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Computer-paced versus self-paced arithmetic drill-and-practice Dyck, Anthony Carey 1971

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COMPUTER-P&CED ARITHMETIC  VERSUS  SELF-PACED  DRILL—AND—PRACTICE  by  ANTHONY CAREY B.  Sc.,  University  A THESIS  of  SUBMITTED  British  IN PARTIAL  MASTER  in  DYCK  OF  the  Columbia,  FULFILLMENT  1969  OF  ARTS  Department of  Education  We a c c e p t required  this  thesis  as  conforming  to  standard  THE U N I V E R S I T Y  OF  JUNE,  BRITISH 1971  COLUMBIA  the  In p r e s e n t i n g an  this  thesis  advanced degree at  the  Library  I further for  shall  agree  scholarly  by  his  of  this  written  the  in p a r t i a l  fulfilment of  University  of  make i t f r e e l y  that permission  p u r p o s e s may  representatives.  be  available  granted  gain  permission.  Department  Date  Q.^^  AH/-?  Columbia  /  for  for extensive by  the  It i s understood  thesis for financial  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a  British  shall  requirements  Columbia,  Head o f my  be  I agree  r e f e r e n c e and copying of  that  not  the  that  study.  this  thesis  Department  copying or  for  or  publication  allowed without  my  An very  a n a l y s i s of the l i t e r a t u r e  little  should  agreement  branch  together  a  with  arithmetic teaching  on  student the  has shown of concepts,  s t u d e n t s working  that  that  program  determined  where  the  of  the  length a  follow  questions.  evaluation  f i e l d of effective  to i n v e s t i g a t e  whether  would  do  t o be where t h e computer be  branched  to  SELF-PACED was d e f i n e d t o when t h e y  by p u s h i n g  were  one o f  presented the  two  terminal.  was done by c o m p a r i n g  COMPUTER-PACED  This,  o r a SELF-PACED program.  was d e f i n e d  k e y s on t h e c o m p u t e r  The  program  questions  the  drill-and-practice  s t u d e n t s determined  more o r l e s s d i f f i c u l t marked  should  in  is  program  program.  when t h e s t u d e n t s s h o u l d  more o r l a s s d i f f i c u l t be  CAI  research  drill  on a r i t h m e t i c  COMPUTER-PACED  a  l e d the author  b e t t e r on a COMPUTER—PACED  there  when and how a computer through  fact  showed t h a t  the achievement  and t h e SELF-PACED g r o u p s .  For the  o f the s t u d y t h e two g r o u p s o f grade s i x s t u d e n t s had  daily  arithmetic  computer  terminal  lesson  followed  by  a  session  at  a  t o work on a r i t h m e t i c d r i l l - a n d - p r a c t i c e  programs.  The pre-test  as  significant Further  r e s u l t s of the p o s t - t e s t a  covariate)  (adjusted  showed  that  by there  using was  a no  d i f f e r e n c e between t h e two s e l e c t i o n mechanisms.  analysis  showed  that  there  was  no  significant  difference that  there  between  the  males  was no s i g n i f i c a n t  and f e m a l e s  performance  interaction  (sex  X  and  groups)  effect. The  results  o f the s t u d y i n d i c a t e  with a r i t h m e t i c  drill-and—practice,  if  program c o n t r o l s  t h e computer  would level  i f the students c o n t r o l of d i f f i c u l t y .  that  students  when  to  when  will branch  when t o b r a n c h  working  do a s as  well they  to a different  Chapter  I.  Page  THE PROBLEM  ,  INTRODUCTION  1  STATEMENT OF THE PROBLEM II.  ....  4  REVIEW OF THE PERTINENT LITERATURE AND THE DEFINITIONS OF TERMS  5  INTRODUCTION  5  DRILL IN ARITHMETIC  5  DECISION STRUCTURES  7  DEFINITIONS  -.11  HYPOTHESES  III.  1  13  Hypothesis 1  13  Hypothesis 2.  13  Hypothesis 3.  13  EXPERIMENTAL DESIGN  15  INTRODUCTION  15  PILOT STUDY  15  FORMATION  OF GROUPS  .......  17  MATERIAL  18  Levels  18  Computer Terminals  19  Test  19  Chapter  IV.  Page PROCEDURE  19  STATISTICAL ANALYSIS  23  Data  23  Design  24  ANALYSIS OF RESULTS  25  TESTING OF HYPOTHESES  25  Hypothesis 1.  26  Hypothesis 2.  27  Hypothesis 3.  27  INTERPRETAION OF RESULTS ............  .... 27  ANALYSIS OF ADDITIONAL DATA V.  CONCLUSION  28  AND SUGGESTIONS FOR  FURTHER RESEARCH  31  SUMMARY  ....  31  DISCUSSION  32  LIMITATIONS OF THE STUDY  33  SUGGESTIONS FOR FURTHER RESEARCH  34  BIBLIOGRAPHY APPENDIXES .......  36 .  .  41  A.  LEVELS  41  B.  EASIER LEVELS  46  C.  TEST..  48  D.  SAMPLE PRINTOUTS  52  E.  ANALYSIS OF A STUDENT'S WORK  55  F.  EXPERIMENTAL DATA  57  L I S T OF TABLES  Table  Page  1.  THE NUMBER OF SUBJECTS IN THE TWO FACTOR  2.  ANALYSIS  OF VARIANCE  3.  ADJUSTED  EXPECTED  TABLE  MEANS  ,  DESIGN .  . 24 25 26  THE PROBLEM  INTRODUCTION A  modern  approach  c h a r a c t e r i z e d by meaningful the  development  concepts,  teaching  arithmetic i s  drill-and-practice  of a r i t h m e t i c concepts.  presents the student the  to  with a c t i v i t i e s  drill-and-practice  and  along  with  a f t e r the teacher illustrations  on  i s given t o r e i n f o r c e the  f a c t s and p r o c e s s e s . The furnishing and the  task  meaningful  checking  understanding teacher.  of  of  is  adequately  to the i n d i v i d u a l  results  diagnose  beyond  time  check  to  the  in  of  the  task  of  responses,  and  identify  quickly.  Drill-and-practice, instruction  interaction  weaknesses  limitations  well  needs,  I t can present the e x e r c i s e s s u i t e d to  the a b i l i t y of the student,  assisted  to  The computer lends i t s e l f  weaknesses very  concepts,  d r i l l suited  often  drill-and-practice.  developing  (CAI),  the  simplest  i s the  form of computer  type  that i s o f i n t e r e s t i n t h i s study.  the computer i s t o provide r e g u l a r review  and  of  computer  The r o l e of practice  to  supplement types of  the  CAI.  complex  established curriculum. The  level  tutorial  of  computer program. The  third  computer c a r r i e s third  level  work  of  the  were t a k i n g  J e r m a n , and In  Brian  1969-70  arithmetic programs.  programs may  be  and  more  the  student  program a c t s a s  the  tutor.  student.  the The  stages.  programs school  in  in  in  over the  details the  pioneered arithmetic  year  lessons More  found  and  where  headed by S u p p e s h a s  drill-and-practice By  second  the d i a l o g u e system  i n the p l a n n i n g  group  other  between  computer is  two  i s the  on a c o n v e r s a t i o n w i t h  drill-and-practice Stanford  the  CAI  Stanford  fundamentals. students  of  is still  The the  interaction Here  type  system  There are  8,000  Stanford about  book  by  the  Suppes,  (42) .  Stanford's  program,  drill-and-practice  programs,  determines  when  the  difficulty  to t h e  the  student  like  teacher moves  from  most or  the one  other program  level  of  next.  At t h e p r e s e n t t i m e we a r e moving the students up and down the l e v e l s o f d i f f i c u l t y on t h e b a s i s o f t h e p r e v i o u s days's performance. I f more t h a n 80 per cent of the e x e r c i s e s a r e c o r r e c t , t h e s t u d e n t moves up one l e v e l , u n l e s s he i s a l r e a d y a t t h e top l e v e l . If less than 60 per cent of the e x e r c i s e s are c o r r e c t , the s t u d e n t moves down a l e v e l , u n l e s s he i s a l r e a d y a t the bottom. If his percentage of c o r r e c t answers f a l l s between 60 per c e n t and 80 per c e n t he s t a y s a t the same level. I t s h o u l d be e m p h a s i z e d t h a t the selection of e x a c t l y f i v e l e v e l s and o f t h e p e r c e n t a g e s 60 and 80 has no firm theoretical basis but is based on p r a c t i c a l - p e d a g o g i c a l judgments. As s y s t e m a t i c d a t a a r e accumulated, we e x p e c t t o modify our choices in the l i g h t o f e x p e r i e n c e ( Suppes. 41:15).  