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IQ, cognitive level, and related information processing variables as predictors of problem finding ability… Porath, Marion 1984

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IQ, COGNITIVE LEVEL, AND RELATED INFORMATION PROCESSING VARIABLES AS PREDICTORS OF PROBLEM FINDING A B I L I T Y IN INTELLECTUALLY GIFTED CHILDREN  by MARION PORATH B.  Ed., U n i v e r s i t y  Of B r i t i s h  A THESIS SUBMITTED  Columbia,  IN PARTIAL FULFILMENT OF  THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY  OF GRADUATE  D e p a r t m e n t Of  We  accept to  Education  this thesis  the r e q u i r e d  STUDIES  as c o n f o r m i n g S/tattdar^)  THE UNIVERSITY OF BRITISH COLUMBIA August  ©  1974  Marion  1984  Porath,  1984  In  presenting  requirements  this f o r an  Columbia,  I  available  for  permission  agree  or  her  of  Department  of  August  the  shall  reference  and  study.  I  extensive granted  by  my  written  copying the It for  Head of is  1984  this thesis my  Columbia  gain  the  of  British  it  freely  agree for  Department  understood  permission.  make  further  financial  Education  22,  of  of  University  Library  The U n i v e r s i t y of B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  Date:  fulfilment  the  this thesis  without  partial  advanced degree at  representatives.  publication allowed  be  in  that  for  p u r p o s e s may  thesis  that  that  scholarly  or  by  copying  shall  not  his or be  i i  Abstract This  study  cognitive  was  an  l e v e l , and  predictors  of  children. contribute  related  problem  It  was  the  to  in  importance  variable  of  insight  of  problem The  and  that  finding  sample  order  to  insight  g r o u p IQ  of  the  variables  cognitive selection  procedure  was  operations.  not to  finding,  maturity  a  information  by  IQ.  in  It  would  finding, processing  was  grades  ability  further prediction  five,  were i n c l u d e d  hypothesized  test  of  six, in  the  predictive  a problem  formal  to  to of  a  insight,  test  the  correlational  on  and  finding  reasoning,  and  the  criterion  the  predictor  IQ.  A  mediation  Backward  and  replacement-deletion of  analyses  insight  by  formal  supplemented  the  analysis. revealed  that of  cognitive  problem  " f l o o r e f f e c t " stemming the  model,  regressed  p r o c e d u r e s were u s e d .  Additional  results  regression was  level,  used  regression  due  problem  were a d m i n i s t e r e d  puzzles,  significant predictors be  of  as  gifted  level  the  the  linear multiple  problem  The  cognitive  children  varying  children  variable,  primary  intellectually  IQ,  test.  Using  stepwise  76  clarify  task,  set  of  variables  l e v e l w o u l d . m e d i a t e the  of  of  The  a  roles  insight.  Subjects  in  secondly  cognitive by  in  prediction by  the  processing  that  firstly  and  relationships.  a  the  sample c o n s i s t e d  seven.  ability  hypothesized  most  of  information  finding  followed  hypothesized  investigation  sample.  IQ  as  l e v e l and  finding. from  a predictor  insight  T h i s was  the of  low  were  thought cognitive  problem  finding  was  i n the expected  accounted  f o r was  Formal  finding  certain  of t h e  It by  was  in  t h e amount  from  Significant  to support that  their  variance  this  mediating  even b r i g h t  are  correlations  schemata and  ability  There  curriculum the  of  to mediate the p r e d i c t i o n  for  findings  to  find  implications  the g i f t e d  of t h e  two  study.  was  of  of  between  the  insight  effect.  children  for age-appropriate d e f i n i t i o n s  appropriate stemming  found  insight.  concluded  puzzles.  constraints  was  formal reasoning  appeared  maturation  insight  by  although  minimal.  reasoning  problem  processes  direction,  are  constrained  p r o b l e m s and inherent  in  of g i f t e d n e s s . another  solve these Age-  implication  iv  Table  of Contents  Abstract L i s t of Tables  i i viii  Chapter I INTRODUCTION  1  1 . STATEMENT OF THE PROBLEM  1  2. CONTEXT OF THE PROBLEM 2 2.1 Q u a n t i t a t i v e V s . Q u a l i t a t i v e D i f f e r e n c e s I n The I n f o r m a t i o n P r o c e s s i n g Of I n t e l l e c t u a l l y G i f t e d Children 3 2.2 P r o b l e m F i n d i n g As A P o s s i b l e Q u a l i t a t i v e l y D i f f e r e n t C o g n i t i v e A t t r i b u t e Of I n t e l l e c t u a l l y Gifted Children 3 2.3 C o g n i t i v e L e v e l As A V a r i a b l e R e l a t i n g To P r o b l e m Finding 4 2.4 I n f o r m a t i o n P r o c e s s i n g V a r i a b l e s R e l a t i n g To P r o b l e m Finding 4 2.5 I n s i g h t As A N o n e n t r e n c h e d Measure Of I n t e l l e c t u a l Giftedness 5 3. SUMMARY OF THE PROBLEM  6  4. J U S T I F I C A T I O N OF THE STUDY  6  5. ORGANIZATION OF THE STUDY  7  6. DEFINITION OF THE VARIABLES 6.1 C r i t e r i o n And P r e d i c t o r V a r i a b l e s 6.2 P r o b l e m F i n d i n g And Terms A s s o c i a t e d W i t h P r o b l e m Finding 6.2.1 P r o b l e m F i n d i n g 6.2.2 E l e m e n t s N e c e s s a r y F o r An O p e r a t i o n a l D e f i n i t i o n Of P r o b l e m F i n d i n g 6.3 Terms A s s o c i a t e d W i t h C o g n i t i v e L e v e l 6.3.1 O p e r a t i o n a l L e v e l 6.3.2 C o n c r e t e O p e r a t i o n a l L e v e l 6.3.3 F o r m a l O p e r a t i o n a l L e v e l 6.3.4 C o g n i t i v e M a t u r i t y 6.3.5 H o r i z o n t a l D e c a l a g e 6.4 Terms A s s o c i a t e d W i t h The R e l a t e d Information Processing Variables 6.4.1 S e l e c t i v e E n c o d i n g 6.4.2 S e l e c t i v e C o m b i n a t i o n 6.4.3 S e l e c t i v e C o m p a r i s o n  7 7  10 10 10 10  7. SUMMARY OF CHAPTER ONE  11  7 7 8 8 8 8 9 9 9  V  Chapter II A REVIEW OF THE LITERATURE  12  1. OVERVIEW OF THE CHAPTER  12  2.  INFORMATION  PROCESSING IN INTELLECTUALLY GIFTED CHILDREN 12 2.1 The I n t e l l e c t u a l l y G i f t e d As Q u a n t i t a t i v e l y D i f f e r e n t Information Processors 12 2.2 The I n t e l l e c t u a l l y G i f t e d As Q u a l i t a t i v e l y D i f f e r e n t Information Processors 14  3. PROBLEM FINDING IN INTELLECTUALLY GIFTED CHILDREN 3.1 The I m p o r t a n c e Of P r o b l e m F i n d i n g And I t s L i n k To G i f t e d Performance 3.2 The Need F o r R e s e a r c h I n t o P r o b l e m F i n d i n g 3.3 I n t e l l i g e n c e And P r o b l e m F i n d i n g 3.4 A F o r m a l S t a t e m e n t Of The F i r s t H y p o t h e s i s  15  4. COGNITIVE LEVEL AND PROBLEM FINDING 4.1 The Need F o r A D e v e l o p m e n t a l F o c u s To D e s c r i p t i o n s Of G i f t e d n e s s 4.2 The P i a g e t i a n P e r s p e c t i v e On G i f t e d n e s s 4.2.1 I n t r a - s t a g e P r e c o c i t y 4.2.2 M a t u r a t i o n a l C o n s t r a i n t s On The G i f t e d ' s A c q u i s i t i o n Of F o r m a l O p e r a t i o n s 4.3 A P i a g e t i a n P e r s p e c t i v e On P r o b l e m F i n d i n g 4.4 A F o r m a l S t a t e m e n t Of The S e c o n d H y p o t h e s i s  18  5.  15 16 17 18  18 19 19 20 23 24  INSIGHT AND PROBLEM FINDING 24 5.1 I n s i g h t As A Component Of I n t e l l e c t u a l G i f t e d n e s s .24 5.2 The R e l a t i o n s h i p Of I n s i g h t To P r o b l e m F i n d i n g ....27 5.3 I n s i g h t As A N o n e n t r e n c h e d M e a s u r e Of I n t e l l e c t u a l Giftedness 28 5.4 C o g n i t i v e L e v e l As A F a c t o r I n I n s i g h t 30 5.5 F o r m a l S t a t e m e n t s Of The T h i r d And F o u r t h H y p o t h e s e s 31 5.6 O r d e r Of E n t r y Of The P r e d i c t o r V a r i a b l e s I n t o The Regression Equation 32 5.7 A F o r m a l S t a t e m e n t Of The F i f t h H y p o t h e s i s 32  6. SUMMARY OF THE F I V E HYPOTHESES  33  Chapter I I I METHOD  34  1. OVERVIEW OF THE CHAPTER  34  2. POPULATION  34  3. SAMPLE  35  4. PROCEDURES 4.1 The P r o b l e m F i n d i n g Task  36 36  vi  4.1.1 Task D e s c r i p t i o n 4.1.2 C l a s s i f i c a t i o n Of The Q u e s t i o n s R a i s e d 4.1.3 S c o r i n g 4.2 P i a g e t i a n A s s e s s m e n t 4.2.1 T e s t D e s c r i p t i o n 4.2.2 T e s t A d m i n i s t r a t i o n 4.2.3 S c o r i n g 4.3 Measurement Of I n s i g h t 4.3.1 I n s i g h t P u z z l e s 4.3.2 A d m i n i s t r a t i o n And S c o r i n g 4.4 Measurement Of IQ  36 36 38 39 39 40 40 41 41 42 42  5. DESIGN  43  6. THE ANALYSIS OF THE DATA 6.1 The L i n e a r M u l t i p l e R e g r e s s i o n Model 6.2 A s s u m p t i o n s U n d e r l y i n g The L i n e a r R e g r e s s i o n  43 44  6.3 Methods Of A n a l y s i s 6.3.1 T e s t Of The F u l l M o d e l 6.3.2 S e l e c t i o n And E s t i m a t i o n Of The R e g r e s s i o n Parameters 6.3.3 C r o s s - v a l i d a t i o n 6.3.4 T e s t Of The M e d i a t i o n Of I n s i g h t By F o r m a l Ope r a t i o n s , 6.3.5 S u p p l e m e n t a r y A n a l y s e s 6.4 Methods Of R e p o r t i n g The D a t a 7. SUMMARY OF CHAPTER THREE  Model 44 45 45 45 46 47 ,,....47 48 ...48  C h a p t e r IV RESULTS OF THE ANALYSIS  49  1. OVERVIEW OF THE CHAPTER  49  2. SUMMARY STATISTICS 2.1 P r o b l e m F i n d i n g 2.2 C o g n i t i v e L e v e l 2.3 I n s i g h t 2.4 The IQ Measure 3. APPROPRIATENESS OF THE LINEAR REGRESSION MODEL  49 50 50 51 52 53  4. RESULTS OF THE REGRESSION ANALYSIS 4.1 T e s t Of The F u l l M o d e l 4.2 Backward E l i m i n a t i o n 4.3 S h r i n k a g e 4.4 T e s t Of The M e d i a t i o n Of I n s i g h t Operations  53 54 55 56 By F o r m a l 56  5. RESULTS OF THE SUPPLEMENTARY ANALYSES 57 5.1 The R e l a t i o n s h i p Of P r o b l e m F i n d i n g Q u a l i t y To The T h r e e P r o c e s s e s Of I n s i g h t 57 5.2 The R e l a t i o n s h i p Between The T h r e e P r o c e s s e s Of  Insight  And The F o r m a l R e a s o n i n g  Schemata  5.3 C o r r e l a t i o n s Among The V a r i a b l e s  58 61  6. QUALITATIVE ANALYSIS  62  7. SUMMARY OF CHAPTER FOUR  65  Chapter V DISCUSSION AND CONCLUSIONS  67  1. OVERVIEW OF THE CHAPTER  67  2. LIMITATIONS OF THE STUDY  68  3. DISCUSSION OF THE RESULTS 68 3.1 C o g n i t i v e L e v e l As A P r e d i c t o r Of P r o b l e m F i n d i n g .69 3.2 I n s i g h t As A P r e d i c t o r Of P r o b l e m F i n d i n g 69 3.3 IQ As A P r e d i c t o r Of P r o b l e m F i n d i n g 70 3.4 F u r t h e r D i s c u s s i o n Of The S u p p l e m e n t a r y A n a l y s i s ..71 4. CONCLUSIONS. 72 5. IMPLICATIONS 73 5.1 D e f i n i t i o n Of G i f t e d n e s s 73 5.2 E d u c a t i o n a l I m p l i c a t i o n s 75 5.2.1 A g e - a p p r o p r i a t e n e s s Of C u r r i c u l u m F o r The G i f t e d 75 5.2.2 I n s t r u c t i o n a l I n t e r v e n t i o n And F o r m a l R e a s o n i n g .76 5.2.3 I n s t r u c t i o n a l I n t e r v e n t i o n And I n s i g h t 76 5.2.4 I n s t r u c t i o n a l I n t e r v e n t i o n And P r o b l e m F i n d i n g ..77 5.2.5 D i r e c t i o n s F o r R e s e a r c h 78 6. SUMMARY OF CHAPTER 5  79  BIBLIOGRAPHY  80  APPENDIX A - DATA USED IN THE REGRESSION ANALYSES  85  APPENDIX B - DATA USED IN THE SUPPLEMENTARY ANALYSIS  87  APPENDIX C - ARLIN PROBLEM FINDING TASK  89  APPENDIX D - SAMPLE PAGE FROM THE ARLIN TEST OF FORMAL REASONING  91  APPENDIX E - THE INSIGHT PUZZLES  92  vi i i  List  I. II.  of T a b l e s  The p r o c e s s e s o f i n s i g h t and c o m p o n e n t i a l thought t o r e l a t e t o each p r o c e s s Hypothesized r e l a t i o n s h i p s problem f i n d i n g a b i l i t y  26  skills  with 28  III.  The i n t e l l e c t u a l  IV.  Cognitive  V.  D i s t r i b u t i o n o f IQ s c o r e s a s compared w i t h t h e n o r m a l distribution 52  VI.  Analysis  VII.  Summary  VIII.  C o r r e l a t i o n matrix of problem three processes of i n s i g h t  IX.  C o r r e l a t i o n matrix of the three processes w i t h t h e f o r m a l r e a s o n i n g schemata  X.  level  product  of i n s i g h t  skills  categories  36  distribution  51  of v a r i a n c e table  Correlations variables  54  o f backward e l i m i n a t i o n  procedure  ....55  f i n d i n g q u a l i t y with the 57  among t h e p r e d i c t o r  of i n s i g h t 60  and c r i t e r i o n 61  ix  Acknowledgement  The Dr.  author  w i s h e s t o a c k n o w l e d g e the  Patricia Arlin  to  guidance  influenced  of  Dr.  Walter Boldt  and  Dr.  also  Stanley  gratefully  principal,  the  completion  e a c h s t a g e of  Blank  in helping i n the  teachers,  and  children  of  t h i s t h e s i s . Her  t h i s s t u d y . The to plan  careful  acknowledged.  significant contribution  the  reading  Additional who  the  thanks  participated  superb  contributions  regression of  of  analysis  thesis  are  go  the  i n the  to  study.  1  I. 1.  in  STATEMENT OF  THE  PROBLEM  Defining  and  identifying  psychology  and  education.  giftedness,  definition  implicitly,  i n terms of  are  seen as  test.  There  gifted have  think been  ability  to  Hildreth,  exists,  think  1966;  question  of  and  the  and 1973;  1970),  the of  with  issues  intellectual  intellectually  from t h e  are  belief  as  that  possessing  of  thinking  Ehrlich,  the  terms  1976)  yet  research  has  flexibility and  with  the 1982;  logical  addressed  differentiation  t h e s e v a r i a b l e s between the  They  Ehrlich,  or not  IQ  cognitive  1970),  1983;  Newland,  d e g r e e of' c o g n i t i v e  1970),  Rice,  1977;  an  intellectually  differential  (Clark,  they  different.  (Rice,  1982;  in that  measured by  qualitatively  as  norm  gifted  as  the  defined  intellectually  gifted  norm.  The actual  The  "intelligence"  in abstract  Kaplan,  (Rice,  terms  1983;  long-debated  dealing  IQ.  a l s o , the  fluency  (Clark,  systems  in  a high  i n ways t h a t  are  most commonly, e i t h e r e x p l i c i t l y or  amount of  s u c h as  thinking  When  is  characterized  attributes  giftedness  quantitatively different  possess a greater  of  INTRODUCTION  lack  of  information  differences  the  norm  has  in thinking been n o t e d  Robinson, Roedell,  emphasizes  that:  a v a i l a b l e concerning  the  issue  between the  intellectually  (Alvino,  Getzels  & Jackson,  1981;  1979).  Sternberg  &  of  gifted Dillon, (1981a)  2  Attempts to understand intellectual giftedness must go beyond merely characterizing t h e a t t r i b u t e s of t h e g i f t e d ... to identifying the underlying differences i n mental s t r u c t u r e s , contents, and p r o c e s s e s t h a t d i f f e r e n t i a t e t h e g i f t e d from t h e i r u n g i f t e d p e e r s . (p.86) Additionally, patterns and  for information abstract  "early"  is  as  1983,  Are these  "early  thinking  sensing  (Clark,  defined.  such  processing:  terms,  generalizations"  all  descriptions  differential  in alternatives  consequences,  p.199)  fail  to  making  address  how  d e s c r i p t i o n s c h a r a c t e r i s t i c of  age l e v e l s ? A further c r i t i c i s m  i s that  characterizing  t e r m s o f a t t r i b u t e s has l a c k e d a t h e o r e t i c a l  giftedness  perspective  in  (Carter  & Kontos,1982). This  study  investigating  of  2.  theory  Robert  perspectives as  gifted  issues  information,and  Sternberg  w e l l , the c o n t e x t u a l  (1980,  raised  above  d i f f e r e n c e i n the  the  by u t i l i z i n g  as a  of q u a l i t a t i v e  of  information  1981a).  by  way  perspectives  and t h e c o m p o n e n t i a l  and t h e n o t i o n  These  Piagetian processing theoretical  difference  provided,  s t r u c t u r e of the problem.  CONTEXT OF THE PROBLEM Discussion  issues  of  of  problem  qualitatively the  process  f o r the i n v e s t i g a t i o n the  developmental theory  the  a possible qualitative  intellectually framework  addressed  the  finding  different  hypothesized  context as  of the problem d e a l s a  information  relationships  of  possible  manifestation  processing IQ,  with the of  i n the g i f t e d ,  cognitive  level,  and  3  insight  to  problem  m e a s u r e s of  Vs.  Qualitative Differences  Of I n t e l l e c t u a l l y  Is a b r i g h t c h i l d (Robinson,  1980),  progressing difference thinking  at  the  different  way?  of  is a  ability  this  w h i c h may  the Or  intellectually  been  hypothesis  way  in  in  1983).  focusing  exist  think  the  & but  quality  hypothesized  1982, by  same  gifted  difference  has  Jackson,  does t h e r e  - a distinction  Davidson,  gifted  c h i l d r e n and on  r e l a t e t o and/or a f f e c t  2.2 P r o b l e m F i n d i n g Cognitive  a of  in a  gifted's  (Sternberg,  This  research  on p r o b l e m f i n d i n g  from many  ill-defined as  the  to deal  ability  Gifted  - the d i s c o v e r y problems  equally  discovery  cognitive to find  processes problems.  As A P o s s i b l e Q u a l i t a t i v e l y D i f f e r e n t  finding  recognized  the  the a b i l i t y  A t t r i b u t e Of I n t e l l e c t u a l l y  Problem  1982;  Roedell,  child  as a p o s s i b l e d i s t i n g u i s h i n g c o g n i t i v e c h a r a c t e r i s t i c of  intellectually  to great  &  1979;  rate?  qualitative  information  Sternberg  investigated  processes  Information  t o an a v e r a g e o l d e r  basically  accelerated  that  there  processing 1981a;  an  in  In The  Children  equal  Jackson,  thinking  such  fundamentally That  &  i n thought -  Gifted  mentally  Roedell,  Robinson,  entrenched  intelligence.  2.1 Q u a n t i t a t i v e Processing  f i n d i n g , and n o n e n t r e n c h e d v s .  with  presented  and t h e  o f many g e n e r a l  (Mackworth,  important  Children  1965)  -  questions has  t o , i f n o t more v a l u a b l e  been than,  p r o b l e m s , and h a s been l i n k e d  advancement  E i n s t e i n & I n f e l d , 1938; G e t z e l s  of  knowledge  (Dillon,  & Csikszentmihalyi,  1975;  4  Mackworth,  1965;  Wertheimer,  p r o b l e m s has  been c a l l e d  (Getzels  Dillon,  &  problem  finding  ability  1965)  measured by  IQ  additional  factors  possibly  m e d i a t e d by  2.3  Cognitive  affect  has  not  the  formal  operational  thinking  problem  f i n d i n g q u a l i t y and.  on  problem  necessary (Arlin, already  not  posed, level  Sternberg  what  (p.52).  1977,  on  and  difference  set  They b e l i e v e  that  problems,  level  Finding  of  the  child  (1975-76)  found  correlated  (1977), level  developmental  with  found on  a  problem  constraints  operational  thinking  a  problem  in  b).  To  the  questions  of  the  e f f e c t of  press  question  finding  ability. Relating  (1983), the  the  be  for  "exceptional  apart  Problem  study  formal  Variables  in  there  condition  finding  Davidson  To  Arlin  i s added t h e  Processing  Might  operational  with  1982;  i n t e l l i g e n c e as  significantly  t h e n , be  1984  problem  propose that  truly  and  sufficient  therefore,  Information  gifted,  age  finding ability,  but  qualitative  of  gifted"  schemes?  Relating  later  truly  in discovering  ability. t o be  discover  (Dillon,  does  developmental  in a  T h e r e may,  1975-76,  cognitive 2.4  effect  quality.  How  to  i n t e l l i g e n c e to  suggested  operational  A Variable  suggests that  the  finding ability?  