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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 ABILITY 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 Columbia, 1974 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES Department Of Education We accept t h i s t h e s i s as conforming to the r e q u i r e d S/tattdar^) THE UNIVERSITY OF BRITISH COLUMBIA August 1984 © Marion Porath, 1984 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree that p ermission f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of Education The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: August 22, 1984 i i A b s t r a c t T h i s study was an i n v e s t i g a t i o n of the r o l e s of IQ, c o g n i t i v e l e v e l , and r e l a t e d 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 as p r e d i c t o r s of problem f i n d i n g a b i l i t y i n 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 . It was hypothesized that c o g n i t i v e l e v e l would c o n t r i b u t e the most to the p r e d i c t i o n of problem f i n d i n g , f o l l o w ed i n importance f i r s t l y by the 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 of i n s i g h t and secondly by IQ. I t was f u r t h e r hypothesized that c o g n i t i v e l e v e l would.mediate the p r e d i c t i o n of problem f i n d i n g by i n s i g h t . The sample c o n s i s t e d of 76 c h i l d r e n in grades f i v e , s i x , and seven. Subj e c t s of v a r y i n g a b i l i t y were in c l u d e d i n the sample in order to c l a r i f y the hypothesized p r e d i c t i v e r e l a t i o n s h i p s . The c h i l d r e n were admi n i s t e r e d a problem f i n d i n g task, a set of i n s i g h t p u z z l e s , a t e s t of formal reasoning, and a group IQ t e s t . Using 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, the c r i t e r i o n v a r i a b l e , problem f i n d i n g , was regressed on the p r e d i c t o r v a r i a b l e s c o g n i t i v e l e v e l , i n s i g h t , and IQ. Backward and stepwise s e l e c t i o n procedures were used. A r e p l a c e m e n t - d e l e t i o n procedure was used to t e s t the mediation of i n s i g h t by formal o p e r a t i o n s . A d d i t i o n a l c o r r e l a t i o n a l analyses supplemented the primary r e g r e s s i o n a n a l y s i s . The r e s u l t s r e v e a l e d that c o g n i t i v e l e v e l and i n s i g h t were not s i g n i f i c a n t p r e d i c t o r s of problem f i n d i n g . T h i s was thought to be due to a " f l o o r e f f e c t " stemming from the low c o g n i t i v e m aturity of the sample. IQ as a p r e d i c t o r of problem f i n d i n g was i n the expected d i r e c t i o n , although the amount of v a r i a n c e accounted f o r was minimal. Formal reasoning was found to mediate the p r e d i c t i o n of problem f i n d i n g by i n s i g h t . S i g n i f i c a n t c o r r e l a t i o n s between c e r t a i n of the formal reasoning schemata and two of the i n s i g h t processes appeared to support t h i s mediating e f f e c t . I t was concluded that even b r i g h t c h i l d r e n are c o n s t r a i n e d by maturation i n t h e i r a b i l i t y to f i n d problems and solve i n s i g h t p u z z l e s . There are i m p l i c a t i o n s inherent i n these c o n s t r a i n t s f o r age-appropriate d e f i n i t i o n s of g i f t e d n e s s . Age-a p p r o p r i a t e c u r r i c u l u m f o r the g i f t e d was another i m p l i c a t i o n stemming from the f i n d i n g s of the study. i v Table of Contents A b s t r a c t i i L i s t of Tables v i i i 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 Vs. Q u a l i t a t i v e D i f f e r e n c e s In The Information 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 C h i l d r e n 3 2.2 Problem 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 G i f t e d C h i l d r e n 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 Problem F i n d i n g 4 2.4 Information 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 Problem F i n d i n g 4 2.5 I n s i g h t As A Nonentrenched Measure Of I n t e l l e c t u a l G i f t e d n e s s 5 3. SUMMARY OF THE PROBLEM 6 4. JUSTIFICATION OF THE STUDY 6 5. ORGANIZATION OF THE STUDY 7 6. DEFINITION OF THE VARIABLES 7 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 7 6.2 Problem F i n d i n g And Terms A s s o c i a t e d With Problem F i n d i n g 7 6.2.1 Problem F i n d i n g 7 6.2.2 Elements Necessary For An O p e r a t i o n a l D e f i n i t i o n Of Problem F i n d i n g 8 6.3 Terms A s s o c i a t e d With C o g n i t i v e L e v e l 8 6.3.1 O p e r a t i o n a l L e v e l 8 6.3.2 Concrete O p e r a t i o n a l L e v e l 8 6.3.3 Formal O p e r a t i o n a l L e v e l 9 6.3.4 C o g n i t i v e M a t u r i t y 9 6.3.5 H o r i z o n t a l Decalage 9 6.4 Terms A s s o c i a t e d With The Rel a t e d Information P r o c e s s i n g V a r i a b l e s 10 6.4.1 S e l e c t i v e Encoding 10 6.4.2 S e l e c t i v e Combination 10 6.4.3 S e l e c t i v e Comparison 10 7. SUMMARY OF CHAPTER ONE 11 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 Pr o c e s s o r s 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 Pr o c e s s o r s 14 3. PROBLEM FINDING IN INTELLECTUALLY GIFTED CHILDREN 15 3.1 The Importance Of Problem F i n d i n g And I t s Link To G i f t e d Performance 15 3.2 The Need For Research Into Problem F i n d i n g 16 3.3 I n t e l l i g e n c e And Problem F i n d i n g 17 3.4 A Formal Statement Of The F i r s t Hypothesis 18 4. COGNITIVE LEVEL AND PROBLEM FINDING 18 4.1 The Need For A Developmental Focus To D e s c r i p t i o n s Of G i f t e d n e s s 18 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 19 4.2.1 I n t r a - s t a g e P r e c o c i t y 19 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 Formal Operations 20 4.3 A P i a g e t i a n P e r s p e c t i v e On Problem F i n d i n g 23 4.4 A Formal Statement Of The Second Hypothesis 24 5. 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 Problem F i n d i n g ....27 5.3 I n s i g h t As A Nonentrenched Measure Of I n t e l l e c t u a l G i f t e d n e s s 28 5.4 C o g n i t i v e L e v e l As A Fac t o r In I n s i g h t 30 5.5 Formal Statements Of The T h i r d And Fourth Hypotheses 31 5.6 Order Of Entry Of The P r e d i c t o r V a r i a b l e s Into The Regression Equation 32 5.7 A Formal Statement Of The F i f t h Hypothesis 32 6. SUMMARY OF THE FIVE HYPOTHESES 33 Chapter III METHOD 34 1. OVERVIEW OF THE CHAPTER 34 2. POPULATION 34 3. SAMPLE 35 4. PROCEDURES 36 4.1 The Problem F i n d i n g Task 36 v i 4.1.1 Task D e s c r i p t i o n 36 4.1.2 C l a s s i f i c a t i o n Of The Questions Raised 36 4.1.3 Sco r i n g 38 4.2 P i a g e t i a n Assessment 39 4.2.1 Test D e s c r i p t i o n 39 4.2.2 Test A d m i n i s t r a t i o n 40 4.2.3 Scoring 40 4.3 Measurement Of In s i g h t 41 4.3.1 I n s i g h t Puzzles 41 4.3.2 A d m i n i s t r a t i o n And Sco r i n g 42 4.4 Measurement Of IQ 42 5. DESIGN 43 6. THE ANALYSIS OF THE DATA 43 6.1 The Li n e a r M u l t i p l e Regression Model 44 6.2 Assumptions U n d e r l y i n g The L i n e a r Regression Model 44 6.3 Methods Of A n a l y s i s 45 6.3.1 Test Of The F u l l Model 45 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 Regression Parameters 45 6.3.3 C r o s s - v a l i d a t i o n 46 6.3.4 Test Of The Mediation Of I n s i g h t By Formal Ope rat ions , 47 6.3.5 Supplementary Analyses ,,....47 6.4 Methods Of Reporting The Data 48 7. SUMMARY OF CHAPTER THREE ...48 Chapter IV RESULTS OF THE ANALYSIS 49 1. OVERVIEW OF THE CHAPTER 49 2. SUMMARY STATISTICS 49 2.1 Problem F i n d i n g 50 2.2 C o g n i t i v e L e v e l 50 2.3 I n s i g h t 51 2.4 The IQ Measure 52 3. APPROPRIATENESS OF THE LINEAR REGRESSION MODEL 53 4. RESULTS OF THE REGRESSION ANALYSIS 53 4.1 Test Of The F u l l Model 54 4.2 Backward E l i m i n a t i o n 55 4.3 Shrinkage 56 4.4 Test Of The Mediation Of I n s i g h t By Formal Operations 56 5. RESULTS OF THE SUPPLEMENTARY ANALYSES 57 5.1 The R e l a t i o n s h i p Of Problem F i n d i n g Q u a l i t y To The Three Processes Of In s i g h t 57 5.2 The R e l a t i o n s h i p Between The Three Processes Of I n s i g h t And The Formal Reasoning Schemata 58 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 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 Problem 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 Problem F i n d i n g 69 3.3 IQ As A P r e d i c t o r Of Problem F i n d i n g 70 3.4 Further D i s c u s s i o n Of The Supplementary 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 Age-appropriateness Of Curr i c u l u m For 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 Formal Reasoning .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 Problem F i n d i n g ..77 5.2.5 D i r e c t i o n s For Research 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 v i i i L i s t of Tables I. The processes of i n s i g h t and componential s k i l l s thought to r e l a t e to each process 26 I I . Hypothesized r e l a t i o n s h i p s of i n s i g h t s k i l l s with problem f i n d i n g a b i l i t y 28 I I I . The i n t e l l e c t u a l product c a t e g o r i e s 36 IV. C o g n i t i v e l e v e l d i s t r i b u t i o n 51 V. D i s t r i b u t i o n of IQ scores as compared with the normal d i s t r i b u t i o n 52 VI. A n a l y s i s of v a r i a n c e 54 VI I . Summary t a b l e of backward e l i m i n a t i o n procedure ....55 V I I I . C o r r e l a t i o n matrix of problem f i n d i n g q u a l i t y with the three processes of i n s i g h t 57 IX. C o r r e l a t i o n matrix of the three processes of i n s i g h t with the formal reasoning schemata 60 X. C o r r e l a t i o n s among the p r e d i c t o r and c r i t e r i o n v a r i a b l e s 61 ix Acknowledgement The author wishes to acknowledge the s i g n i f i c a n t c o n t r i b u t i o n of Dr. P a t r i c i a A r l i n to the completion of t h i s t h e s i s . Her superb guidance i n f l u e n c e d each stage of t h i s study. The c o n t r i b u t i o n s of Dr. Walter Boldt i n h e l p i n g to plan the r e g r e s s i o n a n a l y s i s and Dr. Stanley Blank i n the c a r e f u l reading of the t h e s i s are a l s o g r a t e f u l l y acknowledged. A d d i t i o n a l thanks go to the p r i n c i p a l , t e a chers, and c h i l d r e n who p a r t i c i p a t e d i n the study. 1 I. INTRODUCTION 1. STATEMENT OF THE PROBLEM D e f i n i n g and i d e n t i f y i n g g i f t e d n e s s are long-debated i s s u e s in psychology and education. When d e a l i n g with i n t e l l e c t u a l g i f t e d n e s s , d e f i n i t i o n i s most commonly, e i t h e r e x p l i c i t l y or i m p l i c i t l y , i n terms of a high IQ. The i n t e l l e c t u a l l y g i f t e d are seen as q u a n t i t a t i v e l y d i f f e r e n t from the norm in that they possess a g r e a t e r amount of " i n t e l l i g e n c e " as measured by an IQ t e s t . There e x i s t s , a l s o , the b e l i e f that the i n t e l l e c t u a l l y g i f t e d think i n ways that are q u a l i t a t i v e l y d i f f e r e n t . They have been c h a r a c t e r i z e d as p o s s e s s i n g d i f f e r e n t i a l c o g n i t i v e a t t r i b u t e s such as f l u e n c y of t h i n k i n g (Rice, 1970), f l e x i b i l i t y of t h i n k i n g ( C l a r k , 1983; E h r l i c h , 1982; Rice, 1970), and the a b i l i t y to think in a b s t r a c t terms ( C l a r k , 1983; E h r l i c h , 1982; H i l d r e t h , 1966; Kaplan, 1977; Newland, 1976) or with l o g i c a l systems (Rice, 1970), yet r e s e a r c h has not addressed the q u e s t i o n of the degree of' c o g n i t i v e d i f f e r e n t i a t i o n as d e f i n e d in terms of these v a r i a b l e s between the i n t e l l e c t u a l l y g i f t e d and the norm. The l a c k of i n f o r m a t i o n a v a i l a b l e concerning the i s s u e of a c t u a l d i f f e r e n c e s i n t h i n k i n g between the i n t e l l e c t u a l l y g i f t e d and the norm has been noted ( A l v i n o , 1981; G e t z e l s & D i l l o n , 1973; Robinson, R o e d e l l , & Jackson, 1979). Sternberg (1981a) emphasizes t h a t : 2 Attempts to understand i n t e l l e c t u a l g i f t e d n e s s must go beyond merely c h a r a c t e r i z i n g the a t t r i b u t e s of the g i f t e d ... to i d e n t i f y i n g the u n d e r l y i n g d i f f e r e n c e s i n mental s t r u c t u r e s , c o n t e n t s , and processes that d i f f e r e n t i a t e the g i f t e d from t h e i r u n g i f t e d peers. (p.86) A d d i t i o n a l l y , d e s c r i p t i o n s such as " e a r l y d i f f e r e n t i a l p a t t e r n s f o r in f o r m a t i o n p r o c e s s i n g : t h i n k i n g i n a l t e r n a t i v e s and a b s t r a c t terms, sensing consequences, making g e n e r a l i z a t i o n s " ( C l a r k , 1983, p.199) f a i l to address how " e a r l y " i s d e f i n e d . Are these 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 a l l age l e v e l s ? A f u r t h e r c r i t i c i s m i s that c h a r a c t e r i z i n g g i f t e d n e s s in terms of a t t r i b u t e s has lac k e d a t h e o r e t i c a l p e r s p e c t i v e (Carter & Kontos,1982). T h i s study addressed the i s s u e s r a i s e d above by i n v e s t i g a t i n g a p o s s i b l e q u a l i t a t i v e d i f f e r e n c e i n the way the i n t e l l e c t u a l l y g i f t e d process information,and by u t i l i z i n g as a framework f o r the i n v e s t i g a t i o n the p e r s p e c t i v e s of P i a g e t i a n developmental theory and the componential i n f o r m a t i o n p r o c e s s i n g theory of Robert Sternberg (1980, 1981a). These t h e o r e t i c a l p e r s p e c t i v e s and the no t i o n of q u a l i t a t i v e d i f f e r e n c e provided, as w e l l , the c o n t e x t u a l s t r u c t u r e of the problem. 