDED TO TAKE THE MAIN LESSON. YOU MAY TAKE A SHORT BREAK OR YOU CAN START THE MAIN LESSON RIGHT AWAY. DO YOU WANT TO TAKE A BREAK? no EXCELLENT I KEEP UP THE GOOD WORK.  THEN TYPE...SSOURCE STOP  LESSON  U  •EXECUTION TERMINATED 'source lesson #$RUN CAI.O U=DATAMA!N< LAST+1) S - T X . - • M S O U R C E * 'EXECUTION BEGINS PLEASE ENTER YOUR FIRST AND LAST NAME  "  ~  LET'S STUDY THE MOTION OF A BOAT AS IT LEAVES A DOCK. SUPPOSE THAT I T ' S MOVING. AT A CONSTANT SPEED OF 10 MILES/Hf",R. WHAT IS THE DISTANCE S OF 7H_ BOAT FROM THE DOCK AT ANY TIM5. T? tUU) I DON T RECOGNIZE YOUR RESPONSE. TRY AGAIN lOt OK  THE EQUATION WHiCH DESCRIBES THE MOTION OF THE BOAT is S-10T. THIS IS SIMPLY THt FAMILIAR D I S T M N C E - ( S P E E D H T I M E ) EQUAT I ON, in I TH SPEEO V BEING CONSTANT AT 1 0 MILES/HOUR.  LOOK  AT SHEET 1 THAT WAS GIVEN TO YOU.THE GRAPH INDICATES FAR THIS BOAT i S FROM THE DOCK AT ANY 71.!E. WHAT IS ' H E SLOPE OF THIS STRAIGHT L I N . REfP.ESEi;." i r,G THE BOAT'S MOTION IN A TIME IMTERVAL T - 2 TO T-6 HOURS? 10 HOW  .GOOD. •"•  THE SLOPE IS THE CHANGE IN DISTANCE DIVIDED BY THE CHANGE IN TIME. WE WRITE THIS AS SLOf _»UE_(S >/. S L O ' ) WHICH IS EQUAL TO < 6 0 - 2 0 ) / ( 6 - 2 ) - 1 0 MILES/HOUR.  WHAT IS THE  "10 ' EXCELLENT I  SLOPE OF THE LINE  IN THE TIME  INTERVAL l°k  T J T - 8 HOURS?  THE SLOPE IS CONSTANT AT 10 MI LES/HOUR.THIS l_ A'.WAYS TH*. CASE WHEN THE GRAPli CF THE MOTION IS A STPAI Gil'l LINE.THE C-RAPH !S JUST A PICTURE Or THE EQUATION OF MOTION S»10T,AND SO THE SLOPE OF THE LINE IS THE SPEED OF Trie BOAT. :  SHEET 2 ILLUSTRATES THE MOTION OF A SECOND BOAT COMPUTE THE AVEKAOc SPEED OF THE BOAT IN THE INTERVAL 2  PROM T=2 TO T»6 HRS.  222  EXCELLENT I KEEP UP THt GOOD WORK. THE AVERAGE SPEED IS SIMPLY THE CHANGE IN DISTANCE DIVIDED BY THE CHANGE IN TIME.THIS IS GIVEN BY V«DEL(S)/DELCT)-(9-l)/(6-2)«8/4-2 MILES/HOUR LOOK AT SHEET 3,WHICH IS JUST THE GRAPH IN SHEET 2 WITH THREE POINTS P , Q , AND R INDICATED ON I T . WHAT IS THE SLOPE OF THE LINE SEGMENT JOINING THE POINTS P AND 0.? 2 EXCELLENT! KEEP UP THE GOOO WORK. THE SLOPE OF THE LINE SEGMENT JOINING P AND Q IS GIVEN BY CHANGE IN 01 STANCE DIVIDEO BY CHANGE IN TIME,WHICH IS D E L . S ) / D E L ( T ) ' & / 4 = 2 M/HR. THIS IS THE SAME AS THE AVERAGE SPEED OF THE BOAT BETWEEN P AND Q. L E T ' S TAKE A SMALLER SIZE INTERVAL THAN BEFORE ON THE GRAPH IN SHEET. 3. WHAT IS THE AVERAGE SPEED OF THE BOAT IN THE INTERVAL T - 2 TO T - 4 HOURS? 3/2 EXCELLENT! KEEP UP THE GOOD WORK. THE AVERAGE SPEED IS V=DELCS)/DEL(T) « ( 4 - 1 ) / ( 4 - 2 ) - l . 5 M/HR. THE SLOPE OF THE LINE SEGMENT JOINING P AND R IS AGAIN THE SAME AS THE AVERAGE SPEED OVER THIS INTERVAL. NOTICE THAT THE AVERAGE SPEED IS NO LONGER CONSTANT 11 If THE GRAPH IS NOT A STRAIGHT L I N E , T H E SLOPE IS NO LONGER CONSTANT. WHAT HAPPENS TC THE SPEED AS WE MAKE THE TIME INTERVAL SMALLER AND SMALLER. L E T ' S CONTINUE WHAT WE DID WITH SHEET 3 BY CONSTRUCTING A T/>bLE. LENGTH OF 1 NT E R V A L ( H R S ) * * 4 2 1 .5 .25 0 SLOPE Or L I N E ( M I L E S / H R ) « « 2 1.5 1.06 1.25 1.12 AVERAGE S P E E D ( M I L E S / H R ) * * 2 1.5 1.25 ? 1.12 1.06 WHAT IS THE LIMIT OF AVERAGE SPEED AS THE INTERVAL SHRINKS TO S I Z E 0? 