formal  finding  finding  been  which a f f e c t s k i l l  As  ability  r e l a t i o n s h i p of  articulated.  problem  significant  A  p r e d i c t problem  Level  Research may  but  The  s i g n a l mark of  1973).  Mackworth,  as  "the  1945).  in  thinking  To  Problem  hypothesizing  of  the  insight involves  gifted three  a  intellectually  insight a b i l i t i e s  intellectually  Finding  seem from  to  be  others"  separate  but  5  related  psychological  combination, (1983)  and  and  important  of  major  always  that  inventions,  parallel  the  discovery  and  the  may  research  problem.  Insight  relate  As  of  and  to  the  and  problem  new  understandings  (p.52)  seems  finding ability  knowledge  three  discoveries,  s i m i l a r works - a l m o s t  insights"  of  Davidson's exceptional  significant  problem  advancement That  together  new  intellectual  association  Mackworth,1965).  2.5  and  and  and  scientific  philosophical,  major  Sternberg  "significant  - f o r example, m a j o r  literary,  involve  s e l e c t i v e encoding, s e l e c t i v e  s e l e c t i v e comparison.  statement  accomplishments  processes:  (Arlin,  processes finding  to  of  forms  to  great  1975-76;  insight part  taken  of  the  A N o n e n t r e n c h e d Measure Of I n t e l l e c t u a l  Gi ftedness Sternberg p e r f o r m a n c e on measure  of  for  most  the  (1981b,  nonentrenched,  intellectual part,  insight  ability,  a better  predictor  hypothesized intellectually by  the  reference  or  giftedness  than  gifted?  (Inhelder  that  IQ  of  of  tasks  than  t e s t s which  or  IQ  A d d i t i o n a l l y , might  & Piaget,  of  1958)?  or  of  better include, Might  i n t e l l i g e n c e , be ability,  the  attribute  of  i n s i g h t be  mediated  operational two  a  tasks.  finding  cognitive  coordination  is  familiar,  problem  c e r t a i n formal  measurement  novel,  a n o n e n t r e n c h e d measure of  distinctive  and  believes  entrenched,  as  presence  combinations  1982b)  schemes,  more  the  namely  systems  of  6  3.  SUMMARY OF THE PROBLEM This  study  possible  investigated  differential  gifted  children  relate  t o problem  What  is  the  relative  finding  ability? level.  problem of  the c o g n i t i v e It  importance  processing  intellectually  p r o c e s s e s which  addressed  the  o f IQ, c o g n i t i v e  variables  The s t u d y was aimed The age range was  f i n d i n g as a  in  problem:  l e v e l , and  predicting  at children  may  problem  a t t h e upper  10-14 y e a r s .  J U S T I F I C A T I O N OF THE STUDY Focusing  gifted  to  on an a b i l i t y  i.e.  problem  articulating  information Inclusion  possible  of c o g n i t i v e  level  t h e o r e t i c a l l y based,  inclusion  to  lead  of i n t e l l e c t u a l  (Kerlinger,  problems  giftedness.  1979).  for  of g i f t e d n e s s ,  are  a beginning in  gifted  s p e a k i n g t o t h e need  a  the  children. of  age-  The s t u d y theoretical  and f i n a l l y , t h e  r e f l e c t s the  closer  in  a t t r i b u t e of t h e  to s p e c i f i c a t i o n  independent v a r i a b l e s  "multivariable  ... r e a l i t y "  may  factor  differences  intellectually  investigations  of m u l t i p l e  cognitive  underlying of  definitions  perspective  crucial  f i n d i n g , may h e l p t o p r o v i d e  processing  appropriate  that  t h o u g h t t o be a  p e r f o r m a n c e and a d i f f e r e n t i a l  gifted,  is  in  attribute  finding a b i l i t y .  information  4.  cognitive  and examined  related  elementary  skill  to  belief  psychological  7  5.  ORGANIZATION OF THE STUDY  Chapter problem. study.  One  presents  Chapter  Two  the  rationale  and  F o u r and F i v e discussion  data  deal  of  analysis  with  the  the  research  reviews the l i t e r a t u r e , p e r t i n e n t  Chapter Three o u t l i n e s the  procedure,  for  the  methods,  used  and  design,  i n the r e s e a r c h .  results  results,  subjects,  of  the  Chapters  data  conclusions  to the  analysis,  and i m p l i c a t i o n s  drawn from t h e s t u d y .  6.  DEFINITION OF THE VARIABLES  6.1 C r i t e r i o n The  criterion  predictor in  terms  of  the  6.2 P r o b l e m  and  processes  Finding  Problem  is  variable i s  of  finding level,and  selective  And Terms A s s o c i a t e d  finding i s defined  from many  insight  encoding,  The  defined  selective  With Problem  as the d i s c o v e r y  ill-defined  unknown i n t h e p r o b l e m f o r s o l u t i o n , there  problems  situation,  formulation, be d i s c o v e r e d  Finding  solving  i n terms  situation. i s generally  the  problem  does  (Getzels  general  1965).  o f what  is  In t h e p r e s e n t a t i o n  It  known of a  a known f o r m u l a t i o n ,  not  method of s o l u t i o n , o r s o l u t i o n . and p o s e d  o f many  (Mackworth,  known method o f s o l u t i o n , and a known s o l u t i o n . problem  ability.  Finding  d i s t i n g u i s h e d from p r o b l e m  problem  problem  and s e l e c t i v e c o m p a r i s o n .  Problem  questions  Variables  v a r i a b l e s a r e IQ, c o g n i t i v e  combination,  6.2.1  And P r e d i c t o r  In a  yet  discovered  have  a known  The p r o b l e m  & Csikszentmihalyi,  a  1975).  must  8  6.2.2  Elements Necessary For  Problem  Operational  D e f i n i t i o n Of  Finding  Arlin (1965)  An  (1975-76) s t a t e d  definition  definition  of  that  an  3)  a  necessary  for  an  Mackworth's operational  situation;  opportunity way  latter  are  e l e m e n t s b a s e d on  problem f i n d i n g :  1) a p r o b l e m a t i c 2)  three  of  for subjects  to  c a t e g o r i z i n g the  i s necessary  to  raise questions;  questions  s i n g l e out  the  and  once r a i s e d .  general  The  question,  (p.100) Further task,  d e s c r i p t i o n of  d i r e c t i o n s to  the  questions  6.3  Terms A s s o c i a t e d  6.3.1  the  term  child  subjects,  r e f e r s t o the  categorizing i s found  problem f i n d i n g and  i n the  scoring  third  of  chapter.  Level  level  Piaget's  of  c o g n i t i v e development  genetic  approach  to  of  cognition  1964).  this  level  approximately), knowledge  i . e . the  Level  Concrete Operational At  and  With C o g n i t i v e  i n t e r m s of  (Inhelder, 6.3.2  subjects,  r a i s e d by  Operational This  these elements,  the  of  is  developed  and  conservation  c o g n i t i v e development  child's  is oriented  immediate p r e s e n t  Level  towards c o n c r e t e  (Flavell,  which of  structuring  1963).  An  i s bound t o t h e physical  and  things  (ages 7 t o  organization and  elementary  events form of  classification,  properties.  11-14,  in  of the  logic  seriation,  9  6.3.3  Formal O p e r a t i o n a l The  by of  formal  Level  stage of c o g n i t i v e development  hypotheticodeductive  thought  h y p o t h e s e s and d e d u c t i o n  with  the thought p.25)  of  formal  operational  ideas,to  of p o s s i b l e  bound t o t h e " c o n c r e t e  1964,  and  (Inhelder,  the previous, thinker  think  concrete  i s able  to  is  characterized  1964).  The  forming  consequences  contrasts  h e r e and now"  (Inhelder,  operational manipulate  i n terms o f t h e p o s s i b l e  stage.  The  propositions  and n o t s i m p l y  the  actual. 6.3.4  Cognitive Cognitive  that  most  Maturity maturity  of  "cognitively operational  the  formal  mature"  in  this  operational  subject  is  thus  study  as  evidence  schemata a r e i n u s e . one  who  is  a  A  formal  thinker.  6.3.5 H o r i z o n t a l Horizontal an  i s defined  operational  Decalage decalage  level.  r e f e r s t o the mastery  Flavell's  (1963)  of tasks  description  within  serves  to  clar i fy: A cognitive structure, characteristic of that level, can first be successfully applied t o t a s k X b u t n o t t o t a s k Y; a y e a r or so l a t e r ... t h e same organization of operations c a n now be e x t e n d e d t o Y a s w e l l as X. Moreover, the developmental process whereby Y comes t o be m a s t e r e d ... is essentially the same as that which c h a r a c t e r i z e d t h e m a s t e r y of X. (p.22) As  an  example,  typically  achieved  Flavell earlier  notes than  that  invariance  invariance  of  of w e i g h t .  mass  is  10  6.4  Terms A s s o c i a t e d  W i t h The  Related  Information  Processing  Variables 6.4.1  S e l e c t i v e Encoding Selective  information what  from  information  relevant 6.4.2  encoding  i s relevant  unified  information, to  & Davidson,  to  combination  seem  to  be  whole t h a t may put  implied.  together  (Sternberg  that  out is,  relevant understanding  s o l v i n g a p r o b l e m , and  how  i t is  1982,1983).  involves  isolated  or may pieces  not of  combining  pieces resemble  of  & Davidson,  might  information  its  information  what  parts.  that  are  into a Knowing  relevant  is  1983).  S e l e c t i v e Comparison Selective  comparison  information  to  relationship  between  (Sternberg  involves  information new  & Davidson,  Theory aim  sifting  S e l e c t i v e Combination  originally  6.4.3  irrelevant  (Sternberg  Selective  how  involves  provided  acquired  and  1982, the  relating  old  i n the  variables  the  research.  summarized, s t a t e m e n t s of  as The  defined  hypotheses.  A is  acquired nonobvious discovered  1983). guide  to v a r i a b l e s e l e c t i o n with  supply  the  introduction  preparatory  past.  information  of a t t a i n i n g s u b s t a n t i a l p r e d i c t a b i l i t y  The  newly  to a review  to of  (Pedhazur,  operational the  study  pertinent  the  1982).  structure for can  now  be  literature  and  11  7.  SUMMARY OF Given  gifted  the  this  it  of  problem  f i n d i n g as  seems n e c e s s a r y  important  ability  significant  to address  in conceptions  the  and  lack  in of  research  giftedness. Examining  and  ONE  recognition  performance,  e m p h a s i s on of  CHAPTER  related  problem  recognized  2)  of  importance  processing  ability  1 ) .'to i d e n t i f y processes  relative  information  finding  following  the  is  of  variables  justified  on  IQ,  cognitive  as the  level,  predictors basis  of  of the  needs: possible  intellectually  underlying gifted  differential  cognitive  children;  to a r t i c u l a t e age-appropriate  d e f i n i t i o n s of  giftedness;  perspective  research  and 3)  to  gi ftedness.  provide  a  theoretical  to  on  12  II. 1.  OVERVIEW  OF THE CHAPTER  Chapter of  problem  2 reviews the l i t e r a t u r e p e r t a i n i n g  finding  intellectually five  as  a  gifted  differential children.  the l i t e r a t u r e review  which  deal  on  with problem  problem  problem  finding.  evident  within  The  the nature  the  review,  into  four  the a s s o c i a t i o n  influence  f o r these  of  of i n f o r m a t i o n  of  and t h e r e l a t i o n s h i p  The r e a s o n  the review  of  cognitive  of i n s i g h t t o  categories  will  become  itself.  concludes  with  a  summary  of  the  five  hypotheses.  INFORMATION  PROCESSING IN INTELLECTUALLY GIFTED CHILDREN  propositions  processing  finding,  finding,  chapter  directional  Two  with  i s divided  by i n t e l l e c t u a l l y g i f t e d c h i l d r e n ,  intelligence level  respectively  attribute  a r e s u l t of t h i s  To  processing  concerning  in gifted children  2.1 The I n t e l l e c t u a l l y G i f t e d Information  that  will  the  nature  of  information  be e x a m i n e d .  As Q u a n t i t a t i v e l y  Different  Processors  Intellectually ways  As  formulated.  aid clarity,  t o the question  cognitive  h y p o t h e s e s were  parts  2.  A REVIEW OF THE LITERATURE  indicate  gifted their  difference  (1980)  a  norm  above t h e mean, and an a d v a n c e d m e n t a l a g e . Robinson  denotes  the  significantly  and  metric  from  terms.  Jackson,  IQ  a r e commonly d e s c r i b e d  quantitative  Roedell,  The  children  high  equate  in in  score,  this  13  quantitative belief  difference  i s that  younger  characteristics  children  intellectually  Firstly, in  part,  of  which  change  not  be  differences  correct  one  consideration  of  Secondly, gifted  child  average  of  gifted  different  as  to  from  distinguish  children.  advancement (Webb,  Two  organization  inadequate  imply,  1974)?  change, t h e r e  qualitative.  but  older  however.  of  the  knowledge to  specify  advancement in  at  While  is also  Thus,  developmental  a  said MA  that,  of  This for  information  uses  may  i t s omission  of  be the  thinks  these  f o r example,  13  thinks  may  be  in  thought  8-year-old  i n ways i d e n t i c a l t o an  i t does not processing  an  inadequate a d d r e s s the  Perhaps  ways more t y p i c a l of in  a  of  possibility  strategies.  processes  way  the  his/her  the age  qualitatively  manner. "quantitatively  intellectually  gifted children  achievement  the  gifted's  and  to  is  i t be  giftedness,  The  school  can  8-year-old  g r o u p , but  as  and  Their  q u a l i t a t i v e change.  with  differential  well  less bright  change  structure  sense,  13-year-old?  describing  from  quantitative  viewed  quantitative in  as  developmental  mean  i n the  distinguish  equally  qualitative  can  can  which  from t h i s a s s u m p t i o n , might  "development" notion  apply  gifted children  questions arise  least  w i t h d e v e l o p m e n t a l advancement.  (Kaplan,  ability  r e t a i n more  to p r o c e s s  information  different" applies  also  1977).  This  information (Clark,  "quick" performance n e c e s s a r i l y  description to  their  of  advanced  advancement r e f l e c t s faster  (Clark,  1983;Newland,  synonomous w i t h  1976).  1983) But  "intelligent"  1 4  performance? define  The  question occurs  intelligence  Davidson  (1982,  1983)  Sternberg features  of  assessment optimum  as  and  are  reaction of  to  qualitative  difference  2.2  The  novel,  gifted  are  Davidson, builds  will  be  insofar  literature this  the said  they on  important  cognitive  responses"  "they or  do  occur.  the  provide  the  intellectual  hypothesize,  information  fine  in  not  assessing  They  Gifted  As  processing  Qualitatively  believes  components  rather, between  a the  Different  to possess 1983).  relate problem ability  attribute  of  major  hypotheses,  part  to problem  of  intellectually  what the &  research  possible qualitative gifted  for i t  t h a t the h y p o t h e s i s  represent a  or  (Sternberg  this  subsequently,  finding,  are  particular,  skills  intellectually  i n more d e t a i l  finding  1982b)  In  these  in certain  nonentrenched,  (1981b,  gifted.  Since a  may  on  superior insight  t h i n k i n g of  with  superiority  and  intelligence  intellectually  i n the  dealt as  of  Sternberg's  differences  skills  (1981 a,1982a)  processing  1982,  on  speeded  and  Processors  measures  distinguish  Sternberg  norm.  Sternberg information  or  p.56).  Intellectually  Information  time  in  would  b e l i e v e t h a t " d e s p i t e t h e many  understanding  (1983,  the  performance.  f o r whom the q u e s t i o n does  intellectual  entree  and  of  two  Davidson  giftedness"  gifted  speed  f o r some, whereas o t h e r s  particularly is  from  the  evolved  that  qualitatively gifted  children  children.  different  1 5  3.  PROBLEM FINDING IN INTELLECTUALLY GIFTED CHILDREN Associations  gifted These  have  been  made  between p r o b l e m  p e r f o r m a n c e and between p r o b l e m  f i n d i n g and i n t e l l i g e n c e .  a s s o c i a t i o n s and t h e c o n c o m i t a n t need  examined  in this  s e c t i o n of t h e l i t e r a t u r e  3.1 The I m p o r t a n c e  Of P r o b l e m F i n d i n g  f i n d i n g and  f o r research  will  be  review.  And I t s L i n k  To G i f t e d  Performance Problem general  questions  1965).  This  problem been  f i n d i n g has been  ability  solving  Superior  many  problem  linked  described  of research  1965).  1965; in  &  are  problems  (Getzels  i t  creative comparison  gifted"  is  the  scholar to  t h e pedant have  been  science  to  Dillon,  i s the a b i l i t y  who  work copyist  in scholarship  1965), and t o  to the  of ideas  Helvey,  problem  in  1971;  finding i s  " t h e s i g n a l mark  problems, point scientist,  discovered  who  work  In  in science,  with  i t i s the problem  out  and t h e  problems.  i n a r t , the t e c h n i c i a n  p r e s e n t e d t o them,  1976).  performance.  to find  "(p.721)  than  Infeld,  1975,  1973;  the inventive  with  &  be c r u c i a l  (1973), i n s t a t i n g t h a t  fine a r t i s t ,  "the  gifted  (Mackworth,  1945), and has  and the g e n e r a t i o n  &  many  important  (Mackworth,  believed  of  (Einstein  I t c a n be s e e n , t h e n , t h a t  and D i l l o n  the t r u l y  a s more  Csikszentmihalyi,  t o what c a n be c o n s i d e r e d  Getzels  problems  Wertheimer,  to inventions  finders  disciplines  Mackworth,  that  1965),  i n a r t (Getzels  formulation  and  has been  as t h e d i s c o v e r y  ill-defined  (Mackworth,  Mackworth,  originality  that  many  l i n k e d to breakthroughs  1938;  of  from  defined  problems  f i n d e r s who  16  are  d i s t i n g u i s h e d as g i f t e d . While  the format  criticized  to  giftedness,  a  their  research  gains  critique  of the a  specifies  comprehensive  call  for  credence term  neither  the  type  689).  problem  i t s considered  for  scientific Given  i s scant  example,  1945),  a  orientation  to  context  of t h e i r  the  term  definition,  ability  nor  the  Problem  (Dillon,  the  lack  has  "fori t degree  of  of  emphasis on  may p r o v i d e ,  at least,  Finding  by  many,  1982).  (1975,  research  Getzels  1976), and  research  which  discussions  creat ive  discovery  into  (1964,1975),  Arlin  (1975-76,  i s drawn upon  in this  thinking  the r e c o g n i t i o n of problem  within  can  examined p r i o r  i t  the  between only  of  productive (Henle,  thinking  1975),  ( E i n s t e i n & I n f e l d , 1938; Mackworth,  performance,  association ability  of  but p r i m a r i l y t h e t o p i c has t o be a p p r o a c h e d t a n g e n t i a l l y  (Wertheimer,  finding  the  in their  nature  believe  than  importance  and C s i k s z e n t m i h a l y i  through,  gifted  in  on g i f t e d n e s s  Into  have done s i g n i f i c a n t  study,  the  finding  They  of  on  be  of t h e type of a b i l i t y .  finding  Getzels  put  Addressing  3.2 The Need F o r R e s e a r c h  Despite  problem  rather  can  a s an a f t e r t h o u g h t article  "gifted."  finding i n research  specification  1977)  a when  designation  superiority"(p. problem  and D i l l o n ' s s t a t e m e n t  f o r i t s appearance almost  conclusion  remained  of G e t z e l s  seems  context  intellectual be  implied.  to formulating  to  giftedness.  giftedness These  the f i r s t  1965).  f i n d i n g as s i g n i f i c a n t i n  appropriate of  and  study At  present,  and p r o b l e m  implications will hypothesis  problem an  finding now be  for empirical  1 7  study. 