Gentile research that  said  i n the area  are  using  branching  from  research  in  that o f CAI  CAI  p o i n t e d out i n Chapter  of  Most  decide  to t h e  area  i s a great  (15:24).  to-day  one l e v e l the  there  on  next,  how  support and  funds  courses  decision  can  be  the in  questions  stated  than  now  appropriate student  for  decide  student?  made  i s who  learns.  little  no  As i s  agreement  in  a l l CAI  following  i n a simple  the  theoretical levels  a CAI  possible  80  per c e n t of  program. CAI  has  been  the c o m p u t e r .  decide  the  The b i g  or m a t e r i a l  e d u c a t i o n a l needs.  some e d u c a t o r  for  the u s e o f c o m p u t e r s  what i n s t r u c t i o n  the student's  basis  As  b a s i s c a n be made f o r  for by  making  of d i f f i c u l t y i f  o r more t h a n  a theoretical  through  most  o b j e c t i v e manner.  Hopefully, with  decides  or d o e s  of  v i a CAI.  s t r u c t u r e i f the d e c i s i o n  justification  individualization question  capable  per cent  correct.  major  or  stated that p r a c t i c a l l y  to d i f f e r e n t  60  the s t u d e n t s  The  little  for  s t r u c t u r e s t o use.  he has no f i r m  r e s e a r c h on l e a r n i n g ,  branching  the  making  the s t u d e n t s  he a n s w e r s l e s s  people  criterion  r e s e a r c h on l e a r n i n g  is  o u t by S u p p e s ,  branching  the  the development of systems, equipment,  computer  complicated  pointed  go i n t o  and not i n t o  The  criteria  (15:23-24)  a  the student  t h e r e s e a r c h s t u d i e s on what d e c i s i o n  Gentile  of  with  II there i s very  need f o r more  is  Does t h e  what i s b e s t f o r  Because of the many f a c t o r s t h a t i n f l u e n c e a  person  such  as age l e v e l , a b i l i t y l e v e l , a t t e n t i o n span, a t t i t u d e ,  sex,  anxiety,  individual  etc.  until  differences  more  research  (ID), p o s s i b l y  have c o n t r o l of the path taken through  is  done  the student  on  should  a CAI course.  Because there are no t h e o r e t i c a l grounds on when the program should branch structures  a student, r e s e a r c h on d e c i s i o n  has only s t a r t e d , a student,  and t h e r e are so  factors  that  influence  test  to see i f the s t u d e n t should c o n t r o l the branching  one  level  of  i t i s the concern  many  making  difficulty  t o another  of t h i s study to from  when working on a CAI  program.  STATEMENT OF THE PROBLEM  The the f o l l o w i n g the  level  present i n v e s t i g a t i o n attempts  q u e s t i o n : Do students who  of  difficulty  in a  have  learning  to answer  control  over  sequence achieve  h i g h e r scores than s t u d e n t s who do not have c o n t r o l over the level  of  difficulty  when  working formal  an  drill-and-practice  program?  hypotheses  a t the end of Chapter I I .  i s stated  A  on  statement  arithmetic of the  REVIEW OF THE PERTINENT LITERATURE THE  AND  DEFINITION OF TERMS  INTRODUCTION The f o l l o w i n g review of the  research  investigated. as  used  of  is  applicable  to  the  summarizes  problem  I t i s important to note that the  at which the frames  Programmed I n s t r u c t i o n . the  literature  being  term  PACED  i n COMPUTER—PACED and SELF-PACED does not r e f e r to  the speed in  that  the  LEVELS  questions  of  or m a t e r i a l are  not  as  PACED here r e f e r s t o the c h o i c e  difficulty  presented  presented  or  on how  the  difficulty  of  the  much time a student has to  answer a q u e s t i o n or frame.  DRILL IN ARITHMETIC Many people are s t i l l use  of  drill  confused with r e s p e c t  i n the classroom to-day.  When commenting  r e a d i n e s s f o r d i v i s i o n Brownell  (5) s t a t e d that i f  find  many  the  topics  inadequate  mastery  Jerman  (23)  difficult, of the s k i l l s  and  to  times basic  it  is  facts  the on  children due  to  needed.  c i t e d a study by Anaspaugh i n which 93 percent  of  the e r r o r s  made i n  long  common f r a c t i o n s i n g r a d e s m a s t e r y o f number  grade day  by  and  the d r i l l  three  percent  19.3  percent  and  52.5  of by  items  by  must  an  Their study  by  The the  the  up  and  most  widely  and  as  has  had  Stanford  programs.  As  solution  drill  the i n s t r u c t o r  that only  learned to obtain  that d r i l l  are  can  be of  most  typical  introduced  used  of  pointed  any  out  and  no c o n t r o l o v e r  In  the  of  student  the I, is  on t h e b a s i s o f  Stanford  whether they  programs  i n Chapter  programs t h e  LEVELS o f d i f f i c u l t y  arithmetic  that  teacher.  and  difficulty.  each  guessing,  They c o n c l u d e d  the concepts  known  down t h e  after  two  Stanford arithmetic drill-and-practice  t h e LEVELS o f the  that  indirect  drill,  the s t u d e n t  p r e v i o u s day's performance.  students  dangers of  were o b t a i n e d by  precede  l a c k of  minutes of d r i l l  by  in  processes. the  i n g r a d e one  the Stanford d r i l l — a n d — p r a c t i c e  moved  number  They f o u n d  percent  and  t o the  t o overcome a l a r g e p e r c e n t a g e  the classroom  drill-and—practice in  the  five  p o i n t e d out  in arithmetic a f t e r  discussed  are  procedure  used  18.7  decimals  6 were due  immediate r e c a l l .  the  errors  taught  of  pointed out  responses  reinforces  effectively  (6)  were g i v e n  counting,  teaching  answer.  and  method a l o n e .  the  percent  effective  Chazel  students  f o r a month on  15.4  4,5  f a c t s r a t h e r than  Brownell teaching  division  case  the  moved up o r down  I t i s assumed, i n  programs  like  drill-and-practice  programs,  that  knows what i s b e s t  f o r the  student.  The teaching  studies  should  be  have d e f i n i t e l y presenting  cited  followed  shown  drill  that  to  the  and  summarizing  teacher.  How  the  will  be  branched  the  used  through  Machines use  developed  past  organize  it its  or  must  tutor.  i f  have t h e a b i l i t y  a student  he  learns  machine s h o u l d and  system  take  of  If this  If  d e e p e r and presenting  machine fuller a  to  in  the  decision  the  student  process  Teaching.  system  that  among He  i s to  to students  can  various  attempted  t o be s i m i l a r  and  to  to  t h a t of  be  useful  to  improve  experience.  s l o w and  quickly  these them  needs  than  by b r a n c h i n g material.  give  student  many v i s u a l  others, the  characteristics  in  student  the s t u d e n t  through  It i s possible  subject  for  students  matter  with a l e s s r i g o r o u s  aids  teaching  the  t h e more i n t e l l i g e n t  p r e s e n t a t i o n of the  slower  for  the  how  deciding  so as  t o adapt  more a p p r o p r i a t e b l o c k s o f teaching  is  checking  course?"  decision  more  advantage of  work  the m a t e r i a l .  i s very  detect  "what  as  of  STRUCTURES  process  e f f e c t i v e n e s s with  students'  others  capable  well  model f o r a d e c i s i o n  presentations  private  as  is  i n A D e c i s i o n S t r u c t u r e For  a  his decision  effective  S u p p e s and  computer  is;  a CAI  inputs t o the  alternate  a  (35)  drill.  that  that determines  DECISION S m a l l wood  by the  question  t h a t i s t o be  suggest  students,  responses  structure  above  a a  while  treatment  of t h e  same m a t e r i a l . Smallwood  should  be  'learns'  capable  (36:2).  i n f o r m a t i o n t o r e - e s t i m a t e the  geometry  twenty  to  students. adapt  the  that  Smallwood had  d e c i s i o n s as  He  the  decision  parameters of the study  decision better  that  rule with  computer  He  or  the  his  and  i n making miniature  of  Technology  t h a t h i s model was  used  pointed out  one  as i t  by  taught  Institute  model  know i f t h e  model  caused  p a r a m e t e r s used  more d a t a  though  d i d not  his  as  machine  processes  are  in demonstrating  model.  