2. CONTEXT OF THE PROBLEM D i s c u s s i o n of the context of the problem d e a l s with the iss u e s of problem f i n d i n g as a p o s s i b l e m a n i f e s t a t i o n of q u a l i t a t i v e l y d i f f e r e n t i n f o r m a t i o n p r o c e s s i n g i n the g i f t e d , the hypothesized r e l a t i o n s h i p s of IQ, c o g n i t i v e l e v e l , and 3 i n s i g h t to problem f i n d i n g , and nonentrenched vs. entrenched measures of i n t e l l i g e n c e . 2.1 Q u a n t i t a t i v e Vs. Q u a l i t a t i v e D i f f e r e n c e s In The Information  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 C h i l d r e n Is a b r i g h t c h i l d mentally equal to an average old e r c h i l d (Robinson, R o e d e l l , & Jackson, 1979; R o e d e l l , Jackson, & Robinson, 1980), t h i n k i n g in b a s i c a l l y the same way but p r o g r e s s i n g at an a c c e l e r a t e d rate? Or does there e x i s t a d i f f e r e n c e i n thought processes - a d i s t i n c t i o n i n q u a l i t y of t h i n k i n g - such that the i n t e l l e c t u a l l y g i f t e d think i n a fundamentally d i f f e r e n t way? That there i s a q u a l i t a t i v e d i f f e r e n c e i n the g i f t e d ' s p r o c e s s i n g of in f o r m a t i o n has been hypothesized (Sternberg, 1981a; Sternberg & Davidson, 1982, 1983). T h i s research i n v e s t i g a t e d t h i s hypothesis by f o c u s i n g on problem f i n d i n g a b i l i t y 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 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 and on the c o g n i t i v e processes which may r e l a t e to and/or a f f e c t the a b i l i t y to f i n d problems. 2.2 Problem 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 G i f t e d C h i l d r e n Problem f i n d i n g - the d i s c o v e r y of many general questions from many i l l - d e f i n e d problems (Mackworth, 1965) - has been recognized as e q u a l l y important t o, i f not more v a l u a b l e than, the a b i l i t y to d e a l with presented problems, and has been l i n k e d to great d i s c o v e r y and the advancement of knowledge ( D i l l o n , 1982; E i n s t e i n & I n f e l d , 1938; G e t z e l s & C s i k s z e n t m i h a l y i , 1975; 4 Mackworth, 1965; Wertheimer, 1945). The a b i l i t y to d i s c o v e r problems has been c a l l e d "the s i g n a l mark of the t r u l y g i f t e d " ( G e t z e l s & D i l l o n , 1973). A r e l a t i o n s h i p of i n t e l l i g e n c e to problem f i n d i n g a b i l i t y has been suggested ( D i l l o n , 1982; Mackworth, 1965) but not a r t i c u l a t e d . How does i n t e l l i g e n c e as measured by IQ p r e d i c t problem f i n d i n g a b i l i t y ? Might there be a d d i t i o n a l f a c t o r s which a f f e c t s k i l l i n d i s c o v e r i n g problems, p o s s i b l y as mediated by formal o p e r a t i o n a l schemes? 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 Problem F i n d i n g Research suggests that the developmental l e v e l of the c h i l d may a f f e c t problem f i n d i n g a b i l i t y . A r l i n (1975-76) found formal o p e r a t i o n a l t h i n k i n g to be s i g n i f i c a n t l y c o r r e l a t e d with problem f i n d i n g q u a l i t y and. i n a l a t e r study (1977), found a s i g n i f i c a n t e f f e c t of age and o p e r a t i o n a l l e v e l on problem f i n d i n g q u a l i t y . There may, then, be developmental c o n s t r a i n t s on problem f i n d i n g a b i l i t y , with formal o p e r a t i o n a l t h i n k i n g a necessary but not s u f f i c i e n t c o n d i t i o n f o r problem f i n d i n g ( A r l i n , 1975-76, 1977, 1984 i n press b ) . To the q u e s t i o n s a l r e a d y posed, t h e r e f o r e , i s added the q u e s t i o n of the e f f e c t of c o g n i t i v e l e v e l on problem f i n d i n g a b i l i t y . 2.4 Information Pr 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 Problem F i n d i n g Sternberg and Davidson (1983), in h y p o t h e s i z i n g a q u a l i t a t i v e d i f f e r e n c e i n the t h i n k i n g of the i n t e l l e c t u a l l y g i f t e d , propose that " e x c e p t i o n a l i n s i g h t a b i l i t i e s seem to be what t r u l y set apart the i n t e l l e c t u a l l y g i f t e d from o t h e r s " (p.52). They b e l i e v e that i n s i g h t i n v o l v e s three separate but 5 r e l a t e d p s y c h o l o g i c a l p r o c e s s e s : s e l e c t i v e encoding, s e l e c t i v e combination, and s e l e c t i v e comparison. Sternberg and Davidson's (1983) statement that " s i g n i f i c a n t and e x c e p t i o n a l accomplishments - f o r example, major s c i e n t i f i c d i s c o v e r i e s , new and important i n v e n t i o n s , and new and s i g n i f i c a n t understandings of major l i t e r a r y , p h i l o s o p h i c a l , and s i m i l a r works - almost always i n v o l v e major i n t e l l e c t u a l i n s i g h t s " (p.52) seems to p a r a l l e l the a s s o c i a t i o n of problem f i n d i n g a b i l i t y to great d i s c o v e r y and the advancement of knowledge ( A r l i n , 1975-76; Mackworth,1965). That the three processes of i n s i g h t taken together may r e l a t e to problem f i n d i n g forms part of the r e s e a r c h problem. 2.5 I n s i g h t As A Nonentrenched Measure Of I n t e l l e c t u a l  Gi ftedness Sternberg (1981b, 1982b) b e l i e v e s that measurement of performance on nonentrenched, or novel, tasks i s a b e t t e r measure of i n t e l l e c t u a l g i f t e d n e s s than IQ t e s t s which i n c l u d e , f o r the most p a r t , entrenched, or f a m i l i a r , t a s k s . Might i n s i g h t a b i l i t y , as a nonentrenched measure of i n t e l l i g e n c e , be a b e t t e r p r e d i c t o r than IQ of problem f i n d i n g a b i l i t y , the hypothesized d i s t i n c t i v e c o g n i t i v e a t t r i b u t e of the i n t e l l e c t u a l l y g i f t e d ? A d d i t i o n a l l y , might i n s i g h t be mediated by the presence of c e r t a i n formal o p e r a t i o n a l schemes, namely combinations and c o o r d i n a t i o n of two or more systems of r e f e r e n c e (Inhelder & P i a g e t , 1958)? 6 3. SUMMARY OF THE PROBLEM Th i s study i n v e s t i g a t e d s k i l l in problem f i n d i n g as a p o s s i b l e d i f f e r e n t i a l 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 g i f t e d c h i l d r e n and examined the c o g n i t i v e processes which may r e l a t e to problem f i n d i n g a b i l i t y . I t addressed the problem: What i s the r e l a t i v e importance of IQ, c o g n i t i v e l e v e l , and r e l a t e d 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 in p r e d i c t i n g problem f i n d i n g a b i l i t y ? The study was aimed at c h i l d r e n at the upper elementary l e v e l . The age range was 10-14 ye a r s . 4. JUSTIFICATION OF THE STUDY Focusing on an a b i l i t y thought to be a c r u c i a l f a c t o r i n g i f t e d performance and a d i f f e r e n t i a l c o g n i t i v e a t t r i b u t e of the g i f t e d , i . e . problem f i n d i n g , may he l p to provide a beginning to a r t i c u l a t i n g p o s s i b l e u n d e r l y i n g d i f f e r e n c e s i n the info 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 c h i l d r e n . I n c l u s i o n of c o g n i t i v e l e v e l may lead to s p e c i f i c a t i o n of age-ap p r o p r i a t e d e f i n i t i o n s of i n t e l l e c t u a l g i f t e d n e s s . The study i s t h e o r e t i c a l l y based, speaking to the need f o r a t h e o r e t i c a l p e r s p e c t i v e to i n v e s t i g a t i o n s of g i f t e d n e s s , and f i n a l l y , the i n c l u s i o n of m u l t i p l e independent v a r i a b l e s r e f l e c t s the b e l i e f that " m u l t i v a r i a b l e problems are c l o s e r to p s y c h o l o g i c a l ... r e a l i t y " ( K e r l i n g e r , 1979). 7 5. ORGANIZATION OF THE STUDY Chapter One presents the r a t i o n a l e f o r the re s e a r c h problem. Chapter Two reviews the l i t e r a t u r e , p e r t i n e n t to the study. Chapter Three o u t l i n e s the methods, s u b j e c t s , design, procedure, and data a n a l y s i s used i n the r e s e a r c h . Chapters Four and F i v e deal with the r e s u l t s of the data a n a l y s i s , d i s c u s s i o n of the r e s u l t s , and c o n c l u s i o n s and i m p l i c a t i o n s drawn from the study. 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 The c r i t e r i o n v a r i a b l e i s problem f i n d i n g a b i l i t y . The p r e d i c t o r v a r i a b l e s are IQ, c o g n i t i v e l e v e l , a n d i n s i g h t d e f i n e d in terms of the processes of s e l e c t i v e encoding, s e l e c t i v e combination, and s e l e c t i v e comparison. 6.2 Problem F i n d i n g And Terms A s s o c i a t e d With Problem F i n d i n g 6.2.1 Problem F i n d i n g Problem f i n d i n g i s d e f i n e d as the d i s c o v e r y of many general q u e s t i o n s from many i l l - d e f i n e d problems (Mackworth, 1965). I t i s d i s t i n g u i s h e d from problem s o l v i n g i n terms of what i s known and unknown i n the problem s i t u a t i o n . In the p r e s e n t a t i o n of a problem f o r s o l u t i o n , there i s g e n e r a l l y a known f o r m u l a t i o n , a known method of s o l u t i o n , and a known s o l u t i o n . In a d i s c o v e r e d problem s i t u a t i o n , the problem does not yet have a known fo r m u l a t i o n , method of s o l u t i o n , or s o l u t i o n . The problem must be d i s c o v e r e d and posed (G e t z e l s & C s i k s z e n t m i h a l y i , 1975). 8 6.2.2 Elements Necessary For An O p e r a t i o n a l D e f i n i t i o n Of  Problem F i n d i n g A r l i n (1975-76) s t a t e d three elements based on Mackworth's (1965) d e f i n i t i o n that are necessary fo r an o p e r a t i o n a l d e f i n i t i o n of problem f i n d i n g : 1) a problematic s i t u a t i o n ; 2) an o p p o r t u n i t y f o r s u b j e c t s to r a i s e q u e s t i o n s ; and 3) a way of c a t e g o r i z i n g the q u e s t i o n s once r a i s e d . The l a t t e r i s necessary to s i n g l e out the general q u e s t i o n , (p.100) Furth e r d e s c r i p t i o n of these elements, i . e . the problem f i n d i n g task, d i r e c t i o n s to s u b j e c t s , and c a t e g o r i z i n g and s c o r i n g of the q u e s t i o n s r a i s e d by s u b j e c t s , i s found in the t h i r d chapter. 6.3 Terms A s s o c i a t e d With 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 T h i s term r e f e r s to the l e v e l of c o g n i t i v e development of the c h i l d i n terms of P i a g e t ' s g e n e t i c approach to c o g n i t i o n (Inhelder, 1964). 6.3.2 Concrete O p e r a t i o n a l L e v e l At t h i s l e v e l of c o g n i t i v e development (ages 7 to 11-14, appr o x i m a t e l y ) , the c h i l d ' s s t r u c t u r i n g and o r g a n i z a t i o n of knowledge i s o r i e n t e d towards c o n c r e t e t h i n g s and events in the immediate present ( F l a v e l l , 1963). An elementary form of l o g i c i s developed which i s bound to the c l a s s i f i c a t i o n , s e r i a t i o n , and c o n s e r v a t i o n of p h y s i c a l p r o p e r t i e s . 9 6.3.3 Formal O p e r a t i o n a l L e v e l The formal stage of c o g n i t i v e development i s c h a r a c t e r i z e d by h y p o t h e t i c o d e d u c t i v e thought (Inhelder, 1964). The forming of hypotheses and deduction of p o s s i b l e consequences c o n t r a s t s with the thought bound to the "concrete here and now" (Inhelder, 1964, p.25) of the pr e v i o u s , concrete o p e r a t i o n a l stage. The formal o p e r a t i o n a l t h i n k e r i s able to manipulate p r o p o s i t i o n s and i d e a s , t o t h i n k i n terms of the p o s s i b l e and not simply the a c t u a l . 6.3.4 C o g n i t i v e M a t u r i t y C o g n i t i v e maturity i s d e f i n e d i n t h i s study as evidence that most of the formal o p e r a t i o n a l schemata are i n use. A " c o g n i t i v e l y mature" subject i s thus one who i s a formal o p e r a t i o n a l t h i n k e r . 6.3.5 H o r i z o n t a l Decalage H o r i z o n t a l decalage r e f e r s to the mastery of tasks w i t h i n an o p e r a t i o n a l l e v e l . F l a v e l l ' s (1963) d e s c r i p t i o n serves to c l a r i f y : A c o g n i t i v e s t r u c t u r e , c h a r a c t e r i s t i c of that l e v e l , can f i r s t be s u c c e s s f u l l y a p p l i e d to task X but not to task Y; a year or so l a t e r ... the same o r g a n i z a t i o n of op e r a t i o n s can now be extended to Y as w e l l as X. Moreover, the developmental process whereby Y comes to be mastered ... i s e s s e n t i a l l y the same as that which c h a r a c t e r i z e d the mastery of X. (p.22) As an example, F l a v e l l notes that i n v a r i a n c e of mass i s t y p i c a l l y a c h ieved e a r l i e r than i n v a r i a n c e of weight. 