3.3 I n t e l l i g e n c e And P r o b l e m  Some  references  association formulate  between  relationship  as a " h i g h l y  equated  intelligent  problem  thought  defined  the  (Henle,  (Getzels  distinction  between  finding may  some  the discovered  into  this  problem  Dewey  (1933)  problem.  between i n t e l l i g e n c e  the  nature  For  of  example,  contribute  of problem  the would  significantly  f i n d i n g with  (Getzels  thinking  Kogan  &  inventions  &  Csikszentmihalyi,  (Wertheimer,  1945), and c r e a t i v e  Jackson,  creativity (1965),  may n o t be s t r o n g ,  be  that  1975); t h e low c o r r e l a t i o n f o u n d between IQ and  creativity  and  intelligence  and  and  and  finding?  originality  1975,1976), p r o d u c t i v e  Wallach  process"  i n terms o f IQ  positive  (1965) d e s c r i b e d  necessary.  association  (Mackworth,1965),  thinking  with  of problem  a  to perceive  finding  Mackworth  research  appears  the p r e d i c t i o n Given  problem  of the suggested a s s o c i a t i o n  relationship  to  in  intellectual  finding,  "intelligence"  imply  (1982) s u g g e s t s t h a t  be r e s e a r c h e d .  light  literature  Dillon  variable  finding  and  the  i n t e l l i g e n c e and t h e a b i l i t y  problems.  may be a r e l e v a n t  In  in  Finding  1962; G u i l f o r d , and  the  of  affirmed  by  r e l a t i o n s h i p o f IQ t o p r o b l e m  but t h e r e  contribution  intelligence  1967); and t h e  i s reason  to believe  IQ t o t h e p r e d i c t i o n  there  of problem  f inding. B e i n g o f above a v e r a g e but 120  not s u f f i c i e n t i s thought  to  IQ i s c o n s i d e r e d  condition be  the  for creativity. minimum  level  t o be  a  necessary  An IQ o f a t l e a s t necessary  f o r the  18  inventive  and  production  (Roe,  Problem than IQ.  superior  however,  would  problem  sufficient"  relationship  The  of  of  IQ  forms the  Intelligence  as  problem  the  predictor  4.  COGNITIVE LEVEL AND A  The  variables  developmental  finding  forms t h e  importance  The  creative  for  evident.  4.1  Need F o r  but  IQ  of  to  creativity  some  its  with a  relevance  "necessary  thinking.  but  The  high in not first  relevance.  First  a  Hypothesis  predictor  of  ability  the  first  will  contribute  will  be  of  less  variance  cognitive  level  to  research to  discover  hypothesis:  the  prediction  significant accounted and  in for  its than  insight.  PROBLEM FINDING perspective  following  of  become The  with  associated  have  creative  proportion  the  to  given  to  measured by  to  thinking  appear  as  basis  finding  contribution  more a l l i e d  d e g r e e of  S t a t e m e n t Of  role  problems  is likely  finding  h y p o t h e s i s c o n c e r n s the A Formal  associated  convergent  predicting  3.4  thinking  1976).  f i n d i n g , then,  t o the IQ,  elaborative  on  section  this perspective  of to  giftedness the the  A D e v e l o p m e n t a l F o c u s To  and  problem  literature research  review.  question  Descriptions  will  Of  Gi ftedness The may  criticism  not  "attributes"  be  has  been made t h a t  age-appropriate fail  to  address  in  descriptions that  whether  of  listings these  giftedness of  gifted  attributes  are  19  characteristic necessary theory  o f a l l age l e v e l s .  i n research  provides  contribution  and  secondly  of  provision problem  of  be l o o k e d  Research intra-stage  within  research stage on  as  are  It will  constrained  4.2.1  horizontal  most  children older,  the  differential  suggests  r e l a t e d t o IQ, b u t movement  i s dependent precocity  on  that  maturation.  will  on t h e  maturation  that  be l o o k e d  in  a t f i r s t and  acquisition  while g i f t e d  their  Studies  of  a  children  new excel  stage,  they  progression  to  a  stage. Precocity  (1974) s t u d y decalage  striking  on c o n c r e t e average  showed s u p p o r t  is  sample o f 25 c h i l d r e n "the  in  gifted.  with a p a r t i c u l a r developmental by  Intra-stage  Webb's  of g i f t e d n e s s  a possible  perspective  closely  be seen  for  Giftedness  to constraints  associated  subsequent  is  t o another  relevant  On  Piagetian  to intra-stage  second.  tasks  a  precocity  from one s t a g e pertaining  Perspective  at f i r s t l y  age-appropriateness  finding  appears  developmental  understanding  c o g n i t i v e a t t r i b u t e of t h e i n t e l l e c t u a l l y 4.2 The P i a g e t i a n  focus  and P i a g e t i a n  It will  to a developmental  for  specification  on g i f t e d n e s s  such a f o c u s .  its  A developmental  and S h i e l d s '  gifted  children's  function  i n t h e age r a n g e observation operations  children"  Lovell  a  intelligence.  6 t o 11 y e a r s  problems that  (p.299).  order  of  that With a  (IQ  >160),  was t h e s u c c e s s o f b r i g h t  (1967) s u g g e s t i o n first  for h i s hypothesis  Webb's that  are d i f f i c u l t findings  the  operational  young  support  flexibility  schemas  for  is  of much  20  greater  than  Arlin's stage  ordinary (1984,  precocity  intellectually  pupils'.  in press  a) s t u d y  continues  gifted  to  through  established  be  formal  a  that  intra-  characteristic  of  the  operations:  The argument c a n be made that those identified as g i f t e d appear t o move v e r y q u i c k l y i n the c o n s o l i d a t i o n and i n t e g r a t i o n of t h e c o n c e p t s and o p e r a t i o n s associated with the new stage. Such speed of a c q u i s i t i o n i s not apparent i n l e s s gifted groups of s t u d e n t s with a v e r a g e t o above a v e r a g e I Q ' s . (p.8) W i t h a sample o f 223 c h i l d r e n and  Ormrod  gifted  children  tested"  found  over  10 t o 15  "superiority  years,  Carter  on P i a g e t i a n t a s k s f o r  normal-ability children  a t each  age  level  (p.113).  The stage  (1982)  aged  question  of  of development  expected  precocious  by i n t e l l e c t u a l l y  as a r e s u l t  schemas w i t h i n  whether  the  of f a s t e r previous  acquisition  gifted  children  o f a new could  be  c o n s o l i d a t i o n and i n t e g r a t i o n of stage  may  be  a  logical  one.  Research,  however, has i n d i c a t e d  t h a t t h i s may n o t be t h e c a s e .  Studies  on  of  the  intellectually operational problem 4.2.2  gifted  stage  will  formal  be f o c u s e d  t h a t may be t h e most  operations  by  the  upon, f o r i t i s t h e f o r m a l r e l e v a n t t o the study  of  finding.  M a t u r a t i o n a l C o n s t r a i n t s On The G i f t e d ' s A c q u i s i t i o n Of  Formal  Operations  Support by  acquisition  gifted  (1975).  f o r the precocious  children It will  would a p p e a r  be s e e n ,  acquisition t o come from  of formal  operations  t h e work o f K e a t i n g  however, t h a t t h e number o f t a s k s  used  21  to  test  formal  may  be i m p o r t a n t In a s t u d y  found  that  o p e r a t i o n a l t h i n k i n g and t h e age r a n g e s t u d i e d qualifiers comparing  the  fifth  to Keating's  average grade  than The  the seventh former  found  group  children,  group  cognitive  grade average  g r o u p was  and b r i g h t  bright  months) were a t a more a d v a n c e d  findings.  11 y e a r s  developmental  (M age  t o be f o r m a l  (M age  Keating  13 y e a r s  3  level  1 month).  o p e r a t i o n a l ; the  latter,  transitional. Keating's formal  s u b j e c t s were,  operations  tasks,  sshemata were d e f i n e d by ability  to  do  evidence  of c a p a b i l i t y  be c o m p l e t e l y  three  accurate  however, whereas  Inhelder formal  tested  eight and  Piaget  three  operational  (1958).  While  tasks provides  of a b s t r a c t i o n ( A r l i n , such  only  formal  operational  to c l a s s i f y  on  1984a),  performance  some  i t may not as  "formal  operat i o n a l . " Additionally, precocity younger older  shown  by  bright  average  research,  it  is  Keating's  group  group?  limits  important  to  o p e r a t i o n s c a n be seen  the  6 months), A r l i n  this  group  were  schemes p r e s e n t were  at  the g i f t e d  qualify  group.  would t h e y  viewed  in  precocious  the  t h e e x t e n t of  That also  is,  if  outperform  context  acquisition  of of  a  the  other formal  to e x i s t .  W i t h a g r o u p of s l i g h t l y years  bright  were u s e d When  to  (1984,  identified  in their  younger  gifted  children  i n p r e s s a) f o u n d as low f o r m a l  thinking)  and  t h e upper end o f t h e age r a n g e . g r o u p whose mean age  was  11  (M age  10  that only  21% of  (three to f i v e  formal  that  those  identified  In comparison, years  4  months  55% of were  22  classified  as  comparable gifted  t o those  pupils  operational Webb no  low  formal  of L o v e l l  "do  thought  not  below  results  are  a n d S h i e l d s (1967) who f o u n d  11 y e a r s  The d a t a  formal  These  attain o f age  the l e v e l at  of h i s study  operations  of formal  least"  "suggest  that  (p.206). essentially  a s s o c i a t e d w i t h h i g h IQ's  t h e age o f 11" ( p . 2 9 9 ) . The  studies  demonstrate  of  Arlin,  that the g i f t e d  constrained in  on  formal.  generally  until  (1974) c o n c u r s . precocity  or  Lovell child  i n the a c q u i s i t i o n  comparison  to  precocious,  as  performance  of both  the  shown  they  Keating.  gifted  Shields,  may i n d e e d  of formal  norm, by  and  be  and  developmentally  operations.  c a n be c o n s i d e r e d Arlin,  Webb  However, somewhat  t o o , found  the  g r o u p s t o be above t h a t of a n o r m i n g  group. It  is  precocity is  of  important  to  in acquisition  a  "relatively  note  Webb's  19  years,  expectations" Put gifted  into  low d e g r e e . "  subjects  more  children  In h i s sample of 6- t o 11IQ s c o r e s )  performed  the context as  of t h e  ranged  "closer  discussion  quantitatively  processors presented  from  t o CA t h a n  typical  of  intra-stage  flexibility  qualitative  difference  his/her of from  of  10 MA  intellectually  or q u a l i t a t i v e l y  earlier,  P i a g e t i a n t e r m s , an i n t e l l e c t u a l l y  ways  that  (p.299) on t a s k s o f f o r m a l t h i n k i n g .  children  information in  but  emphasis  of f o r m a l o p e r a t i o n s by b r i g h t  y e a r - o l d s , m e n t a l age ( e s t i m a t e d from to  (1974)  different  i t would a p p e a r  gifted  child  that,  does t h i n k i n  age g r o u p and t h a t t h e g r e a t e r  thought t h e norm.  could  be  How t h e s e  considered  a  developmental  23  characteristics problem 4.3  A Piagetian has  been  problem  of  greater  Webb,  is  more a d e p t finders, their  a at  (Arlin,  superior  young  1975-76),  at  to  developmental Arlin  and  mainly Can  discovering  level  of  (1975-76)  appeared the  to c o n f i r m  the  problem  1977, problem  found problem  problem may  p.298).  There  a  of  may  finding capability,  gifted  who  that  &  that  the  in  greater  would  allow  c h i l d r e n would  perceive a gifted  perceive  to  problems scholar  alone  may  in who  not  ability.  operational  be  problem  p r o b l e m s as  a relevant  a be The  variable. thinking  to  be  f i n d i n g q u a l i t y and,  in  a  operational  with  Lovell  problems.  finding quality.  t h e n be  schemas  variance  gifted  significant  posing  of  a;  the  finding be  formal  formal  finding s k i l l  to  appear  suggestion  be  flexibility  child  found  that  of  assume t h a t  (1977), on  some  that  later  level  the  posing  c o r r e l a t e d with problem  operational  With  i t might  significantly study  in press  problems could  for  flexibility  1984,  to a d u l t s  we  children  S p e c i f i c references  Intra-stage account  gifted  intellectually  hypothesis  study.  child?  sufficient  for  f i n d i n g problems.  of  relate  Finding  than average  i n the  likely  however, a r e  fields  Problem  1974).  (Arlin,  schemas  c h i l d r e n may  intellectually  superiority in perceiving It  is  On  thought accounts  of  gifted  explored.  development  finding  flexibility for  a  1967;  flexibility  be  seen t h a t  s t a g e s of  Shields,  now  Perspective  demonstrate  within  intellectually  finding will  It to  of  general  effect  of  This  second  thinking  age  study  "relates  questions"  level  a  to  (Arlin,  developmental c o n s t r a i n t s cognitive  and  on  relevant  24  consideration  when p r e d i c t i n g  4.4 A F o r m a l S t a t e m e n t The finding  role  of  ability level  of  finding  problem  general questions 5.  cognitive the  will  to discover  problems.  Of The S e c o n d H y p o t h e s i s  forms  Cognitive  the a b i l i t y  level  basis  contribute  ability,  that  as  for  a predictor the  second  significantly is,  from i l l - d e f i n e d  the  hypothesis:  to the p r e d i c t i o n  ability  problems  of problem  to  discover  (Mackworth,  1965).  INSIGHT AND PROBLEM FINDING . The  and  role  of i n s i g h t f u l  the r e l a t i o n s h i p  considered. insight  5.1 I n s i g h t  possible  some t h e o r e t i c a l  processing  the  main  finding  giftedness  will  now  be  d e v e l o p m e n t a l i n f l u e n c e s on  variable  Giftedness  background relevant  to  insight  as  an  t o the study of problem  i d e a s of a c o m p o n e n t i a l t h e o r y  of g i f t e d n e s s  be p r e s e n t e d . Recognizing  constitute formulated this  t o problem  As A Component Of I n t e l l e c t u a l  information  will  in intellectual  be e x a m i n e d .  To p r o v i d e  finding,  of i n s i g h t  Additionally,  will  thinking  need  intelligent  to  intellectual  to superiority  specify  performance,  a componential theory  theory,  primarily  the  the  Sternberg  of i n t e l l e c t u a l  giftedness  processes  i s viewed  i n the f o l l o w i n g  (1980,  that 1981a)  giftedness. as  In  attributable  componential  (a) "Metacomponential" or executive processing skills, such as problem recognition, process selection, strategy selection, solution monitoring, and the like; (b) p e r f o r m a n c e - c o m p o n e n t i a l s k i l l s , s u c h a s  skills:  25  the abilities t o make inferences and t o apply previously made inferences i n new doma i n s ; (c) learning skills, s u c h a s e n c o d i n g and r e t r i e v a l of i n f o r m a t i o n that resides in l o n g - t e r m memory; and (d) interactions among t h e s e v a r i o u s k i n d s of componential skills. (Sternberg & D a v i d s o n , 1983, p.52) Drawing subtheory  that  encoding, defined gifted  combination,  Chapter  (Sternberg  1) t h a t  & Davidson,  c a n be seen  problem  that  problem  ability. strategy  Sternberg hypothesizes a  comparison,  t o be s o l v e d  i t s role and/or  contributes  irrelevancies solutions.  refinement  what to  a  deriving  a conclusion  superior  at  is  relevant  selective  in  encoding  the problem), in  tandem  to  o f t h e e n c o d i n g p r o c e s s by d e t e c t i n g  person  and/or  skilled  from p r e m i s e s  selectively  skill  i n determining the  needed t o s o l v e  i n t h e s t r a t e g i e s used Too,  of the  "metacomponential"  s e l e c t i o n , and s o l u t i o n m o n i t o r i n g work to  as  1982, 1983).  Process s e l e c t i o n (steps  contribute  (selective  are d i s t i n g u i s h i n g features  through  situation,  thinking  selective  the superior  recognition,  n a t u r e of the problem the  view,  i t i s p r o c e s s e s of i n s i g h t f u l  selective in  It of  on t h e c o m p o n e n t i a l  encoding  in  inconsistencies making  inferences, in  o r e v i d e n c e , would information  in  likely  relevant  to  be a  problem. Skill selective several  in  making  combination inferences  Similarly,  greater  selection  may  inferences as w e l l ,  may skill  need  may  for  to superior  drawing  conclusion,  t o be combined  i n process  contribute  in  contribute  initially  selection  a  i n a unique and/or  way.  strategy  to s e l e c t i v e combination,  26  that  i s , to  information  "knowing  that  how  are  to  put  relevant"  together  the  (Sternberg  pieces  of  & D a v i d s o n , 1983,  p. 53) . Superior  performance-componential  skills  can  ability  to apply  closely of  retrieve  t o be  basic  Problem  encoding  recognition  Process s e l e c t i o n  in  selective  information  & Davidson,  in  new  s o l v i n g by a n a l o g y ,  learning  greater  The  domains  one example ability  comparison  to information  process  componential  s k i l l s can  be  to the p r o c e s s e s of i n s i g h t .  S e l e c t i v e combination  Ability  t o make  inferences  Selective  Ability  comparison  to apply  previously  made  Process s e l e c t i o n  inferences in  Solution  monitoring  Strategy  new domains  inferences  of  acquired in  selection  t o make  to  l o n g - t e r m memory would  Strategy  Ability  is  1983, p . 5 4 ) .  I summarizes how s u p e r i o r  to contribute  Selective  inferences  resides  the  and  to s e l e c t i v e comparison.  Additionally,  that to  (Sternberg  Table seen  comparison.  newly a c q u i r e d  past"  made  with problem  information  "relating the  to contribute  previously  associated  selective  appear  be seen  skills  selection  R e t r i e v a l of information  that  resides in l o n g - t e r m memory  Table  I - The p r o c e s s e s o f i n s i g h t and c o m p o n e n t i a l thought t o r e l a t e t o each p r o c e s s  skills  27  Sternberg  and D a v i d s o n  will  have s e v e r a l ,  their  lifetimes,  from  the  variable, study of  p e r h a p s many, m a j o r  and i n t h i s  norm.  theoretical  The  background for  (1983) b e l i e v e  of problem  subtheory  for  superior finding  respect,  the  the t r u l y  gifted  intellectual insights in  they d i f f e r  qualitatively  of  provides  insight  choice  insight  that  of  skills  a  third  the  predictor  may be s i g n i f i c a n t  as a q u a l i t a t i v e l y  different  in a  attribute  the g i f t e d .  5.2 The R e l a t i o n s h i p Of I n s i g h t Chapter  1  outcomes o f m a j o r 1983)  and  1965).  pointed  out  I t was h y p o t h e s i z e d  taken  together  references  in  the  intellectual  t h o s e of p r o b l e m  may the  To P r o b l e m  parallel  insights  finding that  relate  seen  between  (Sternberg  (Arlin,  &  problem  would  the  Davidson,  1975-76; Mackworth,  t h e t h r e e p r o c e s s e s of  to  literature  Finding  finding.  appear  to  insight  Two  other  support  this  hypothesis. Henle question need  (1975),  in  and t h e p r o b l e m  for  a  principle  speaking  in creative of  significance  when i d e a s a r e  finder,  the  in  (Mackworth, encode  1965), c o u l d  information  more s i g n i f i c a n t the  most To  raising  relevant Dewey  of the importance thinking,  selection generated.  of q u e s t i o n s thus  either  and  from  points  the  The  questions  (1933), d i s c o v e r y  the  problem  i l l - d e f i n e d problems  effectively  selectively  from t h o s e  out  r e c o g n i t i o n of  superior  from t h e i l l - d e f i n e d p r o b l e m  q u e s t i o n s and/or  of both the  selectively  space t o r a i s e  encode t o s i f t o u t  raised.  