0 NO.THE LENGTH OF THE INTERVAL TENDS TO 0 BUT AVERAGE SPEED DOES NOT. LENGTH .5 .25 .15 .10 0 SLOPE *• 1.12 1.06 1.04 1.02 ? AVERAGE S P E E D * * 1.12 1.06 1.04 1.02 ? WHAT IS THE LIMIT OF AVERAGE SPEED AS THE INTERVAL SHRINKS T O S I Z E 0? 1  OK  THE LIMIT OF AVERAGE SPEED AS THE INTERVAL APPROACHES ZERO IS 1 M/HR. WE SEE THAT A S T H E IMTtKVAL KEEPS GETTING SMALLER.IT SHRINKS TO A POINT  AT T-=2,.*S SH.~>WN O N S H E E T  3.THE  SPEED  AT  T  =2  iS JUST  T H E SLOPE OF  THE LINE L WHICH TORCHES T H E CURVE AT ONLY ONE POINT P. THIS LINE CALLED THE T A N G E N T 10 THE CURVE AT POINT P. WHAT IS THE INSTANTANEOUS SPEED OF THE BOAT M T THE T I M E , T - 2 1 GOOD.  IS  HOURS?  -  THE SPEED AT TIME T=2 H0U.7S IS DEFINED AS THE LIMIT OF THE AVERAGE SPEED AS THE TI Mt INTS-RV/A'. ABOUT T=>2 SHRINKS TO ZERO.THE SHORTER THE TIME  INTERV/AI  USEI'. H t T  CLOSER  T H E AVERAGE  A T THAT INSTANT. Y H E A C T U A L SPEED AT THAT O F THE TANGENT TO TriE CURVE.  f.PEED  IS  TO THE A C T U A L  SPEED  INSTANT IS JUST THE SLOPE  LOOK AT SHEET 4 WHICH I S THE GRAPH OF THE MOTION 0? A FEAThER DROPPED FrfOM A TOWER, i RtPREb 1 N T S T H E D iSTANCE OF T H E FEATHER FROM THE GROUND. WHAT IS THE SPEED OF THE FEATHER AT T - 2 S E C ?  * YOU'RE .'.'.MOST RIGHT.T!'E CHANGE IN DISTANCE D L L ( S ) IS GIVEN BY (FINAL DiSTAiJCt)-< INITIAL DISTANCE). SINCE DISTANCE IS GETTING SMALLER  AS TIMt -4  - t T S B I G G t R , D t L ( S ) WILL BE N E G A T I V E .  TRY AGAIN.  OK  THE ACTUAL S P t E D AT T-2 S E C . IS -4 F E E T / S E C . THIS IS THE S L O P E OF THE LINE WHICH TUUCHtS THE CURVE AT ONLY ONE POINT P.THE S L O P E IS N E G A T I V E S I N C E THE D I S T A N C E S I S G E T T I N G SMALLER AS THE T I M E T I N C R E A S E S THIS MEANS THAT D E L ( S ) WILL BE N E - A T I V E . THIS ACTUAL SPEED I S CALLED THE INSTANTANEOUS SPEED OF THE FEATHER A T T-- S E C . THE INSTANTANEOUS S P E t D I S THE SLOPE OF THE STRAIGHT L I N E WHICH TOUCHES TriE CURVE IN SHEET 0 « T THE POINT P. T H I S L I N E I S CALLED THE TANGENT TO TriE CURVE AT POINT P. OO YOU UNDERSTAND? yes  GOOD.  TriE INSTANTANEOUS SPEED IS WRITTEN AS V - L I M I T ( O E L C S ) / D E L ( T ) ) AS D E L ( T ) APPROACHES 0. T H I S IS A B B R E V I A T E D BY WRITING V « O S / D T - L I M I T ( D E L ( S ) / D E L ( T ) ) AS D E L ( T ) TENDS TO 0. DS/DT IS C A L L E D THE D E R I V A T I V E S F S WITH RESPECT TO T AND R E P R E S E N T S THE S L O P E OF A L I N E TOUCHING THE CURVE OF S V S . T AT ONLY ONE P O I N T . NOW L E T ' S F I N D THE INSTANTANEOUS -SPEED BY U S I N G THE EQUATION OF MOTION. SHEET 5 I L L U S T R A T E S THE GRAPH OF THE EQUATION OF MOTION, S-3T*2 F I R S T L O O K AT THE TIME INTERVAL B E G I N N I N G AT T - l S E C . WHAT IS T H E D I S T A N C E S AT THE B E G I N N I N G OF T H I S TIME I N T E R V A L ? 3 EXCELLENTI THE D I S T A N C E S IS E A S I L Y OBTAINED FROM THE EQUATION OF MOTION. S»JT»2«3C1)«2»3. WE A R E S I M P L Y C A L C U L A T I N G THE D I S T A N C E AT ONE POINT. THE LENGTH O F THE T I M E INTERVAL I N D I C A T E D ON THE GRAPH I S D E L ( T ) . WHICH O F THE FOLLOWING REPRESENTS THE D I S T A N C E AT THE END OF THE TIME INTERVAL,THAT I S , A T TIME T - 1 + D E L C T ) ? P L E A S E ANSWER A,B,C,0,OR E. A 3(DEL(T))*2 B 3(1+DEL(T))«2 C 3(1+DEL(T)> D 3T*2 E NONE OF THE ABOVE 3  b  I DON T R E C O G N I Z E  YOUR RESPONSE.  