10 6.4 Terms A s s o c i a t e d With The R e l a t e d Information P r o c e s s i n g  V a r i a b l e s 6.4.1 S e l e c t i v e Encoding S e l e c t i v e encoding i n v o l v e s s i f t i n g out r e l e v a n t i n f o r m a t i o n from i r r e l e v a n t i n f o r m a t i o n , that i s , understanding what in f o r m a t i o n i s r e l e v a n t to s o l v i n g a problem, and how i t i s r e l e v a n t (Sternberg & Davidson, 1982,1983). 6.4.2 S e l e c t i v e Combination S e l e c t i v e combination i n v o l v e s combining what might o r i g i n a l l y seem to be i s o l a t e d p i e c e s of i n f o r m a t i o n i n t o a u n i f i e d whole that may or may not resemble i t s p a r t s . Knowing how to put together p i e c e s of i n f o r m a t i o n that are r e l e v a n t i s i m p l i e d . (Sternberg & Davidson, 1983). 6.4.3 S e l e c t i v e Comparison S e l e c t i v e comparison i n v o l v e s r e l a t i n g newly a c q u i r e d i n f o r m a t i o n to i n f o r m a t i o n a c q u i r e d i n the p a s t . A nonobvious r e l a t i o n s h i p between new and o l d i n f o r m a t i o n i s d i s c o v e r e d (Sternberg & Davidson, 1982, 1983). Theory p r o v i d e d the guide to v a r i a b l e s e l e c t i o n with the aim 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 (Pedhazur, 1982). The v a r i a b l e s as d e f i n e d supply the o p e r a t i o n a l s t r u c t u r e f o r the r e s e a r c h . The i n t r o d u c t i o n to the study can now be summarized, p r e p a r a t o r y to a review of p e r t i n e n t l i t e r a t u r e and statements of hypotheses. 11 7. SUMMARY OF CHAPTER ONE Given the r e c o g n i t i o n of problem f i n d i n g as s i g n i f i c a n t i n g i f t e d performance, i t seems necessary to address the lack of emphasis on t h i s important a b i l i t y i n conceptions and r e s e a r c h of g i f t e d n e s s . Examining the r e l a t i v e importance of IQ, c o g n i t i v e l e v e l , and r e l a t e d 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 as p r e d i c t o r s of problem f i n d i n g a b i l i t y i s j u s t i f i e d on the b a s i s of the f o l l o w i n g recognized needs: 1 ) .'to i d e n t i f y p o s s i b l e u n d e r l y i n g d i f f e r e n t i a l c o g n i t i v e processes of 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 ; 2) 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 g i f t e d n e s s ; and 3) to provide a t h e o r e t i c a l p e r s p e c t i v e to research on g i f t e d n e s s . 12 I I . A REVIEW OF THE LITERATURE 1. OVERVIEW OF THE CHAPTER Chapter 2 reviews the l i t e r a t u r e p e r t a i n i n g to the quest i o n of problem f i n d i n g as a d i f f e r e n t i a l 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 g i f t e d c h i l d r e n . As a r e s u l t of t h i s review, f i v e hypotheses were formulated. To a i d c l a r i t y , the l i t e r a t u r e review i s d i v i d e d i n t o four p a r t s which d e a l r e s p e c t i v e l y with the nature of in f o r m a t i o n p r o c e s s i n g 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 , the a s s o c i a t i o n of i n t e l l i g e n c e with problem f i n d i n g , the i n f l u e n c e of c o g n i t i v e l e v e l on problem f i n d i n g , and the r e l a t i o n s h i p of i n s i g h t to problem f i n d i n g . The reason f o r these c a t e g o r i e s w i l l become evident w i t h i n the review i t s e l f . The chapter concludes with a summary of the f i v e d i r e c t i o n a l hypotheses. 2. INFORMATION PROCESSING IN INTELLECTUALLY GIFTED CHILDREN Two p r o p o s i t i o n s concerning the nature of information p r o c e s s i n g i n g i f t e d c h i l d r e n w i l l be examined. 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 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 are commonly d e s c r i b e d in ways that i n d i c a t e t h e i r d i f f e r e n c e from the norm in q u a n t i t a t i v e terms. The IQ metric denotes a high score, s i g n i f i c a n t l y above the mean, and an advanced mental age. R o e d e l l , Jackson, and Robinson (1980) equate t h i s 13 q u a n t i t a t i v e d i f f e r e n c e with developmental advancement. T h e i r b e l i e f i s that c h a r a c t e r i s t i c s which d i s t i n g u i s h o l d e r from younger c h i l d r e n apply e q u a l l y as w e l l to d i s t i n g u i s h 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 from l e s s b r i g h t c h i l d r e n . Two q u e s t i o n s a r i s e from t h i s assumption, however. F i r s t l y , might not developmental advancement imply, at l e a s t in p a r t , q u a l i t a t i v e change (Webb, 1974)? While "development" can mean q u a n t i t a t i v e change, there i s a l s o the n o t i o n of change in the s t r u c t u r e and o r g a n i z a t i o n of knowledge which can be viewed as q u a l i t a t i v e . Thus, to s p e c i f y q u a n t i t a t i v e d i f f e r e n c e s as developmental advancement may be c o r r e c t in one sense, but inadequate i n i t s omission of the c o n s i d e r a t i o n of q u a l i t a t i v e change. Secondly, can i t be s a i d t h a t , f o r example, an 8-year-old g i f t e d c h i l d with a MA of 13 t h i n k s i n ways i d e n t i c a l to the average 13-year-old? T h i s may be an inadequate way of d e s c r i b i n g g i f t e d n e s s , f o r i t does not address the p o s s i b i l i t y of d i f f e r e n t i a l i n f o r m a t i o n p r o c e s s i n g s t r a t e g i e s . Perhaps the g i f t e d 8-year-old t h i n k s i n ways more t y p i c a l of h i s / h e r age group, but uses these thought processes in a q u a l i t a t i v e l y d i f f e r e n t manner. The " q u a n t i t a t i v e l y d i f f e r e n t " d e s c r i p t i o n of 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 a p p l i e s a l s o to t h e i r advanced school achievement (Kaplan, 1977). T h i s advancement r e f l e c t s the g i f t e d ' s a b i l i t y to process i n f o r m a t i o n f a s t e r ( C l a r k , 1983) and to r e t a i n more in f o r m a t i o n ( C l a r k , 1983;Newland, 1976). But i s "quick" performance n e c e s s a r i l y synonomous with " i n t e l l i g e n t " 1 4 performance? The q u e s t i o n occurs f o r some, whereas others would d e f i n e i n t e l l i g e n c e as speed of performance. Sternberg and Davidson (1982, 1983) are two f o r whom the q u e s t i o n does occur. Sternberg and Davidson b e l i e v e that " d e s p i t e the many f i n e f e a t u r e s of r e a c t i o n time or speeded responses" i n the assessment of i n t e l l e c t u a l s k i l l s "they do not provide the optimum entree to understanding or a s s e s s i n g i n t e l l e c t u a l g i f t e d n e s s " (1983, p.56). They hypothesize, r a t h e r , a q u a l i t a t i v e d i f f e r e n c e i n i n f o r m a t i o n p r o c e s s i n g between the g i f t e d and the norm. 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 Sternberg (1981 a,1982a) b e l i e v e s s u p e r i o r i t y i n c e r t a i n i n f o r m a t i o n p r o c e s s i n g components and on nonentrenched, or novel, measures of i n t e l l i g e n c e (1981b, 1982b) are what d i s t i n g u i s h the i n t e l l e c t u a l l y g i f t e d . In p a r t i c u l a r , the g i f t e d are s a i d to possess s u p e r i o r i n s i g h t s k i l l s (Sternberg & Davidson, 1982, 1983). Since a major p a r t of t h i s research b u i l d s on Sternberg's hypotheses, these p o s s i b l e 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 t h i n k i n g of 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 w i l l be d e a l t with i n more d e t a i l subsequently, p a r t i c u l a r l y i n s o f a r as they r e l a t e to problem f i n d i n g , f o r i t i s from the l i t e r a t u r e on problem f i n d i n g that the hypothesis evolved that t h i s important a b i l i t y may represent a 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 g i f t e d c h i l d r e n . 1 5 3. PROBLEM FINDING IN INTELLECTUALLY GIFTED CHILDREN A s s o c i a t i o n s have been made between problem f i n d i n g and g i f t e d performance and between problem f i n d i n g and i n t e l l i g e n c e . These a s s o c i a t i o n s and the concomitant need f o r resea r c h w i l l be examined i n t h i s s e c t i o n of the l i t e r a t u r e review. 3.1 The Importance Of Problem F i n d i n g And I t s Link To G i f t e d  Performance Problem f i n d i n g has been d e f i n e d as the d i s c o v e r y of many gene r a l q u e s t i o n s from many i l l - d e f i n e d problems (Mackworth, 1965). T h i s a b i l i t y has been d e s c r i b e d as more important than problem s o l v i n g (Mackworth, 1965; Wertheimer, 1945), and has been l i n k e d to breakthroughs i n sc i e n c e ( E i n s t e i n & I n f e l d , 1938; Mackworth, 1965), to i n v e n t i o n s (Mackworth, 1965), and to o r i g i n a l i t y i n a r t (Getzels & C s i k s z e n t m i h a l y i , 1975, 1976). Superior problem f i n d e r s are b e l i e v e d to be c r u c i a l to the for m u l a t i o n of re s e a r c h problems and the ge n e r a t i o n of ideas i n many d i s c i p l i n e s ( Getzels & D i l l o n , 1973; Helvey, 1971; Mackworth, 1965). I t can be seen, then, that problem f i n d i n g i s l i n k e d to what can be co n s i d e r e d g i f t e d performance. G e t z e l s and D i l l o n (1973), i n s t a t i n g that "the s i g n a l mark of the t r u l y g i f t e d " i s the a b i l i t y to f i n d problems, p o i n t out that i t i s the f i n e a r t i s t , the i n v e n t i v e s c i e n t i s t , and the c r e a t i v e s c h o l a r who work with d i s c o v e r e d problems. In comparison to "the c o p y i s t i n a r t , the t e c h n i c i a n i n s c i e n c e , and the pedant i n s c h o l a r s h i p "(p.721) who work with problems that have been presented to them, i t i s the problem 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 of G e t z e l s and D i l l o n ' s statement can be c r i t i c i z e d f o r i t s appearance almost as an a f t e r t h o u g h t i n t h e i r c o n c l u s i o n to a comprehensive a r t i c l e on the nature of g i f t e d n e s s , t h e i r c a l l for a problem f i n d i n g o r i e n t a t i o n to re s e a r c h gains credence when put i n the context of t h e i r c r i t i q u e of the term " g i f t e d . " They b e l i e v e the term has remained a d e s i g n a t i o n rather than a d e f i n i t i o n , " f o r i t s p e c i f i e s n e i t h e r the type of a b i l i t y nor the degree of s u p e r i o r i t y " ( p . 689). Addressing the lack of emphasis on problem f i n d i n g i n resea r c h on g i f t e d n e s s may pr o v i d e , at l e a s t , s p e c i f i c a t i o n of the type of a b i l i t y . 3.2 The Need For Research Into Problem F i n d i n g Despite i t s c o n s i d e r e d importance by many, research i n t o problem f i n d i n g i s scant ( D i l l o n , 1982). G e t z e l s (1964,1975), G e t z e l s and C s i k s z e n t m i h a l y i (1975, 1976), and A r l i n (1975-76, 1977) have done s i g n i f i c a n t r e s e a r c h which i s drawn upon i n t h i s study, but p r i m a r i l y the t o p i c has to be approached t a n g e n t i a l l y through, f o r example, d i s c u s s i o n s of p r o d u c t i v e t h i n k i n g (Wertheimer, 1945), c r e a t ive t h i n k i n g (Henle, 1975), and s c i e n t i f i c d i s c o v e r y ( E i n s t e i n & I n f e l d , 1938; Mackworth, 1965). Given the r e c o g n i t i o n of problem f i n d i n g as s i g n i f i c a n t i n g i f t e d performance, i t seems a p p r o p r i a t e to study problem f i n d i n g w i t h i n the context of g i f t e d n e s s . At present, an a s s o c i a t i o n between i n t e l l e c t u a l g i f t e d n e s s and problem f i n d i n g a b i l i t y can only be i m p l i e d . These i m p l i c a t i o n s w i l l now be examined p r i o r to f o r m u l a t i n g the f i r s t h ypothesis f o r e m p i r i c a l 1 7 study. 