o f a p r o b l e m was t h e f u n c t i o n o f  28  thinking, expands Insight  and  "insight  the  into  suggestion  into a  selectively  that  discovered  encoding  the  problem  corrects,  modifies,  originally  occurred"  (p.109).  problem  the  could,  therefore,  ideas that o r i g i n a l l y  involve  occurred,  correcting  t o o b t a i n t h e most  relevant idea;  seemingly  isolated  information to s e l e c t i v e l y  with  the o r i g i n a l  comparing  the  expanding  on i t .  Superior discovering  p i e c e s of idea,  original  insight,  problem  finding  conceived  of by Mackworth  it  i s necessary  nature  as  influences 5.3  may  Table  insight  to  II  nature  t o examine two  a measure of  and  on  the  problem  model  of  finding  as  this  relationship,  intelligence  and  of  in  hypothesized  process  facets  thus  ability  formally  other  combine  ideas,  Before of  other  selectively  to s u p e r i o r  cognitive  1975-76)  and  past  summarizes  (1965).  the  it;  with  relate  the  (Arlin,  concerning  modifying  suggestion  then,  problems.  r e l a t i o n s h i p of  hypothesis  thus  drawing  thus  stating  however,  insight  possible  a  -  its  developmental  on i t .  I n s i g h t As  A N o n e n t r e n c h e d Measure Of  Intellectual  Gi ftedness The Davidson that  subtheory  of  insight  skills  (1983) as a c l a r i f i c a t i o n  "intelligence  a c q u i r e and  think in  conceptual  systems  comprises terms ..."  " n o n e n t r e n c h e d " t a s k s and (Sternberg  & Davidson,  in  of  and  Sternberg  and  e l a b o r a t i o n of t h e i r  view  large  novel  (p.54). concepts  1982,  i s viewed  1983),  part  kinds When  such the  by  the of  ability  concepts  faced with  as t h e  novel,  "insight  intellectually  to and or  puzzles" gifted  29  C o g n i t i v e p r o c e s s model of p r o b l e m f i n d i n g " T A r l i n , 1975-76)  Insight  skills  Problem  f inding  (Sternberg & D a v i d s o n , 1983)  (Mackworth,1965)  D i s c r i m i n a t ion  Selective  encoding  D e t e c t i o n of the need f o r a new program  Differentiation  Selective  comparison  Comparing existing and e x p e c t e d f u t u r e programs  Integration  Selective  combination  D e v i s i n g o f new programs  Selects  formal  operations  Transformat i o n s / Implications  OUTCOMES Problem f i n d i n g o u t p u t : The g e n e r a l question.  Table  are  Insights that d i f f e r i n kind from t h o s e o f ordinary individuals in their striking o r i g i n a l i t y and consequence.  The d i s c o v e r y o f many g e n e r a l questions from many i l l - d e f i n e d problems.  II - H y p o t h e s i z e d r e l a t i o n s h i p s of i n s i g h t with problem f i n d i n g a b i l i t y  distinguished  formulation  by  of the p u z z l e s '  "Insight  puzzles"  of  intelligence.  in  Chapter  is  important  3.  will  the  at this  thus provide  i n the  a nonentrenched  themselves are discussed  classification point  demonstrated  solutions.  The p u z z l e s  Their  insights  skills  as a  nonentrenched  as a t h e o r e t i c a l  measure  in detail measure  consideration.  30  Sternberg the  ability  "this  (1982b)  to deal  ability  tests  believes  seems o n l y  variance  of  problem  than  IQ.  t h e mark of g i f t e d n e s s i s  with nonentrenched  I t may  finding,  This  tasks  and  concepts,  t o be p e r i p h e r a l l y measured by  of i n t e l l i g e n c e " ( p . 6 5 ) .  predictor  that  be,  insight  hypothesis  then, will  arises  from  current  that,  account the  and  as  a  f o r more following  considerations: 1.  As  subjects  a  measure  to  raise  nonentrenched 2.  of  problem  questions  f i n d i n g , a task  (Arlin,  requiring  1975-76,1977)  is  i n nature.  Insight,  would, t h e r e f o r e ,  as  a n o n e n t r e n c h e d measure o f i n t e l l i g e n c e ,  seem  t o be a " b e t t e r "  predictor  than  IQ,  an  entrenched measure. 5.4  Cognitive  Level  Arlin's formal the  operational  also  thinking  finding be  Sternberg's initial  (1981a)  research  more r e c e n t  research  1984)  concluded  failed  to take that  skill  and  of p o s i n g  general  only to  the g i f t e d  gifted to  thinking  solve.  this question  does,  Since  can  in fact,  be  a  cogent  i s the f a c t  superior number  i n the f o u r t h ,  (1982,1983)  is  (Davidson  possessed  It  insight?  this  the s i g n i f i c a n t  children  Might  on  adults,  for  questions.  and D a v i d s o n ' s  done w i t h c h i l d r e n  i n t o account  but n o t s u f f i c i e n t  constraints  validity  that  g r a d e s were u n a b l e  suggests the importance of  Sternberg  included  Adding  operational  Insight  as n e c e s s a r y  developmental  question.  puzzles  In  (1975-76,1977) r e s e a r c h  problem  there  As A F a c t o r  &  Sternberg, i n s i g h t , but of  fifth,  seen  have l i k e l y  that  insight and s i x t h  that  formal  connection  to  31  the  insight  processes.  Combinatorial systems  of  reference  operational insight  schemata  -  reference  of  encode  The h y p o t h e s i z e d may,  thought.  This  be  mediating  i n a separate  two  or  of  information  mediated  relationship  Piagetian finding  of  reference  be  Insight  finding  ability,  is the  problem  operational statistically  analysis.  and  the  t o the t h i r d  a)  to  to  Hypotheses  a s a n o n e n t r e n c h e d measure o f g i f t e d n e s s ,  theory,  lead  instances  formal  5.5 F o r m a l S t a t e m e n t s Of The T h i r d And F o u r t h Insight  of  relevant  will  to  systems  insight  by  formal  of s e l e c t i v e  more  frame  more  relevant  and t o c e r t a i n  one  or  1958) a r e two  r e l a t i o n s h i p of  therefore,  two  to the process  comparison  correctly  of  particularly  reasoning  selective  to  & Piaget,  appear  e n c o d i n g where more t h a n  problem.  tested  that  and the c o o r d i n a t i o n to  necessary  finding  and c o o r d i n a t i o n  (Inhelder  combinatorial  combination  selective  reasoning  will  relationships  and f o u r t h  be  accounting  a  of  both  to  relevant problem  hypotheses:  significant  predictor  for significantly  of problem  more v a r i a n c e  than  IQ. b) The r e l a t i o n s h i p o f i n s i g h t t o p r o b l e m m e d i a t e d by f o r m a l Having  stated  significance concerning prediction  operational the  the  order  equation  of  will  be  thinking.  hypotheses  of the independent  finding  concerning  variables,  entry  i s considered  of  the  important.  a  the p r e d i c t i v e final  variables  hypothesis into  the  32  5.6 O r d e r Of E n t r y Regression  All  predictor  significantly  the  to  order  of  entry  (Pedhazur,  As a r e s u l t level  first  relationship problem  are  The  hypothesized  equation.  underlying  of v a r i a b l e s  to  add  A d d i t i o n a l l y , the  it  should  determine  i n t o the m u l t i p l e  regression  1982).  of the l i t e r a t u r e  of d e v e l o p m e n t a l (Arlin,  reviewed,  entering  seems a p p r o p r i a t e level  1975-76,  1977).  to enter  than  IQ.  of t h e  v a r i a b l e of  Cognitive  s e c o n d due t o t h e  a "better" predictor  cognitive  in light  to the c r i t e r i o n  most t o t h e p r e d i c t i o n of p r o b l e m  hypothesized  being  prediction  i n t o the equation  finding  contribute is  the  variables  p r o b l e m and t h e t h e o r y  equation  Into  Equation  the  research  Of The P r e d i c t o r V a r i a b l e s  level  finding  .  may  Insight  possibility  of  IQ, t h e n , would be  its  entered  last. A fifth variables  multiple + IQ.  therefore,  i n t o the p r e d i c t i o n  5.7 A F o r m a l The  hypothesis,  of  entry  regression  of  equation  the order  of entry  of  equation.  S t a t e m e n t Of The F i f t h  order  states  the  Hypothesis predictor  variables  w i l l be: c o g n i t i v e  level  in  the  + insight  33  6.  SUMMARY OF THE F I V E  HYPOTHESES  As a r e s u l t o f t h e were  formulated.  entrenched  (IQ)  literature  Two and  nonentrenched  as  further  hypotheses  constraints order  of e n t r y  regression 1) ability, level  predictors  equation.  IQ w i l l  (insight)  problem to  measures  finding  ability.  possible  predictor The f i v e  variables  the  multiple  h y p o t h e s e s a r e summarized  be a weaker p r e d i c t o r  of problem  than  A  concerned the  into  t o the p r e d i c t i o n  of  developmental  f i n d i n g , while the f i f t h  contribute  but w i l l  of  related  problem of the  hypotheses  either  below: finding  cognitive  or i n s i g h t . 2)  will  on  five  of the hypotheses c o n c e r n e d the r o l e of  intelligence two  reviewed,  Insight,  account  as  a  n o n e n t r e n c h e d measure o f i n t e l l i g e n c e ,  f o r more o f t h e v a r i a n c e  in  problem  finding  than  IQ. 3)  Cognitive  prediction  of problem  4) C o g n i t i v e finding 5) multiple  level  will  contribute  significantly  t o the  finding.  level  will  mediate  the p r e d i c t i o n  of  problem  by i n s i g h t . The  order  regression  of  entry  of the p r e d i c t o r  equation w i l l  be: c o g n i t i v e  variables level  +  i n the insight  + IQ. The analyze chapter.  methodology the  resulting  used data  to  test is  the f i v e  described  hypotheses and t o in  the  following  34  III. 1.  OVERVIEW This  finding  OF THE CHAPTER  study may  research four  refers  2.  gifted  children  may  predict  ascertain  forms t h e f i r s t  part  finding  i s contained concerning  Lastly,  attribute  of  ability.  The  i n the f o l l o w i n g  the population  in parts  of the study  problem  examine t h e c o g n i t i v e  of t h e d i s c u s s i o n .  to t e s t i n g procedures. the design  to  problem  Information  whether  cognitive  and  f o r the study  discussion.  on  to  differential  methodology  information data  designed  a  which  part  sample  was  be  intellectually processes  METHOD  and  The s e c o n d three  and  part four,  and t h e a n a l y s i s o f t h e  are presented. POPULATION The  target  population  elementary  grades  Vancouver.  The  students schools included  in  in  five  i n the d i s t r i c t .  relationships.  gifted  a suburban-rural  accessible  grades  for  was  population to  seven  Students  clarification  of  of the  students school was in  in  the  upper  d i s t r i c t east of  three  classes  of  one o f t h e e l e m e n t a r y  varying  abiltites  hypothesized  were  predictive  35  3.  SAMPLE  The the  sample  exception  sufficiently sample years 6  included of  one  understand  size  was  the e n t i r e  76  foreign oral  accessible student  directions  (37 g i r l s  population,  who  was  unable  in English.  and 39 b o y s ) .  with  The  total  Age range  was 10  8 months t o 14 y e a r s 9 m o n t h s , w i t h a mean age o f 12  months.  Subjects  were  predominantly,  w h i t e and E n g l i s h - s p e a k i n g . school's Several  catchment  area  s t u d e n t s from  enrichment  program  years  Piagetian  grade  level  offered  reviewed  by A r l i n  (1984,in p r e s s a ) , C a r t e r  clarify  finding, formal  the  i n that, thought  condition  either  in  approximates,  ( 1 9 7 5 ) , and Webb ( 1 9 7 4 ) .  to  of  middle  the  class.  participated  in  at the school.  i n c h o o s i n g t h e age range  on t h e i n v e s t i g a t i o n s  perspective  level  an  Testing  1984.  studied  also  had  years  but not e x c l u s i v e l y ,  socio-economic  lower-middle  previously  involved  centered  is  each  took p l a c e d u r i n g J u n e , Rationale  The  to  Chapter  i s expected  2.  The  i n whole o r i n p a r t ,  relationship  and  of  10  -  14  o f g i f t e d n e s s done from a  Ormrod  I t was hoped t h a t  on t h e b a s i s  of  this  cognitive  of A r l i n ' s  age that  (1982),  range studied  Keating  age g r o u p level  would  t o problem  (1975-76,1977)  work,  t o be a n e c e s s a r y b u t n o t s u f f i c i e n t  f o r the p o s i n g of g e n e r a l q u e s t i o n s .  36  4.  PROCEDURES Four p r o c e d u r e s  include  the  problem  finding,  cognitive 4.1  The  4.1.1  task  level,  for and  described  in  measurement measures  insight,  and  this  section.  of t h e c r i t e r i o n  of  the  These  variable,  predictor  variables  IQ.  P r o b l e m F i n d i n g Task  Task D e s c r i p t i o n Subjects  completed  1975-76,1977).  The  a r e appended. and  are  the  The  elements  finding.  A  for  (1956);  an  that  corresponding  Of  The  by  they the  six  - two  element,  of a  of  the  problem way  of  follows.  Raised  the  subjects  product  were  situation  definition  third  Questions  intellectual  is, to  the  once r a i s e d ,  generated  t o the  the p r o b l e m a t i c  operational  of  the q u e s t i o n s  Classification  according  both  (Arlin,  for i t s administration  for subjects to r a i s e questions  description  Questions  P r o b l e m F i n d i n g Task  instructions  task provides  necessary  4.1.2  t a s k and  opportunity  categorizing  the A r l i n  were  categories  of  c a t e g o r i z e d from one  categories  of  classified  the  Guilford  through  six  intellectual  products: Category  1 - Units  Category  4 - Systems  Category  2 - Classes  Category  5 -  Category  3 - Relations  Category  6 - Implications  Examples  of q u e s t i o n s  Transformations  f o r each c a t e g o r y  are  found  i n Table  III. A  higher  order  question  (that  is,  tranformations,  37  Category  Def i n i t i o n  u n i t s of  Example  information  "How many o b j e c t s a r e there here?"  1.Units  Basic  2 .Classes  C l a s s can be embodied d i f f e r e n t s e t s of part i c u l a r s .  using  "Can I a r r a n g e these according to s i z e , o r c o l o r , or s h a p e ? "  3.Relations  C o n n e c t i o n s between o b j e c t s or u n i t s s u c h a s opposition, part-whole, agent-action, etc.  "If t h i s paper's hole was b i g g e r , I c o u l d put t h i s q u a r t e r t h r o u g h i t . Maybe, can I put the quarter through the h o l e without ripping i t ? "  4. Systems  To t a l k about r u l e s , p r i n c i p l e s , orders, o r i e n t a t i o n s , and s t r u c t u r e s i s t o speak of the p s y c h o l o g i c a l product of s y s t e m .  "I b e t t h i s box, open up, how do you open i t , t h e r e i s a way, isn't there?"  5 .Transformat i o n s  A t r a n s f o r m a t i o n i s any k i n d o f change s u c h as expanding, r e v e r s a l , i n t e r c h a n g e , and so on.  " I f you were g i v e n this steel thing, what c o u l d you change i t i n t o ? What c o u l d you make?"  6.Implications  A c o n n e c t i o n between two u n i t s of i n f o r m a t i o n . Relations are d e f i n a b l e kinds of c o n n e c t i o n s . . . comes n e a r e s t t o t h e t r a d i t i o n a l n o t i o n of association.  "In what ways c a n y o u arrange the o b j e c t s on t h e t a b l e t o r e p r e s e n t how you f e e l a t t h i s moment? How c o u l d t h e s e m a t c h e s be man's enemy?"  A d a p t e d from t h e chapter, "New Psychological Conceptions of Memory" in I n t e l l i g e n c e , C r e a t i v i t y and t h e i r E d u c a t i o n a l I m p l i c a t i o n s , J.P. G u i l f o r d , 1968. Cited in Arlin (1975-76, p.102) . Table  I I I - The  intellectual  i m p l i c a t i o n s ) more c l o s e l y  product  categories  approaches the g e n e r a l  question  than  38  a  lower  order  transformations stimuli  in  questions  question  questions  new  ways"  " r e q u i r e the  general  quality  apparent  i n the  which  (Arlin,1977; order,  4.1.3  combination  p.297) and the  (Arlin,  1977,  1965). which  The  processes  is  It  is  i s thought  so  the  that  i s not  p.298).  outcome  of  implications  stimuli  i s abstracted that  expected  questions  Specifically,  a  readily  outcome  of  the  general  for  problem  finding  the  posing  to r e s u l t  of  higher  in a  higher  finding.  Scoring  Units  questions  implications,  the  calculated  the  20  1977,  implications  i s the  of p r o b l e m  the  o r g a n i z a t i o n of  stimuli" and  1975-76).  for  (Arlin,  Mackworth,  general  quality  "call  or p r i n c i p l e  transformations question,  (Arlin,  on  problem  quality  represents category,  given  (6).  the  tasks,  and  calculated  lowest  Inter-rater  s c o r i n g of q u e s t i o n s ,  was  the as  highest  finding  score  were  using  w e i g h t e d a v e r a g e of  each the  was  a random sample  of  agreement.  subject.  questions  asked  i n each  Quality=1(cat.1)+2(cat.2)+3(cat.3)+4(cat.4)+5(cat.5)+6(cat.6)  (Arlin,  number of q u e s t i o n s  1975-76).  asked.  A  Quality  follows:  Total  (1);  reliability  r e s u l t e d i n 87% for  score  39  4.2  Piagetian  4.2.1  Test  Assessment  Description  Subjects (Arlin,  were g i v e n  1984c).  administration, Piagetian measure  the  (Arlin,  test  items  represents  a  1982,  of  provides  32  1984a).  are formal  organize  from t h e  beginning  certain  kinds  of d a t a ,  (Inhelder-  Test answers posed to the  of  followed  interviews  of  the  items eight  Reasoning  Piaget,  and  include to basic  by the  formal  when f a c e d  1958,  p.308)  outside and  direct of  two  reasoning"  are can with these  volume),  proportional verification  or more  systems  equilibrium. of  explanations  " T h i s p r o c e d u r e of a  in  which  include  of  reasoning,  beyond  test.  potentially  manifest  selection  method  the  schemata  not  a r a t i o n a l e f o r the  to assess  level  reliable  e a c h of  formal  formal  mechanical  and  of  i s appended.  (conservation  problems.  clinical  page  subject  combinatorial  the  valid  subtests,  the  f o r group  measurement  comprise  eight  which are  conservation  reference,  given  Formal  a  test  of momentum), c o o r d i n a t i o n  items  use  which  compensations  forms  f r a m e s of  &  correlations,  (conservation or  but  The  of  is  sample  into  scheme. concepts  multiplicative  A  organized  "the  reasoning,  of  objective  It  multiple-choice  as  probability,  Test  an  level.  defined  conditions"  Arlin  A p a p e r - a n d - p e n c i 1 measure d e s i g n e d  developmental  A total These  the  answer c h o s e n the  use  (Arlin,  for  problem  i s analogous  of  1984a).  individual  40  4.2.2 T e s t  Administration  Since  the  test  was a d m i n i s t e r e d and  orally  t o the s i x t h  of c h i l d r e n  i n the c l a s s is  seventh  class  grade  Introductory  minutes, complete  a  level  t o the f i f t h  grade c l a s s  administration  t h e manual  readability  who  grade c l a s s  as w e l l , had  feature  but  1984a).  the  to f i n i s h  (Arlin,  test  Time r e q u i r e d was  at  a  the  sample  time  Oral  1984a).  The  independently.  were g i v e n  p r o v i s i o n was made f o r t h o s e  the t e s t  in  the t e s t  difficulties.  