TRY A G A I N  OK  THE  TIML AT THE END O F THE T I M E I N T E R V A L I S T » 1 + D E L ( T ) . THEN THE O l S T A N C t AT T r i i S V A L U F OF T I M E I S G I V E N EV S-3T«2 ?(1+DEL(T))«2 WHICH I S ALSO EQUAL TO 3+6DEL(T)•30EL(T>*2 C  WE WOULD L I K E TO FIND THE AVERAGE SPEED I N T H I S TIME I N T E R V A L FROM T - l t O T=:-.*DEL(Y).THE CHANliE IN D I S T A N C E , D E L ( S j , I S G I V E N BY ( D I S T A N C E AT END O F I N T E R V A L ) - ( D I STANCE AT START OF I N T E R V A L ) . THEN DEL(S; (3+6DEL(T>-JDELCT)*2}-3 . WHAT I S THE S I M P L I F I E D FORM DEL(T) (1+DEL(T))-1 OF D E L ( S ) / D E L ( T ) ? 3<2+de1(C))  GOOD.  D E L ( S ) / D E L < T ) = < 6 D E L ( T ) * 3 0 E L ( T ) * 2 ) / D E L ( T ) - 6 * J 0 E L < T J SINCE DEL!T) IN BOTH NUMERATOR >ND DENOMINATOR. T H I S I S THE AVERAGE S P E E D IN THE !NTEPVAL. R E C A L L I N G THAT INSTANTANEOUS S P E F D I S THE L I M I T OF AVERAGE T I M E I N T E R V A L S H R I N K S TO ZERO,THAT I S , A S D E L ( T ) APPROACHES WHAT i S THE INSTANTANEOUS S P E E D AT TIME T»i S E C ? 6 EXCELLENT !  CANCEL-  SPEED A S THE ZERO.  224  LET'S TAKE A SHORT BREAK FROM THE L E S S O N . I ' D L I K E TO KNOW HOW YOU F E E L . . . ..RIGHT NOW. WHICH OF THE CATEGORIES BELOW D E S C R I B E BEST YOUR REACTION..NOW.. TO THE STATEMENT I AM T E N S E . A NOT AT A L L C MODERATELY SO 8 SOMEWHAT D VERY MUCH SO PLEASE ANSWER A,B,C,OR 0 . •>  WHICH CATEGORY dELOW..A,B,C,OR D..BEST D E S C R I B E S YOUR R E A C T I O N TO THE STATEMENT. I F E E L AT E A S E . A NOT AT A L L C MODERATELY SO B SOMEWHAT D VERY MUCH SO ANSWER A,B,C,OR 0 . C  • .  I AM R E L A X E D . A NOT AT A L L C MODERATELY SO B SOMEWHAT 0 VERY MUCH SO P L E A S E ANSWER A,B,C,OR 0.  c  I FEEL CALM. NOT AT ALL C MODERATELY SO SOMEWHAT D VERY MUCH SO ANSWER A, B,C, OR D.  • '  •  A B  I AM JITTERY. NOT AT ALL C MODERATE:Y SO SOMEWHAT 0 VERY MUCH SO ANSWER A,B,C,OR D.  LET'S TRY ONCE MORE TO FIND THE INSTANTANEOUS SPEEO U S I N G THE EQUATION OF MOTION, S=T*2. F I R S T , W H I C H OF THE FOLLOWING I S THE AVERAGE SPEED BETWEEN T-2 AND T»2*DEL(T)? ANSWER A,B,C,D,OR E. A <2*DEL(T))*2 S (2+DEL(T))*2-2»2 C <2*DEL(T>)*2-2«2 / ( 2 + D E L ( T ) ) - 2 D (2+DEL(T))»2-DEL(T)*2 / D E L ( T ) E NONE OF THE ABOVE  •  NO. T H I S R E P R E S E N T S DISTANCE.THE D I S T A N C E AT T-2 IS S*T»2 = 2*2-k AND THE D I S T A N C E AT 1-=2*D EL C T ) I S S - < 2 + D E L ( T ) ) * 2 . YO'J MUST D I V I D E D E L C i ^ BY O E L ( T ) . YOU SHOULD REPEAT THE M A T E R I A L D E A L I N G WITH SHEET 5 TO BECOME CLEAR ABOUT T H I S . E I T H E R |-.'Pt ...REVIEW ,0R ANSWER A G A I N .  e  NO. THE AVERAGE SPEED I S D E L ( S 2 , ' D E L ( T ) IN THE I N T E R V A L . DEL( S )"F INAL 01 STAN CE- I NI T i AL D I ST ANCE= ( 2+L'ELCT) W - 2 * 2 AND ' O E L ( T ) = F I N A L TI M E - I N I T I A L T I M E = ( 2 + D E L ( T ) ) - 2 . S I M P L I F Y D E L ( S ) AND D E L ( T ) AND D I V I D C THLM.YOU SHOULD REPEAT THE M A T E R I A L O t A H N G WITH SHEET i TO EE '-LEAP. AEOUT T H I S . T Y P E . . .REV I EW .OR TRY A G A I N , review NOW LET'S F I N D THE INSTANTANEOUS SPEED BY U S I N G THE £QUATION OF MOTION. SHEET 5 I L L U S T R A T E S THE GRAPH OF THE EQUATION 0'- MOTION, S-=3T»2 F l k S T L00£ AT THE T I M E INTERVAL B E G I N N I N G AT J"X S E C . WHAT IS THE D I S T A N C E S AT THE B E G I N N I N G OF T H I S TIME I N T E R V A L ? 