3.3 I n t e l l i g e n c e And Problem F i n d i n g Some re f e r e n c e s i n the l i t e r a t u r e imply a p o s i t i v e a s s o c i a t i o n between i n t e l l i g e n c e and the a b i l i t y to p e r c e i v e and formulate problems. D i l l o n (1982) suggests that i n t e l l i g e n c e may be a r e l e v a n t v a r i a b l e i n problem f i n d i n g and that t h i s r e l a t i o n s h i p be researched. Mackworth (1965) d e s c r i b e d problem f i n d i n g as a " h i g h l y i n t e l l e c t u a l process" and Dewey (1933) equated i n t e l l i g e n t thought with the d i s c o v e r e d problem. In l i g h t of the suggested a s s o c i a t i o n between i n t e l l i g e n c e and problem f i n d i n g , research i n t o the nature of the r e l a t i o n s h i p appears necessary. For example, would " i n t e l l i g e n c e " d e f i n e d i n terms of IQ c o n t r i b u t e s i g n i f i c a n t l y to the p r e d i c t i o n of problem f i n d i n g ? Given the a s s o c i a t i o n of problem f i n d i n g with i n v e n t i o n s (Mackworth,1965), o r i g i n a l i t y ( G e t z e l s & C s i k s z e n t m i h a l y i , 1975,1976), p r o d u c t i v e t h i n k i n g (Wertheimer, 1945), and c r e a t i v e t h i n k i n g (Henle, 1975); the low c o r r e l a t i o n found between IQ and c r e a t i v i t y ( G e t z e l s & Jackson, 1962; G u i l f o r d , 1967); and the d i s t i n c t i o n between c r e a t i v i t y and i n t e l l i g e n c e a f f i r m e d by Wallach and Kogan (1965), the r e l a t i o n s h i p of IQ to problem f i n d i n g may not be strong, but there i s reason to b e l i e v e there may be some c o n t r i b u t i o n of IQ to the p r e d i c t i o n of problem f i n d i n g . Being of above average IQ i s con s i d e r e d to be a necessary but not s u f f i c i e n t c o n d i t i o n f o r c r e a t i v i t y . An IQ of at l e a s t 120 i s thought to be the minimum l e v e l necessary f o r the 18 i n v e n t i v e and e l a b o r a t i v e t h i n k i n g a s s o c i a t e d with c r e a t i v e p r o d u c t i o n (Roe, 1976). Problem f i n d i n g , then, i s l i k e l y more a l l i e d to c r e a t i v i t y than to the s u p e r i o r convergent t h i n k i n g a s s o c i a t e d with a high IQ. IQ, however, would appear to have some relevance i n p r e d i c t i n g problem f i n d i n g given i t s "necessary but not s u f f i c i e n t " r e l a t i o n s h i p to c r e a t i v e t h i n k i n g . The f i r s t h y pothesis concerns the degree of r e l e v a n c e . 3.4 A Formal Statement Of The F i r s t Hypothesis The r o l e of IQ as a p r e d i c t o r of a b i l i t y to d i s c o v e r problems forms the b a s i s f o r the f i r s t r e s e a r c h h y p o t h e s i s : I n t e l l i g e n c e as measured by IQ w i l l c o n t r i b u t e to the p r e d i c t i o n of problem f i n d i n g but w i l l be l e s s s i g n i f i c a n t in i t s c o n t r i b u t i o n to the p r o p o r t i o n of v a r i a n c e accounted f o r than the 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 l e v e l and i n s i g h t . 4. COGNITIVE LEVEL AND PROBLEM FINDING A developmental p e r s p e c t i v e on g i f t e d n e s s and problem f i n d i n g forms the f o l l o w i n g s e c t i o n of the l i t e r a t u r e review. The importance of t h i s p e r s p e c t i v e to the r e s e a r c h q u e s t i o n w i l l become e v i d e n t . 4.1 The Need For A Developmental Focus To D e s c r i p t i o n s Of  Gi ftedness The c r i t i c i s m has been made that d e s c r i p t i o n s of g i f t e d n e s s may not be age-appropriate i n that l i s t i n g s of g i f t e d " a t t r i b u t e s " f a i l to address whether these a t t r i b u t e s are 19 c h a r a c t e r i s t i c of a l l age l e v e l s . A developmental focus appears necessary i n resea r c h on g i f t e d n e s s and P i a g e t i a n developmental theory p r o v i d e s such a focus . I t w i l l be looked at f i r s t l y f o r i t s c o n t r i b u t i o n to a developmental understanding of g i f t e d n e s s and secondly f o r p r o v i s i o n of age-appropriateness i n the s p e c i f i c a t i o n of problem f i n d i n g as a p o s s i b l e d i f f e r e n t i a l c o g n i t i v e a t t r i b u t e of the i n t e l l e c t u a l l y g i f t e d . 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 Research w i t h i n a P i a g e t i a n p e r s p e c t i v e suggests that i n t r a - s t a g e p r e c o c i t y i s c l o s e l y r e l a t e d to IQ, but movement from one stage to another i s dependent on maturation. Studies p e r t a i n i n g to i n t r a - s t a g e p r e c o c i t y w i l l be looked at f i r s t and re s e a r c h r e l e v a n t to c o n s t r a i n t s on the a c q u i s i t i o n of a new stage second. I t w i l l be seen that while g i f t e d c h i l d r e n e x c e l on tasks a s s o c i a t e d with a p a r t i c u l a r developmental stage, they are c o n s t r a i n e d by maturation i n t h e i r p r o g r e s s i o n to a subsequent stage. 4.2.1 I n t r a - s t a g e P r e c o c i t y Webb's (1974) study showed support f o r h i s hypothesis that h o r i z o n t a l decalage i s a f u n c t i o n of i n t e l l i g e n c e . With a sample of 25 c h i l d r e n i n the age range 6 to 11 years (IQ >160), "the most s t r i k i n g o b s e r v a t i o n was the success of b r i g h t young c h i l d r e n on concrete o p e r a t i o n s problems that are d i f f i c u l t f o r o l d e r , average c h i l d r e n " (p.299). Webb's f i n d i n g s support L o v e l l and S h i e l d s ' (1967) suggestion that the f l e x i b i l i t y of g i f t e d c h i l d r e n ' s f i r s t order o p e r a t i o n a l schemas i s much 20 g r e a t e r than o r d i n a r y p u p i l s ' . A r l i n ' s (1984, in press a) study e s t a b l i s h e d that i n t r a -stage p r e c o c i t y continues to be a c h a r a c t e r i s t i c of the i n t e l l e c t u a l l y g i f t e d through formal o p e r a t i o n s : The argument can be made that those i d e n t i f i e d as g i f t e d appear to move very q u i c k l y in 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 the concepts and o p e r a t i o n s a s s o c i a t e d with the new stage. Such speed of a c q u i s i t i o n i s not apparent in l e s s g i f t e d groups of students with average to above average IQ's. (p.8) With a sample of 223 c h i l d r e n aged 10 to 15 years, C a r t e r and Ormrod (1982) found " s u p e r i o r i t y on P i a g e t i a n tasks f o r g i f t e d c h i l d r e n over n o r m a l - a b i l i t y c h i l d r e n at each age l e v e l t e s t e d " (p.113). The q u e s t i o n of whether p r e c o c i o u s a c q u i s i t i o n of a new stage of development 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 c o u l d be expected as a r e s u l t of f a s t e r 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 schemas w i t h i n the previous stage may be a l o g i c a l one. Research, however, has i n d i c a t e d that t h i s may not be the case. S t u d i e s on the a c q u i s i t i o n of formal o p e r a t i o n s by the i n t e l l e c t u a l l y g i f t e d w i l l be focused upon, f o r i t i s the formal o p e r a t i o n a l stage that may be the most r e l e v a n t to the study of problem f i n d i n g . 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  Formal Operations Support f o r the pr e c o c i o u s a c q u i s i t i o n of formal o p e r a t i o n s by g i f t e d c h i l d r e n would appear to come from the work of Keating (1975). I t w i l l be seen, however, that the number of tasks used 21 to t e s t formal o p e r a t i o n a l t h i n k i n g and the age range s t u d i e d may be important q u a l i f i e r s to Keating's f i n d i n g s . In a study comparing average and b r i g h t c h i l d r e n , Keating found that the f i f t h grade b r i g h t group (M age 11 years 3 months) were at a more advanced c o g n i t i v e developmental l e v e l than the seventh grade average group (M age 13 years 1 month). The former group was found to be formal o p e r a t i o n a l ; the l a t t e r , t r a n s i t i o n a l . Keating's s u b j e c t s were, however, t e s t e d on only three formal o p e r a t i o n s t a s k s , whereas ei g h t formal o p e r a t i o n a l sshemata were d e f i n e d by Inhelder and Piaget (1958). While a b i l i t y to do three formal o p e r a t i o n a l tasks p r o v i d e s some evidence of c a p a b i l i t y of a b s t r a c t i o n ( A r l i n , 1984a), i t may not be completely accurate to c l a s s i f y such performance as "formal operat i o n a l . " A d d i t i o n a l l y , i t i s important to q u a l i f y the extent of p r e c o c i t y shown by Keating's b r i g h t group. That i s , i f a younger b r i g h t group were used would they a l s o outperform the ol d e r average group? When viewed i n the context of other r e s e a r c h , l i m i t s to the p r e c o c i o u s a c q u i s i t i o n of formal o p e r a t i o n s can be seen to e x i s t . With a group of s l i g h t l y younger g i f t e d c h i l d r e n (M age 10 years 6 months), A r l i n (1984, i n press a) found that only 21% of t h i s group were i d e n t i f i e d as low formal (three to f i v e formal schemes present i n t h e i r t h i n k i n g ) and that those i d e n t i f i e d were at the upper end of the age range. In comparison, 55% of the g i f t e d group whose mean age was 11 years 4 months were 22 c l a s s i f i e d as low formal or formal. These r e s u l t s are comparable to those of L o v e l l and S h i e l d s (1967) who found that g i f t e d p u p i l s "do not g e n e r a l l y a t t a i n the l e v e l of formal o p e r a t i o n a l thought u n t i l 11 years of age at l e a s t " (p.206). Webb (1974) concurs. The data of h i s study "suggest e s s e n t i a l l y no p r e c o c i t y on formal o p e r a t i o n s a s s o c i a t e d with high IQ's below the age of 11" (p.299). The s t u d i e s of A r l i n , L o v e l l and S h i e l d s , and Webb demonstrate that the g i f t e d c h i l d may indeed be developmentally c o n s t r a i n e d i n the a c q u i s i t i o n of formal o p e r a t i o n s . However, in comparison to the norm, they can be co n s i d e r e d somewhat pr e c o c i o u s , as shown by Kea t i n g . A r l i n , too, found the performance of both g i f t e d groups to be above that of a norming group. It i s important to note Webb's (1974) emphasis that p r e c o c i t y i n a c q u i s i t i o n of formal o p e r a t i o n s by b r i g h t c h i l d r e n i s of a " r e l a t i v e l y low degree." In h i s sample of 6- to 11-y e a r - o l d s , mental age (estimated from IQ scores) ranged from 10 to 19 years, but s u b j e c t s performed " c l o s e r to CA than MA ex p e c t a t i o n s " (p.299) on tasks of formal t h i n k i n g . Put i n t o the context of the d i s c u s s i o n of 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 as q u a n t i t a t i v e l y or q u a l i t a t i v e l y d i f f e r e n t i n f o r m a t i o n p r o c e s s o r s presented e a r l i e r , i t would appear t h a t , i n P i a g e t i a n terms, an 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 does think i n ways more t y p i c a l of h i s / h e r age group and that the grea t e r i n t r a - s t a g e f l e x i b i l i t y of thought c o u l d be con s i d e r e d a q u a l i t a t i v e d i f f e r e n c e from the norm. How these developmental 23 c h a r a c t e r i s t i c s of 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 may r e l a t e to problem f i n d i n g w i l l now be e x p l o r e d . 4.3 A P i a g e t i a n P e r s p e c t i v e On Problem F i n d i n g I t has been seen that 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 appear to demonstrate a greater than average f l e x i b i l i t y of schemas w i t h i n stages of development ( A r l i n , 1984, i n press a; L o v e l l & S h i e l d s , 1967; Webb, 1974). With the suggestion that f l e x i b i l i t y of thought accounts for some of the v a r i a n c e i n problem f i n d i n g ( A r l i n , 1975-76), i t might be that the g r e a t e r f l e x i b i l i t y of schemas in the i n t e l l e c t u a l l y g i f t e d would allow f o r s u p e r i o r i t y i n p e r c e i v i n g and posing problems. It i s a l i k e l y h ypothesis that g i f t e d c h i l d r e n would be more adept at f i n d i n g problems. S p e c i f i c r e f e r e n c e s to problem f i n d e r s , however, are mainly to a d u l t s who p e r c e i v e problems i n t h e i r f i e l d s of study. Can we assume that a g i f t e d s c h o l a r who i s s u p e r i o r at d i s c o v e r i n g problems c o u l d p e r c e i v e problems as a young c h i l d ? I n t r a - s t a g e f l e x i b i l i t y alone may not be s u f f i c i e n t to account for problem f i n d i n g a b i l i t y . The developmental l e v e l of the c h i l d may be a r e l e v a n t v a r i a b l e . A r l i n (1975-76) found formal o p e r a t i o n a l t h i n k i n g to be s i g n i f i c a n t l y c o r r e l a t e d with problem f i n d i n g q u a l i t y and, i n a l a t e r study (1977), found a s i g n i f i c a n t e f f e c t of age and o p e r a t i o n a l l e v e l on problem f i n d i n g q u a l i t y . T h i s second study appeared to c o n f i r m that formal o p e r a t i o n a l t h i n k i n g " r e l a t e s to the problem f i n d i n g s k i l l of posing general q u e s t i o n s " ( A r l i n , 1977, p.298). There may then be developmental c o n s t r a i n t s on problem f i n d i n g c a p a b i l i t y , with c o g n i t i v e l e v e l a r e l e v a n t 24 c o n s i d e r a t i o n when p r e d i c t i n g the a b i l i t y to d i s c o v e r problems. 4.4 A Formal Statement Of The Second Hypothesis The r o l e of 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 problem f i n d i n g a b i l i t y forms the b a s i s f o r the second h y p o t h e s i s : C o g n i t i v e l e v e l w i l l c o n t r i b u t e s i g n i f i c a n t l y to the p r e d i c t i o n of problem f i n d i n g a b i l i t y , that i s , the a b i l i t y to d i s c o v e r g e n e r a l q u e s t i o n s from i l l - d e f i n e d problems (Mackworth, 1965). 