even  he  the  rule  teaching  the computer c o l l e c t  Massachusetts  succeeded  good  i t s decision  effects  the branching  the  t h a t "a  of improving  more about t h e  decisions" use  p o i n t e d out  estimate  at the would  students  that did  to  did  end  of  adapt  the  learned  not a d a p t  any  to  past  information.  Stolurow instructional  has  been  closely  system,  SOCRATES,  Illinois.  Stolurow  associated that  University  Of  attempting  to c o n s t r u c t a d e c i s i o n  all  the p r e v i o u s  predict the  responses student  started  of  the  through  t o s o l v e the  the  course  t h e CAI of  i n order  and  course.  the  to o p t i m i z e  the  where  that,  given  the s t u d e n t ,  could  a CAI  course. was  appropriately  using a l l the  at  associates  program  The  another  designed  making s y s t e m  should s t a r t  student  b e s t way  about a student  his  i n f o r m a t i o n p o s s i b l e on  where t h e s t u d e n t  student  and  was  with  problem  Once  to adapt branch  of  to the  attempting  information available  the  teaching  strategy  used was  w i t h him working  i s very  with,  Stolurow  research  must  be  b e f o r e we  w i l l have a  Other discussed decision  short—term  satisfactory  reading  reading  (2:163).  Stolurow  Davis  of  and  individual  methods o f i n s t r u c t i o n in  a  variety  They f i n i s h e d  their  tremendous  aid  interactions  and  Two reviewed  and of  in  points  years  and  in  learning  interaction instruction  of ID and (PI)  course.  The  interest  tests.  relationship  concluded  in  method a  (ID)  and  research  reported  treatments  with  interactions  in  and  were  ID  a  ID-method  Harzocco  and  on  the  programmed mathematics  attitude,  no  (9)  individual  variables of  be  instruction.  remedial  t h a t the  methods.  will  research  i n CAI  still  variables  on  ID i n c l u d e d n u m e r o u s n e s s a b i l i t y ,  with the  are  of  t h a t CAI  college-level  They c o n c l u d e d  which  s e t t i n g s and  Denny  i f  studies  t h a t such  variables  "even  that i s optimal  research  empirical and  that  individualized  Davis,  some  elementary  be d e v i s e d  suggesting  conducting  later  for  out  were  worked on  reviewed  instructional  theory  differences  (38)  i n implementing  has  programs  differences  p a p e r by  more  strategies  Ha  curriculum  been a c h i e v e d  t h a t much  model.  (2:143-165).  in  Smallwood  of d e c i s i o n s t r u c t u r e s  optimization  Atkinson  a total  interaction  occur  p o i n t e d out  o p t i m i z a t i o n s t r a t e g i e s can  effective, not  problem t h a t  i n the area  Atkinson  children.  t o the  (37)  term  strategies  school  has  done  short  by  similar  had  value  and no in  prescribing It what  instructional should  be c l e a r  variables,  decison  a decision  student,  a g r e e m e n t on  t h e r e i s some agreement on  i ti s  impossible  to  decide  model t o c o n t r o l t h e i n s t r u c t i o n a l  Because of  is little  s h o u l d be i n c l u d e d i n a d e c i s i o n  Until  are important  making  that there  i f any,  making model f o r CAI. variables  treatments.  of  t h e l a c k o f agreement  making  assuming  model  his  the  better  internal  mental processes  can b e s t  select  author  what on  a  strategy.  as t o t h e make up suggests  self-awareness  that  of  a  a l l his  and i m m e d i a t e s t a t e s o f a w a r e n e s s ,  h i s own s t r a t e g y  for  acquiring  a  s e t of  concepts. Gay males w i l l difficulty controls  (14)  h a s done some r e s e a r c h t h a t s u g g e s t s  do b e t t e r i f t h e y while  the l e v e l  females  they  girls  achieved  that  they  memory  will  equations,  controlled  their  better results  were  retention.  do  of d i f f i c u l t y .  c o u r s e on p o l y n o m i a l when  have c o n t r o l o v e r  given  that  the l e v e l  of  b e t t e r i f t h e computer  Gay f o u n d  boys a c h i e v e d  that  in  better  a  results  own l e v e l o f d i f f i c u l t y when t h e number  a t any one LEVEL  of  was based  CAI  while  questions on  their  LEVELS: A s e r i e s of problems or types of q u e s t i o n s sequentially  according  to  the order  of  arranged  difficulty  as  determined by the author, other teachers, and the p r o f e s s o r s consulted.  See Appendix A f o r a l i s t i n g of  the 60  LEVELS  used.  PATH:  a r e c o r d of the branches t o EASIER LEVELS.  The f i r s t  time the student s i g n s onto the computer t e r m i n a l  h i s PATH  is an  null,  and i t w i l l stay n u l l  EASIER LEVEL.  until  the program branches to  For example i f the program branched to an  EASIER LEVEL, e.g. 34, from LEVEL v e c t o r of one element,38.  38  PATH  would  be the  Now i f the program branches again  to  an EASIER LEVEL, say 32, from LEVEL 34 PATH would now be  the  v e c t o r PATH=34,38.  HARDER  Now when the program branches  to a  LEVEL from LEVEL 32 the program w i l l branch to LEVEL  34 not the next LEVEL,33.  HARDER: a higher LEVEL. branch  to  the next  requested. obvious  In higher  There a r e two  in  most  cases  LEVEL  LEVEL  null  will  exceptions.  The  first  one i s  that i f the program i s a t LEVEL 60 and a HARDER  61  does  s t a y s a t LEVEL 60. the  program  whan a HARDER LEVEL i s  LEVEL i s requested the program cannot since  the  not e x i s t .  branch  to  LEVEL  61  In t h i s case the program  The other exception i s when PATH i s not  v e c t o r , the program has reached the c u r r e n t LEVEL  by branching to an EASIER LEVEL. the  program  vector  will  branch  I f PATH i s not  null  then  to the f i r s t element of the PATH  (see d e f i n i t i o n of PATH).  EASIER: a lower LEVEL of that operation  wherever  possible.  I f a student i s at an a d d i t i o n question then an EASIER would  ba  an  addition  There i s a l i s t LEVELS  in  question  of the EASIER  Appendix  B.  LEVEL  t h a t i s at a lower LEVEL.  LEVELS  used  for  a l l sixty  Note t h a t i n some cases the EASIER  LEVEL i s of a d i f f e r e n t o p e r a t i o n : the EASIER LEVEL f o r  the  lowest LEVEL of m u l t i p l i c a t i o n i s an a d d i t i o n LEVEL.  COMPUTER-PACED:  the  program  EASIER LEVEL  depending  student  answered  has  on  w i l l branch to a HARDER or an the  correctly  number at  of  questions  the  any g i v e n LEVEL.  The  frequency o r the number of q u e s t i o n s given at any one was  initialized  to  2.  LEVEL  The freguency would remain a t two  u n t i l the program branched to an EASIER LEVEL i n which  case  the  frequency would be i n c r e a s e d by two to a maximum of ten.  If  the  student  answered  more than one-half the questions  i n c o r r e c t l y at any given LEVEL then the program w i l l that to  the student does not understand  an EASIER LEVEL.  LEVEL  if  the  The program w i l l  number  assume  the concept and branch branch  to  a  HARDER  c o r r e c t i s greater than one-half the  freguency at any given LEVEL.  SELF-PACED: the student determines when he w i l l branch to  a  HABDEB  o r an EASIEB LEVEL.  question marked  he may push 'E»  given  the  YOU MAY  pushed  message  GO ON  answered  t h e key marked  f o r EASIEB  When t h e s t u d e n t  instead  of answering  key  the question.  'H* t h e  student  was  " I F YOU ANSWER THIS QUESTION CORRECTLY LEVEL)."  question correctly  HARDER LEVEL.  