of the t e s t  completed  grade,  s i n c e t h e r e were a number  reading  remarks and i n s t r u c t i o n s  (Arlin,  i s sixth  as o u t l i n e d i n  approximately  students  closely  45  who d i d n o t  following  the  original administration. 4.2.3 S c o r i n g A total  score  i s used t o determine c o g n i t i v e l e v e l ,  below: Concrete  00-07 p o i n t s  High concrete  08-14 p o i n t s  Transitional  15-17 p o i n t s  Low  18-24 p o i n t s  High Arlin  formal formal  (1984a) p r o v i d e s  25-32 p o i n t s a description  of each  level:  CONCRETE represents performance on t h e formal tasks which i s best described as providing no e v i d e n c e o f a b s t r a c t r e a s o n i n g and some d i f f i c u l t y with reasoning skills t h a t a r e problem s p e c i f i c . HIGH CONCRETE r e p r e s e n t s p e r f o r m a n c e on t h e formal tasks which i s best described as providing some evidence of a systematic approach t o problems but not evidence of  a s seen  41  forming a g e n e r a l r u l e o r a b s t r a c t i o n from the problems. This level i n d i c a t e s some a b i l i t y t o c l a s s i f y and o r g a n i z e i n f o r m a t i o n but p r o v i d e s l i t t l e e v i d e n c e of the a b i l i t y t o make i n f e r e n c e s . TRANSITIONAL r e p r e s e n t s p e r f o r m a n c e on t h e formal tasks which i s best d e s c r i b e d as p r o v i d i n g evidence of a systematic approach t o t h e p r o b l e m s a n d some u s e of a b s t r a c t i o n s and i n f e r e n c e s but the performance i s q u i t e inconsi stent. LOW FORMAL r e p r e s e n t s a p e r f o r m a n c e on t h e formal tasks which g i v e s c l e a r evidence of t h r e e - t o - f i v e of t h e formal schemes being present i n t h e i r t h i n k i n g . HIGH FORMAL r e p r e s e n t s a p e r f o r m a n c e on t h e f o r m a l t a s k s which g i v e s c l e a r evidence of most o f t h e f o r m a l schemes b e i n g i n e v i d e n c e i n t h e i r t h i n k i n g . (p.7) Total Subtest  scores  scores  recorded  for  as w e l l  were  recorded  f o r the r e g r e s s i o n  each  of  eight  the  schemata  were  formed t h e measure o f i n s i g h t .  Four  f o r a supplementary  formal  analysis.  analysis.  4.3 Measurement Of I n s i g h t 4.3.1  Insight Eight  of  these  Davidson of  insight  (1982,1983).  a  those  written  Sternberg puzzle  used  by  Sternberg  f o u r were t a k e n  for children  for clarity.  p r o b l e m used by S t e r n b e r g  more s u i t a b l e  conducted  from  The r e m a i n i n g  m o d i f i c a t i o n s made  exactly  each  puzzles  p u z z l e s were c h o s e n  "brain-teasers"  slight  text  Puzzles  from a book  (Brandreth,1979)  Of t h e s e ,  one  and D a v i d s o n ,  and  with  parallels  but c o n t a i n s  for children.  and D a v i d s o n emphasized.  on t h e r e m a i n i n g  d e s c r i b e d the p r o c e s s e s An  inter-rater  p u z z l e s , with  100%  of  insight  reliability agreement  as  was to  42  the  processes The  the  insight  puzzles,  processes  4.3.2  concerned.  together  with  emphasized, are  A d m i n i s t r a t i o n And The  was  of  insight  their  and  timed,  but  took  approximately  A  score  on  the  puzzles  T h i s s c o r e was Scores  separately  for  each  for  of  of  use  process  purpose  The  30 m i n u t e s t o  consists  recorded  for  the  of  Scoring  p u z z l e s were g r o u p a d m i n i s t e r e d .  analysis.  listings  appended.  not  correct.  sources  of  complete.  the in  measure  total  the  insight  number  regression  were  supplementary  recorded  statistical  analysis. 4.4  Measurement Of Subjects  (Otis  completed  & Lennon,  mental  1968).  processes,  p e r f o r m a n c e on valid  IQ  and  the  individually The  Otis-Lennon  Subjects Level  test.  four.  Two  retested  I t was  IQ  i n grades Median  five  and  reading  test  (Otis  of  is  & Lennon,  this  the  test  s c o r e s of more t h a n  Intermediate  Level  test.  is  a  which  has  with  the  .60. minutes  according  s i x completed  level  1969)  r e q u i r e s 40  administered  i n t h e manual  test  correlation  i s a g r o u p measure and  time.  the  Its  of  summarizing  The  & Lennon,  Test  variety  score  1969).  Stanford-Binet  p u p i l s r e c e i v e d raw with  (Otis  Ability  wide  total  & Lennon,  1972).  Mental  sample a  single  instrument  (Buros,  provided  items  a  (Otis  administered  of a c t u a l w o r k i n g directions  with  reliable  Otis-Lennon  Eighty  test  been w e l l r e v i e w e d  the  to  the  1969). Elementary i s below 73 This  and  II  grade were  procedure  43  e n s u r e s more e f f i c i e n t Lennon,  majority  of  Intermediate Level grade.  Since  slower p u p i l s next  ability  (Otis  &  for  lowest  level  in  grade  Elementary  level  is  below  administration  grade w i t h i n  i n the  seven c o m p l e t e d  level  s e r i e s , seven p u p i l s  II L e v e l  seventh  recommends  a given  the  be  that given  i n grade  seven  test.  DESIGN The  study  manipulation all  subjects  6.  THE  entry  of  nonexperimental; the  and  variables.  analyzed THE  level,  of  the  cognitive  problem  followed  prediction  of  mediated  cognitive  by  test  variables  level,  The  is,  it  involved  same d a t a was  through p r e d i c t i v e  the  i n s i g h t , and  p r e d i c t i o n of  that  no  c o l l e c t e d on  regression.  DATA  statistically  cognitive the  was  ANALYSIS OF  To  to  mental  Its reading  manual  i n the  the  subjects  test.  the  lower  completed 5.  of  1969).  The  the  measurement  problem  IQ  the  contribute  and  that  ability  a multiple  IQ; by  that  significantly the  order  p r e d i c t i o n equation  insight  finding  level,  will  hypotheses  finding ability;  into by  research  and  regression  will  that  insight  of  the  will  analysis  be  be was  used. In  the  prediction clarity, several used.  of  analysis, a regression problem  discussion subsections,  finding ability of  the  data  beginning with a  equation  was  would be analysis  sought  so  optimized. i s be  statement  of  divided the  that For into model  44  6.1  The  Linear  Using finding  Multiple Regression  the  linear  model,  was  regressed  ability,  cognitive  level,  regression  model  where i=  1,...,N  j=  independent  1,2,3  Y = observed  the  insight,  is written  Model criterion  on  and  as  the  variable,  predictor  IQ.  The  problem  variables  linear  multiple  follows:  subjects;  score  variables;  of  i*  the  person  h  on  Y;  3  flo  ftjX'j  +  = the  variables y&> fij  = the =  which  constant; applied  Ei  to  = the  the  the  effect  them's  X j ' 's  r e s i d u a l or  partial Y;  ts*~ Y; ], as  (Kirk,  are  X  of  independent  account  for  Y;  hyperplane; on  partial  unaccounted  Y,  a l l other  regression  to optimally  i s C'»  The  assumed  J  <?£'i  underlying  Linear  be  Further =  of  X's  held  coefficients  predict Y  (Kirk,  *•*") ;  Y  (Y-Y).  assumptions.  Regression  coefficients  to  (0, * " * ^ i " ) .  (<r y; =  for part  several  regression  is  variances  and Ci  of  in order  model c o n t a i n s  linear.  c  satisfactorily  regression  Assumptions Underlying The  of  is,  of  to  combination  and  This 6.2  marginal that  weighted  i s expected  Y-intercept  the  1982);  linear,  are  normally  Model assumed  distributed  assumptions  independence  are  to  be  [£~(Y/),  homogeneity  otCi , t h a t  is,^f/  ' are  uncorrelated  1982);  independent  and  variables.  so no  that error  the in  covariances the  equal  measurements  of  zero the  45  Having methods of 6.3  stated  analysis  of  statistical  procedure.  Since  Test In  chosen  Of  The  f o r t e s t s of  Full  statistical  tested  i s the  h y p o t h e s e s as The  the  of  the  REGRESSION p r o c e d u r e s  criterion  6.3.2  of  would be  was  then  regression  the  =/^=/^=0  a l l y t ? / ' s=0.  of  the  ) was  ( L a i , 1983).  f o r by  An  of  the  This  first  three  done u s i n g  NEW  F-statistic  was  variance  in  the  predictor variables.  F-statistic,  If a s i g n i f i c a n t  s t a g e of  Of  The  the  null  F-statistic  were  Regression  from t h e the  This  predictor one  thaty^/  proceed.  planned.  equation  0.05.  not  ( R * y . tz$  non-significant  procedures  elimination  study,  2.  proportion  Estimation  for this  model,  f r o m SPSS  a n a l y s i s would  were p l a n n e d  describing  exploratory  hypothesis  equivalent  model  tenable.  selection  i s an  parts  significance is  in Chapter  full  a  S e l e c t i o n And Two  The  into five  a l t e r n a t i v e that  i f a significant  case  hypothesis  steps.  several  this  null  v a r i a b l e i s accounted  the  obtained,  the  statistical  summarized  test  to t e s t  the  Model  terms,  against  alternative  In  consisted divided  level  assumptions,  discussed.  therefore,  6.3.1  used  be  is,  t h e c*C  was  now  i t s underlying  Analysis  data  discussion each  model and  a n a l y s i s can  Methods Of  The  the  SPSS r e g r e s s i o n  analysis. procedure  variables  Parameters  Firstly,  program backward  s t a r t s with  the  full  deleted  from  the  are  at a time, a l l o w i n g  examination  of  the  46  loss  in proportion  variable. the  "It  least  of v a r i a n c e  i s thus p o s s i b l e  when e n t e r e d  REGRESSION estimates  program of  accounted  the  last"  also  t o the  deleted  t o observe which v a r i a b l e adds  (Pedhazur,  supplies  regression  f o r due  1982,  p.158).  t-statistics,  parameters  The  so  NEW  that  the  tested  for  (b's)  could  be  was  also  planned.  significance. The  stepwise  selection  procedure  In  stepwise s e l e c t i o n , tests are performed at each step to d e t e r m i n e the c o n t r i b u t i o n of e a c h p r e d i c t o r a l r e a d y i n t h e e q u a t i o n i f i t were t o enter last. It is thus possible to identify p r e d i c t o r s t h a t were c o n s i d e r e d t o be 'good' a t an e a r l i e r stage but have lost their usefulness when a d d i t i o n a l p r e d i c t o r s were b r o u g h t i n t o t h e e q u a t i o n and may therefore be removed from i t . ( P e d h a z u r , 1982,p.160) In s e n s e of  order the  selection  equation  "best"  regression  were  to  be  y . y , r e s u l t s from  examined  regression  and  the both  compared  coefficients  c o r r e l a t i o n s are  error-free.  The  i s an  (Pedhazur,  1982).  the  the  the  zero-order result  If these  predictor  would a l m o s t for  in  with  Cross-validation  y.y ,  to  equation,  expectations.  In c a l c u l a t i n g R  the  which maximizes R  procedures  theoretical 6.3.3  to obtain  which  phenomenon correlation"  scores  a l w a y s be  weights  is  referred  (Pedhazur,  of  another than  were to 1982,  t r e a t e d as  which  regression  smaller  the  V- H  R  the  the  is  sample,  biased  pp.147-148).  applied  resulting R  i n the  calculated. of  were  upwards  were  "the  R obtained  shrinkage  maximize  i f they  coefficients  originally as  to  the  sample This  multiple  47  In the c a s e  of a s i g n i f i c a n t r e s u l t  model, a c r o s s - v a l i d a t i o n shrinkage. form  a  The  screening  regression sample  would  6.3.4  T e s t Of was  finding  The  program  In  order  as  variable  .  U  F-statistic: statistic insight ability 6.3.5  2  but  Using correlation  reasoning provide  test. further  and  of  of  was  were  enhanced.  Operations of  problem  operational  hypothesis,  used  the  shrinkage  formal  used.  The  screening  scores  a predictor  insight  . .  null  the  computer  Designating  formal  as  variable  t o d e r i v e the  .  by  .  hypothesis  therefore,  2,  the  following  A non-significant that^ =0  d i r e c t l y predict  formal  tenable  l  problem  Fand  finding  reasoning.  Analyses  coefficients  processes  f o r the  to  / /'  SPSS program  of  in half  sample.  Formal  by  this was  1  By  i n s i g h t as  1980)  y . a -  i s mediated  three processes  Insight  mediated  4 j  not,  the  Of  full  estimate  g e n e r a l i z a b i l i t y would be  test  would make t h e does  r e s u l t i n g estimate  procedure  F=  Supplementary  three  to  (Le,  replacement-deletion  .  predictor  be  BMD:03R  reasoning  the  the  to  split  calibration  to  that  would  randomly  equation  Mediation  t e s t of  order  the  and  hypothesized  a  in  from  I f the  accuracy  ability  thinking.  and  applied  sample.  predictive  It  sample  be  planned  sample would be  coefficients  calibration low,  total  was  i n the  ( L a i , 1983), P e a r s o n were c a l c u l a t e d  i n s i g h t and of  problem  i n s i g h t and  I t was  felt  understanding  of  between s c o r e s on  f i n d i n g and  sub-test  that  product-moment  these the  scores  between  from t h e  correlations variables  under  the the  formal should study,  48  particularly reasoning  i n regard to the formal  and frames o f r e f e r e n c e t h o u g h t  6.4 Methods Of R e p o r t i n g  The  data  statistical sources  used were  are  of  combinatorial  t o mediate  insight.  The D a t a  reported  procedure,  of  supplemented 7.  schemata  for  variation  in  tables  example,  and  appropriate  an  ANOVA  correlation  by w r i t t e n i n t e r p r e t a t i o n  to  table  matrices,  each  showing and  are  of the r e s u l t s .  SUMMARY OF CHAPTER THREE Chapter  T h r e e was c o n c e r n e d  to test  the f i v e  with p r e s e n t i n g the methodology  hypotheses.  d e s c r i b e d and p r o c e d u r e s  The  concerned  and  s c o r i n g o f t h e IQ measure, t h e t e s t  the  insight  chapter  and  concluded  problem with  finding  with  of  and  sample  the a d m i n i s t r a t i o n  of f o r m a l  tasks  descriptions  a n a l y s i s and d a t a r e p o r t i n g .  population  were the  r e a s o n i n g , and detailed.  The  methods o f d a t a  49  IV. 1.  OVERVIEW OF  THE  This chapter of  the  In o r d e r  consist  of  five  will  presented  appropriateness sections w i l l  those  parts.  of  the  results  will  be  apparent  in  operationally formal  defined  schemes b e i n g  development  (Arlin,  t h e a b s e n c e o f , or Attainment alone 2.  of  does not  SUMMARY  finding  insight, IQ and  high  a  and  s c o r e s on  discussion  sample.  in this  study  incomplete  that  the  Subsequent  analysis,  the  e a c h of  the  to the  Cognitive as e v i d e n c e  i s , the  "high  variables. maturational maturity  is  of most of  the  formal"  stage  M a t u r a t i o n a l c o n s t r a i n t s thus development  operations  guarantee t h i s  model.  of  a qualitative analysis  made i n t h e c h a p t e r the  will  f o r each v a r i a b l e  regression  analyses,  1984a).  and  concerning and  the  IQ and  cognitive level  chapter.  the  results  of,  formal  of  imply  operations.  i s u s u a l l y a g e - r e l a t e d , but  age  attainment.  STATISTICS  Statistics problem  statistics by  the  the p r e s e n t a t i o n  regression  of  i n use,  formal  p r e s e n t a t i o n of  followed linear  subjects earning  constraints  to the  Summary  first,  detail  Reference  ANALYSIS  to a i d c l a r i t y ,  supplementary c o r r e l a t i o n a l of  THE  CHAPTER  i s devoted  analysis.  be  RESULTS OF  scores  on  the  criterion  v a r i a b l e of  p r e d i c t o r v a r i a b l e s of c o g n i t i v e  information concerning i n the  sample  form  the  level,  the d i s t r i b u t i o n first  p a r t of  of  this  50  2.1 P r o b l e m F i n d i n g  The with  range of problem  a  mean  subjects  of  No  level  finding  2.99  i n the s i x t h  question. higher  of  standard  is  the asking  which  found  finding  a  with  The l a c k o f  previous  problem  a significant  quality.  requiring  Two  transformation  a  effect  The low  level  below,  seemed  o f t h e sample, a s i n d i c a t e d of q u e s t i o n s  4.33,  of 1.09.  were a s k e d .  consistent  on p r o b l e m  cognitive maturity  posed  questions  (Arlin,1977)  s c o r e s was 0 t o  deviation  grade group each  questions  research  to preclude  and  implications  operational level  of  finding quality  high  level  of  abstraction. 2.2 C o g n i t i v e L e v e l Scores of  b a s e d on t h e P i a g e t i a n a s s e s s m e n t  4 t o 21 w i t h  mean  score  majority  a maximum  was  10.99  sample.  There  Classification accomplished Arlin  Test The  level  with  a standard  of s u b j e c t s no  high  formal  translated  reference  with  of l e v e l s  expectations The f i f t h  academic  level  Table  a t t a i n e d by  from t h e  (Arlin,  i n the seventh  This  of the s i x t h  The IV this  t h i n k e r s i n the sample.  children  grade group i s  would be e x p e c t e d .  thinkers.  raw  scores,  to the cut points provided  for  The  d e v i a t i o n of 4.07.  i n the l e v e l s  o f F o r m a l R e a s o n i n g manual  1984a).  than  overall  with  by l e v e l s ,  distribution  consistent (Arlin,  were  i n the range  p o s s i b l e a t t a i n a b l e s c o r e o f 32.  o f t h e sample were h i g h c o n c r e t e  shows t h e p e r c e n t a g e s  were  fact,  was  i n the  1984a). grade of t h i s  higher  in  group  is  age g r o u p cognitive  i n a d d i t i o n t o t h e low  g r a d e g r o u p , would a p p e a r t o  51  explain  the  distributions  of  differences  between  the  s i x t h grade  f i f t h and  the  cognitive  groups.  Grade 7  Grade 6  Grade 5  Concrete  14%  25%  21%  20%  High Concrete  62%  71%  63%  66%  Transitional  14%  11%  8%  Low  10%  5%  6%  Formal Table  2.3  IV  . 0 % 4% - Cognitive  level  Total  Sample  level distribution  Insight S c o r e s on  r e s p o n s e s out The standard  the of  mean  subjects  will  be  score  general,  even  and  the  1.42.  i n the the  section  is  Sternberg  developmental considerations specifying gifted  insight  children.  chapter insight.  would  as  a  to  on  (1984). must be  0 to  was 7.  scores  qualitative  children  i n the with It  differential  correct  with  Profiles on  the  sample the be  into  cognitive  i n subsequent  1.25  a of  puzzles  analysis.  will  taken  of  8.  puzzles  high  consistent  Data p r e s e n t e d appear  few  number  of  range was  the  brightest This  score  insight  The  obtained  difficult.  Davidson  on  of  who  analyzed  were t h e  a maximum p o s s i b l e  deviation  the  puzzles  insight puzzles  In  found  the  findings  of  seen  that  account  when  attribute  sections  of  i n d i c a t e developmental c o n s t r a i n t s  of the on  52  2.4 The IQ M e a s u r e  IQ  s c o r e s ranged  standard deviation standard (Otis  &  o f 15.09.  Lennon,  attain  (1968).  1968).  summarizes  comparison  to  of  97.72  distribution  scores  as  range  normal  normally.  of c h i l d r e n  the  Otis-Lennon  manual  fell  within  distribution.  