5. INSIGHT AND PROBLEM FINDING . The r o l e of i n s i g h t f u l t h i n k i n g i n i n t e l l e c t u a l g i f t e d n e s s and the r e l a t i o n s h i p of i n s i g h t to problem f i n d i n g w i l l now be co n s i d e r e d . A d d i t i o n a l l y , p o s s i b l e developmental i n f l u e n c e s on i n s i g h t w i l l be examined. 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 To p r o v i d e some t h e o r e t i c a l background to i n s i g h t as an inf 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 r e l e v a n t to the study of problem f i n d i n g , the main ideas of a componential theory of g i f t e d n e s s w i l l be presented. Recognizing the need to s p e c i f y the processes that c o n s t i t u t e i n t e l l i g e n t performance, Sternberg (1980, 1981a) formulated a componential theory of i n t e l l e c t u a l g i f t e d n e s s . In t h i s theory, i n t e l l e c t u a l g i f t e d n e s s i s viewed as a t t r i b u t a b l e p r i m a r i l y to s u p e r i o r i t y i n the f o l l o w i n g componential s k i l l s : (a) "Metacomponential" or ex e c u t i v e p r o c e s s i n g s k i l l s , such as problem r e c o g n i t i o n , process s e l e c t i o n , s t r a t e g y s e l e c t i o n , s o l u t i o n m o n i t o r i n g , and the l i k e ; (b) performance-componential s k i l l s , such as 25 the a b i l i t i e s to make i n f e r e n c e s and to apply p r e v i o u s l y made i n f e r e n c e s i n new doma i n s ; (c) l e a r n i n g s k i l l s , such as encoding and r e t r i e v a l of in f o r m a t i o n that r e s i d e s i n long-term memory; and (d) i n t e r a c t i o n s among these v a r i o u s kinds of componential s k i l l s . (Sternberg & Davidson, 1983, p.52) Drawing on the componential view, Sternberg hypothesizes a subtheory that i t i s processes of i n s i g h t f u l t h i n k i n g ( s e l e c t i v e encoding, s e l e c t i v e combination, s e l e c t i v e comparison, as d e f i n e d i n Chapter 1) that are d i s t i n g u i s h i n g f e a t u r e s of the g i f t e d (Sternberg & Davidson, 1982, 1983). It can be seen that the s u p e r i o r "metacomponential" s k i l l of problem r e c o g n i t i o n , through i t s r o l e i n determining the nature of the problem to be solv e d and/or what i s r e l e v a n t in the problem s i t u a t i o n , c o n t r i b u t e s to s e l e c t i v e encoding a b i l i t y . Process s e l e c t i o n (steps needed to sol v e the problem), s t r a t e g y s e l e c t i o n , and s o l u t i o n monitoring work i n tandem to c o n t r i b u t e to refinement of the encoding process by d e t e c t i n g i r r e l e v a n c i e s i n the s t r a t e g i e s used and/or i n c o n s i s t e n c i e s in s o l u t i o n s . Too, a person s k i l l e d i n making i n f e r e n c e s , i n d e r i v i n g a c o n c l u s i o n from premises or evidence, would l i k e l y be s u p e r i o r at s e l e c t i v e l y encoding i n f o r m a t i o n r e l e v a n t to a problem. S k i l l i n making i n f e r e n c e s may c o n t r i b u t e to s u p e r i o r s e l e c t i v e combination as w e l l , f o r i n drawing a c o n c l u s i o n , s e v e r a l i n f e r e n c e s may need to be combined i n a unique way. S i m i l a r l y , g r e a t e r s k i l l i n process s e l e c t i o n and/or s t r a t e g y s e l e c t i o n may c o n t r i b u t e i n i t i a l l y to s e l e c t i v e combination, 26 that i s , to "knowing how to put together the p i e c e s of inform a t i o n that are r e l e v a n t " (Sternberg & Davidson, 1983, p. 53) . Superior performance-componential s k i l l s and l e a r n i n g s k i l l s can be seen to c o n t r i b u t e to s e l e c t i v e comparison. The a b i l i t y to apply p r e v i o u s l y made i n f e r e n c e s in new domains i s c l o s e l y a s s o c i a t e d with problem s o l v i n g by analogy, one example of s e l e c t i v e comparison. A d d i t i o n a l l y , g r e a t e r a b i l i t y to r e t r i e v e i n f o r m a t i o n that r e s i d e s i n long-term memory would appear to be b a s i c to the s e l e c t i v e comparison process of " r e l a t i n g newly a c q u i r e d i n f o r m a t i o n to inf o r m a t i o n a c q u i r e d i n the past" (Sternberg & Davidson, 1983, p.54). Table I summarizes how s u p e r i o r componential s k i l l s can be seen to c o n t r i b u t e to the processes of i n s i g h t . S e l e c t i v e encoding S e l e c t i v e combination S e l e c t i v e comparison Problem r e c o g n i t i o n Process s e l e c t i o n S t r a t e g y s e l e c t i o n S o l u t i o n m o nitoring A b i l i t y to make in f e r e n c e s A b i l i t y to make i n f e r e n c e s Process s e l e c t i o n S t r a t e g y s e l e c t i o n A b i l i t y to apply p r e v i o u s l y made i n f e r e n c e s i n new domains R e t r i e v a l of in f o r m a t i o n that r e s i d e s i n long-term memory Table I - The processes of i n s i g h t and componential s k i l l s thought to r e l a t e to each process 27 Sternberg and Davidson (1983) b e l i e v e that the t r u l y g i f t e d w i l l have s e v e r a l , perhaps many, major i n t e l l e c t u a l i n s i g h t s i n t h e i r l i f e t i m e s , and i n t h i s r e s p e c t , they d i f f e r q u a l i t a t i v e l y from the norm. The subtheory of i n s i g h t p r o v i d e s the t h e o r e t i c a l background f o r the ch o i c e of a t h i r d p r e d i c t o r v a r i a b l e , f o r s u p e r i o r i n s i g h t s k i l l s may be s i g n i f i c a n t i n a study of problem f i n d i n g as a q u a l i t a t i v e l y d i f f e r e n t a t t r i b u t e of 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 To Problem F i n d i n g Chapter 1 p o i n t e d out the p a r a l l e l seen between the outcomes of major i n t e l l e c t u a l i n s i g h t s (Sternberg & Davidson, 1983) and those of problem f i n d i n g ( A r l i n , 1975-76; Mackworth, 1965). I t was hypothesized that the three processes of i n s i g h t taken together may r e l a t e to problem f i n d i n g . Two other r e f e r e n c e s i n the l i t e r a t u r e would appear to support t h i s h y p o t h e s i s . Henle (1975), i n speaking of the importance of both the questi o n and the problem i n c r e a t i v e t h i n k i n g , p o i n t s out the need f o r a p r i n c i p l e of s e l e c t i o n and the r e c o g n i t i o n of s i g n i f i c a n c e when ideas are generated. The s u p e r i o r problem f i n d e r , i n the r a i s i n g of q u e s t i o n s from i l l - d e f i n e d problems (Mackworth, 1965), c o u l d thus e i t h e r e f f e c t i v e l y s e l e c t i v e l y encode i n f o r m a t i o n from the i l l - d e f i n e d problem space to r a i s e more s i g n i f i c a n t q u e s t i o n s and/or s e l e c t i v e l y encode to s i f t out the most r e l e v a n t q u e s t i o n s from those r a i s e d . To Dewey (1933), d i s c o v e r y of a problem was the f u n c t i o n of 28 t h i n k i n g , and " i n s i g h t i n t o the problem c o r r e c t s , m o d i f i e s , expands the suggestion that o r i g i n a l l y o c curred" (p.109). I n s i g h t i n t o a d i s c o v e r e d problem c o u l d , t h e r e f o r e , i n v o l v e s e l e c t i v e l y encoding the ideas that o r i g i n a l l y occurred, thus c o r r e c t i n g to o b t a i n the most r e l e v a n t idea; drawing on other seemingly i s o l a t e d p i e c e s of i n f o r m a t i o n to s e l e c t i v e l y combine with the o r i g i n a l idea, thus modifying i t ; and s e l e c t i v e l y comparing the o r i g i n a l suggestion with past ideas, thus expanding on i t . Superior i n s i g h t , then, may r e l a t e to s u p e r i o r a b i l i t y i n d i s c o v e r i n g problems. Table II summarizes the hypothesized r e l a t i o n s h i p of i n s i g h t to the c o g n i t i v e process model of problem f i n d i n g ( A r l i n , 1975-76) and problem f i n d i n g as conceived of by Mackworth (1965). Before f o r m a l l y s t a t i n g a hypothesis concerning the nature of t h i s r e l a t i o n s h i p , however, i t i s necessary to examine two other f a c e t s of i n s i g h t - i t s nature as a measure of i n t e l l i g e n c e and p o s s i b l e developmental i n f l u e n c e s on i t . 5.3 I n s i g h t As A Nonentrenched Measure Of I n t e l l e c t u a l  Gi ftedness The subtheory of i n s i g h t s k i l l s i s viewed by Sternberg and Davidson (1983) as a c l a r i f i c a t i o n and e l a b o r a t i o n of t h e i r view that " i n t e l l i g e n c e comprises i n l a r g e p a r t the a b i l i t y to a c q u i r e and think i n terms of novel kinds of concepts and conceptual systems ..." (p.54). When faced with novel, or "nonentrenched" tasks and concepts such as the " i n s i g h t p u z z l e s " (Sternberg & Davidson, 1982, 1983), the i n t e l l e c t u a l l y g i f t e d 29 C o g n i t i v e process model of problem f i n d i n g " T A r l i n , 1975-76) In s i g h t s k i l l s (Sternberg & Davidson, 1983) Problem f i n d i n g (Mackworth,1965) D i s c r i m i n a t ion D i f f e r e n t i a t i o n S e l e c t i v e encoding D e t e c t i o n of the need f o r a new program I n t e g r a t i o n S e l e c t s formal o p e r a t i o n s Transformat i o n s / I m p l i c a t i o n s S e l e c t i v e comparison Comparing e x i s t i n g and expected f u t u r e programs S e l e c t i v e combination D e v i s i n g of new programs Problem f i n d i n g output: The general q u e s t i o n . OUTCOMES I n s i g h t s that d i f f e r i n kind from those of o r d i n a r y i n d i v i d u a l s i n t h e i r s t r i k i n g o r i g i n a l i t y and consequence. The d i s c o v e r y of many general q u e s t i o n s from many i l l - d e f i n e d problems. Table II - Hypothesized r e l a t i o n s h i p s of i n s i g h t s k i l l s with problem f i n d i n g a b i l i t y are d i s t i n g u i s h e d by the i n s i g h t s demonstrated i n the formulation of the p u z z l e s ' s o l u t i o n s . " I n s i g h t p u z z l e s " w i l l thus p r o v i d e a nonentrenched measure of i n t e l l i g e n c e . The pu z z l e s themselves are d i s c u s s e d i n d e t a i l in Chapter 3. T h e i r c l a s s i f i c a t i o n as a nonentrenched measure i s important at t h i s p o i n t as a t h e o r e t i c a l c o n s i d e r a t i o n . 30 Sternberg (1982b) b e l i e v e s that the mark of g i f t e d n e s s i s the a b i l i t y to d e a l with nonentrenched tasks and concepts, and " t h i s a b i l i t y seems only to be p e r i p h e r a l l y measured by c u r r e n t t e s t s of i n t e l l i g e n c e " (p.65). I t may be, then, t h a t , as a p r e d i c t o r of problem f i n d i n g , i n s i g h t w i l l account f o r more v a r i a n c e than IQ. T h i s hypothesis a r i s e s from the f o l l o w i n g c o n s i d e r a t i o n s : 1. As a measure of problem f i n d i n g , a task r e q u i r i n g s u b j e c t s to r a i s e q u e s t i o n s ( A r l i n , 1975-76,1977) i s nonentrenched i n nature. 2. I n s i g h t , as a nonentrenched measure of i n t e l l i g e n c e , would, t h e r e f o r e , seem to be a " b e t t e r " p r e d i c t o r than IQ, an entrenched measure. 5.4 C o g n i t i v e L e v e l As A F a c t o r In I n s i g h t A r l i n ' s (1975-76,1977) r e s e a r c h suggests the importance of formal o p e r a t i o n a l t h i n k i n g as necessary but not s u f f i c i e n t f o r the problem f i n d i n g s k i l l of posing g e n e r a l q u e s t i o n s . Might there a l s o be developmental c o n s t r a i n t s on i n s i g h t ? Since Sternberg's (1981a) and Sternberg and Davidson's (1982,1983) i n i t i a l r e s e a r c h i n c l u d e d only a d u l t s , t h i s i s a cogent q u e s t i o n . Adding v a l i d i t y to t h i s q u e s t i o n i s the f a c t that more recent r e s e a r c h done with c h i l d r e n (Davidson & Sternberg, 1984) concluded that the g i f t e d possessed s u p e r i o r i n s i g h t , but f a i l e d to take i n t o account the s i g n i f i c a n t number of i n s i g h t p u z z l e s that g i f t e d c h i l d r e n i n the f o u r t h , f i f t h , and s i x t h grades were unable to s o l v e . I t can be seen that formal o p e r a t i o n a l t h i n k i n g does, i n f a c t , have l i k e l y connection to 31 the i n s i g h t processes. Combinatorial reasoning and c o o r d i n a t i o n of two or more systems of re f e r e n c e (Inhelder & P i a g e t , 1958) are two formal o p e r a t i o n a l schemata that appear p a r t i c u l a r l y r e l e v a n t to i n s i g h t - c o m b i n a t o r i a l reasoning to the process of s e l e c t i v e combination and the c o o r d i n a t i o n of two or more systems of re f e r e n c e to s e l e c t i v e comparison and to c e r t a i n i n s t a n c e s of s e l e c t i v e encoding where more than one frame of r e f e r e n c e i s necessary to c o r r e c t l y encode i n f o r m a t i o n r e l e v a n t to the problem. The hypothesized r e l a t i o n s h i p of i n s i g h t to problem f i n d i n g may, t h e r e f o r e , be mediated by formal o p e r a t i o n a l thought. T h i s mediating r e l a t i o n s h i p w i l l be s t a t i s t i c a l l y t e s t e d i n a separate a n a l y s i s . 