3  OK  THE  D I S T A N C E S I S E A S I L V O B T M fit, ) F R O " THE EQUATION OF MOTION. S«;T«2=i(l)«2-3. WE ARE S l h P L V C A L C U L A T I N G THE D I S T A N C E AT ONE POINT. 1  T H E LENGTH OF THE TIME INTERVAL I NO ICATED ON THE GRAPH IS D E L ( T ) . W H I C H OF THE FOLLOWING REPRESENTS THE DISTANCE AT THE END OF THE T I M E INTERVAL,THAT I S , A T TIME T - 1 + D E L < T ) ? PLEASE ANSWER A , B , C , D , O R E . A 3(DEL(T))*B 3{l+DELCT))*1 C 3U*DEL(T)) D 3T*2 E  c  NONE  OF THE ABOVE  WRONG. THE DISTANCE IS GIVEN BY S - 3 T * _ . YOU HAVE CHOSEN THE DISTANCE A T T H E E N D OF THE INTERVAL FOR AN EQUATION OF MOTION S - 3 T « 3 { l + D E L C T ) ) .  b  TRY  AGAIN,  OK.  T H E T I M E A T THE ENO OF THE TIME INTERVAL IS T - 1 + D E L l T ) . THEN THE D I S T A N C E A T THIS VALUE OF TIME IS GIVEN BY S«3T»_»3(1+DEL(T)) W H I C H IS ALSO EQUAL TO . 3 + 6 D E L C T ) * 3 D E L ( T ) * 2 WE WOULD LIKE TO FIND THE AVERAGE SPEED IN THIS TIME INTERVAL FROM T » l T O T - 1 + D E L ( T ) . T H £ CHANGE IN DI STAN CE, DEL( S ) , I S GIVEN BY (DISTANCE AT END OF I M T E R V A L ) - ( 0 I STANCE AT START OF INTERVAL). DEL(S)  THEN  (3+6DELCT)+3DELCT)*2)-3  .  WHAT U*0EL(T))-1  OEL(T)  3(2*dei(t)) GOOD.  ............  OF .  IS THE SIMPLIFIED FORM DEL(S)/DEL(T>? -  •  .  O E L ( S ) / D E L ( T > » ( 6 D E L ( T ) * 3 D E L C T ) * 2 ) / D E L ( T ) « 6 + 5 D E L ( T ) SINCE D E L ( T ) CANCELS I N BOTH NUMERATOR AND DENOMINATOR. THIS IS THE AVERAGE SPEED I N T H E INTERVAL. R E C A L L I N G THAT INSTANTANEOUS SPEED IS THE LIMIT OF AVERAGE SPEED AS T H E TIME INTERVAL SHRINKS TO ZERO,THAT IS,AS DEL(T) APPROACHES ZERO. WHAT I S THE INSTANTANEOUS SPEED AT TIME T - l S E C . ? 6 EXCELLENT 1  L E T ' S TAKE A SHORT BREAK FROM THE L E S S O N . I ' D LIKE TO KNOW HOW YOU F E E L . . . . . R I G H T NOW. WHICH OF THE CATEGORIES BELOW DESCRI3E BEST YOUR REACT ION..NOW.. TO T H E STATEMENT I AM TENSE. A NOT AT ALL C MODERATELY SO B SOMEWHAT D VERY MUCH SO P L E A S E ANSWER A , B , C , O R D. i> WHICH CA7--0RY . - L G W . A , B , C , OR D. .BEST DESCRIBES I FEEL AT E A S E . A NOT AT ALL C MODERATELY SO B SOMEWHAT D VERY MUCH SO C . I AM RELAXED. A NOT AT ALL C MODERATELY sn B SOMEWHAT 0 VERY MUCH SO PLF„',F. ANSWER A , B , C , O R D. .  C A 8  c  I FEEL CALM. NOT A T ALL C MODERATELY SO SOMEWHAT D VERY MUCH SO ANSWER A , B , C , OR D.  .  A B  I AH J I T T E R Y . NOT AT A L L C SOMEWHAT D  ....  MODERATELY SO VERY MUCH SO  "CUR REACTION  TO THE STATEMENT  ANSWER A , B , C , O R 0. -  •. •  .  •  226  ANSWER A,B,C,OR 0.  •  LET'S TRY ONCE MORE TO FIND THE INSTANTANEOUS SPEED U S I N G THE EQUATION OF MOTION, S » T * 2 . F I R S T , W H I C H OF THE FOLLOWING I S THE AVERAGE SPEEO BETWEEN T « 2 AND T » 2 + D E L ( T )? ANSWER A,B,C,D,OR E. A (2*DEL(T)W B ( 2 * D E L ( T ) ) «2-2«2 C <2*DEL(T))*2-2«2 / ( 2 * D E L ( T ) ) - 2 D ( 2 * D E L ( T ) ) « 2 - D E L ( T ) » 2 / DEL(T) E NONE OF THE ABOVE C EXCELLENT! K E E P U P THE GOOD WORK. THE AVERAGE SPEED IS S I M P L Y D E L ( S ) / D E L C T ) IN THE INTERVAL,WHICH IS GIVEN BY ( 2 * D E L ( T ) W - 2 « 2 / ( 2 + D E L ( T ) > - 2 .  