'H» f o r HABDER o r a  t h e key marked  (to t h e next  the  When t h e s t u d e n t i s p r e s e n t e d a  When t h e s t u d e n t answering  then  i f the  t h e computer  pushed  the guesticn  the  student  branched  key  marked  *E  1  instead  of  branched  to an EASIER LEVEL and p r e s e n t e d t h e s t u d e n t w i t h a  guestion  from  t h e EASIER  t h e program  to a  immediately  LEVEL.  HYPOTHESES  On  the b a s i s  o f the reviewed  expects the f o l l o w i n g  H1.  Students  who  difficulty scores the H2.  have  control  students  achieve  females  over  achieve  the  level  higher  of  post-test over  (group C) .  higher  when  author  who do n o t have c o n t r o l  of d i f f i c u l t y  will  the  t o be t r u e :  (group S) w i l l  than  level  Males  hypotheses  literature  post-test  working  scores  on  than  arithmetic  drill-and-practice. H3.  There groups  will  be  and  interaction  an  interaction  sex. that  The  will  effect  between  a u t h o r i s assuming  occur i s as f o l l o w s :  the  that the (1) t h e  males  in  post-test group group  the  SELF-PACED group  s c o r e s than  and will  (2)  the females  the  achieve  females  higher  the  same  marked  i n the  higher  SELF-PACED  i n t h e COMPUTER—PACED than  the  group.  more o p e r a t i o n a l t e r m s , t h e s t u d e n t s t h a t s t a y a t level  HARDER  of d i f f i c u l t y  o r EASIER w i l l  arithmetic  test  their  of d i f f i c u l t y .  level  achieve  post-test scores  m a l e s i n t h e COMPUTER-PACED In  will  than  (LEVEL)  achieve  students  that  until higher have  they  push  scores  a key on  no c o n t r o l  an over  EXPERIMENTAL  DESIGN  INTRODUCTION The that  i t  would  difficulty the  rationale  these students  students  tested  by  students  who  a  SELF-PACED  the s t u d e n t s  of q u e s t i o n s presented  freedom  than  allow  f o r having  freedom  comparing  would m a s t e r the  answering  questions  decision  when t o t r y a HARDER or an  other  LEVEL s h o u l d  group be  the  students  computer  material  of  two  had  groups  the  of  was of  material  control  EASIER  the  better  hypothesis  concerning  One  the  of  as a r e s u l t  The  performance  presented. of  group  the  was  i n selecting  t o them and  were COMPUTER-PACED,  program  over  the  L E V E L , and  program d e t e r m i n e d  when  for the  changed.  PILOT STUDY A pilot grade  study  six students.  were t o d e t e r m i n e  conducted  The  main o b j e c t i v e s o f  whether the  the i n s t r u c t i o n s  were  follow  any  without  was  clear  with  two  program  was  enough  for  difficulty,  and  above the  pilot  working the  five  average study  correctly,  students twenty  to  minute  s e s s i o n s on t h e d r i l l - a n d - p r a c t i c e The Of  two s t u d e n t s  British  Columbia  were b r o u g h t  to  work  programs f o r t h r e e h a l f - d a y s . was  the  same  teletypewriter computer  by  program  type  connected telephone  on The  as  used  to  the  lines.  the  in  minute  session.  The g i r l  SELF-PACED  Both  the  program  students  were  w h i l e t h e y were w o r k i n g a t t h e  and  they  some of  guestions  their  the  had f i n i s h e d  guestions u n t i l  one  student  student  except  360/67  working  on  took  his  encouraged computer  twenty to  Both s t u d e n t s  computer  watching  ask  terminal  s e s s i o n was f i n i s h e d -  the  the  first,  a t t h e t e r m i n a l but saved  their on  IBM  a  asked most While  t e r m i n a l the other  guestions  the other  o r t o engage i n student  working  t h e computer t e r m i n a l .  There pilot  were  study.  sessions the  was  turn.  was a b l e t o a s k t h e a u t h o r  other a c t i v i t i e s at  their  while working  study,  minute s e s s i o n  questions after  main  used  The two s t u d e n t s a l t e r n a t e d  had h e r t w e n t y  the  terminal  university's  COMPUTER—PACED t h e boy on  University  drill-and-practice  computer  terminal.  then  reasonable.  out to the  working a t the computer program  were  same  few t e c h n i c a l p r o b l e m s d u r i n g t h e  The c o m p u t e r s h u t  but  the author  point  interference  very  in  the  down onca d u r i n g  was a b l e t o r e s t a r t program.  on t h e t e l e p h o n e  lines but this  p r o b l e m s e v e n t h o u g h i n some c a s e s r e t y p e h i s answer.  There  one o f  the  the student at was  also  caused  the student  would  some  v e r y few have t o  The for  three  student LEVEL that  students days  reached  51.  for  a  total  An a n a l y s i s o f t h e  and  as  even when t h e y involved  understood  a result  and  that  five  twenty  amount o f time both  the concept  o f the p i l o t were c l e a r  involved.  study  minute  that  The a u t h o r  also  they  A school is  grade  class  i n Vancouver, B r i t i s h  situated  buildings. type  children  being  computation.  concluded  felt  presented.  felt  that  that  to  since  computation  The  the  students  twenty  stated  minute that  he  be i n c r e a s e d .  OF GROUPS was  selected  Columbia.  i n a lower—middle  t h e o l d homes a r e  the  six  LEVELS  be an a p p r o p r i a t e  per s e s s i o n should  FORMATION  mistakes  The  less  s e s s i o n s would  material  t h e l e n g t h of time  reached  enough f o r t h e s t u d e n t s  s e s s i o n s were not t o o l o n g and one s t u d e n t felt  One  indicated  the a u t h o r  were c h a n g e d t o i n v o l v e  f o r the  indicated  progress  t h e s t u d e n t s were making  t o understand.  some o f t h e LEVELS  students  so as t o n e c e s s i t a t e l e s s  the i n s t r u c t i o n s  follow  s i x s e s s i o n s each.  was i n v o l v e d i n some o f t h e h i g h e r  a result  were changed  As  of  t h e L E V E L 53 w h i l e t h e o t h e r s t u d e n t  t o o much c a l c u l a t i o n  LEVELS,  that  had two t w e n t y m i n u t e s e s s i o n s e a c h day  from  by  parochial  The s e l e c t e d  class district  replaced  a  school  where most o f  high-rise  apartment  The c l a s s c o u l d be c o n s i d e r e d r e p r e s e n t a t i v e f o r of  district  the  school  i n the school i s d e c l i n i n g  is every  i n . T h e number o f year  because  many  of  t h e new a p a r t m e n t  Canadian recent  buildings  Basic S k i l l s standardized  Test  will  In  test  not take c h i l d r e n .  Mathematics  that  these  was  the  students  test  was w r i t t e n i n the f o u r t h month o f t h e s i x t h  and  the  students  eight  month  with a range  eight  years four  The study. then  five  years  zero  groups  class  was  divided  into  to  four groups f o r t h i s  assigned  groups.  t o the  The  the ten g i r l s , SELF-PACED  girls  were  t o t h e COMPOTER-PACED and SELF-PACED random a s s i g n m e n t  fairly  months  months.  COMPOTER-PACED  The  year  equivalent of s i x years  The f o u r t e e n b o y s were s e p a r a t e d f r o m  assigned  to  from  t h e boys were r a n d o m l y  the  a grade  most  had t a k e n .  This  averaged  The  similarly  groups.  t o g r o u p s a i d e d i n making  equal b u t a p r e - t e s t  a d j u s t f o r any r e m a i n i n g  and  was used  the  as a c o v a r i a t e  differences.  MATERIAL  Levels The  two  COMPUTER-PACED, material  complete  both  consisting  operations  in  groups,  the  worked  SELF-PACED  on t h e same  of questions i n v o l v i n g  whole  numbers  list  of the s i x t y  p r o b l e m s used  can be found  the  LEVELS  i n A p p e n d i x A.  the  drill-and-practice  and i n d e c i m a l  different  and  four  basic  fractions. or  types  A of  Computer  TerminaIs Two  where the  teletypewriters  twenty f o u r  drill-and-practice connected Columbia  by IBM  was  plastic  The  lines  computer  The  i n the worked  school on  the  teletypewriters  to the U n i v e r s i t y  terminals  always used  by  t e r m i n a l was  ENTER and  these keys e a s i l y . keys  HARDER and  students  questions.  