expected  in a  distribution  Percentage obtaining  o f sample these  scores  3%  117-132  14%  9%  85-116  68%  72%  69-84  14%  13%  2%  3%  and lower  in  expected  2%  68  132  in  o f 16  received  i n g e n e r a l , t h e sample  f o r a normal  Percentage  scores  percentages  given  that,  of  and  IQ i s a n o r m a l i z e d  The sample was d i s t r i b u t e d  the  I t c a n be seen  score  Above  The O t i s - L e n n o n  the approximate  these  the expected  IQ  65 t o 136 w i t h a mean  s c o r e w i t h a mean o f 100 and a s t a n d a r d d e v i a t i o n  Table V  to  from  T a b l e V - D i s t r i b u t i o n o f IQ s c o r e s a s compared w i t h t h e normal d i s t r i b u t i o n  Given the l i n e a r  these d e s c r i p t i v e  r e g r e s s i o n model t o a n a l y z e  the p r e d i c t o r discussed.  statistics,  variable  the a p p r o p r i a t e n e s s of  the r e l a t i o n s h i p  and t h e s e c r i t e r i o n  variables  will  between now be  53  3.  APPROPRIATENESS OF  Since the  it  linear  are  criterion  analysis (Lai,  to  model be  done  be  the  using  the  met  if  of  valid  r e l a t i o n s h i p between  the  predictor  NEW  REGRESSION p r o c e d u r e s  Durbin-Watson  error  terms  t e s t supported  were  not  probability  plot  standardized  s c a t t e r p l o t s confirmed  showed  appropriateness One  outlier  proved  problem  of  was  to  variables,  this  the  linear  residual from  SPSS  On  the  subject's  the  over  had  basis  of  predicted  that  [D(=2.10)  error  homogeneity  regression  who  hypothesis  r e s i d u a l s and  of  slightly  a subject  f i n d i n g task.  variables,  normality  null  correlated  standardized  found at  be  the  serially  A h i s t o g r a m of  This  assumptions  satisfactorily  d#(=1.7l)].  the  underlying  drawn r e g a r d i n g  v a r i a b l e s and  was  that  1983). The  the  LINEAR REGRESSION MODEL  important  regression  inferences the  is  THE  of  a  >  normal  terms,  and  variances  and  function. -3  failed scores problem  S.D. to  (-3.15).  respond to  on  the  the  predictor  f i n d i n g score  was  3.38. It  was  regression validly 4.  RESULTS OF  Results  of  the  underlying  been met  regression  THE  and  assumptions  that  of  inferences  the  could  linear be  drawn  analysis.  REGRESSION ANALYSIS  regression  analysis  the  the  t e s t of  subsequent  procedures,  that  model had  from t h e  The  with  felt  sections  full  consisted model w i l l  detailing  shrinkage estimates,  and  of be  results  the  several  steps.  presented of  outcome of  the the  first,  selection test  of  54  the  mediation  4.1  Test  Of  The  sum  the  The  insight Full  f o r by  of  the  of  S o u r c e of  of  operations.  variance  errors  variables  in  the  variables of  was  Sum  of  squares  significant.  not  VI  df  4.78  minimized  by  summarizes  the  72  Total _ (Y;- Y)  89.66  75  T a b l e VI  Since F a  hypotheses  ( = 1.35)  - Analysis  <  3 7Z  relating  Thus,  to  the  of  F  1.59 1.18  1.35  variance  ( = 2.74), the  t  tenable.  s  Mean s q u a r e  3  84.88  w  was  Table  Residual (Y;Y)  =  not  variable  variance.  variation  ft,Px fi*-Q  criterion  prediction  chosen.  Regression (Y - y)  =  formal  predictor  squared  predictor  analysis  the  by  Model  proportion  accounted The  of  none  of  prediction  null  the of  hypothesis  three  problem  that  research  finding  were  supported. Despite model,  the  carried  the  elimination  out  predictor  non-significant  in  variables  qualified  procedure,  but  believed  be  to  procedures planned  order  variables  r e s u l t s on  to  for for  backward relevant  to  examine possible entry  for  the  test  of  the  study  in  the  prediction  the  contributions  significant  elimination the  the  were of  trends.  stepwise  provided of  full  problem  the No  selection information finding.  55  4.2  Backward  In  the  forced This  following  done t o  the  multiple +  backward e l i m i n a t i o n  in i n the  was  that  Elimination  order:  investigate  order  of  regression  entry  cognitive  the of  equation  procedure,  will  be:  variables  level,  research the  the  were  insight,  hypothesis  IQ.  stating  predictor  variables  cognitive  level  the  step  in  the  +  insight  of  backward  IQ. Cognitive  level  was  removed on  first  a. elimination, insight  was  equation,  the  Step  removed  an  significant of  resulting  R  of  at  the  in on  the  0.05 0.06  R  F  change  second  in  step.  was  obtained,  level.  T a b l e VII  backward e l i m i n a t i o n  R  little  R  .  W i t h IQ a  Similarly, only  result  in  which  summarizes the  procedure.  Sig.F  R*  change  Variable In:  2  In:  Insight  IQ  In:  Cog.  Level Level  3  0.05  0.01  1.35  0.26  0.05  4  0.05  0.02  1.95  0.15  -0.003  Out:  Cog.  5  0.05  0.03  3.69  0.06  -0.003  Out:  Insight  It little  can to  likely subjects  - Summary t a b l e  be  the  to at  seen t h a t prediction  the  small  the  low  of  backward e l i m i n a t i o n  cognitive of  problem  number of formal  was  results  1  T a b l e VII  the  level  insight  contributed  finding, cognitive  formal  stage)  and  procedure  thinkers  and  i n the  insight,  as  level  due  sample  (5  will  be  56  discussed  later  maturational While expected  in  the  chapter,  due  likely  to  the  same  constraints.  IQ a s a  predictor  direction,  of  problem  finding  is  in  the p r o p o r t i o n of v a r i a n c e accounted  the  for  is  slight. Results  from  backward e l i m i n a t i o n  research  hypothesis  variables  was n o t  4.3  concerning  also  order  indicated  that  the  of e n t r y of the p r e d i c t o r  supported.  Shrinkaqe Since the t e s t  of the f u l l  model  was  not  significant,  a  z. cross-validation on  the  SPSS  acceptable  was n o t done.  NEW  limits.  REGRESSION  the  output,  in R  was r e p o r t e d  however,  and i s w i t h i n  T a b l e V I I r e p o r t s t h e a d j u s t e d R^ CR*) .  4.4 T e s t Of The M e d i a t i o n The  The s h r i n k a g e  Of I n s i g h t By F o r m a l  following F-statistic  replacement-deletion  was d e r i v e d  procedure  Operations  using  results  w i t h i n t h e computer  from  program  *V/*->eV / A BMD: 03R  : F=—^3  Le,l980  Formal variable  reasoning  2.  hypothesis directly  that/? =0 t e n a b l e and x  problem  reasoning.  S i n c e F( = 0.69)  t h a t fix =0  was f o u n d  The  supports  < ,fs  the  effect research  insight but  does is  There  insight reasoning  hypothesis  that  1;  insight  as  w o u l d make t h e n u l l not,  therefore,  m e d i a t e d by f o r m a l  7* (= 3 . 97 ) , t h e  t o be t e n a b l e .  of f o r m a l  as v a r i a b l e  F-statistic  finding  r e l a t i o n s h i p between  mediating  , , = 0.69.  was d e s i g n a t e d  A non-significant  predict  predictive  .  null  i s thus  not a d i r e c t  and. problem found  finding.  in this  cognitive  hypothesis  analysis  level  will  57  mediate  the  therefore, is  an  i n t e r m s of  Results their  under 5.  the  THE  taken  reasoning  for  up  in d e t a i l  the  there i s ,  and  insight  for definition  curriculum  supplementary analyses to  That  planning.  i n Chapter  will  now  understanding  be  of  of  5.  looked  at  the v a r i a b l e s  SUPPLEMENTARY ANALYSES  between  the p r o c e s s e s addition,  indicated  the p r o c e s s e s of  insight  since  correlational  relationships will,  of  these  relationships  The  R e l a t i o n s h i p Of  No  Of  which problem  formal  were  and  reasoning  done  finding,  variables  to  the  to  test  the  out  schemata.  the  important  D i s c u s s i o n of of  problem  among  was  carried  study, these  supplementary  three parts r e f l e c t i n g  each  in turn. P r o b l e m F i n d i n g Q u a l i t y To  The  Three  Insight  and  in Table Given  the  analysis  therefore, consist  significant  processes  insight  considered  for significance.  analyses  Processes  and  of  analyses  intercorrelations  relationships  another  found  and  supplementary c o r r e l a t i o n a l  as p l a n n e d  5.1  be  formal  i m p l i c a t i o n s both  insight  contribution  RESULTS OF  In  between  finding.  study.  Two  and  of  problem  issue with  implications will  for  of  a relationship  important  giftedness These  prediction  correlations  problem  finding.  finding  found  Results  between  of  insight  the a n a l y s i s are  VIII.  the m a t u r a t i o n a l  resulted  were  in only t a s k and  constraints operative  lower very  order few  questions  high  insight  i n the  being  posed  scores,  sample i n the  i t is  to  58  Problem  finding  Selective  encoding  0.02  Selective  combination  0.12  Selective  comparison  0.16  quality  N=76 Table VIII  - C o r r e l a t i o n m a t r i x of p r o b l e m f i n d i n g w i t h the t h r e e p r o c e s s e s of i n s i g h t  be  expected  due  to a " f l o o r  in  that c o r r e l a t i o n s  responses  an  effect."  and  inadequate  An  would be  insufficient  a therefore limited test  the  and  5.2  The  R e l a t i o n s h i p Between The  The  Formal Reasoning was  systems  with  combinatorial process  of  concept  The  of  comparison  to c e r t a i n  one  frame  of  of  scheme  all when be  in  between  Insight  And  was  i n s t a n c e s of reference  seen  for this  a  of  is  as  scheme  believed new  encoding  necessary  to  or more most the the  "involves  the  of a  solution  for" (Arlin,  of  relevant to  combinations  relating  selective  of two  In p a r t i c u l a r ,  problem's  was  schemes  correlate  insight.  accounted  process  reasoning  would  possible  r e f e r e n c e scheme  and  Of  coordination  reference  ...  a l l possibilities  selective  the  combination  generating  frames of  formal  the p r o c e s s e s  selective  of  relationship  Three Processes  the  and  reasoning  number of v a r i a b l e s that  that  frames  significantly  scores resulted  Schemata  reasoning  or  r a n g e of  abstraction  finding.  expected  combinatorial  in a l l probability  d e g r e e of  hypothesized  insight  It  problem  of  low,  quality  given  requires  1984a,  relevant  p.10). to  the  to o l d information where  more  correctly  than encode  59  information  relevant  Significant processes the  of  selective  as  Correlations e n c o d i n g and  selective  correlation  between  reference  may  to e x i s t  frames  of  be  necessary  "isolated may  not  resemble  The  due,  comparison,  in  that  i t s parts"  of  at  not  only  one  insight  of  one  which  encoding  with  frame of  reference seemingly  whole t h a t may  f r a m e s of  in this  The  frames  t o the  & Davidson,  to a p o s s i b l y i n s u f f i c i e n t that  selective  combining  into a unified  supported  facts,  reference.  and  i s , more t h a n one  (Sternberg  that  involves  both  selective  r e l a t i o n s h i p between was  between  of  and  a solution.  f r a m e s of  instances  appear  relevant  combination  correlation  insight  combination,  in that  and  the  combination  would  relationship similar  information  comparison  in part,  a  in c e r t a i n of  It  to a r r i v e  combination  i n the  expected  selective be  pieces  selective  selective  reasoning  selective  reference;  between  also significant  represent  appears  may  w e l l as  combined  were  and  scheme.  of c o m b i n a t o r i a l  once e n c o d e d , must be  found  encoding  reasoning  encoding,  some n o t i o n  problem.  c o r r e l a t i o n s were  combinatorial  selective  to the  1983,  measure of  puzzle  p.53).  reference  study.  or  This  and may  selective  emphasized  this  process. Additional  significant  selective  e n c o d i n g and  selective  combination  relate  to the  propositional It  can  be  c o r r e l a t i o n s were  both p r o p o r t i o n and  "combinatorial logic  of  formal  and  proportion. system" thought  seen t h a t a c o m b i n a t o r i a l  obtained  momentum, and  between between  These c o r r e l a t i o n s  thought (Piaget  to  underlie  & Inhelder,  may the  1977).  s y s t e m w h i c h would e n a b l e  a  60  subject  " t o combine among t h e m s e l v e s  factors given  with  reality  based  required  or a t h e o r y  i n the t e s t  form  combining  of t h o u g h t  1983),  items  processes  IX  summarizes  of i n s i g h t  objects  " t o reason  reality,  an  sense  1977,  t o the n o t i o n a unified  selectively  propositions in a relevant  Table  with  the  about a  explanation of a group of  pp.398-399)  Selective Encoding  of  (Sternberg factors  or  way.  reasoning  between t h e t h r e e schemata.  Select ive Combinat i o n  Selective Comparison  Volume  0.03  -0.04  0.08  Probability  0.13  0.05  -0.09  Correlations  0.22  0.15  0.13  Combinations  0.27*  0.49**  0.17  Proportion  0.29*  0.23*  0.09  Momentum  0.25*  0.08  0.08  Mechanical E q u i l i b r i u m  0.05  0.18  0.11  Frames o f  0.23*  0.32**  0.11  N=76; * p<0.05; ** p<0.0l Table  as  selectively  whole  encoding  correlations  and t h e f o r m a l  Reference  or  f o r momentum and p r o p o r t i o n i s a  related  and/or  or  i n the simple  p i e c e s of i n f o r m a t i o n i n t o  Davidson,  related  physical  p r o p o s i t i o n s " (Piaget & Inhelder,  selective  &  (physical,etc.)"  (a segment o f  on f a c t o r s ,  related is  factors  objects  IX - C o r r e l a t i o n m a t r i x o f t h e t h r e e p r o c e s s e s o f i n s i g h t w i t h t h e f o r m a l r e a s o n i n g schemata  61  5.3 C o r r e l a t i o n s  Among The  C o r r e l a t i o n s among relationships correlations  which  Variables  the v a r i a b l e s are  relevant  are presented  i n Table  Insight Cognitive  Level  Insight  some  to  research.  the  significant These  X.  IQ  0.43**  revealed  Problem  0.55**  0.09  0.34**  0.13  IQ  Finding  0.22  N=76;  ** p<0.0l  T a b l e X - C o r r e l a t i o n s among t h e p r e d i c t o r variables  The insight  significant  discussion  Maturational of  cognitive  level  i n s i g h t i s mediated  c o n s t r a i n t s a r e thus  i n s i g h t as a d i f f e r e n t i a l  by  important  cognitive  and formal  in  any  a t t r i b u t e of  gifted. The  c o r r e l a t i o n between IQ  research  cited  attainment will  between  supports the f i n d i n g that  operations.  the  correlation  and c r i t e r i o n  of formal  be  discussed  qualitative That hypothesis processing (Davidson  in  the  and  review  operations further  cognitive  level  of t h e l i t e r a t u r e by g i f t e d in  the  children. subsequent  supports  dealing This  with issue  section  on  analysis.  i n s i g h t c o r r e l a t e s with that  i n s i g h t may  characteristic  IQ  represent in  appears  support  a differential  intellectually  & Sternberg,1984; Sternberg  to  &  information  gifted  Davidson,  the  children  1982,1983).  62  In  their  study  D a v i d s o n and between  while  appears  to  predictor  weak and  The  formal  the  maturational  their 6.  of  on  a  the  found  for  the  level  0.55  problem  IQ  and  reflect  and  as  a  problem  once  insight of  this  and  more  mature  with  post-  suggests  sample would be  relationships.  in Chapter  findings  problem  more  study  older  hypothesized  5 since  relevant  to  there the  a  This are age-  giftedness.  a qualitative analysis to  and  been a s s o c i a t e d  and  further  d e f i n i t i o n of  contribution  IQ  sample  i n s i g h t , an  a r i s i n g from t h e s e  of  of  expected d i r e c t i o n  between  with  1984b)  explored  Results  six,  sample.  f i n d i n g has  (Arlin,  issue  appropriate  i n the  testing  test  implications  between  f i n d i n g may  relationships  constraints  be  and  correlation  between c o g n i t i v e  constraints  more a p p r o p r i a t e will  five,  measure.  problem  Since problem  thought  a  directionality  correlations  further  four,  finding.  hypothesized  thinkers.  found  relationship  i n s i g h t and  need  grades  s i g n i f i c a n t , i s i n the  problem  maturational  finding  a g r o u p IQ  support  of  The  not  in  (1984)  correlational  finding,  finding  children  Sternberg  i n s i g h t and  The  the  of  research  will  now  be  presented  for  findings.  QUALITATIVE ANALYSIS Results  variables, scores,  do  significant  of  while  a  qualitative  tentative  appear findings  due  to c o n f i r m of  the  analysis  of  high  to  the  the  maturational  study.  small  s c o r e s on a l l  number  of  constraints  high and  63  Those or  transitional  subjects 134) B  subjects with  who  was  (IQ  Of  scored  the  136)  stage.  only  the  highest  particular  highest  low  formal  on  the  thinker  i n the  low  formal  That  b r i g h t e r c h i l d r e n were a t a more  will  be  peers  d e a l t with  i n the  low one IQ,  highest  formal  a  score at and  t h i n k e r s and  exception was  the  had  place.  a subject  high  concrete  highest  limit  transitional  thinker.  emerge  some e x p e r i e n c e  of  reference  by  The  group.  cognitive  those  f r a m e s of  1984b)  and  was the  last  t o do  The  average  of  schemes i n more  formal, her  to  w e l l on  of  frames the  i t i s unusual  which enabled and  IQ's.  classification  since  below h i g h  were  d i d , however,  reference  subject  the  questions  which  who  above  This subject  be  level  an  high concrete  this  to  (Arlin,  may  frames  and  (IQ  Subject  grade  advanced  having  Alternatively,  i n place at a  have had  while  that  scheme t o be  A  chapter.  thinker.  scheme i s b e l i e v e d to  seventh  two  grade.  a v e r a g e or above a v e r a g e  f o r the  indicate  grade;  fifth  were o b t a i n e d  who,  correlations  T h i s may  schemes  scores had  the  implications for instruction  following  was  the  reference  insight  has  formal  Subject  sixth  i n the  t h i n k e r s were i n t h e  their  The  thinker  low  were  IQ measure.  remaining  than  the  interest  only  level  formal  were a t  the  these  low  IQ's  this  of  formal for  this  subject  answer the  a  the  insight  puzzles. The scores  seventh on  suggested high  the  g r a d e g r o u p had  insight  maturational  problem  finding  puzzles  the  w h i c h would a p p e a r  c o n s t r a i n t s on  scores  was  smallest proportion  less  insight. conclusive.  of  to support  The  pattern  low the of  64  A  high  frequent only  problem  use o f r e l a t i o n s  Systems q u e s t i o n s  This  formal  Examination reasons two  in  the  1977; A r l i n , in  questions  this  posed  since, in general,  were  sample. reasoners.  of a  transition  1984 i n p r e s s b ) . sample,  indicated  however.  two p o s s i b l e  systems q u e s t i o n s  fell  into  categories. It  you  r e f l e c t e d the  since there  some e v i d e n c e  indicated  systems  for this,  study  i n samples of c o n c r e t e  (Arlin,  not  in this  questions  usually indicate  was of  order  a r e common  operations  pattern  score  and s y s t e m s q u e s t i o n s  two i n s t a n c e s o f h i g h e r  Relations questions  to  finding  may be t h a t t h e example g i v e n  form  provided  four  triangles  out  of  these  a " s e t " which t h e c h i l d r e n  questions.  The  which appeared  following  are  you  make  up  a  used  s i x match in  examples  t o match t h e example  Can  i n the i n s t r u c t i o n s ,  "Can  sticks?"  formulating  of systems  their  questions  given:  game  using  the s i x  matches? Could How of  many 3 - s i d e d  matches?  