WHAT IS THE INSTANTANEOUS SPEED AT T - 2 ? ft EXCELLENT 1 K E E P UP THE GOOD WORK.  THE AVERAGE SPEED I S D E L ( S ) / D E L ( T ) = ( 2 + D E L ( T ) ) « 2 - 2 * 2 / 2+OEL(T)-2 S I M P L I F Y I N G THE NUMERATOR AND DENOMINATOR G I V E S DEL(S)/DEL(T)=ltDEL( T)+DEL(T)*2 / O E L ( T ) NOW CANCEL D E L ( T ) FROM NUMERATOR AND DENOMINATOR AND WE END UP WITH i»*DEL(T). THE LIMIT OF <**OEL(T) AS D E L ( T ) TENDS TO ZERO I S U,WHICH IS THE INST.  SPEED  CONGRATULATIONS! YOU HAVE COMPLETED A CAI LESSON.I HOPE THAT YOU ENJOYED OUR CONVERSATION AS MUCH AS I DIO AND THAT YOU LEARNED SOMETHING TOO. DID YOU ENJOY T H I S METHOD OF L E A R N I N G ? ANSWER YES OR NO.  yes EXCELLENT! K E E P U P THE GOOD WORK.  IF YOU WISH TO MAKE ANY COMMENTS ABOUT THE LESSON,ASK THE PROVIDE YOU WITH A COMMENT S H E E T . GOOD-BYE FOR NOW... STOP 0 • E X E C U T I O N TERMINATED  *slg s 'OFF AT l i t : 32: 39  60.580 20.13 15,55 fW 06.006 •D 2188 « $26.02 t P . " . '$252.«6 #E  / 'C | 'C  SUN MAR 1 8 / 7 3 $3.02 $1.00 $.26 $13.92 . ..  .  .  INSTRUCTOR TO  -  227  APPENDIX F  Post t e s t  228  F I N A L  INSTRUCTIONS:  T E S T  Please answer a l l q u e s t i o n s .  Enter your c h o i c e  i n the space p r o v i d e d on the answer  sheet.  Use the s c r a p paper p r o v i d e d f o r your calculations.  229 What i s the name f o r the slope of a s t r a i g h t segment j o i n i n g vs.  line  two p o i n t s on the graph o f d i s t a n c e  time? a b c d e  tangent derivative average speed speed i n s t a n t a n e o u s speed  What i s the name f o r the slope o f a s t r a i g h t  l i n e segment  which i s tangent to the curve o f d i s t a n c e v s . time? a b c d e  average speed i n s t a n t a n e o u s speed tangent change speed  What i s the name f o r the l i m i t o f average speed i n an i n t e r v a l as the s i z e o f that i n t e r v a l approaches z e r o ? a b c d e  derivative average speed i n s t a n t a n e o u s speed tangent speed  What i s the name f o r the slope of a s t r a i g h t  l i n e segment  which i s tangent t o the curve o f S v s . T and i s w r i t t e n as DS/DT? a b c d e  derivative slope tangent change speed  230  50 Q) rH •H  CO  40 30  w <  H CO  20  M  Q  10  >  0 0  10  15  20 TIME T  25 (hours)  Figure 1  5.  Refer to the graph i n f i g u r e  1.  Calculate  the average  speed i n the i n t e r v a l between T = 5 and T = 20 hours. a b c d e  15 20 2 1  231  14 Graph of S vs. T  12 OJ t-i  •H  ~ ?  10  J  8  10  w.  ••  CO  0  y 7  •  4 5 TIME T (hours) Figure 2  6.  Refer to the graph shown i n F i g u r e 2. Compute the average speed i n the i n t e r v a l from T = 1 to T = 3 hours. a b c d e  7.  3.3  4.0 4.5  Refer to the graph shown i n F i g u r e 2. i n s t a n t a n e o u s speed at T = 2 hours. a b c d e  8.  0.2 1.0  Compute the  1 2 3  4 5  R e f e r to the graph shewn i n F i g u r e 2. Compute the d e r i v a t i v e of d i s t a n c e with r e s p e c t to time, that i s DS/DT at the point T = 2 a 1 b 2 c 3 d 4 e 5  232 9.  