tape so t h a t  additional  six  installed  of  were  British  360/67 c o m p u t e r .  o t h e r computer group.  grade  telephone  Both terminal  were  were  the  same  t h e COMPUTER-PACED group a l w a y s used  by  the  the s t u d e n t s  would  be  SELF-PACED computer  marked  with  plastic  tape,  one  and  marked  able  with  to  find  t e r m i n a l had one  the  SELF—PACED  DECIMAL k e y s were c l e a r l y  The  but  marked  two  H for  t h e o t h e r marked E f o r EASIER .  Test All at  t h e s t u d e n t s were g i v e n a p r e - t e s t  C)  and  the end  as  a post-test.  of t h e The  s t u d y t h e y were g i v e n t h e  test  computer program g e n e r a t e  (see  was one  same  test  by  having  the  each  LEVEL.  contructed  q u e s t i o n from  Appendix  PROCEDURE All University university's  the students  i n the study  of  Columbia  British  Computing  Centre  and  were t a k e n  for to  a  tour see  out of  t h e IBM  to  the the  360/67  computer  so t h a t  computer  is,  such so  they  The s t u d e n t s  have  some  were g i v e n  a l l had some f a m i l i a r i t y terminals  their  told  study s t a r t e d  t h a t they  exercises  on  the students they  were  students all  before  would be computer  had been given  what  t h e IBM  360/67  a  pushing  computer  the  keys  on  using the terminals  on a F r i d a y whan t h e s t u d e n t s starting  to  the  after  their  opportunity  hour  to  were  arithmetic  ask  After  questions  t o complete the p r e — t e s t . they  were a s k e d  to  The do  A t the e n d o f t h e hour t h e t e s t s and a l l  were c o l l e c t e d .  on  do  t e r m i n a l s t h e f o l l o w i n g week.  were g i v e n e x t r a p a p e r where  papers  until  of  a c h a n c e t o p l a y games  they s t a r t e d  given  one  calculations.  results  with  idea  school. The  the  would  a s TICTACTOE and COINFLIP w i t h  computer at  they  test;  The s t u d e n t s  n o r were t h e y  were not g i v e n  given  their  tests  the back  t h e end o f t h e s t u d y .  The f o l l o w i n g Monday was t h e f i r s t  day t h a t  was a s c h o o l h o l i d a y so T u e s d a y  t h e s t u d e n t s worked  at  the  computer  terminals. The o n l y i n i t i a t i o n the  playing  university author  of  games  was t h e i r  e x p l a i n e d how  on  first  that the students the  computer  t w e n t y minute  to e n t e r  their  terminals.  None o f t h e s t u d e n t s  were h e l p e d  e n t e r i n g the f i r s t  had o t h e r  than  t e r m i n a l s a t the session  answers  when  on t h e c o m p u t e r  had any t r o u b l e a f t e r  two o r t h r e e  the  answers.  they  The HARDEE  SELF-PACED students were shown how  LEVEL  and  demonstrated  an  that  EASIER  they  were  e n t e r i n g t h e i r answers. three  3 was  not  This  having  usually  after any  took  they  difficulty  about  two  or  The  students might have needed a longer i n t r o d u c t i o n  if  the  beginning q u e s t i o n s had been more d i f f i c u l t  since  the  first  = ? ,  the  +  U  LEVEL only  contained difficulty  questions  like  with the f i r s t  LEVEL  g e t t i n g used t o the computer t e r m i n a l . For the length of t h i s study  thirty  minute  four  basic  fractions  the  The  l e s s o n s c o n s i s t e d of  operations which  in  included  drill-and-practice  whole all  program  classes.  blackboard  in  The  the  sixty  listed  the  drill-and—practice one  list The  'SELF-PACED' classroom. worked  students  order  that  a  numbers  in  t h e i r a r i t h m e t i c l e s s o n the students normal  author  taught  a r i t h m e t i c l e s s o n t o the students a t 9  every morning.  was  only  minutes.  period but  LEVEL  t o request a  review and  they  were were  in  the  A.  After  with  their  listed to  the  i n decimal  Appendix  names  A.M.  of  LEVELS  continued  a  on  the  have  their  s e s s i o n at the computer t e r m i n a l .  There  of names f o r each t e r m i n a l . two  t e r m i n a l s were marked  as were the two The  students  on  lists the  'COMPUTES-PACED•  on  the blackboard  SELF-PACED  list  i n the always  on the computer t e r m i n a l marked 'SELF-PACED* and  s t u d e n t s on the COMPUTER—PACED l i s t  always  worked  and  on  the the  terminal  marked  helpful  in  'COMPUTER-PACED',  that  the  terminal  to  program.  The v e r y  were w o r k i n g other  group  were b o t h  go  fact  experimental  on  the  then q u i e t l y  each  student  This turn.  Each  t h e same s u b j e c t e a c h day.  even  students  on  take so at  of  the  list  position  they i n the  have  been  t h e next for  was  list  to  stay  of  to  d i d not f i n i s h .  session  until  a l l the  miss  involved the  lunch  school  two  the  time  per  students  breaks.  The  i f a l l the  One s t u d e n t  o f t h e names on one l i s t  by  not be w o r k i n g  have  during  student  his  rotated  sudants  after  to f a l l  h i s lesson  day and t h u s  necessary  h i s t u r n i f i t happened the  finished  t h e i r r e c e s s and t h e i r  agreed a  that  should  continued  every  number  t e r m i n a l i t was  students  on a l i s t  process  in  through  t h e wrong  on the outcome b u t t h e y  day s o t h a t t h e s t u d e n t s would  Because  which  the s t u d e n t s  leave the classroom  t h e t e r m i n a l t h e same time  continue  from  knew  groups so t h e e f f e c t  at  computer  students  t e r m i n a l he would n o t i f y  had t h e i r  students  exactly  groups.  terminal.  students  knew  t o be v e r y  was e v e r g i v e n  may have had some e f f e c t  computer  who would  that the  on a d i f f e r e n t program  When t h e f i r s t the  soon  t o and no s t u d e n t  t h e same f o r both  on  students  T h i s proved  c o u l d not  lunch  had t o be  hour  altered  times.  The p.m.  last  student  finished  on Monday, t h e f i f t h  his  turn  at  about  3:10  s c h o o l day t h a t t h e s t u d e n t s h a d  been w o r k i n g students Eleven  were g i v e n calendar  wrote the the  a t the computer  student  students  The  the  hour  to  had  passed  same t e s t  only  would  had  the papers writing  days  test.  post—test  any  one  remember  no i d e a  test  test were  any  had  the t e s t  had  r e c o g n i z e d any  some o f t h e g u e s t i o n s he  written  was  sure that  the  the  i t was  The  used.  while  questions  between  to those  on  post-test  thought  only  t h e same  test  on  problems  the q u e s t i o n s .  b e f o r e and  All  and  the  t h a t they  that  children,  similar  of  and  unlikely  for calculations  written  one-fourth of the students s a i d  that  used  first  pre—test  would be  the  again.  questions.  a g r e a t number o f  the students i f they  the  the  with  a d m i n i s t r a t i o n s of  seen  of  discussed  test  extremely  ever  calculated  asked  as  None o f  the  were  used  were c o l l e c t e d .  had  After  was  the  s i n c e the s t u d e n t s  t h a t t h e same t e s t  students  test.  Tuesday morning  complete  b e c a u s e i t was  that the students  the  two  terminals.  one  the  the they  About  they  had  student  said  that  they  had  before.  STATISTICAL  ANALYSIS  Data For The  first  each  was  h i s s c o r e on  his  score  that  each s t u d e n t  in  Appendix  on  E.  of the  students the  t h e same t e s t achieved  two  scores  p r e — t e s t and  used  daily  were o b t a i n e d .  the  second  as a p o s t - t e s t . was  recorded.  