c a n y o u make o u t  square  out of  matches?  was  the  question,  "Can  asked  by s u b j e c t s  i n response  "Do y o u have any q u e s t i o n s may have p r o v i d e d numerous  triangles  y o u make a 3 - d i m e n s i o n a l  Additionally, questions?"  out of f i v e  30 t a c k s ?  Could six  y o u make a s q u a r e  systems  f o r me b e f o r e  a direction questions  be  to  This, too,  the  t o resemble  math,  to the query,  beginning?"  f o r responses appeared  they  task,  for  mathematical  65  problems  such  curriculum.  as  students  The  encounter  following  are  in  the  mathematics  some examples o f t h i s  t y p e of  question: How many 20.5 cm p i e c e s c a n y o u c u t from one of  the cords?  How  l o n g do y o u  three  think  candles  i t would  t o burn  t a k e s one c a n d l e  a 2-metre c o r d  cut  it  for if  i t  one h o u r ?  How many p i e c e s o f c o r d would you  take  in  half  you  and  each  have  if  half  in  quarters? If  a box i s p e r f e c t l y  side  is  5  appears  into either scores more  that,  and  o f t h e b o t t o m and l e f t  since  systems  questions  o f t h e above c l a s s i f i c a t i o n s ,  reflecting t o these  the  right  cm and t h e t o p i s 5 cm, what i s  t h e measurement It  square  side? generally  higher problem  finding  f r e q u e n t u s e o f s y s t e m s q u e s t i o n s were  "sets"  than  to evidence  of a t r a n s i t i o n  fell  related  t o formal  operations. 7.  SUMMARY OF CHAPTER FOUR Chapter  analysis insight This  4 presented  of  the  full  the r e s u l t s model  were n o t s i g n i f i c a n t result,  considerations cognitive  however, important  of the  showed  that  predictors  lent  support  t o a study  study. cognitive  l e v e l and  of  problem  finding.  to  the  of problem  m a t u r i t y o f t h e sample a p p e a r e d  Regression  to  developmental  finding.  The low  militate  against  66  high  level  finding  task.  expected for  was  responses  the  IQ as a p r e d i c t o r  direction, minimal.  predictor  in  although  Significant  variables  insight  p u z z l e s and  of p r o b l e m  finding  the was  t h e amount of v a r i a n c e correlations  which supplement  the  were f o u n d findings  of  problem in  the  accounted among  the  the  primary  analysis. Formal problem  reasoning  finding  certain processes appeared  of  by  the of  was  insight. formal  selective  to support  Conclusions, research  stemming  presented  i n the  found  to mediate  Significant  reasoning encoding  correlations  schemata and  effect.  implications,  and  the  results  following chapter.  of  and  selective  t h i s mediating  from  the p r e d i c t i o n  suggestions this  the  of  between insight  combination  for  research  future will  be  67  V. 1.  OVERVIEW  This problem  was  finding  intellectually  of  revealed  that  finding  concrete  level  general  questions.  as  a  The  the  account  f o r only  Chapter some will  in  be n o t e d ;  classroom  regression  that  some c o n c l u s i o n s  a  order  t h e low o v e r a l l the asking  "floor  of  effect"  i n s i g h t emerging The  that  regression IQ was i n t h e  finding  equation.  It did,  i n problem  finding.  research.  as  i n s i g h t i s m e d i a t e d by  problem  to discussion  for future  presented.  lower  showed  of  5% o f t h e v a r i a n c e  5 i s devoted  suggestions  predicted  predictor.  elimination  their  analysis  emerge  to preclude  that  significant  the  the  not  l i k e w i s e worked a g a i n s t  backward  appeared  of  and t h e d e v e l o p m e n t a l  expected d i r e c t i o n as a p r e d i c t o r alone  sense  finding  thinking  i n t h e sample  of  in  for  f o r i n the c r i t e r i o n  did  i t  o f t h e sample a p p e a r e d  statistically  procedure  predictor,  of  v a r i a b l e s of  analyzed  results  level  related to  attribute  predictor  were  The  cognitive  ability  operational  operative  The  accounted  finding.  significant  cognitive  insight  variance  while  t e s t hypotheses  differential  and  the  problem  to  children.  IQ,  problem  formal  a  gifted  to  statistically  conducted  as  level,  contribution variable  CONCLUSIONS  OF THE CHAPTER  study  cognitive  DISCUSSION AND  of these  when  however,  results,  Limitations  i t  with  of the study  drawn; and i m p l i c a t i o n s  f o r the  68  2.  LIMITATIONS OF  The While  sample  the  limits,  independent  appropriate A low  STUDY  was  limited  shrinkage  acceptable of  THE  of  i t is felt  did  serve  to  of  the  and  insight,  correlation  a smaller  sample  in a  "floor  sample.  subjects. was  of  i s s u e which  this  been  1982). to  "floor  in  number  have  due  regression issue  within  the  would  effect"  While  maturational  an  ratio  size  r e s u l t s i n the  t o h i g h l i g h t the  number of  i n r e s u l t s (Pedhazur,  also existed  non-significant  finding  that  f o r more s t a b i l i t y  cognitive maturity to  multiple  variables  limitation  led  the  i n t e r m s of  the  effect"  analysis, i t both  problem  i s l a r g e l y ignored  in  the  literature. Rationale in  the  study  Chapter  involved  3,  perspective Keating,  for using  (Arlin,  1975;  (1984)  suggested  the  information  3.  DISCUSSION OF  insight, of  the  IQ  not  a;  Shields,  of  1967;  may  upper be  gifted  as  done from a  Carter  group.  with  there  Firstly,  &  level  stated  Piagetian  Ormrod,  Webb, 1974)  Secondly,  1982;  were done  Davidson  elementary  and  school-aged  qualtitative differences children  in  in this  age  in  group.  RESULTS  the  will  predictor  be  will  covered  upper e l e m e n t a r y  giftedness  same age  that  e f f e c t s of and  &  work  THE  of  in press  processing  discussion  analyses  the  the  considerations.  1984,  Lovell  Sternberg's  The  two  investigations  with approximately  children  c h i l d r e n at  discussed  concern  under  the  v a r i a b l e s of separately.  results above  from  headings.  cognitive A the  fourth  level, section  supplementary  69  3.1 C o g n i t i v e While  Level the  As A P r e d i c t o r  regression  analysis  failed  to  confirm  that  of  f i n d i n g , t h e r e l a t i o n s h i p between t h e mean  level  of  problem a  relevant  problems.  appears to confirm  consideration There  appear  when to  questions  that  be  failure  criterion  variable  cognitive  finding  of c o g n i t i v e  level,  scores  would a p p e a r  due t o t h e f a i l u r e  of  t r a n s i t i o n to formal  to  represent,  rather,  i n the  level  is  to find  constraints  on  children. with the  t o be due t o t h e l i m i t e d range t h e l i m i t e d range of problem  This  l a c k o f c o r r e l a t i o n may  of systems q u e s t i o n s operations.  to represent  Systems q u e s t i o n s  a "set" created  of the problem  posed  to correlate highly  and, t h e r e f o r e ,  be  completion  level  i n t h e sample.  cognitive  cognitive  developmental  the  predictor  p r e d i c t i n g the a b i l i t y  f i n d i n g c a p a b i l i t y , even among b r i g h t  The  of  would be a s i g n i f i c a n t  t h e sample and t h e l o w e r o r d e r  f i n d i n g task  problem  level  Finding  hypothesis problem  cognitive  Of P r o b l e m  evidence were  by examples g i v e n  f i n d i n g task,  as d i s c u s s e d  also  felt  p r i o r to  in  Chapter  4. 3.2 I n s i g h t  of  The  hypothesis  problem  finding  maturational posing to  As A P r e d i c t o r  than  IQ  in  limited  that  not  appeared  supported.  t o be c o n f i r m e d level  to  predictor  Again,  the  to m i l i t a t e against the  i n the problem  responses  cognitive  Finding  i n s i g h t as a " b e t t e r "  was  that  questions  c o n s t r a i n t s appeared hypothesis  concerning  constraints  of g e n e r a l  result  Of P r o b l e m  finding  task  seemed  the i n s i g h t task.  by t h e  acceptance  These of  the  would m e d i a t e t h e p r e d i c t i o n o f  70  problem  finding  by  between c o g n i t i v e Further between the problem  research three  (Arlin,  1984b), an  thinkers  IQ  As  The  between  in  the  elimination,  direction,  either again,  level  seen t o While  cognitive  has  been  post-formal, of  Since  relationship  more  suitable  test  problem  finding.  to  further  adult  thought  sophisticated  of  a  possible  Finding  IQ  as  the  a relevant extent  equation  account this  of  Given  IQ,  and  greater insight  Additionally,  of  problem  level  role  level  exploration  and  relationships  that,  generated  for  5%  result small  of  the  was  predictor  in  proportion  of  appearing  by  backward  variance  in  the  expected  of  variance  for.  fruitful.  high  of  to  prediction  i t was  correlation  finding.  bear a  finding  Problem  supported  hypothesized  cognitive  and  i t represents a very  prediction  of  insight  finding.  The  more  concerning  alone  accounted  a  hypothesis was  to  sample c o n s i s t i n g  Of  finding  possible  problem  appear  A Predictor  problem  problem  p r o c e s s e s and  characteristic older  significant  investigate  problem  would p r o v i d e  relationship  the  insight.  insight  and  be  by  should  and  to  and  and  insight  operations  hypothesized  3.3  level  finding  formal  insight  such  of  a weaker p r e d i c t o r  insight  was  the  research  hypotheses d e a l i n g  using  an  not  supported.  older  sample  significant correlations  insight, cognitive being a  as  or  finding  the  IQ  i t may  of  IQ  be  that,  with older  maturity  would  result  stronger  sample may  predictors  better  test  the  in  than Once  with  the  would  be  with  both  subjects cognitive  than  IQ.  hypothesis  of  71  problem  f i n d i n g as a d i f f e r e n t i a l  cognitive  attribute  of  the  gi f ted. 3.4 F u r t h e r It  Discussion  has  insight  been  the  gifted  (Davidson  possible  insight  suggested  Of  0.01)  a  1984;  closer for  in this  four,  c o n s i s t e n t l y outperformed  selective  problems  &  Davidson,  a t one o f t h e s e  studies  constraints  with  in  a  their  been  included  on  peers,  While  scores  subsequent  section  inherent  cognitive  level  i n Davidson  (1984) gifted  are s t i l l  12 on s e l e c t i v e  o f 6.50 o u t o f a p o s s i b l e  problems.  example, one o f t h e p r o b l e m s u s e d was a s f o l l o w s :  and s i x .  16  The s e l e c t i v e c o m p a r i s o n  different testing conditions  implications  may be t h a t  five,  o f 4.08 o u t o f a p o s s i b l e  combination  represented  instructional  have  c o g n i t i v e a t t r i b u t e of  maturational  e n c o d i n g p r o b l e m s and a mean s c o r e  It  research  research.  i n grades  w i t h a mean s c o r e  dealt  support  between  p a r t i c u l a r i n t e r e s t i s t h e D a v i d s o n and S t e r n b e r g  children  on  to  found  Sternberg  look  the  Analysis  correlation  appears  & Sternberg,  support  with c h i l d r e n  low,  the  as a d i f f e r e n t i a l  However,  reveals  that  p<  insight  1982,1983).  work  noted  and IQ (0.34;  hypothesizing  Of The S u p p l e m e n t a r y  of  and  the chapter  will  be  f o r the  i n the r e s u l t s . isa  variable  and S t e r n b e r g ' s  that research.  to test s e l e c t i v e  should For  combination  72  At a dinner party, there are f i v e people sitting in a row a t a table. Scott i s seated a t one end o f t h e row. Z i g g y i s s e a t e d next t o Matt. Joshua i s not sitting next t o Matt or S c o t t . Only 1 person i s s i t t i n g next t o W a l t e r . Who i s s i t t i n g n e x t to Walter? (Davidson & S t e r n b e r g , 1984, p.61 ) Formal with  operational  thinking  i d e a s o n l y , as i n such a v e r b a l  Particularly scheme, this  as  relevant  would  indicated  by  would be r e l e v a n t  research  to  problems,  with the  problems  that  what  carefully  be  problem  the  (Donaldson,  combinatorial  the s i g n i f i c a n t  r e s e a r c h between t h i s It  i n the Davidson  following  the  and  in  most o f t h e sample a r e u n a b l e  i s the n a t u r e of  these  a c r o s s grade  confirm  that  insight  as a d i f f e r e n t i a l  problems?  levels?  cognitive  How  found i n  combination. . Sternberg  responses  questions  1978).  reasoning  correlation  scheme and s e l e c t i v e  examine  differ  4.  i s c o n s i d e r e d necessary t o reason  (1984)  to the i n s i g h t  mind.  Are  t o answer? does  there I f so,  performance  Answers t o s u c h q u e s t i o n s may  maturity i s relevant cognitive  well  to the d i s c u s s i o n of  attribute  of the g i f t e d .  CONCLUSIONS The  important finding.  developmental in This  implications of g i f t e d n e s s dealt  with  terms  of  level  of  the  constraints  i s e v i d e n t even  for instruction  on  appears  insight  among b r i g h t  to  and  children.  be  problem  There a r e  and f o r a g e - a p p r o p r i a t e d e f i n i t i o n s  inherent i n this  i n the f o l l o w i n g  child  finding.  section  These  implications  of the c h a p t e r .  are  73  5.  IMPLICATIONS Implications  categories.  from  The  appropriate  first  this category  d e f i n i t i o n s of  appropriateness  intervention  form t h e  will,  these 5.1  Firstly, gifted the  as  1982; with  t o a l l age more  transitional, are  at  first" It  level implied  not  1977;  1970)  parts  general  for  age-  implications  and  This  than  fully  two  or  with  instructional  section dealing  of  Chapter  with each  descriptions  cognitive  (Clark, Newland, be  children  1983; 1976)  seen  of  three  three  to  (Arlin,  as  the  to  five  applicable  below  while  average  of  the  Some formal  others These  were  findings  (1967) s t a t e m e n t  child  as  think  thinkers.  schemes p r e s e n t .  a v a i l a b l e to  or  1984a);  Shields'  the  Ehrlich,  i n t h i s sample,  formal o p e r a t i o n a l with  of  a t t r i b u t e s such  t h e i r a v e r a g e and  L o v e l l and  i s not  that  cannot  brightest  thinkers,  with  thinking  Educational  terms  in t h e i r thinking  consistent  "formal  (Rice, The  formal  schemes p r e s e n t  Kaplan,  mature  were s t i l l  suggests  in abstract  systems  groups.  low  two  differential  1966;  cognitively  peers, were  think  Hildreth, logical  implications  curriculum  of  two  Giftedness  t h i s research  to  into  turn.  possessing  ability  of  consist  in  D e f i n i t i o n Of  concerns  second c a t e g o r y .  therefore,  implications  fall  giftedness.  concerning  5  research  that  in a l l s i t u a t i o n s  (p.206).  would cannot in  seem t h a t think lists  g i f t e d c h i l d r e n at  abstractly of  or  the  employ  characteristics  upper  l o g i c to of  the  elementary the  extent  gifted.  74  Qualification extent for  of  is  "abstraction"  instruction also  later  the  cognitive  finding  seen  hypothesis  that  problem  the  gifted.  this  i n d i c a t e that  skills  constraints  on  between  in  this  Even  maturity  giftedness  i n t e r m s of  be  be  presented  the  presented.  may  necessary  a  differential  a  hypothesis (1975-76,  i n terms  is 1977)  of  problem  i n t e r m s of  superior  in  and  children  superior  developmental  of  the  of  elementary  constraints in  the  on  this  general,  insight  germane t o  and  relationship  upper  children,  insight  Davidson  positive  are  number be  that  at  there  brightest  well  possible  c o r r e l a t i o n s between  significant  implications  is  be  Arlin  the  research  significant  Cognitive  Educational  the  indicate that the  of  giftedness  While  insight  u n a b l e t o answer a  concerning  and  age-appropriate.  recognize  insight.  such  defined  also  studies  superiority.  that  of  need t o  more r e s e a r c h  If  definitions  and  both  age  Implications  will  f i n d i n g may  giftedness  (1984) i n d i c a t e a IQ  that  and  need t o be  obtained  Sternberg  level,  research  would a l s o  IQ  thinking."  been  Thirdly, insight  "logical  i n terms of  chapter.  a t t r i b u t e of  to  lists  i t has  supported, appear  and  these  from t h i s i s s u e and  i n the  into  on  stem  Secondly,  and  needed  are  problems.  d e f i n i t i o n of  insight.  stemming  from  a g e - a p p r o p r i a t e d e f i n i t i o n of  the  issues  giftedness  raised will  now  75  5.2  Educational Two  this  Implications  issues  research.  concerning  Appropriateness  the  issues presented  be  discussed  giftedness. reasoning, 5.2.1  is  will  insight,  be  and  considerations.  operations,  in their  formulate  insight, children and  general  curriculum should  logical  take  the  gifted  becoming  be  useful  curriculum  tied  g i f t e d n e s s and of  to  will  instructional  reference  to  on  formal  finding.  in  their  ability  For  The  and  these  gifted  involves  c h i l d r e n appear  acquisition  use  of  problems the  for elementary  i n t o account  Gifted  f o r the  to d i s c o v e r  questions)  curriculum child  more  (1982) and  is closely  from  to  be  formal  (that i s ,  processes  school-aged  c o n s t r a i n t s on  of  gifted abstract  reasoning.  Secondly, for  with  since gifted  materials  arise  developmental perspective  curriculum  Firstly,  of  gifted  issue  Curriculum  of  constrained  to  a  problem  developmentally and  the  discussed  Age-appropriateness two  to  A g e - a p p r o p r i a t e n e s s Of  the  of c u r r i c u l u m  Secondly,  important  This  of  involving definition  first.  intervention  education  of  Arlin for  who a  needs t o be  i s entering  formal  determining  that  Carter  Piagetian  cognitive  challenging  operations  propositional thinker.  (1984a) s u g g e s t  accordingly.  sufficiently  level  and  and  Ormrod  assessment and  is  can  planning  76  5.2.2  Instructional Inhelder  I n t e r v e n t i o n And  and  Piaget  schemata  as  organize  from  certain  k i n d s of d a t a ,  conditions"  "the the  concepts beginning  (p.308).  nourishment"  and  but  transitional students  5.2.3  Instructional  in  benefit  from  who  showing are  low  experiment  revealed that (p.63).  intervention discussed well low  this  in  above  stage.  "cognitive  formal  by  of  of  students formal  the  examples  of  at  reasoning  in  skills  the  gifted their  A subsequent  "insight  may  be  between  research  promoting appear  Piaget  thought,  may of the or  to  when  most  indicate  appeared  to  solving  of  least  somewhat to  specify  effective.  the  formal  of  training  are at  insight and  role  insight  I t d o e s , however, seem n e c e s s a r y  be most e f f e c t i v e formal  the  these  Insight  giftedness,  training  this  outside  seen  (1984) s t u d y  problems.  relationship by  some e v i d e n c e  receipt  comparison  suggested  vis-a-vis  with  i n c o r p o r a t i n g the p r i n c i p l e s  Sternberg's  selective  The  of  when f a c e d  not m a n i f e s t  stimulation"  I n t e r v e n t i o n And  and  the  what s t a g e  level  can  formal t h i n k e r s .  