What i s the value of the e x p r e s s i o n g i v e n below? LIMIT OF (3T+4DEL(T)-6) AS DEL(T) TENDS TO O. a b c d e  3T 3T+4 3T-6 -6 3  10. What i s the value of the e x p r e s s i o n g i v e n below? LIMIT OF (4TDEL(T)*2+DEL(T)+5) AS DEL(T) TENDS TO O. a b c d e  5 4 2 4T 4T+5  11. D e f i n e the i n s t a n t a n e o u s speed V, at any time T, as a f u n c t i o n o f d i s t a n c e ( T ) and time ( T ) . a b c d ,  e  V V V V V  = = = = =  S/T DEL(S)/DEL(T) LIMIT (S/T) AS T TENDS TO O. LIMIT (PEL(S)/DEL(T)) AS DEL(T) TENDS TO O. LIMIT (3/T) AS DEL(T ) TENDS TO O.  12. Given that S = 2T r e p r e s e n t s the d i s t a n c e S of a boat at any  time T, compute the average speed o f the boat between  T = 1 and T = 1+DSL(T). a b c d e  0 2 4 6 8  13. For . the boat in' problem spaed a t T~3. a 0 b 2 c -3 d t e h  12, compute the i n s t a n t a n e o u s  233 14.  Given that S=T*2+8 r e p r e s e n t s the d i s t a n c e S o f a boat at any time T, compute the average speed of the boat between T=l and T=1+DEL(T). a b c  (1+DEL(T))*2+8 (1+DEL(T))*2-l (1+DEL (T) ) * 2 - l DEL(T)  d  (1+DEL(T) )*2+8  DEL(T) e  15.  (1+DEL (T) ) - l DEL(T)  For the boat i n problem  14, compute the i n s t a n t a n e o u s  speed at T = 1. a b c d e 16.  (1+DEL(T))*2 2+DEL(T) 8 1 2  Given an e q u a t i o n S = 6T, c a l c u l a t e the d e r i v a t i v e o f S with r e s p e c t a b c d e  17.  to T, DS/DT, a t the p o i n t T = 2.  0 2 6 12 36  Given an e q u a t i o n S=T*2, c a l c u l a t e a b c d e  2T (T+DEL(T))*2 T+D£L(T) 2T+DEL(T) DEL(T)*2  DEL(S)/DEL(T)  234 G i v e n an e q u a t i o n S=T*2, c a l c u l a t e the d e r i v a t i v e of S with r e s p e c t to T, DS/DT, at the. p o i n t T = 4, u s i n g the limit a b c d e  definition. 2T T*2 2 4 8  235 NAME:  ANSWER SHEET  1. 2. 3. 4. 5. 6. 7. 8. 9.  r  10. 11. 12. 13. 14. 15. 16. 17. 18.  236 KEY  1.  C  2.  B  3.  C  4.  A  5.  D  6.  E  7.  D  8.  D  9.  C  10. A 11. D 12. B 13. B 14. C 15. E 16. C 17. D 18. E  237  APPENDIX G  S t a t e - T r a i t Anxiety  Inventory  SELF-EVALUATION QUESTIONNAIRE  Developed by C. D. Spielberger, R. L. Gorsuch and R. Lushene  238  STAI FORM X-1  NAME  :  '.  DATE  DIRECTIONS: A number of statements which people have used to describe themselves are given below. Read each statement and then blacken in the appropriate circle to the right of the statement to indicate how you feel right now, that is, at t h i s moment. There are no right or wrong answers. Do not spend too much time on any one statement but give the answer which seems to describe your present feelings best.  o  S m  f  2. I feel s e c u i ^ ^ ^ v  -'.  -  :  ,  .^^s^.  5. I feel at e a & r ^  ./..  6. I feel upset  L  »•  ...^1.  . . ^ r ^  7. I am presently worrying over"possible misfortunes/:.  ..A  y/.^TSv^^.  8. I feel rested  «;  3 e o  s  r  ©  4. I am legretful  M  a  >  1. I feel calm  3. I am tyense  3 o a n s > H  9. J feel anxious  \.. .  1 jL.  ©  © ©  ® ©  © ©  ©  ©  ®  ©  ©  ©  ©  ©  ©  ©  ©  ©  ©  ©  ©  ©  ©  ©  ©  ©  ©  ®  ®  ©  ©  ©  ©^,® ©  ®  ®  ©  ©  ©  ®  ©  ©  ©  ®  ©  ©  ©  ©  ©  ®  ®  ®  ©  ©  ©  ®  ©  16. I feel content  ©  ©  ®  ©  17. I am worried  ©  ©  ©  ©  13. I feel over-excited and rattled  ©  ©  19. I feel joyful  ©  ©  @  ©  20. I feel pleasant  Q  ®  ©  ®  10. I feel comfortable 11. I feel self-confident  :  /.  