The  was LEVEL  This data i s  THE NUMBER OF SUBJECTS IN THE TWO FACTOR DESIGN USED  N=7  N=5  N=7  N=5  i  In order t o make i t e a s i e r f o r l a b e l i n g t h e diagrams the  groups  were  labeled  as  M  (male),  F  (female),  S  (SELF-PACED), and C (COMPUTER—PACED) , A University  standard  analysis  of B r i t i s h Columbia  of  c o v a r i a n c e program  a t the  (BMDX64) was used to analyze  the data f o r t h i s two f a c t o r f i x e d design. An alpha l e v e l of 0.05 was s e l e c t e d . value  for F  with  The  critical  one and nineteen degrees of freedom f o r  t h i s alpha l e v e l i s 4.38.  ANALYSIS OF RESULTS  TESTING OF HYPOTHESES A summary using  of the a n a l y s i s of  the p r e — t e s t s c o r e s  following  the  as a c o v a r i a t e  post-test  scores  may be found i n the  table.  TABLE 2 ANALYSIS OF VARIANCE  SOURCE  SUM  MEAN GROUPS SEX GROUP X SEX COVS COV. 1 ERROR  OF SQUARES  158.38185 35.86396 67.08819 1.29 310 1252.86695 1252.86694 634.27590  Table 3 c o n t a i n s four scores  TABLE  D.F.  MEAN SQUARE  19  158. 381 85 3 5.863 95 67.08818 1.293 10 1252. 86694 1252. 86694 33. 3 82 93  the expected scores  c e l l s of two by two f a c t o r i a l were used as a c o v a r i a t e .  design  See  F  4.74440 1.07432 2.00965 0.03874 37.53015 37.53015  f o r each of the  when the p r e — t e s t  Appendix  F  f o r the  observed means f o r both the p r e - t e s t and the p o s t - t e s t . TABLE  3  ADJUSTED EXPECTED MEANS  M  F  i  1  S  |  46.83  |  49.74  |  48.29*  C  |  43.84  |  47.72  |  45.78*  45.34*  48. 73*  47.04**  * THE AVERAGE OF THE TWO MEANS ** THE EXPECTED GRAND MEAN  S.229.%.h§sis I  (H 1)  Since the F value of 1.07 was l e s s than t h e c r i t i c a l value  of  4.38  H1 was r e j e c t e d .  T h i s i n d i c a t e s t h a t there  was no s i g n i f i c a n t d i f f e r e n c e i n achievement scores  between  thoses  l e v e l of d i f f i c u l t y  students  (group.S)  who  post-test  had c o n t r o l over the  and those that  c o n t r o l over the l e v e l of d i f f i c u l t y  of  d i d not have  (group C ) .  Since t h e F v a l u e of 2.01 was l e s s than t h e c r i t i c a l value of 4.3 8 H2 was r e j e c t e d . significant between  difference  males  and  in  females  T h i s means that t h e r e was no  achievement when  of p o s t — t e s t scores  working  on  arithmetic  drill-and-practice.  I l f o t h e s i s 3 (H3) The  hypothesis  that  there  would be a s i g n i f i c a n t  i n t e r a c t i o n e f f e c t between groups and sex, H3, was because  rejected  the F value o f 0.04 i s l e s s than the c r i t i c a l  value  of 4,38.  INTERPRETATION OF RESULTS The expected v a l u e s i n TABLE students  on  Even  significantly to  indicate  that  the  t h e COMPUTER—PACED program s c o r e d higher than  those on the SELF-PACED higher.  3  though  program  though  the  females  not  significantly  d i d not  achieve  higher s c o r e s than the males i t i s i n t e r e s t i n g  note that the g i r l s  SELF-PACED groups  i n both the COMPUTER—PACED  and the  d i d b e t t e r on t h e p o s t — t e s t .  I t was expected that the females would do r e l a t i v e l y b e t t e r on the COMPUTER—PACED than the SELF-PACED program but it  was not expected t h a t the females would do b e t t e r on the  COMPUTER—PACED than the SELF-PACED program.  ANALYSIS OF ADDITIONAL DATA  LEVELS  The  students i n the SELF-PACED group achieved  on  the average  COMPUTER-PACED  group  Appendix  It  F).  SELF-PACED  than  every  day  appeared  students  d i d the s t u d e n t s  to  except take  on  some  higher  in  day  the  one (see  time  f o r the  to become f a m i l i a r with how t o ask f o r  q u e s t i o n s from HARDER o r EASIER LEVELS.  fairly  The LEVELS  achieved  well  the c r i t e r i o n  with  on  the  fifth  day  correlate  scores on t h e p o s t — t e s t .  T h i s was expected s i n c e the t e s t was c o n s t r u c t e d  by  taking  one question from each LEVEL. The  SELF-PACED  students answered approximately the  same number of q u e s t i o n s as d i d the COMPUTER—PACED group but the number of q u e s t i o n s that they varied  a  great  amount.  SELF-PACED would answer LEVELS  and  trivial. there did that  only  one  Some more  from  the  LEVELS  at  each  LEVEL  students from the on  that  the  they  T h i s was the behavior the author  difficult considered  hoped  f o r but  were about four students i n the SELF-PACED group that  just  the o p p o s i t e .  was  easy  When these students came t o a  they  LEVEL  f o r them they would stay on t h a t LEVEL f o r on  to  a  HARDER  LEVEL.  were presented a question from a LEVEL t h a t they  considered d i f f i c u l t else  of  questions  about t e n g u e s t i o n s b e f o r e moving When  answered  they  would request an EASIER  LEVEL  or  request a HARDER LEVEL and guess at the answer j u s t so  that they c o u l d get t o another LEVEL  that  they  considered  easy. Student one  o r two  other  had  time  students that  he  7  3  -  #15  quickly  ?,  then  from he  two  had  was  and  this  student, class  Other excitement  and  over the  the gain  averaged  able  the  second ahead  a n s w e r s on t h e  #15  for  guestions like  doing  the  where  provided  i s a very  only  one  slow  in  the  nothing  but  year.  there  was  toward  the  shown i n A p p e n d i x F marks  novelty  arithmetic,  computer t e r m i n a l s and  pressure  paper  He  i s the  As  the  to guestions  scrap  T h i s i s a g a i n o f 20  teacher  the  other  questions  day  shown  a gain of eight  the  The  with  work f o r him.  student  of  t o use  to s e e  classroom  t h e computer t e r m i n a l f o r  grade s i x next  i s because  different  at  exercises.  pre-test.  done.  thrilled  enthusiasm  drill-and-practice students  really  t o o much  than  back t o t h e  first  two.  after  repeat  h i s t u r n . . The  about doing  dreams a g r e a t d e a l and  that w i l l  from  he had  s t u d e n t s f o r c e d him  became day  him  exercises  to c a l c u l a t e the  given h i s printout  finished  exerted  LEVEL the  at his printout teased  days b u t  the o t h e r  was  much p a s t by  his printout  which i s LEVEL  #15  pressure  many q u e s t i o n s  looked  drill-and-practice first  student  brought  d i d and  Student  the  have v e n t u r e d  been f o r t h e  Each  a b o u t how  =  not  t e r m i n a l when he  student  bragged  would  i t not  students.  t h e computer  he  #15  on  the  per  cent.  effect  of  post-test Some of having  some b e c a u s e t h e y  some  because  the  they  a  were were  re-taught  the  material  s i m i l a r to those on the  ana test.  were  given  questions  to do  CONCLUSION AND SUGGESTIONS FOB FURTHER RESEARCH  SUMMARY T h i s study was designed t o determine whether o r not it  makes  any d i f f e r e n c e  i f the student c o n t r o l l e d  computer program branched to a d i f f e r e n t computer LEVEL. methods  program c o n t r o l l e d  of  the s e l e c t i o n  drill-and-practice, controls  students c o n t r o l  of d i f f e r e n t LEVELS.  that  to  when  working  branch  when to branch  difficulty.  Further  significant  difference  performance  and  that  (group X sex) e f f e c t .  i f the  between the  analysis between  to  as a  showed the  they  arithmetic  i f the computer would  different that males  two  The r e s u l t s  with  students w i l l do as well when  or  when i t branched t o a d i f f e r e n t  There was no s i g n i f i c a n t d i f f e r e n c e  of t h i s study i n d i c a t e  program  LEVEL  when the  level  there and  there was no s i g n i f i c a n t  i f the of  was no females  interaction  future  The  author of t h i s study  of  the  computer  in  is  the  arithmetic drill-and-practice.  getting  used  in  appendix  they had  very  to the computer t e r m i n a l s .  