5.5 Formal Statements Of The T h i r d And Fourth Hypotheses I n s i g h t as a nonentrenched measure of g i f t e d n e s s , r e l e v a n t P i a g e t i a n theory, and the r e l a t i o n s h i p s of both to problem f i n d i n g l e a d to the t h i r d and f o u r t h hypotheses: a) I n s i g h t w i l l be a s i g n i f i c a n t p r e d i c t o r of problem f i n d i n g a b i l i t y , accounting f o r s i g n i f i c a n t l y 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 of i n s i g h t to problem f i n d i n g w i l l be mediated by formal o p e r a t i o n a l t h i n k i n g . Having s t a t e d the hypotheses concerning the p r e d i c t i v e s i g n i f i c a n c e of the independent v a r i a b l e s , a f i n a l hypothesis concerning the order of entry of the v a r i a b l e s i n t o the p r e d i c t i o n equation i s co n s i d e r e d important. 32 5.6 Order Of Entry Of The P r e d i c t o r V a r i a b l e s Into The  Regression Equation A l l the p r e d i c t o r v a r i a b l e s are hypothesized to add s i g n i f i c a n t l y to the p r e d i c t i o n equation. A d d i t i o n a l l y , the re s e a r c h problem and the theory u n d e r l y i n g i t should determine the order of entry of v a r i a b l e s i n t o the m u l t i p l e r e g r e s s i o n equation (Pedhazur, 1982). As a r e s u l t of the l i t e r a t u r e reviewed, e n t e r i n g c o g n i t i v e l e v e l f i r s t i n t o the equation seems a p p r o p r i a t e i n l i g h t of the r e l a t i o n s h i p of developmental l e v e l to the c r i t e r i o n v a r i a b l e of problem f i n d i n g ( A r l i n , 1975-76, 1977). C o g n i t i v e l e v e l may c o n t r i b u t e most to the p r e d i c t i o n of problem f i n d i n g . I n s i g h t i s hypothesized to enter second due to the p o s s i b i l i t y of i t s being a " b e t t e r " p r e d i c t o r than IQ. IQ, then, would be entered l a s t . A f i f t h h y p o t h e s i s , t h e r e f o r e , s t a t e s the order of entry of v a r i a b l e s i n t o the p r e d i c t i o n equation. 5.7 A Formal Statement Of The F i f t h Hypothesis The order of entry of the p r e d i c t o r v a r i a b l e s in the m u l t i p l e r e g r e s s i o n equation w i l l be: c o g n i t i v e l e v e l + i n s i g h t + IQ. 33 6 . SUMMARY OF THE FIVE HYPOTHESES As a r e s u l t of the l i t e r a t u r e reviewed, f i v e hypotheses were formulated. Two of the hypotheses concerned the r o l e of entrenched (IQ) and nonentrenched ( i n s i g h t ) measures of i n t e l l i g e n c e as p r e d i c t o r s of problem f i n d i n g a b i l i t y . A f u r t h e r two hypotheses r e l a t e d to p o s s i b l e developmental c o n s t r a i n t s on problem f i n d i n g , while the f i f t h concerned the order of entry 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 m u l t i p l e r e g r e s s i o n e quation. The f i v e hypotheses are summarized below: 1) IQ w i l l c o n t r i b u t e to the p r e d i c t i o n of problem f i n d i n g a b i l i t y , but w i l l be a weaker p r e d i c t o r than e i t h e r c o g n i t i v e l e v e l or i n s i g h t . 2) I n s i g h t , as a nonentrenched measure of i n t e l l i g e n c e , w i l l account f o r more of the va r i a n c e in problem f i n d i n g than IQ. 3) C o g n i t i v e l e v e l w i l l c o n t r i b u t e s i g n i f i c a n t l y to the p r e d i c t i o n of problem f i n d i n g . 4) C o g n i t i v e l e v e l w i l l mediate the p r e d i c t i o n of problem f i n d i n g by i n s i g h t . 5) The order of entry of the p r e d i c t o r v a r i a b l e s i n the m u l t i p l e r e g r e s s i o n equation w i l l be: c o g n i t i v e l e v e l + i n s i g h t + IQ. The methodology used to t e s t the f i v e hypotheses and to analyze the r e s u l t i n g data i s d e s c r i b e d i n the f o l l o w i n g c h a p ter. 34 I I I . METHOD 1. OVERVIEW OF THE CHAPTER T h i s study was designed to a s c e r t a i n whether problem f i n d i n g may be a d i f f e r e n t i a l 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 g i f t e d c h i l d r e n and to examine the c o g n i t i v e processes which may p r e d i c t problem f i n d i n g a b i l i t y . The re s e a r c h methodology f o r the study i s contained i n the f o l l o w i n g four p a r t d i s c u s s i o n . Information concerning the p o p u l a t i o n and sample forms the f i r s t p art of the d i s c u s s i o n . The second part r e f e r s to t e s t i n g procedures. L a s t l y , i n p a r t s three and fou r , i n f o r m a t i o n on the design of the study and the a n a l y s i s of the data are presented. 2. POPULATION The t a r g e t p o p u l a t i o n was g i f t e d students i n the upper elementary grades i n a suburban-rural school d i s t r i c t east of Vancouver. The a c c e s s i b l e p o p u l a t i o n was three c l a s s e s of students i n grades f i v e to seven i n one of the elementary sc h o o l s i n the d i s t r i c t . Students of v a r y i n g a b i l t i t e s were i n c l u d e d f o r c l a r i f i c a t i o n of the hypothesized p r e d i c t i v e r e l a t i o n s h i p s . 35 3. SAMPLE The sample i n c l u d e d the e n t i r e a c c e s s i b l e p o p u l a t i o n , with the exception of one f o r e i g n student who was unable to s u f f i c i e n t l y understand o r a l d i r e c t i o n s in E n g l i s h . The t o t a l sample s i z e was 76 (37 g i r l s and 39 boys). Age range was 10 years 8 months to 14 years 9 months,with a mean age of 12 years 6 months. Subjects were predominantly, but not e x c l u s i v e l y , white and E n g l i s h - s p e a k i n g . The socio-economic l e v e l of the school's catchment area i s lower-middle to middle c l a s s . S e v e r a l students from each grade l e v e l had p a r t i c i p a t e d i n an enrichment program p r e v i o u s l y o f f e r e d at the s c h o o l . T e s t i n g took p l a c e d u r i n g June, 1984. R a t i o n a l e i n v o l v e d in choosing the age range of 10 - 14 years centered on the i n v e s t i g a t i o n s of g i f t e d n e s s done from a P i a g e t i a n p e r s p e c t i v e reviewed i n Chapter 2. The age range s t u d i e d approximates, e i t h e r i n whole or i n p a r t , that s t u d i e d by A r l i n (1984,in press a ) , C a r t e r and Ormrod (1982), Keating (1975), and Webb (1974). I t was hoped that t h i s age group would a l s o c l a r i f y the r e l a t i o n s h i p of c o g n i t i v e l e v e l to problem f i n d i n g , i n t h a t , on the b a s i s of A r l i n ' s (1975-76,1977) work, formal thought i s expected to be a necessary but not s u f f i c i e n t c o n d i t i o n f o r the posing of gen e r a l q u e s t i o n s . 36 4. PROCEDURES Four procedures are d e s c r i b e d i n t h i s s e c t i o n . These i n c l u d e the task f o r measurement of the c r i t e r i o n v a r i a b l e , problem f i n d i n g , and measures of the p r e d i c t o r v a r i a b l e s c o g n i t i v e l e v e l , i n s i g h t , and IQ. 4.1 The Problem F i n d i n g Task 4.1.1 Task D e s c r i p t i o n Subjects completed the A r l i n Problem F i n d i n g Task ( A r l i n , 1975-76,1977). The task and i n s t r u c t i o n s f o r i t s a d m i n i s t r a t i o n are appended. The task p r o v i d e s both the problematic s i t u a t i o n and the o p p o r t u n i t y f o r s u b j e c t s to r a i s e q u e s t i o n s - two of the necessary elements 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 problem f i n d i n g . A d e s c r i p t i o n of the t h i r d element, a way of c a t e g o r i z i n g the q u e s t i o n s once r a i s e d , f o l l o w s . 4.1.2 C l a s s i f i c a t i o n Of The Questions Raised Questions generated by the s u b j e c t s were c l a s s i f i e d a c c o r d i n g to the i n t e l l e c t u a l product c a t e g o r i e s of G u i l f o r d (1956); that i s , they were c a t e g o r i z e d from one through s i x corresponding to the s i x c a t e g o r i e s of the i n t e l l e c t u a l p roducts: Category 1 - U n i t s Category 4 - Systems Category 2 - C l a s s e s Category 5 - Transformations Category 3 - R e l a t i o n s Category 6 - I m p l i c a t i o n s Examples of q u e s t i o n s f o r each category are found i n Table I I I . A higher order q u e s t i o n (that i s , t r a n f o r m a t i o n s , 37 Category Def i n i t i o n Example 1.Units 2 .Classes 3.Relations 4. Systems 5 .Transfor-mat ions Basic u n i t s of inf o r m a t i o n C l a s s can be embodied using d i f f e r e n t s e t s of part i c u l a r s . Connections between o b j e c t s or u n i t s such as o p p o s i t i o n , part-whole, a g e n t - a c t i o n , e t c . To t a l k about r u l e s , p r i n c i p l e s , o r d e r s , 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 to speak of the p s y c h o l o g i c a l product of system. A t r a n s f o r m a t i o n i s any kind of change such as expanding, r e v e r s a l , interchange, and so on. 6. I m p l i c a t i o n s A connection between two u n i t s of i n f o r m a t i o n . R e l a t i o n s are d e f i n a b l e kinds of con n e c t i o n s . . . comes nearest to the t r a d i t i o n a l n o t i o n of a s s o c i a t i o n . "How many o b j e c t s are there here?" "Can I arrange these a c c o r d i n g to s i z e , or c o l o r , or shape?" " I f t h i s paper's hole was bigger, I c o u l d put t h i s q uarter through i t . Maybe, can I put the qua r t e r through the hole without r i p p i n g i t ? " "I bet t h i s box, open up, how do you open i t , there i s a way, i s n ' t there?" " I f you were given t h i s s t e e l t h i n g , what c o u l d you change i t in t o ? What could you make?" "In what ways can you arrange the o b j e c t s on the t a b l e to represent how you f e e l at t h i s moment? How c o u l d these matches be man's enemy?" Adapted from the chapter, "New P s y c h o l o g i c a l Conceptions of Memory" i n 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. C i t e d i n A r l i n (1975-76, p.102) . Table III - The i n t e l l e c t u a l product c a t e g o r i e s i m p l i c a t i o n s ) more c l o s e l y approaches the ge n e r a l q u e s t i o n than 38 a lower order question ( A r l i n , 1975-76). S p e c i f i c a l l y , t r a n s f o r m a t i o n s questions " c a l l f o r the combination of the s t i m u l i i n new ways" ( A r l i n , 1977, p.297) and i m p l i c a t i o n s q u e s t i o n s " r e q u i r e the o r g a n i z a t i o n of the s t i m u l i so that a general q u a l i t y or p r i n c i p l e i s a b s t r a c t e d that i s not r e a d i l y apparent i n the s t i m u l i " ( A r l i n , 1977, p.298). The outcome of t r a n s f o r m a t i o n s and i m p l i c a t i o n s processes i s the g e n e r a l q u e s t i o n , which i s the expected outcome f o r problem f i n d i n g ( A r lin,1977; Mackworth, 1965). I t i s the posing of higher order, general q u e s t i o n s which i s thought to r e s u l t in a higher q u a l i t y of problem f i n d i n g . 4.1.3 S c o r i n g U n i t s q u e s t i o n s were given the lowest score (1); i m p l i c a t i o n s , the highest ( 6 ) . I n t e r - r a t e r r e l i a b i l i t y was c a l c u l a t e d on the s c o r i n g of q u e s t i o n s , using a random sample of 20 problem f i n d i n g t a s k s , and r e s u l t e d i n 87% agreement. A q u a l i t y score was c a l c u l a t e d f o r each s u b j e c t . Q u a l i t y represents the weighted average of the q u e s t i o n s asked i n each category, as f o l l o w s : Quality=1(cat.1)+2(cat.2)+3(cat.3)+4(cat.4)+5(cat.5)+6(cat.6) T o t a l number of q u e s t i o n s asked. ( A r l i n , 1975-76). 39 4.2 P i a g e t i a n Assessment 4.2.1 Test D e s c r i p t i o n Subjects were given the A r l i n Test of Formal Reasoning ( A r l i n , 1984c). A paper-and-penci1 measure designed f o r group a d m i n i s t r a t i o n , the t e s t p r o v i d e s an o b j e c t i v e measurement of P i a g e t i a n developmental l e v e l . I t i s a v a l i d and r e l i a b l e measure ( A r l i n , 1982, 1984a). A sample t e s t page i s appended. A t o t a l of 32 m u l t i p l e - c h o i c e items comprise the t e s t . These items are organized i n t o e i g h t s u b t e s t s , each of which repr e s e n t s a formal scheme. The e i g h t formal schemata are d e f i n e d as "the concepts which the subject p o t e n t i a l l y can organize from the beginning of the formal l e v e l when faced with c e r t a i n kinds of data, but which are not manifest o u t s i d e these c o n d i t i o n s " ( I n h e l d e r - & P i a g e t , 1958, p.308) and i n c l u d e m u l t i p l i c a t i v e compensations ( c o n s e r v a t i o n of 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 o r i a l reasoning, p r o p o r t i o n a l reasoning, forms of 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 ( c o n s e r v a t i o n of momentum), c o o r d i n a t i o n of two or more systems or frames of r e f e r e n c e , and mechanical e q u i l i b r i u m . Test items i n c l u d e the s e l e c t i o n of e x p l a n a t i o n s f o r answers given to b a s i c problems. "This procedure of a problem posed followed by a r a t i o n a l e f o r the answer chosen i s analogous to the use of the c l i n i c a l method i n the use of i n d i v i d u a l i n t e r v i e w s to assess formal reasoning" ( A r l i n , 1984a). 