12. I feel nervous 13. I am jittery  *  14. I feel "high strung" 15. I a:n relaxed  '.  imjFki 'y^i^jj  CONSULTING PSYCHOLOGISTS PRESS 577 Colieye Avenuo, Palo Alto, California 94306  v  r  ©  SELF-EVALUATION QUESTIONNAIRE STAI FORM X-2  NAME  :  :  :  239 :  '. DATE  DIRECTIONS: A number of statements which people have used to describe themselves are given below. Read each statement and then blacken in the appropriate circle to the right of the statement to indicate how you generally feel. There are no right or wrong answers. Do not spend too much time on any one statement but give the answer which seems to describe how you generally feel.  >  o  01  O  3  r >  3 S w  CO  m  21. I feel pleasant  ©  ®  ® '©  22. I tire q u i c l d j ^ ^  ©  ©  ®  ©  ©  ®  ®  ©  ©  ®  ®  ©  23. I feel like crying  ;  24. I wish I could be as happy asc_th^rs seem to be  25. I am losing out on things/because I can't make up my mind soon enough .... ©  L^......^Z  26. I feel rested  27. I am '-'calm, cool, and collected"  ...J...  -?^>v.  J^^*^^S..  © 1  ® ©  ©  ® ®  ®  © ©  ©  ©  28. I feel that difficulties a^e piling up so that I cannot overcome \ner^r^....  G  ©  ®  ©  2i*. I worry too much over something that really doesn't matteeT.  ©  ®  ®  ®  30. I am happy  ©  ®  ®  ©  31. I am inclined to take things hard  ©  @  ®  ©  32. f lack self-confidence  ©  ®  ®  ©  33. I teel secure  ©  ©  ®  ©  34. I try to avoid facing a crisis or difficulty  ©  ®  ®  ©  36. I f~el blue  ©  ©  ®  ^  :  36. 1 ara content  :  ;  -  37. Some unimportant thought runs through my mil-d and bothers mc  ©  ©  ©  38. I take disappointments so keenly that I can't put them out of my mind .... ©  ®  ® ®  ©  ®  ©  ,©  ©  SO. I am a steady person  © ^©  ®  ©  40. I become tense ai:d upset when I think about my present concerns  ©  ®  ©  Copyright (_"> I96S by Charles thcrci,' by nny prwess without  D. Spiclb'T^rr. [{"production of thin test or any written p.-rinisvirr. of t'nr Publisher is prohibited.  portion  ©  240  APPENDIX H  T a b l e s of C o r r e l a t i o n  Coefficients  241  ft".  TABLE  I :i y<  17  v.. INTERCORRELATION  1  Vatiabie  2  3 '  5  6  MATRIX  FOR  7  8  COMBINE'D  GROUPS  10  9  11  If  i  1. 2. 3. 4. 5. 6.  Posttest T o t a l E r r o r s - Main L e s s o n T o t a l Responses - Main L e s s o n P r o p o r t i o n o f E r r o r s - Main L e s s o n T o t a l C o r r e c t - Main L e s s o n Do you u n d e r s t a n d ? - Main L e s s o n  7. 3. 9. 10. 11. 12. 13.  Time to Answer (7) Above - Main L e s s o n Had L i m i t S s c t i o n - Main L e s s o n Average F i r s t Latency - Main Lesson A v e r a g e T o t a l L a t e n c y - Main L e s s o n Enjoyment - M a m L e s s o n p r e l e s s o n score p r e l e s s o n C o r r e c t on F i t s t T r y  14. 15. 16.  A v e r a g e F i r s t '.atvncy - P r e l e s s o n Average T o t a l Latency - Prelesson. Math A b i l i t y - F i r s t T e s t i n g  17. 18. 19. 20. 21.  F u l l A-Siate - f i r s t Testing A-Trait - First Testing S h o r t /.-State - F i r s t T e s t i n g A- S t a t e - P r e l e s s o n A - S t a t e - Main L e s s o n  1.00 -.42* -.33* -.42* .46* .13 -.12 -.24 -.12 -.lb .21 .27* .21 - .2?  -.30*  .41* .08  .13  .01 .07 -.29*  1.00 . 96* . 