F,  or  the  The students seemed to enjoy  that one can summarize a student's shown  about  classroom e s p e c i a l l y f o r  working a t the computer terminals and trouble  optimistic  for  work the  for  little The  the  fact  day,  as  week or month and  see  e x a c t l y where the student i s having d i f f i c u l t y  is  the  computerized  most  important  aspect  of  probably  drill-and-practice. The r e s u l t t h a t the females not s i g n i f i c a n t l y  scored  higher,  though  higher, on both the COMPUTER—PACED and  SELF-PACED programs i s c o n t r a r y t o the r e s u l t s t h a t Gay found when he had s t u d e n t s working a t a CAI written  to  equations. been  teach  first  (14)  t u t o r i a l program  c o l l e g e students  polynomial  The reason f o r the d i f f e r e n t r e s u l t s could  because  than those i n "undoubtedly  the  instruction,  Gay's there  younger  another  have  s t u d e n t s i n t h i s study were much younger  the extent to which  (33:51).  year  the  study. will the  Silberman  be an age student  pointed  out  that  g r a d i e n t i n determining  should  control  his  own  c h i l d r e n w i l l r e g u i r e more s t r u c t u r e "  reason f o r  the  have been that the m a t e r i a l was  different  different.  results  could  LIMITATIONS OF THE STUDY The LEVELS.  students  They  finished  were  their  be t o l d  student  would  told  between  than  their  at  finished.  their LEVEL  author  of  each  they  t e r m i n a l they  would  and  60  F o r many  t o see i f they Some o f  before  the  was  a  students  five told  the  set  s e s s i o n s were that there  their  results  of  could reach a  the  the  had n o t been t o l d  session  This  the student, the  h i s own LEVEL.  friend.  were 60  after  asked.  I f t h e s t u d e n t s had not been  LEVELS and i f t h e y end  the  there  everyday  i f they  was a c o m p e t i t i o n  h i g h e r LEVEL goal  that  that  only  o n l y be t o l d  i t  a l l told  s e s s i o n a t t h e computer  thing  students  the  also  t h e LEVEL a c h i e v e d  personal  60  were  own  might  were  LEVEL have  at been  different. A grade selected  from  six  class  been  twenty  a parochial school.  may have been d i f f e r e n t had  of  selected.  four  students  The r e s u l t s  of the study  i f a large class i n a public The  students  that  was  school  attend p a r o c h i a l  s c h o o l s may n o t be r e p r e s e n t a t i v e o f a l l s t u d e n t s . The twenty  s u b j e c t s chosen  four students.  The c l a s s  always p l a y e d t o g e t h e r a group with in  more  experimental  were  a  interaction than  between  small  class  was v e r y c l o s e i n t h a t  a t r e c e s s , noons,  vey few o u t s i d e r s .  program  from  and a f t e r  i f the c l a s s  students were  they  s c h o o l as  T h i s c l o s e n e s s would the  of  result  about  the  not s o c l o s e .  The  decision  model used  number o f p o s s i b l e d e c i s i o n model the  was used  results  followed that  of  The s t u d e n t s  students  concepts  infinite  If a different  decision  different.  the  presented  teacher  were  was n o t r e a l l y  were n o t  new  or  concepts  achieved i n  concepts  by t h e d r i l l - a n d — p r a c t i c e  re-taught,  and t h e r e v i e w  teaching  had p r e v i o u s l y been t a u g h t  the m a t e r i a l covered  The  very  drill-and-parctice  the concepts  students. all  situation  by  models.  an  f o r t h e s t u d e n t s i n t h e COMPUTES—PAC ED g r o u p  may have been  The  i s o n l y one o f  given  to t h e how  t o do  programs.  a review  of,  the  was f o l l o w e d by d r i l l - a n d - p r a c t i c e .  SUGGESTIONS FOR FURTHER RESEARCH A study with  a  group.  different The s t u d y  the study study  should  be c o n d u c t e d  decision could  using  model  may show t h a t one d e c i s i o n  material  f o r t h e COMPUTER-PACED  have many d e c i s i o n  i n v o l v e d enough s t u d e n t s  t h e same  making m o d e l s  t o make more g r o u p s .  The  making model t h a t was  used  was s u p e r i o r t o t h e o t h e r s o r i t may show t h a t i t make little  difference  which d e c i s i o n  SELF-PACED g r o u p may a c h i e v e some o f t h e COMPUTER-PACED  Another conducted results six,  study  with s t u d e n t s may  and n i n e .  i f  very  making model i s u s e d .  higher  post-test  score  The than  groups.  similar over  be v e r y d i f f e r e n t  to many  this  study  grades.  f o r students  should  Possibly i n grade  be the  three,  T h e r e i s a need f o r more r e s e a r c h i n t o person  learns.  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"The Use of Computers I n Education," S c i e n t i f i c American^ 2.15, (19 66), 2 06-2 33.  42.  Suppes, P., M. Jerman, and D. B r i a n . Computer-Assisted I n s t r u c t i o n : Stanford's J 9 6 5 6 6 A r i t h m e t i c Program . New York: Academic Press, 1968. r  43.  Suppes, P., M. Jerman, and G. T. Groen. " A r i t h m e t i c Drills and Review on a Computer-Based T e l e t y p e , " A r i t h m e t i c Teacher, 1966. Pp. 303-308.  44.  Suppes, P., Solving 166,  E. on  F. L o f t u s , and M. Jerman. "Problema Computer-Based T e l e t y p e , " Science^  (1969) , 343-350.  45.  Swenson, E. "How to Teach f o r Memory and A p p l i c a t i o n , " Research i n the Three R_ls, eds. C. W. Hunnicutt and W. J . Iverson (New York: Harper, 1958).  46.  Thorndike, E. L. The Psychology York: Macmillan, 1922.  of  Arithmetic.  New  APPENDIX A  LEVELS  A,B AND 7 ABE WHOLE NUMBERS FOR LEVELS #1 TO #24 1  A + B= 7  4 + 2 = ?  0<A, B<10  2  A — B= 7  8 - 3 = ?  0<A, B<10; B<A  3  A + B=  12 + 46 = ?  10<A,B<100; NO CARRYING  4  A — B= 7  347 - 221 = ?  10<A,B<1000; NO BORROWING  5  A + B=  709 + 231 = ?  10<A,B<1000; CARRYING ON DIGIT 1  6  A — B= 7  870 - 454 = ?  100<A<1000 B<=A; BORROWING ON DIGIT 1  A + B = ?  61 + 146 = ?  10<A,B<1000; CARRYING ON DIGIT 2  745 - 684 = ?  100<A<1000; B<=A; BORROWING ON DIGIT 2  7  8  A  9  A + B = ?  9 8 + 665 = ?  10<A,B<1000; CARRYING ON DIGITS 1 AND 2  10  A — B = ?  910 + 641 = ?  100<A<1000; B<=A; BORROWING ON DIGITS 1&2  11  A X B =  7  3 X 4=  7  0<A, B<10  12  A X B  7  54 X 10  -  13  A X B =  7  12 X 27  14  A / B = ?  15  A /  16 17  —  B = ?  B =  =  7  0<A<100; B=10 OR 100  7  0<A, B< 100  7  72 / 8 =  0<B ? < 1 0 #  7  994 / 7  =  A / B  7  100 / 5  — 7  A +  7  B  751 + ? = 780  ONE OF #4,#6,#8,OR #10  18  7  +  A = B  ? + 38 = 379  ONE OF #4,#6,#8,OR #10  19  A  —7  902 - ? = 23  ONE OF #4,#6,#8,OR  •=  B  7  10<A<1000 A = 1 0 , 100,OR 1000  —A  =  B  7  7  -  B  14 X  20  7  21  A X  22  •>  23  A /  24  7  X A = B 7  =  B  / A = B  _  72 = 21  ONE OF #3,#5,#7,OR #9  ? = 84  10<A<99; 2<?<19  ? X 13 = 65  10<A<99; 2<?<19  156 / ? = 13  10<B<99; 2<?<19  ? / 12=6  REFER TO #13  A,B AND  7  ABE DECIMAL FRACTIONS UNLESS OTHEBWIS E SPECIFIED  25  +  B  A  -  7  0.3 + 0.4 = ?  0.0<A,B<1.0,1  DEC  PL;  NO CARRYING 26  A  —B  27  A  +  28  A  29  7  0.7 - 0.2 = ?  0.0<A,B<1.0,1 DEC PL; NO BORROWING  B =  7  2. 1 + 7. 8 = ?  1. 0<A, B<10.0, 1DEC PL; NO CARRYING  -  B  7  2.5 - 1.4 = ?  1.0<A B<10.0, 1DEC PL; NO BORROWING  A  +  B -  7  8.81 + 1.16 =  7  1.0<A,B<10.0,2 DEC PL; NO CARRYING  30  A  —B  7  8.88 - 3.62 =  7  1.0<A B< 10.0,2 DEC PL; NO BORROWING  31  A + B  7  0.7 + 0.02 =  7  0.0<A,B<1.0; A 1 DEC PL; B 2 DEC PL; NO CARRYING  32  A  —B — 7  0.5 - 0.34 =  7  0.0<A,B<1.0; A 1 DEC PL; B 2 DEC PL; NO BORROWING  33  A  +  B =  7  151. 48 + 833. 34  -  7  100<A,B<1000,2 DEC PL; CARRYING ON D1  34  A  -  B •=  7  772. 81 - 562. 77 =  7  100<A,B<1000,2 DEC PL; BORROWING ON D1  35  A + B =  7  4 + 8.2 = ?  A IS A WHOLE NUMBER; 1.0<B< 10.0,1 DEC PL  36  A  7  8 - 1.6 = ?  A IS A WHOLE NUMBER; 1.0<B<10.0,1 DEC PL  37  A + B  7  23.57 + 104.2=  -  B =  r  r  7  A HAS 2 OR 3 DEC PL; B HAS 1 DEC PL  38  A - B = ?  