40 4.2.2 Test A d m i n i s t r a t i o n Since the t e s t r e a d a b i l i t y l e v e l i s s i x t h grade, the t e s t was a d m i n i s t e r e d o r a l l y to the f i f t h grade c l a s s in the sample and to the s i x t h grade c l a s s as w e l l , s i n c e there were a number of c h i l d r e n i n the c l a s s who had reading d i f f i c u l t i e s . O r a l a d m i n i s t r a t i o n i s a f e a t u r e of the t e s t ( A r l i n , 1984a). The seventh grade c l a s s completed the t e s t independently. I n t r o d u c t o r y remarks and i n s t r u c t i o n s were given as o u t l i n e d in the manual ( A r l i n , 1984a). Time r e q u i r e d was approximately 45 minutes, but p r o v i s i o n was made f o r those students who d i d not complete the t e s t to f i n i s h at a time c l o s e l y f o l l o w i n g the o r i g i n a l a d m i n i s t r a t i o n . 4.2.3 S c o r i n g A t o t a l score i s used to determine c o g n i t i v e l e v e l , as seen below: Concrete 00-07 p o i n t s High concrete 08-14 p o i n t s T r a n s i t i o n a l 15-17 p o i n t s Low formal 18-24 p o i n t s High formal 25-32 p o i n t s A r l i n (1984a) prov i d e s a d e s c r i p t i o n of each l e v e l : CONCRETE repr e s e n t s performance on the 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 no evidence of a b s t r a c t reasoning and some d i f f i c u l t y with reasoning s k i l l s t h a t are problem s p e c i f i c . HIGH CONCRETE repr e s e n t s performance on the 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 some evidence of a systematic approach to problems but not evidence of 41 forming a general r u l e or a b s t r a c t i o n from the problems. T h i s l e v e l i n d i c a t e s some a b i l i t y to c l a s s i f y and organize 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 evidence of the a b i l i t y to make i n f e r e n c e s . TRANSITIONAL re p r e s e n t s performance on the 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 to the problems and some use 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 i n c o n s i s t e n t . LOW FORMAL repr e s e n t s a performance on the 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 the formal schemes being present i n t h e i r t h i n k i n g . HIGH FORMAL repr e s e n t s a performance on the formal tasks which g i v e s c l e a r evidence of most of the formal schemes being i n evidence in t h e i r t h i n k i n g . (p.7) T o t a l scores were recorded f o r the r e g r e s s i o n a n a l y s i s . Subtest scores f o r each of the e i g h t formal schemata were recorded as w e l l f o r a supplementary a n a l y s i s . 4.3 Measurement Of I n s i g h t 4.3.1 I n s i g h t Puzzles E i g h t i n s i g h t p u z zles formed the measure of i n s i g h t . Four of these p u z z l e s were chosen from those used by Sternberg and Davidson (1982,1983). The remaining four were taken from a book of " b r a i n - t e a s e r s " w r i t t e n f o r c h i l d r e n (Brandreth,1979) with s l i g h t m o d i f i c a t i o n s made f o r c l a r i t y . Of these, one p a r a l l e l s e x a c t l y a problem used by Sternberg and Davidson, but c o n t a i n s text more s u i t a b l e for c h i l d r e n . Sternberg and Davidson d e s c r i b e d the processes of i n s i g h t each p u z z l e emphasized. An i n t e r - r a t e r r e l i a b i l i t y was conducted on the remaining p u z z l e s , with 100% agreement as to 42 the processes of i n s i g h t concerned. The p u z z l e s , together with t h e i r sources and l i s t i n g s of the processes emphasized, are appended. 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 The i n s i g h t p u z z l e s were group a d m i n i s t e r e d . The measure was not timed, but took approximately 30 minutes to complete. A score on the p u z z l e s c o n s i s t s of the t o t a l number c o r r e c t . T h i s score was recorded f o r use in the r e g r e s s i o n a n a l y s i s . Scores f o r each process of i n s i g h t were recorded s e p a r a t e l y f o r the purpose of supplementary s t a t i s t i c a l a n a l y s i s . 4.4 Measurement Of IQ Subjects completed the Otis-Lennon Mental A b i l i t y Test ( O t i s & Lennon, 1968). E i g h t y items sample a wide v a r i e t y of mental processes, with a s i n g l e t o t a l score summarizing performance on the t e s t ( O t i s & Lennon, 1969). The t e s t i s a v a l i d and r e l i a b l e instrument ( O t i s & Lennon, 1969) which has been w e l l reviewed (Buros, 1972). I t s c o r r e l a t i o n with the i n d i v i d u a l l y a dministered S t a n f o r d - B i n e t IQ t e s t i s .60. The Otis-Lennon i s a group measure and r e q u i r e s 40 minutes of a c t u a l working time. I t was administered a c c o r d i n g to the d i r e c t i o n s p rovided i n the manual ( O t i s & Lennon, 1969). Subjects i n grades f i v e and s i x completed the Elementary II L e v e l t e s t . Median reading l e v e l of t h i s t e s t i s below grade f o u r . Two p u p i l s r e c e i v e d raw scores of more than 73 and were r e t e s t e d with the Intermediate L e v e l t e s t . T h i s procedure 43 ensures more e f f i c i e n t measurement of mental a b i l i t y ( O t i s & Lennon, 1969). The m a j o r i t y of s u b j e c t s i n grade seven completed the Intermediate L e v e l t e s t . I t s reading l e v e l i s below seventh grade. Since the manual for a d m i n i s t r a t i o n recommends that slower p u p i l s i n the lowest grade w i t h i n a given l e v e l be given the next lower l e v e l i n the s e r i e s , seven p u p i l s i n grade seven completed the Elementary II L e v e l t e s t . 5. DESIGN The study was nonexperimental; that i s , i t i n v o l v e d no manipulation of the v a r i a b l e s . The same data was c o l l e c t e d on a l l s u b j e c t s and analyzed through p r e d i c t i v e r e g r e s s i o n . 6. THE ANALYSIS OF THE DATA To s t a t i s t i c a l l y t e s t the r e s e a r c h hypotheses that c o g n i t i v e l e v e l , i n s i g h t , and IQ w i l l c o n t r i b u t e s i g n i f i c a n t l y to the p r e d i c t i o n of problem f i n d i n g a b i l i t y ; that the order of entry of the v a r i a b l e s i n t o the p r e d i c t i o n equation w i l l be c o g n i t i v e l e v e l , f o l l o w e d by i n s i g h t and IQ; and that the p r e d i c t i o n of problem f i n d i n g a b i l i t y by i n s i g h t w i l l be mediated by c o g n i t i v e l e v e l , a m u l t i p l e r e g r e s s i o n a n a l y s i s was used. In the a n a l y s i s , a r e g r e s s i o n equation was sought so that p r e d i c t i o n of problem f i n d i n g a b i l i t y would be o p t i m i z e d . For c l a r i t y , d i s c u s s i o n of the data a n a l y s i s i s be d i v i d e d i n t o s e v e r a l s u b s e c t i o n s , beginning with a statement of the model used. 44 6.1 The L i n e a r M u l t i p l e Regression Model Using the l i n e a r model, the c r i t e r i o n v a r i a b l e , problem f i n d i n g a b i l i t y , was regressed on the p r e d i c t o r v a r i a b l e s c o g n i t i v e l e v e l , i n s i g h t , and IQ. 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 i s w r i t t e n as f o l l o w s : where i= 1,...,N s u b j e c t s ; j= 1,2,3 independent v a r i a b l e s ; Y = observed score of the i*h person on Y; 3 flo + ftjX'j = the l i n e a r , weighted combination of independent v a r i a b l e s which i s expected to s a t i s f a c t o r i l y account f o r Y; y&> = the Y - i n t e r c e p t of the r e g r e s s i o n hyperplane; fij = the marginal e f f e c t of X on Y, a l l other X's h e l d constant; that i s , them's are p a r t i a l r e g r e s s i o n c o e f f i c i e n t s a p p l i e d to the Xj' 's i n order to o p t i m a l l y p r e d i c t Y ( K i r k , 1982); and Ei = the r e s i d u a l or unaccounted f o r p a r t of Y (Y-Y). T h i s model c o n t a i n s s e v e r a l u n d e r l y i n g assumptions. 6.2 Assumptions Underlying The L i n e a r Regression Model The p a r t i a l r e g r e s s i o n c o e f f i c i e n t s are assumed to be l i n e a r . Y; i s assumed to be normally d i s t r i b u t e d [£~(Y/), ts*~ Y; ], as i s C'» (0, * " * ^ i " ) . F u r t h e r assumptions are homogeneity of v a r i a n c e s ( < r J y ; = <?£'i = *•*") ; independence otCi , that i s , ^ f / c ' and Ci are u n c o r r e l a t e d so that the c o v a r i a n c e s equal zero ( K i r k , 1982); and no e r r o r i n the measurements of the independent v a r i a b l e s . 45 Having s t a t e d the model and i t s u n d e r l y i n g assumptions, the methods of a n a l y s i s can now be d i s c u s s e d . 6.3 Methods Of A n a l y s i s The data a n a l y s i s c o n s i s t e d of s e v e r a l steps. The d i s c u s s i o n i s , t h e r e f o r e , d i v i d e d i n t o f i v e p a r t s d e s c r i b i n g each s t a t i s t i c a l procedure. Since t h i s i s an e x p l o r a t o r y study, the c*C l e v e l chosen for t e s t s of s i g n i f i c a n c e i s 0.05. 6.3.1 Test Of The F u l l Model In s t a t i s t i c a l terms, the n u l l h y p othesis thaty^/ =/^=/^=0 was t e s t e d a g a i n s t the a l t e r n a t i v e that not a l l y t ? / ' s=0. T h i s a l t e r n a t i v e i s the s t a t i s t i c a l e q u i v a l e n t of the f i r s t three hypotheses as summarized in Chapter 2. The t e s t of the f u l l model (R*y. tz$ ) was done using NEW REGRESSION procedures from SPSS ( L a i , 1983). An F - s t a t i s t i c was used to t e s t i f a s i g n i f i c a n t p r o p o r t i o n of v a r i a n c e i n the c r i t e r i o n v a r i a b l e i s accounted fo r by the p r e d i c t o r v a r i a b l e s . In the case of a n o n - s i g n i f i c a n t F - s t a t i s t i c , the n u l l hypothesis would be t e n a b l e . If a s i g n i f i c a n t F - s t a t i s t i c were obtained, a n a l y s i s would proceed. 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 Regression Parameters Two s e l e c t i o n procedures from the SPSS r e g r e s s i o n program were planned f o r t h i s stage of the a n a l y s i s . F i r s t l y , backward e l i m i n a t i o n was planned. T h i s procedure s t a r t s with the f u l l model, then the p r e d i c t o r v a r i a b l e s are d e l e t e d from the r e g r e s s i o n equation one at a time, a l l o w i n g examination of the 46 l o s s i n p r o p o r t i o n of v a r i a n c e accounted fo r due to the d e l e t e d v a r i a b l e . " I t i s thus p o s s i b l e to observe which v a r i a b l e adds the l e a s t when entered l a s t " (Pedhazur, 1982, p.158). The NEW REGRESSION program a l s o s u p p l i e s t - s t a t i s t i c s , so that the estimates of the r e g r e s s i o n parameters (b's) c o u l d be t e s t e d for s i g n i f i c a n c e . The stepwise s e l e c t i o n procedure was a l s o planned. In stepwise s e l e c t i o n , t e s t s are performed at each step to determine the c o n t r i b u t i o n of each p r e d i c t o r a l r e a d y i n the equation i f i t were to enter l a s t . I t i s thus p o s s i b l e to i d e n t i f y p r e d i c t o r s that were c o n s i d e r e d to be 'good' at an e a r l i e r stage but have l o s t t h e i r u s e f u l n e s s when a d d i t i o n a l p r e d i c t o r s were brought i n t o the equation and may t h e r e f o r e be removed from i t . (Pedhazur, 1982,p.160) In order to o b t a i n the "best" r e g r e s s i o n equation, in the sense of the equation which maximizes R y . y , r e s u l t s from both s e l e c t i o n procedures were to be examined and compared with t h e o r e t i c a l e x p e c t a t i o n s . 6.3.3 C r o s s - v a l i d a t i o n In c a l c u l a t i n g the r e g r e s s i o n c o e f f i c i e n t s to maximize R y . y , the zero-order c o r r e l a t i o n s are t r e a t e d as i f they were e r r o r - f r e e . The r e s u l t i s an R V- H which i s b i a s e d upwards (Pedhazur, 1982). If these r e g r e s s i o n c o e f f i c i e n t s were a p p l i e d to the p r e d i c t o r scores of another sample, "the r e s u l t i n g R would almost always be smaller than the R obtained i n the sample for which the weights were o r i g i n a l l y c a l c u l a t e d . T h i s phenomenon i s r e f e r r e d to as the shrinkage of the m u l t i p l e c o r r e l a t i o n " (Pedhazur, 1982, pp.147-148). 47 In the case of a s i g n i f i c a n t r e s u l t i n the t e s t of the f u l l model, a c r o s s - v a l i d a t i o n was planned i n order to estimate shrinkage. The t o t a l sample would be randomly s p l i t i n h a l f to form a s c r e e n i n g sample and a c a l i b r a t i o n sample. The r e g r e s s i o n c o e f f i c i e n t s from the equation f o r the screening sample would be a p p l i e d to the p r e d i c t o r scores of the c a l i b r a t i o n sample. If the r e s u l t i n g estimate of shrinkage were low, p r e d i c t i v e accuracy and g e n e r a l i z a b i l i t y would be enhanced. 