95* -.78* -.26* .08 .26* .00 .33* -.17 -.34* -.31* .05 . 17 -.27* -.10 -.08 -.07 -.13 .31*  'V' -162!'  1.00  . 38*  ,i*2Q* Li' it ,\ 5P'„  -.23  -.32*  ri, •  -.06 f /  i'mk  -.06 -.21 .10  .3.1*U i, V ..3.5*  -,Z6*"r  -.26*|  f  -.02 .11 ' <  it  -.21 t p -|y3>i*.' -.14 f*  !  fj  -.10 -.13-i') -.:.o  1  ;'  .'34*  .48* .42* -.19 - .28* . 30*  - . 04 ' .03 -.0.8 .17 -.28*  1.00 -.56* -.10 -.01 .12 -.04 .26* .23 - . 05 .01 .20 -.02 -.06.02 .03 -.13  V  t, 1. 00 .20 .23 .09 .13 - .10 -.03  1.00 . 10  . 09 - . 06 -.17 - . 18  t —  .13  - . 04  1  .00  -.05 .09  •19  >  - . 32* -.04  -'• IV  -.08 -.06  1.00 .81* .06 .14 . 53* . 49*  -.04 -.04 - .21 - .20 -.10  .03 -.07  -.39*  -.07 -.07 .,04 •' - .2C* j .10. ;  .01  .25 i s s i g n i f i c a n t  ..  .  15  16  17  18  19  20  21  tj„  ( I  .o)  ^  !  '<>• i  re  \\>';<;; 1.00 .02 .07 .16 .49* .50*  v  _.  * jr|  14 '/.',  .  <..  1.C0 .24 .2 6* .09 .00 .19 .16 .03 .03 -. 17 -.35*  |  .  .  1. 00  '.[oq  4.01 ' >..ii i  .00<' . ool-  •:.b4 ! " * ..C6 1  - , ; i i ' • , -. 0l • . 03> ;  V  02  .'./.•fv-'k  ^  & i. t h e o ( = .05 l e v - j l  •/vl  *' L >  1;00 ' .'87*  .  1.00 . 94* -.38* -.03 .00 .09 -.11 .00  1.00 -.47* -.04 ~. 02 .11 -. 08 . 06  1.00 • .05 -.01 .07 •12 J8  1.00 -.05 .09 -.05 . 11  1.00 •  .33* -.20 .41"  1.00 -.08 .31'*  1.00 -.12  1 ;  1.00-  TA3LE 18 COMPARISON OF SELECTED CORRELATION COEFFICIENTS FOR T, T T  C o r r e l a t i o n Between V a r i a b l e s  P o s t t e s t and P r o p o r t i o n of E r r o r s P o s t t e s t and T o t a l Correct-main P o s t t e s t and Prelesson Scc?:e P o s t t e s t and Prelesson Latency P o s t t e s t and Math A b i l i t y P o s t t e s t and A-State-main P r o p o r t i o n of E r r o r s and Response to "Do you understand?" P r o p o r t i o n o f E r r o r s and L i m i t Section P r o p o r t i o n of E r r o r s and T o t a l Latency-main P r o p o r t i o n of E r r o r s and P r e l e s s o n Score P r o p o r t i o n of E r r o r s and Math A b i l i t y P r o p o r t i o n of E r r o r s and A-State PraJesson Score and Response • to "Do you understand?" T o t a l Lacency-main and T o t a l Laten';y-prelesson Moth A b i l i t y and T o t a l Latency-mai.-. A-Stace P r e l e s s o n and Total. Latency-main Enjoyuuent and P r e l e s s o n Score Enjoyment and A-State-main A-State-main and Math A b i l i t y A - T r a i t and A-State-main A - S t e t e Short (Day 1) and A-State-main  Pooled  T  l  T  2  Aobs  1  3.87  -.42 .46 .27 -.30 . 41 -.29  -.48 .64 .39 -.51 .71 -.14  -.50 .56 .30 -.30 .26 -.53  -.03 -.07 .09 .19 .36 -.12  5. 32 4. 05 2.54  -.29 .33 .35 -.37 -.31 .34-  -.40 .03 .30 - .29 - .35 .32  -.27 .55 .38 -.44 -.39 .33  -.37 .12 .39 -.49 -.27 .36  .23 3.62 .13 .59 .18 .03  . 12 .41 - .24 -.34 .49 -.45 -.11 .24 .35  .62 .41 -.45 -.50 .28 -.01 -.12 .46 .09  .16 .62 -.44 . 05 -.05 -.57 -.34 .4.3 .40  4. 11 1. 14 .68 3.37 3 . 1.2 3. 97 .68 .89 • 1.1J  .26 . 50 -.39 ' -.28 .24 -.35 -.18 .41 ' .31  7.22* . 97  1  + "y~ ^ obs > T n i  c  w a i  v /-,\ = 5.99 i s s i g n i f i c a n t a t the / - .05 l e v e l A. (2 ) n c <; c A i n u l a t e d r s i n a a F o r t r a n computer pro.grair w r i t t e n by the author.  

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