267.8 - 63.37 = ?  A HAS 1 DEC PL; B HAS 2 OR 3 DEC PL  39  A X B = ?  2 X 0.3 = ?  A IS A WHOLE # <10; 0. 0<E<0.7,1 DEC PL  40  A X B = ?  4 X 1.2 = ?  A IS A WHOLE # <10; 1.0<B<10.0,1 DEC PL  41  A X B = ?  46 X 4. 8 = ?  10<A IS A WHOLE #<100; 1.0<B<10.0,1 DEC PL  42  A / B = ?  62.4 / 2.6 = ?  10<? IS A WHOLE #<100; 1.0<B<10.0;  43  A / B = ?  34.8 / 0.29 = ?  100<? IS A WHOLE #<1000; A HAS 1 DEC PL; 0. 1<B<1.0,2 DEC PL  44  ? X A= B  ? X 0.4 = 2.4  ? IS A WHOLE #<10; 1.0<=A<=9.0,1 DEC PL  45  ? X A = B  ? X 1.6 = 36.8  10<? IS A WHOLE #<100; 1.0<A<2.0,1 DEC PL  46  A X ? = B  1.8 X ? = 111.6  10<? IS A WHOLE #<100; 1.0<A<2.0,1 DEC PL  47  A X B = ?  86.6 X 0.344 = ?  A=0. 1**N X T WHERE 10<T<1000,N=1,2, OR 3 B=0.1**N X T WHERE 10<T<1000,N=1,2, OR 3  48  A X B = ?  10 X 3.4 = ?  A=10 100, OR 1000; 1. 0<B< 100.0, 1 DEC PL  49  A X B = ?  0.01 X 3.41 = ?  A=0. 1,0.01, OR 0.001 ; B=0. 1**N X T WHERE 10<T<1000,N=1 OR 2  50  A X B = ?  7.62 X 0.01 = ?  B=0. 1, 0. 0 1,0.00 1 ; A=0, 1**S X T WHERE 10<T<1000,N=1 OR 2  51  A + ? = B  38.37 + ? = 892.7  REFER TO #38  52  ? + A = B  ? + 6.653 = 974.7  REFER TO #38  53  A - ? = B  896.3 - ? = 7.873  REFER TO #38  54  ? — A = B  ? - 4.2 = 1.6  ONE OF f27,#29,#31,OR #33  r  55  56  57  ? / A = B  ? / 2. 88 = 0.352  REFER TO #47  16.984 / 4.4 = ?  1.0<B<10.0, 1 DEC PL; ACB ?=0.1**N X T WHERE 10<T<1000, N=0 OR 1  1.8122 / 8. 2 = ?  1.0<B<10.0 1 DEC PL; A<B; ?=0.1**N X T WHERE 10<T<1000,N=3 OR 4  ? X 4.6 = 2. 1068  ONE OF #56 OR #57  A / B = ?  A / B = ?  f  58  ? X A = B  6.2 X ? = 3.9928  ONE OF #56 OR #57  59 60  A X ? = B A / ? =B  6.0918 / ? = 7. 1  ONE OF #56 OR #57  APPENDIX B EASIER LEVELS  A LISTING OF THE EASIEB LEVELS FOB EACH OF THE 60 LEVELS  LEVEL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  EASIER 1 2 1 2 3 4 5 6 7 8 9 11 11 13 14 15 10 10 10 9 15 21 15 13 1 2 25 26 27 28  LEVEL 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60  EASIEB 29 30 31 32 27 34 33 34 25 39 40 16 42 43 44 45 41 12 48 49 17 51 19 53 47 43 56 57 58 23  APPENDIX TEST  1.  8  +  9  = ?  2.  8  -  2  = ?  3.  41  4.  459  -  12  5.  706  +  246  = ?  6.  291  -  285  = ?  7.  371  +  458  = ?  8.  709  -  518  = ?  9.  293  +  628  = ?  68  = ?  10. 11.  +  57  815  -  = ? = ?  6 x 5 = ?  12.  59  x  100  13.  82  x  36  14.  24  /  3  15.  558  /  93  16.  100  /  4  = ?  17.  334  +  ?  =411  18.  ?  63  = 886  19.  512  ?  = 233  20.  ?  -  129  21.  25  x  ?  22.  ?  x  66  23.  468  24.  ?  25.  0.1  +  0.7  = ?  26.  0.9  -  0.1  = ?  27.  8.1  +  1.8  = ?  + -  / /  = ? = ?  = ? = ?  = 243  = 75 = 462  ?  = 26  79  = 97  28.  6.5  -  5.4  29.  1.11  30.  4. 76  31.  0.4  +  0.48  = ?  32.  0. 8  -  0.17  = ?  33.  1 11. 49  34.  778.56  35.  9  +  4.1  = ?  36.  9  -  4.6  = ?  37.  52. 92  +  411.2  = ?  38.  391. 9  -  17.38  = ?  39.  1  x  0. 1  = ?  40.  5  x  7.8  = ?  41.  83  42.  275.4  /  3.4  43.  210.8  /  0.62  +  = ?  8.83  -  4.55  +  = ?  786. 31  -  x  = ?  115.39  5.9  = ?  = ? = ? = ?  44.  ?  x  0.8  = 2.4  45.  ?  x  1.8  = 97.2  46.  1.3  47.  0.541  48.  1000  49.  0. 01  50.  7.52  51.  67. 94  52. 53.  ?  x  ?  892. 9  7.28 57.7  x x  +  =33.8  x x  = ?  = ? = ?  8.88  = ?  0.001  = ?  +  ?  7.587 -  ?  54.  ?  -  0.1  55.  ?  /  0.72  = 698.6 = 795.7 = 7.839 = 0.61 = 0.373  225. 05  /  0.22661 ?  x  3.1 129.6  3.5 /  4.3  2.1  x  ? /  •= ? = ?  = 0.8715 = 2.4397 ?  =1.5  APPENDIX D SAMPLE PRINTOUTS  SAMPLE OF A SELF-PACED PRINTOUT NOTE THE USE OF THE »H» ANS 'E« RESPONSE HI  GOOD LOCK IN YOOR WORK TO-DAY  PLEASE TYPE IN YOUR I.D. NOMBER #: 14 TYPE 1 IF YOUR NAME IS WENDY #: 1 GOOD NOW ON WITH TO-DAYS QUESTIONS 658.71 - 618.32 #: 40.39 JOLLY GOOD SHOW  = ?  OTHERWISE TYPE 0  ?=  (34)*  879.95 - 317. 18 = ? ?= #: H ANSWER THIS QUESTION CORRECTLY THEN YOU WILL GO ON #: 562.77 O.K.  (34)  3 + 3.2 = ? ?= #: H ANSWER THIS QUESTION CORRECTLY THEN YOU WILL GO ON #: 6.2 O.K.  (35)  9 3.3 = ? #: 12.3 TRY AGAIN 9 - 3.3 = ? #: 5.7 THAT IS CORRECT  (36)  ?= ?= WENDY  6 - 5.9 = ? ?= #: H ANSWER THIS QUESTION CORRECTLY THEN YOU WILL GO ON #: 0. 1 O.K.  (36)  •22.76 #:  (37)  152. 56 #:  + E  727. 1  + 41 1.37 563.93  GOODBYE FOR NOW,  *  = ? = ?  ?= ?=  SEE YOU AGAIN  (33) WENDY  THE NUMBER WITHIN THE PARENTHESES WERE ADDED LATER ONLY TO INDICATE THE LEVEL  SAMPLE OF A COMPUTER-PACED  PRINTOUT  NOTE THE 'TRY AGAIN' AND 'THE ANSWER IS 101.75' RESPONSES HI  GOOD LUCK IN YOUR WORK TO-DAY  PLEASE TYPE IN YOUR I.D. NUMBER #: 7 TYPE 1 IF YOUR NAME IS JOHN #: 1 GOOD NOW ON WITH TO-DAYS QUESTIONS 0.6 - 0. 15 #: 0.55 TRY AGAIN 0.6 - 0. 15 #: 0.45 THAT IS RIGHT  = ?  OTHERWISE TYPE 0  ?=  = ?  (32)  ?=  JOHN  356.09 + 423.81 #: 779. 90 GOOD WORK  = ?  ?=  232. 38 + 24 1.47 = ? #: 473. 85 GOOD NOW TRY THE NEXT ONE 879.94 - 778. 19 = ? #: 101.85 TRY AGAIN 879.94 - 778.19 = ? #: 100.85 THE ANSWER IS 101.75  (33)  ?=  (33)  ?=  (34)  ?=  0.9 - 0.85 = ? #: 0.05 CORRECT ANSWER  ?=  (32)  0.6 - 0.29 = ? #: 0.31 GREAT  ?=  (32)  996.91 - 231.32 #: 765.59 FANTASTIC JOHN GOODBYE FOR NOW,  = ?  ?=  SEE YOU AGAIN  (34)  JOHN  * THE NUMBERS WITHIN THE PARENTHESES WERE ADDED LATER ONLY TO INDICATE THE LEVEL  APPENDIX E ANALYSIS OF A STUDENT'S WORK  SAMPLE ANALYSIS OF A STUDENTS WORK FOR THE DAY ANALYSIS OF CORRECTLY SOLVED PROBLEMS FOR DARRELL I. D. NO,2 DATE JUNE 2, 1971 PROBLEM  RESPONSE TIME  483.07 + 212.77 — 7 + 7 514.09 2 84.71 + 7 121.25 553.28 + 161.56 737. 17 •= ? 7 214.08 + 552.52 + 7 1.092 815.7 = + 20.51 355.1 = 7 + 72.74 213.2 = 7 3. 384 + 256.4 = 7 772.3 — 51.41 = 7 693.7 — 5. 167 = 7 572.8 — 15.66 = 7 988.9 — 1.799 = 7 - 7 4 X 0.2 3 X 0. 6 = 7 1 X 0.5 - 7 4 X 0.2 - 7 7 8 X 8.7 7 X 4. 8 - 7 5 X 1.2 — 7 9 X 7.2 - 7 7 28 X 8.6 85 X 2. 7 = ? 7 8,4 22 X 87 X 7.6 - 7 1000 / 5 = ? MEDIAN RESPONSE TIME: =  =  =  =  =  48. 3 48.9 35.0 31.8 28.7 42.9 30.7 33. 2 38.2 54.0 43.9 4 1.4 34.4 7.9 8.2 7.6 6.7 52.9 23.4 15.8 13.6 53.9 29.6 3 1.7 64. 1 17.5 31.8 SECONDS  NO. OF TRIALS  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2  LEVEL  33 33 33 33 33 37 37 37 37 38 38 38 38 39 39 39 39 40 40 40 40 41 41 41 41 16  ANALYSIS OF UNSOLVED PROBLEMS: PROBLEM  426.23 + 233.38 = ? 77.4 / 1.8 = ? MEDIAN RESPONSE TIME:  RESPONSE TIME 66.1 11.3 11.3 SECONDS  ANSWER GIVEN 66000 37. 3  LEVEL  33 42  APPENDIX F EXPERIMENTAL DATA  SUMMARY OF THE LEVELS ACHIEVED AND THE TEST SCORES FOR THE COMPUTER-PACED GROUP  COMPUTER—PACED STUDENT NO. 1 2 3 4 5 6 7  MALES  LEVELS ACHIEVED ON DAY 4 1 3 5 2  PRE—TEST SCORE (A)  POST-TEST SCORE (B)  37 33 45 41 21 42 45  38 30 47 36 31 38 52  55 45 50 46 34 52 51  38.9  47.6  21 19 21 23 8 22 23  31 25 37 34 17 38 4 1  42 37 49 45 29 43 51  42 42 54 47 36 45 55  AVERAGES 19. 6 3 1.9 37.8 42. 3 45.9  COMPUTER—PACED STUDENT NO. 8 9 10 11 12  38 37 10 30 14  38 42 13 35 15  42 47 14 41 21  17 15 3 10 3 15 -1 8. '  FEMALES  LEVELS ACHIEVED ON DAY 4 1 3 2 5 24 27 10 20 17  B-A  43 52 19 43 28  AVERAGES 19. 6 25.8 28.6 33.2 37.0  PRE—TEST SCORE (A)  POST-TEST SCORE (B)  B-A  34 45 23 36 36  47 55 34 50 48  13 10 1 1 14 12  34. 8  46.8  12. '  SUMMARY OF THE LEVELS ACHIEVED AND THE TEST SCORES FOR THE SELF-PACED GROUP  SELF- PACED MALES STUDENT NO. 13 14 15 16 17 18 19 AVERAGES  LEVELS ACHIEVED ON DAY 3 4 1 2 5 6 13 2 8 11 14 15  15 29 12 13 23 25 34  23 37 14 23 35 33 44  39 44 20 31 42 40 57  46 53 30 37 46 48 60 +  9. 9 21.6 29.9 39.0 45.8  PRE—TEST SCORE (A)  POST-TEST SCORE (B)  37 40 24 37 36 41 47  39 53 16 47 44 47 55  2 13 -6 10 8 6 8  37.5  43.3  5. 9  PRE—TEST SCORE (A)  POST-TEST SCORE (B)  37 56 50 25 37  49 60 56 33 54  12 4 6 8 17  41.0  50.4  9.4  B-A  SELF- PACED FEMALES STUDENT NO. 20 21 22 23 24  LEVELS ACHIEVED ON DAY 1 3 4 2 5 15 11 15 7 22  29 40 33 16 37  37 57 45 24 45  43 60 + 59 29 57  53 6 0+ 60+ 33 60 +  AVERAGES 14. 0 31.0 41.6 59. 6 53.2  B-A  NOTE: 60+ INDICATES THAT THE STUDENT HAS REACHED LEVEL 60 AND HAS STARTED OVER AT LEVEL 25.  

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