intellectual  trainable"  formal  This potential,  operational  subject potentially  i n the c u r r i c u l u m f o r those  those  insight  formal  f o r t h e c o n s t r u c t i o n of  level  In D a v i d s o n  the  the  which are  the a p p r o p r i a t e n e s s  formal operations  at  of  Reasoning  define  which  "intellectual  (1972) as n e c e s s a r y indicate  (1958)  Formal  and role  formal of  operational that  introduced at  insight the  reasoning  instructional thought  as  training  may  transitional  or  77  5.2.4 I n s t r u c t i o n a l The  connection  (Arlin,  a  child  from  problematic  formulation,  indicate  be  introduced  in  solution,  1975).  becomes  and p r o b l e m  that  thinker.  or  Support  apparent  problem  situations  Getzels  (1964)  the  no  are either  these  "omits  the c l a s s r o o m discovered In believed  significant  i s considered. (1973) e m p h a s i z e  avoided  or  ignored  o u t t h a t Bloom's  group  of  problems  we  1 i t was seen t h a t s u p e r i o r p r o b l e m  generation 1973; H e l v e y ,  t o the f o r m u l a t i o n of of  ideas  in  in  taxonomy, f o r the  time  may  call  1971; Mackworth,  in curriculum  finders are  research  many d i s c i p l i n e s 1965).  t h e r e f o r e , t o i n c l u d e problem  the a p p r o p r i a t e  that  (p.241).  t o be c r u c i a l  important,  of  from c o n s i d e r a t i o n and seems n o t t o r e c o g n i z e i n  problems"  Chapter  the  Dillon,  a  &  t y p e s of focus  i s u s e d a s t h e b a s i s f o r much c u r r i c u l u m p l a n n i n g  gifted,  known  (Getzels  traditional  situations  points  questions  is  solution  the  experiences  to raise there  finding  curriculum  These  for including  when  problem  which  finding  problem  into  (1982) and G e t z e l s and D i l l o n  education.  and  of  on p r e s e n t e d  discovered  may  situations  method  Dillon  reasoning  of o p p o r t u n i t i e s f o r c h i l d r e n  Csikszentmihalyi,  education  formal  i s becoming a f o r m a l  consist  experiences  1977)  t o o , may b e s t  should  which  between  1975-76,  experiences, when  I n t e r v e n t i o n And P r o b l e m F i n d i n g  It  finding  f o r the g i f t e d .  problems (Getzels &  would  seem  experiences at  78  5.2.5  Directions The  are  of  important  which are  issues  stemming  t o be  pursued.  intervention  applicable  to  from  the  this  In  particular,  the  questions  for  curriculum  for  suggests planning  research  of  gifted. How  might  (Piaget,  the  1972)  incorporating  associated function  1974), but important  and  with  provision  in  formal  consolidation  a  implications  instructional  research the  Research  educational  seen as  notion  For  the  form  operational  "intellectual  of  of  thought?  instructional  the  (Arlin,  instructional intervention component  i n the  experiences rate  c o n c e p t s and  Horizontal  intelligence  stimulation"  p r i n c i p l e s a f f e c t the  integration  formal  of  of  decalage  1984, may  a c q u i s i t i o n and  operations i s seen  i n p r e s s a;  well  be  an  mastery  of  as  Webb,  additional  of  the  formal  schemes. Instructional facilitation well.  How  insight  of  problem  might tasks  intervention  the  into  may  well  be  f i n d i n g c a p a b i l i t y and incorporation  curriculum  for  of  vital  insight s k i l l s  problem  the  to  finding  gifted  the as and  affect their  ability  to pose g e n e r a l  q u e s t i o n s and/or demonstrate s i g n i f i c a n t  insight  i n t o problems?  A d d i t i o n a l l y , what  way  of  presenting  these  the  tasks  of  operational  formal  insight  provide  a  the  n a t u r e of  appropriate  optimum the  thought, agenda  for  time  for  intervention,  to encourage the  full  most e f f e c t i v e  experiences?  Questions concerning intervention,  i s the  development problem future  and and  instructional the  design  integration  finding a b i l i t y , research.  of  and  79  6.  SUMMARY OF CHAPTER 5 This  insight  chapter and  discussed  problem  these c o n s t r a i n t s Definition  in  the  finding  maturational  and t h e i m p l i c a t i o n s  for age-appropriate d e f i n i t i o n s terms  qualitatively  of  problem  different gifted  with  sample t o d e t e r m i n e  definition. to  be  superior  in  found  to  inherent i n  of  as  giftedness. a  possible  attribute  need  further  of  the  investigation  the a p p r o p r i a t e n e s s of such a  d e v e l o p m e n t a l c o n s i d e r a t i o n s were the  on  definition  of g i f t e d n e s s  found  i n t e r m s of  insight.  discussed.  finding  Similarly,  important  Optimal  employed  was  finding  cognitive  intellectually an o l d e r  constraints  times It  to  for effective  was  suggested  determine  a  instructional that  gifted  e x p e r i e n c e s and i n s t r u c t i o n  o p e r a t i o n s and i n s i g h t  skills.  intervention  Piagetian  child's  were  assessment  readiness  i n the p r i n c i p l e s  be  f o r problem of  formal  80  BIBLIOGRAPHY Alvino, J. (1981) Do g i f t e d and differently? P r i n c i p a l , 60  nongifted children learn ( 5 ) , 39-40.  Arlin,P.K. (1975-76) A c o g n i t i v e p r o c e s s model of p r o b l e m rinding. E d u c a t i o n a l H o r i z o n s , 54 ( 2 ) , 99-106. Arlin,P.K. (1977) P i a g e t i a n o p e r a t i o n s i n p r o b l e m D e v e l o p m e n t a l P s y c h o l o g y , 13 ( 4 ) , 2 9 7 - 2 9 8 .  finding.  A r l i n , P.K. (1982) A m u l t i t r a i t - m u l t i m e t h o d v a l i d i t y s t u d y of t e s t of f o r m a l r e a s o n i n g . E d u c a t i o n a l and P s y c h o l o g i c a l Measurement, 42, 103-109. A r l i n , P.K.(1984a) A d m i n i s t r a t i o n manual f o r the formal reasoning. E a s t A u r o r a , NY: S l o s s o n P u b l i c a t i o n s , Inc.  a  A r l i n t e s t of Educational  A r l i n , P.K.(1984b) A d o l e s c e n t and a d u l t t h o u g h t : A s t r u c t u r a l interpretation. In M.L. Commons, F . A . R i c h a r d s , & C. 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E h r l i c h , V.Z. teachers.  minds.  Glasgow:  The e v o l u t i o n o f p h y s i c s .  New  (1982) G i f t e d c h i l d r e n : A g u i d e f o r p a r e n t s and Englewood C l i f f s , NJ: P r e n t i c e - H a l l .  F l a v e l l , J.H. (1963) The d e v e l o p m e n t a l p s y c h o l o g y Piaget. P r i n c e t o n , N J : D. Van N o s t r a n d .  of J e a n  Getzels,J.W. (1964) C r e a t i v e t h i n k i n g , p r o b l e m - s o l v i n g , and instruction. In E.R. H i l g a r d ( E d . ) , T h e o r i e s of l e a r n i n g and i n s t r u c t i o n . C h i c a g o : N a t i o n a l S o c i e t y f o r the Study of E d u c a t i o n . Getzels,J.W. (1975) P r o b l e m - f i n d i n g and t h e i n v e n t i v e n e s s o f solutions. The J o u r n a l o f C r e a t i v e B e h a v i o r , 9 ( 1 ) , 12-18. Getzels,J.W., & Csikszentmihalyi,M. (1975) From p r o b l e m s o l v i n g to problem f i n d i n g . I n I.A. T a y l o r & J.W. 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(1981a) A c o m p o n e n t i a l t h e o r y o f i n t e l l e c t u a l G i f t e d C h i l d Q u a r t e r l y 25 ( 2 ) , 86-93.  S t e r n b e r g , R . J . (1981b) I n t e l l i g e n c e and n o n e n t r e n c h m e n t . J o u r n a l o f E d u c a t i o n a l P s y c h o l o g y , 73 ( 1 ) , 1-16. S t e r n b e r g , R . J . (1982a) L i e s we l i v e t e s t s i n i d e n t i f y i n g the g i f t e d . 26 ( 4 ) , 157-161.  by: M i s a p p l i c a t i o n of Gifted Child Quarterly,  S t e r n b e r g , R . J . (1982b) N o n e n t r e n c h m e n t i n t h e a s s e s s m e n t o f intellectual giftedness. G i f t e d C h i l d Q u a r t e r l y , 26 ( 2 ) , 63-67. Sternberg,  R.J., & Davidson, J . E .  (1982) The mind o f t h e  84  puzzler.  P s y c h o l o g y Today,  37-44.  S t e r n b e r g , R . J . , & D a v i d s o n , J . E . (1983) I n s i g h t E d u c a t i o n a l P s y c h o l o g i s t , 18 ( 1 ) , 51-57.  i n the g i f t e d .  W a l l a c h , M.A., & Kogan, N. (1965) Modes o f t h i n k i n g i n young c h i l d r e n : A study of the c r e a t i v i t y - i n t e l l i g e n c e distinction. New Y o r k : H o l t , R i n e h a r t , & W i n s t o n . Webb, R.A. (1974) C o n c r e t e a n d f o r m a l o p e r a t i o n s i n v e r y b r i g h t 6- t o 11-year o l d s . Human D e v e l o p m e n t , 17, 292-300. W e r t h e i m e r , M. (1945) P r o d u c t i v e and B r o t h e r s Publishers.  thinking.  New Y o r k : H a r p e r  85  APPENDIX A - DATA USED IN THE REGRESSION  ANALYSES  The f i r s t two columns r e p r e s e n t s c o r e s on t h e A r l i n T e s t Formal Reasoning ( A r l i n , 1984c). The maximum p o s s i b l e s c o r e 32. S u b s e q u e n t columns l i s t s c o r e s on t h e i n s i g h t p u z z l e s (maximum p o s s i b l e , 8 ) , t h e IQ t e s t , and t h e p r o b l e m f i n d i n g task. 10 1 11 1 1 6 3 1 6 1 10 0 05 0 15 1 10 1 1 13 1 2 0 06 1 1 2 1 21 7 07 1 1 3 0 09 0 21 6 08 1 1 5 2 07 2 21 1 1 3 2 1 3 0 10 4 1 4 1 08 2 1 2 0 1 12 1 1 2 1 2 2 1 3 1 08 1 1 1 1 1 1 2 04 0 1 2 0 08 0 19 2 1 4 1 1 3 1 06 1 1 4 0 1 4 7 13 2  078 3. 20 1 22 0. 00 1 28 4. 00 1 05 3. 1 4 098 3. 20 086 3. 00 1 16 3. 00 1 02 3. 67 1 1 5 3. 00 1 07 3. 38 082 3. 00 097 3. 00 121 3. 67 095 2. 38 085 3. 1 3 105 3. 75 090 2. 44 094 3. 10 101 4. 00 098 2. 00 093 2. 83 121 3. 60 096 2. 71 086 1 .40 090 4. 00 088 4. 00 082 1 .75 101 4. 00 097 0. 00 109 3. 25 1 04 3. 33 085 4. 00 089 3. 00 093 4. 00 068 3. 00 076 0. 00 075 1 .60 1 34 4. 00 1 1 03. 50 100 3. 20 086 0. 00 109 4. 00 1 1 7 4. 33 093 2. 83  07 1 05 0 14 0 06 0 05 0 08 1 1 3 1 08 0 09 0 1 10 08 2 07 1 1 10 05 1 1 72 1 41 1 20 18 1 10 2 1 62 04 1 1 22 08 1 04 0 1 41 04 1 09 0 1 20 13 2 08 2 1 3 1 10 2  072 2 .50 072 1 .00 077 2 .00 097 4.00 089 3 .00 065 4.00 099 1 .67 095 2 .50 099 3 .40 071 3 .50 097 3 .67 088 4.00 1 05 3 .50 090 3 .33 1 24 2 .63 1 12 4.00 1 03 1 .75 1 36 3 .50 1 06 4.00 099 4.00 091 4.00 118 3 .75 098 3 .00 083 4.00 1 10 4.00 092 3 .25 1 10 1 .88 1 1 13 .00 102 0 .00 091 2 .67 093 4.00 1 05 4.00  87  APPENDIX B - DATA USED IN THE SUPPLEMENTARY ANALYSIS R e a d i n g from l e f t t o r i g h t , t h e f i r s t e i g h t s c o r e s a r e t h e sub-test scores, r e s p e c t i v e l y , f o r the f o l l o w i n g formal r e a s o n i n g s c h e m a t a : volume, p r o b a b i l i t y , c o r r e l a t i o n s , c o m b i n a t i o n s , p r o p o r t i o n a l r e a s o n i n g , forms o f c o n s e r v a t i o n beyond d i r e c t v e r i f i c a t i o n (momentum), m e c h a n i c a l e q u i l i b r i u m , and f r a m e s o f r e f e r e n c e . The next t h r e e s c o r e s a r e s c o r e s f o r the t h r e e i n s i g h t p r o c e s s e s : s e l e c t i v e encoding, selective c o m b i n a t i o n , and s e l e c t i v e c o m p a r i s o n . The f i n a l s c o r e i s t h e problem f i n d i n g score. T h i s d a t a was used i n t h e s u p p l e m e n t a r y correlational analysis.  1 0 4 4 2 0 1 1 2 3 0 1 1 2 0 4 2 0 4 0 2 2 2 2 2 0 2 2 1 0 2 1 1 2 1  2 1 4 4  0 4 2 1  2 1  2 2 1 2 2 3 2 1 1  2 4 2 1  1 4 2 3 2 2 1  2 3 2 1 2 1  2 1 0 2 2 2 2  3 3 3 3 2 1 4 3 4 4 1  4 3 1 3 1 4 4 4 4 4 4 4 1 2 1 4 2 3 3 2 3 3 2 1 0 2 4 4  0 0 1 1 0 0 1 1 0 0 1 0 4 0 0 0 2 0 0 0 2 0 2 1  0 0 0 0 1 1 1 0 2 1 1 1 0 2 0  2 1 2 1 2 0 2 1  0 1 0 1 4 1 2 0 4 1 2 1 4 2 0 2 2 2 1 1 1 1 1 1 0 2 1 3 2 2 0  1 1 0 2 0 1 2 0 3 0 0 1 2 0 2 1 0 1  0 0 0 0 1 1 0 1 0 0 1 3 1 1 0 1 0 1  1 1 1  3  0  1  1  2 1 2 1 1 0 1 1 1 2 2 0 4  2 3 0 1 2 2 0 1 1 0 3 2  1  3 0 2 1  2 1 1 1  3 0 1 1  1 2 2 0 2 3 0 2 0 1 1  1  0 2 0 2 0 3 2 0 0 3 3 2 2 1  1 2 1 1 0 0 1 0 3 2  0 1 1 0 0 0 1 1  2 0 0 0 3 0 0 0 2 0 1 1 1 2 0 3 0 1 0 1 2 1 0 1 0 1 0 0 0 1  0  0 0 1 0 0 0 0 0 0 0 0 0 3 1  0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0  1 0 1 1 0 0 0 0 1 0 1  1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 1  3.20 0.00 4.00 3.14 3.20 3.00 3.00 3.67 3.00 3.38 3.00 3.00 3.67 2.38 3.13 3.75 2.44 3.10 4.00 2.00 2.83 3.60 2.71 1 . 40 4.00 4.00 1 .75 4.00 0.00 3.25 3.33 4.00 3.00 4.00 3.00 0.00 1 .60 4.00 3.50  o o o n n o o o o o o r ~ o o o r - o o r o r o o m o o o o i r > o o o t n c o o o t ^ o o  N o o n o i D o o o o o u i n f i n w o m n u j o M n o o o h o o o N o o o o w o o  O  —O-— 0<—  O O O O ' - O O O O ' - ' - O O ' - O O O ' - ' r - O ^ - ^ O O O O O ' ^ - O O ' r -  O O O r 0 O O O O O O O ' ^ - O O O O O O O O O O - ~ O O « - > - O O O O O O O ' - O < «— O O r O C N O O O O O O O O O O ^ O O * - - - ' — O O ' - ' - C O O O ' - ' - O O - - ' - " — o n o n n ( \ o o r i i ' - ' - ' - o o o o o ( N N ' - i  r  ) f O ' - c ) 0 ( M O ( \ o o ^ O ' - ' - ' - ^ o r o  ^O^<N<N^^^^O(N)(^^rsi<NCNCN00--C\l(N'-"-^'-r\l'-CNO<N'--.-•<*  CN  CO ••-  O O O C N O ^ ^ ^ ^ ^ O O O O ^ O O O O O O ^ O O < N O O O O O C ^ l O ^ O ^ 0 ' ^ ' ^ - O ' - O ' - ' - O ' - ' - ' - ' - ' - O O O ' - O O ' - ' - ' - ' - ' ^ ' - C M O O ' ^ ' r - O O O O ' - ' - O ' - O  '-'-OCNl  —* - 0 0 0 0  —  O O O — ' - ^ C N I ' - C O C O ' - O O ' - O ' - O O O O O O O C N  '— »— CN O * ^ CN CN '— O C\l CN CN CO »— CO CN O '— O CN CO O CO CN •— «— CN *— •— '— <— *— — '— <— CN 1  r 0 ^ r O r - o o ^ ^ O O O N ' - ( M m ( N - - n O ^ O N O ' - * 0 ( N I O ' - ^ 0 ( N ^ ' t N ^ O  o  89  APPENDIX C - ARLIN PROBLEM FINDING TASK (Arlin  1975-76,1977)  Instructions: In f i v e m i n u t e s p l e a s e make up a s few o r a s many q u e s t i o n s as y o u c a n a b o u t any o b j e c t o r o b j e c t s i n f r o n t o f y o u . Your q u e s t i o n s c a n t a k e any form t h a t y o u w i s h them t o t a k e . They can be b r a i n t e a s e r s , p u z z l e s t o s o l v e , n o v e l q u e s t i o n s . An example i s , "Can y o u form f o u r t r i a n g l e s o u t o f t h e s e s i x match sticks?" Your q u e s t i o n s c a n be any t y p e t h a t y o u w i s h them t o be. The o n l y t h i n g t h a t y o u have t o be s u r e t o do i s t o r e f e r t o one o r more o f t h e o b j e c t s b e f o r e y o u i n e a c h o f y o u r questions. Do y o u have any q u e s t i o n s f o r me b e f o r e b e g i n n i n g ?  90  A r l i n P r o b l e m F i n d i n g Task ( A r l i n , 1975-76, 1977)  SOME OBJECTS 1  C-clamp  1  b l a c k w o o d e n block f 2 c m  1  p l a i n w o o d e n block (1cm  1  s m a l l index card (3" X  1  25 c e n t p i e c e  1  s m a l l box top  T  s m a l l box b o t t o m  3  s m a l l c o l o r e d candles  6  w o o d e n matches  10  1. 2. 3. 4.  5. 6  8  t h u m b tacks  2  2-meter long cords  1  pair of scissors  X x  2 cm.) 1 cm.)  5") with a d i m e - s i z e d hole in the center  91  APPENDIX D - SAMPLE PAGE FROM THE ARLIN TEST OF FORMAL REASONING (Arlin,  1984c)  There 5s a new computer game in the stores. The object of the game is to light up the triangle at the top of the game board. The light goes on when one or more of these buttons are pressed down at the same time. These buttons are marked A to F. Pressing any wrong button will prevent the light from coming on. 11. How  would you find out which of these buttons when pushed down at the same time will make the light go on?  A. Try all possible pairs of the buttons to make the light go on. B. Try the buttons one-at-a-time and then two-at-a-time until the triangle lights up. C. Try all six at a time and then all of the burtons taken five-at-a-time, four-at-a-time, and so forth, until the light goes on. D. Try the bottons, six-at-a-time,five-at-a-time,four-at-a-time or three-at-a-time. 12, What is the reason for choosing your answer? A. The problem requires that you test all combinations of the buttons from one-at-a-time to all six-at-a-time. B. The word "combination" implies a pair, or two-at-a-time. C. The information given in the problem requires that you test nil combinations of the buttons taken three, four, five and six-at-a-time. D. The problem can NOT be solved with the information that is provided even if you had the actual game and could work with it.  92  APPENDIX E - THE INSIGHT PUZZLES  On t h e f o l l o w i n g t h r e e p a g e s a r e some p u z z l e s f o r you t o s o l v e . You may t a k e a s t o work o u t y o u r a n s w e r s . You may use t h e p r o v i d e d t o f i g u r e o u t your a n s w e r s i f y o u any q u e s t i o n s b e f o r e y o u b e g i n ?  "brain-teaser" much t i m e a s you need s c r a t c h paper wish. Do y o u have  93  Name School Grade 1. Suppose you must I g i v e you  and I have t h e same amount of money. How much so t h a t you have t e n d o l l a r s more t h a n I ?  2. Water l i l i e s d o u b l e i n a r e a e v e r y 24 h o u r s . At t h e b e g i n n i n g of t h e summer t h e r e i s one water l i l y on a l a k e . It t a k e s 60 d a y s f o r the l a k e t o become c o v e r e d w i t h water l i l i e s . On what day i s t h e l a k e h a l f c o v e r e d ? 3. W i t h a s e v e n - m i n u t e h o u r g l a s s and an 11-minute h o u r g l a s s , what i s t h e s i m p l e s t way t o t i m e t h e b o i l i n g of an egg f o r 15 minutes?  4. the  How c o u l d two men p l a y f i v e games o f c h e c k e r s and same number o f games w i t h o u t any t i e s ?  each  win  5. I f on t h e l a s t day o f F e b r u a r y 1980 - and remember, 1980 was a L e a p Year - you had gone t o bed a t seven o ' c l o c k , h a v i n g s e t y o u r a l a r m c l o c k t o wake you up a t 8:15 i n t h e m o r n i n g , how much s l e e p would you have had?  6. In h i s c o z y l i t t l e i g l o o n e a r t h e N o r t h P o l e , S a n t a C l a u s keeps a l a r g e c h e s t of d r a w e r s . In t h e bottom drawer S a n t a keeps h i s s o c k s . S a n t a C l a u s has c o l d f e e t so he needs a l o t o f socks. He has 36 s o c k s i n a l l , and 18 of them a r e r e d and 18 of them a r e g r e e n . S i n c e i t ' s v e r y d a r k a t t h e N o r t h P o l e , S a n t a C l a u s can n e v e r see what he's d o i n g , so when he opens h i s b o t t o m drawer t o f i s h o u t a p a i r of s o c k s he i s n ' t a b l e t o t e l l w h i c h c o l o u r he has p i c k e d . To make s u r e of h a v i n g one m a t c h i n g p a i r of s o c k s , how many s o c k s must S a n t a t a k e o u t of h i s b o t t o m d r a w e r ? 7. W i t h n o t h i n g a t hand e x c e p t a t h r e e - l i t r e j u g and a l i t r e j u g , how can you measure out e x a c t l y one l i t r e of  fivewater?  94  8. I have two c l o c k s . One o f them has s t o p p e d c o m p l e t e l y . The o t h e r one g a i n s h a l f a m i n u t e e v e r y 24 h o u r s . Which of t h e two c l o c k s t e l l s t h e e x a c t time more o f t e n ?  95  Process  emphasized  Selective Selective Selective  Puzzle  encoding combination comparison  4,5,6 1,2,3,7 8  Source Sternberg & Davidson B r a n d r e t h (1979)  number  Puzzle (1982,1983)  number  1,2,3,4 5,6,7,8  * P u z z l e 6 i s v e r y s i m i l a r t o t h e f o l l o w i n g p r o b l e m from S t e r n b e r g and D a v i d s o n : " I f y o u have b l a c k s o c k s and brown s o c k s i n y o u r drawer, m i x e d i n t h e r a t i o o f 4 t o 5, how many s o c k s w i l l y o u have t o t a k e o u t t o make s u r e o f h a v i n g a p a i r t h e same color?" (1982, p . 4 2 ) .  

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