6.3.4 Test Of The Mediation Of I n s i g h t By Formal Operations It was hypothesized that i n s i g h t as a p r e d i c t o r of problem f i n d i n g a b i l i t y would be mediated by formal o p e r a t i o n a l t h i n k i n g . In order to t e s t t h i s h y p o t h e s i s , the computer program BMD:03R (Le, 1980) was used. D e s i g n a t i n g formal reasoning as v a r i a b l e 1 and i n s i g h t as v a r i a b l e 2, the r e p l a c e m e n t - d e l e t i o n procedure was used to d e r i v e the f o l l o w i n g . . U 2 y . a - / / ' F - s t a t i s t i c : F = 4 j . . . . A n o n - s i g n i f i c a n t F-s t a t i s t i c would make the n u l l h y p o thesis t h a t ^ l = 0 tenable and i n s i g h t does not, t h e r e f o r e , d i r e c t l y p r e d i c t problem f i n d i n g a b i l i t y but i s mediated by formal r e a s o n i n g . 6.3.5 Supplementary Analyses Using the SPSS program ( L a i , 1983), Pearson product-moment c o r r e l a t i o n c o e f f i c i e n t s were c a l c u l a t e d between scores on the three processes of i n s i g h t and problem f i n d i n g and between the three processes of i n s i g h t and s u b - t e s t scores from the formal reasoning t e s t . I t was f e l t that these c o r r e l a t i o n s should provide f u r t h e r understanding of the v a r i a b l e s under study, 48 p a r t i c u l a r l y i n regard to the formal schemata of c o m b i n a t o r i a l reasoning and frames of re f e r e n c e thought to mediate i n s i g h t . 6.4 Methods Of Reporting The Data The data are repo r t e d i n t a b l e s a p p r o p r i a t e to each s t a t i s t i c a l procedure, f o r example, an ANOVA t a b l e showing sources of v a r i a t i o n and c o r r e l a t i o n m a t r i c e s , and are supplemented by w r i t t e n i n t e r p r e t a t i o n of the r e s u l t s . 7. SUMMARY OF CHAPTER THREE Chapter Three was concerned with p r e s e n t i n g the methodology used to t e s t the f i v e hypotheses. The p o p u l a t i o n and sample were d e s c r i b e d and procedures concerned with the a d m i n i s t r a t i o n and s c o r i n g of the IQ measure, the t e s t of formal reasoning, and the i n s i g h t and problem f i n d i n g tasks were d e t a i l e d . The chapter concluded with d e s c r i p t i o n s of the methods of data a n a l y s i s and data r e p o r t i n g . 49 IV. RESULTS OF THE ANALYSIS 1. OVERVIEW OF THE CHAPTER T h i s chapter i s devoted to the p r e s e n t a t i o n of the r e s u l t s of the a n a l y s i s . In order to a i d c l a r i t y , the p r e s e n t a t i o n w i l l c o n s i s t of f i v e p a r t s . Summary s t a t i s t i c s f o r each v a r i a b l e w i l l be presented f i r s t , f o l l o w e d by a d i s c u s s i o n of the a p p r o p r i a t e n e s s of the l i n e a r r e g r e s s i o n model. Subsequent s e c t i o n s w i l l d e t a i l r e s u l t s of the r e g r e s s i o n a n a l y s i s , the supplementary c o r r e l a t i o n a l a n a l y s e s , and a q u a l i t a t i v e a n a l y s i s of those s u b j e c t s earning high scores on each of the v a r i a b l e s . Reference w i l l be made in the chapter to the m a t u r a t i o n a l c o n s t r a i n t s apparent i n the sample. C o g n i t i v e m a t u r i t y i s o p e r a t i o n a l l y d e f i n e d i n t h i s study as evidence of most of the formal schemes being i n use, that i s , the "high formal" stage of development ( A r l i n , 1984a). M a t u r a t i o n a l c o n s t r a i n t s thus imply the absence of, or incomplete development of, formal o p e r a t i o n s . Attainment of formal o p e r a t i o n s i s u s u a l l y a g e - r e l a t e d , but age alone does not guarantee t h i s attainment. 2. SUMMARY STATISTICS S t a t i s t i c s concerning scores on the c r i t e r i o n v a r i a b l e of problem f i n d i n g and the 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 l e v e l , i n s i g h t , and IQ and i n f o r m a t i o n concerning the d i s t r i b u t i o n of IQ and c o g n i t i v e l e v e l i n the sample form the f i r s t p a r t of t h i s c hapter. 50 2.1 Problem F i n d i n g The range of problem f i n d i n g q u a l i t y scores was 0 to 4.33, with a mean of 2.99 and standard d e v i a t i o n of 1.09. Two s u b j e c t s i n the s i x t h grade group each posed a t r a n s f o r m a t i o n q u e s t i o n . No i m p l i c a t i o n s q u e s t i o n s were asked. The lack of higher l e v e l q u e s t i o n s i s c o n s i s t e n t with previous problem f i n d i n g r e s e a r c h (Arlin,1977) which found a s i g n i f i c a n t e f f e c t of o p e r a t i o n a l l e v e l on problem f i n d i n g q u a l i t y . The low l e v e l of c o g n i t i v e m a t u r i t y of the sample, as i n d i c a t e d below, seemed to preclude the asking of ques t i o n s r e q u i r i n g a high l e v e l of a b s t r a c t i o n . 2.2 C o g n i t i v e L e v e l Scores based on the P i a g e t i a n assessment were i n the range of 4 to 21 with a maximum p o s s i b l e a t t a i n a b l e score of 32. The mean score was 10.99 with a standard d e v i a t i o n of 4.07. The m a j o r i t y of the sample were high concrete t h i n k e r s . Table IV shows the percentages of s u b j e c t s i n the l e v e l s a t t a i n e d by t h i s sample. There were no high formal t h i n k e r s i n the sample. C l a s s i f i c a t i o n by l e v e l s , t r a n s l a t e d from the raw scores, was accomplished with r e f e r e n c e to the cut p o i n t s p r o v i d e d i n the A r l i n Test of Formal Reasoning manual ( A r l i n , 1984a). The d i s t r i b u t i o n of l e v e l s i n the seventh grade group i s c o n s i s t e n t with e x p e c t a t i o n s f o r c h i l d r e n of t h i s age group ( A r l i n , 1984a). The f i f t h grade group i s higher i n c o g n i t i v e l e v e l than would be expected. T h i s f a c t , i n a d d i t i o n to the low o v e r a l l academic l e v e l of the s i x t h grade group, would appear to 51 e x p l a i n the d i f f e r e n c e s between the c o g n i t i v e l e v e l d i s t r i b u t i o n s of the f i f t h and s i x t h grade groups. Grade 7 Grade 6 Grade 5 T o t a l Sample Concrete 14% 25% 21% 20% High Concrete 62% 71% 63% 66% T r a n s i t i o n a l 14% . 0 % 11% 8% Low Formal 10% 4% 5% 6% Table IV - C o g n i t i v e l e v e l d i s t r i b u t i o n 2.3 I n s i g h t Scores on the i n s i g h t p u z z l e s were the number of c o r r e c t responses out of a maximum p o s s i b l e score of 8. The mean score on the i n s i g h t p u z z l e s was 1.25 with a standard d e v i a t i o n of 1.42. The range was 0 to 7. P r o f i l e s of the s u b j e c t s who obtained the few high scores on the p u z z l e s w i l l be analyzed i n the s e c t i o n on q u a l i t a t i v e a n a l y s i s . In g e n e r a l , even the b r i g h t e s t c h i l d r e n i n the sample found the p u z z l e s d i f f i c u l t . T h i s i s c o n s i s t e n t with the f i n d i n g s of Davidson and Sternberg (1984). I t w i l l be seen that developmental c o n s i d e r a t i o n s must be taken i n t o account when s p e c i f y i n g i n s i g h t as a d i f f e r e n t i a l c o g n i t i v e a t t r i b u t e of g i f t e d c h i l d r e n . Data presented in subsequent s e c t i o n s of the chapter would appear to i n d i c a t e developmental c o n s t r a i n t s on i n s i g h t . 52 2.4 The IQ Measure IQ scores ranged from 65 to 136 with a mean of 97.72 and standard d e v i a t i o n of 15.09. The Otis-Lennon IQ i s a normalized standard score with a mean of 100 and a standard d e v i a t i o n of 16 ( O t i s & Lennon, 1968). The sample was d i s t r i b u t e d normally. Table V summarizes the d i s t r i b u t i o n of scores r e c e i v e d i n comparison to the approximate percentages of c h i l d r e n expected to a t t a i n these scores as given i n the Otis-Lennon manual (1968). I t can be seen t h a t , in g e n e r a l , the sample f e l l w i t h i n the expected range f o r a normal d i s t r i b u t i o n . IQ score Percentage expected i n a Percentage of sample normal d i s t r i b u t i o n o b t a i n i n g these scores Above 132 2% 3% 117-132 14% 9% 85-116 68% 72% 69-84 14% 13% 68 and lower 2% 3% Table V - D i s t r i b u t i o n of IQ scores as compared with the normal d i s t r i b u t i o n Given these d e s c r i p t i v e s t a t i s t i c s , the a p p r o p r i a t e n e s s of the l i n e a r r e g r e s s i o n model to analyze the r e l a t i o n s h i p between the p r e d i c t o r v a r i a b l e and these c r i t e r i o n v a r i a b l e s w i l l now be d i s c u s s e d . 53 3. APPROPRIATENESS OF THE LINEAR REGRESSION MODEL Since i t i s important that the u n d e r l y i n g assumptions of the l i n e a r r e g r e s s i o n model be s a t i s f a c t o r i l y met i f v a l i d i n f e r e n c e s are to be drawn regarding the r e l a t i o n s h i p between the c r i t e r i o n v a r i a b l e s and the p r e d i c t o r v a r i a b l e s , r e s i d u a l a n a l y s i s was done using NEW REGRESSION procedures from SPSS ( L a i , 1983). The Durbin-Watson t e s t supported the n u l l h ypothesis that the e r r o r terms were not s e r i a l l y c o r r e l a t e d [D(=2.10) > d#(=1.7l)]. A histogram of s t a n d a r d i z e d r e s i d u a l s and a normal p r o b a b i l i t y p l o t showed nor m a l i t y of the e r r o r terms, and s t a n d a r d i z e d s c a t t e r p l o t s confirmed homogeneity of v a r i a n c e s and the a p p r o p r i a t e n e s s of the l i n e a r r e g r e s s i o n f u n c t i o n . One o u t l i e r was found at s l i g h t l y over -3 S.D. (-3.15). T h i s proved to be a s u b j e c t who had f a i l e d to respond to the problem f i n d i n g task. On the b a s i s of scores on the p r e d i c t o r v a r i a b l e s , t h i s s u b j e c t ' s p r e d i c t e d problem f i n d i n g score was 3.38. It was f e l t that the u n d e r l y i n g assumptions of the l i n e a r r e g r e s s i o n model had been met and that i n f e r e n c e s c o u l d be drawn v a l i d l y from the r e g r e s s i o n a n a l y s i s . 4. RESULTS OF THE REGRESSION ANALYSIS The r e g r e s s i o n a n a l y s i s c o n s i s t e d of s e v e r a l s t e p s . R e s u l t s of the t e s t of the f u l l model w i l l be presented f i r s t , with subsequent s e c t i o n s d e t a i l i n g r e s u l t s of the s e l e c t i o n procedures, shrinkage estimates, and the outcome of the t e s t of 54 the mediation of i n s i g h t by formal o p e r a t i o n s . 4.1 Test Of The F u l l Model The p r o p o r t i o n of v a r i a n c e i n the c r i t e r i o n v a r i a b l e accounted for by the p r e d i c t o r v a r i a b l e s was not s i g n i f i c a n t . The sum of the squared e r r o r s of p r e d i c t i o n was not minimized by the p r e d i c t o r v a r i a b l e s chosen. Table VI summarizes the a n a l y s i s of v a r i a n c e . Source of v a r i a t i o n Sum of squares df Mean square F Regression 4.78 3 1.59 (Y - y) R e s i d u a l 84.88 72 1.18 1.35 (Y;- Y) T o t a l _ 89.66 75 (Y;- Y) Table VI - A n a l y s i s of v a r i a n c e Since F ( = 1.35) < 3t7Z ( = 2.74), the n u l l hypothesis that ft, =Px=fi*-Q w a s t e n a b l e . Thus, none of the three r e s e a r c h hypotheses r e l a t i n g to the p r e d i c t i o n of problem f i n d i n g were supported. D e s p i t e the n o n - s i g n i f i c a n t r e s u l t s on the t e s t of the f u l l model, the e l i m i n a t i o n procedures planned f o r the study were c a r r i e d out i n order to examine the c o n t r i b u t i o n s of the p r e d i c t o r v a r i a b l e s f o r p o s s i b l e s i g n i f i c a n t t r e n d s . No v a r i a b l e s q u a l i f i e d f o r entry i n the stepwise s e l e c t i o n procedure, but backward e l i m i n a t i o n p r o v i d e d information b e l i e v e d to be r e l e v a n t to the p r e d i c t i o n of problem f i n d i n g . 55 4.2 Backward E l i m i n a t i o n In the backward e l i m i n a t i o n procedure, the v a r i a b l e s were fo r c e d in i n the f o l l o w i n g order: c o g n i t i v e l e v e l , i n s i g h t , IQ. T h i s was done to i n v e s t i g a t e the r e s e a r c h hypothesis s t a t i n g that the order of entry of the p r e d i c t o r v a r i a b l e s i n the m u l t i p l e r e g r e s s i o n equation w i l l be: c o g n i t i v e l e v e l + i n s i g h t + IQ. C o g n i t i v e l e v e l was removed on the f i r s t step of backward a. e l i m i n a t i o n , r e s u l t i n g i n l i t t l e change i n R . S i m i l a r l y , i n s i g h t was removed on the second step. With IQ only i n the equation, an R of 0.05 was obtained, a r e s u l t which was s i g n i f i c a n t at the 0.06 l e v e l . Table VII summarizes the r e s u l t s of the backward e l i m i n a t i o n procedure. Step R R F Sig.F R* change V a r i a b l e 1 In: IQ 2 In: I n s i g h t 3 0.05 0.01 1.35 0.26 0.05 In: Cog. L e v e l 4 0.05 0.02 1.95 0.15 -0.003 Out: Cog. L e v e l 5 0.05 0.03 3.69 0.06 -0.003 Out: I n s i g h t Table VII - Summary t a b l e of backward e l i m i n a t i o n procedure It can be seen that c o g n i t i v e l e v e l and i n s i g h t c o n t r i b u t e d l i t t l e to the p r e d i c t i o n of problem f i n d i n g , c o g n i t i v e l e v e l due l i k e l y to the small number of formal t h i n k e r s in the sample (5 s u b j e c t s at the low formal stage) and i n s i g h t , as w i l l be 56 d i s c u s s e d l a t e r i n the chapter, due l i k e l y to the same ma t u r a t i o n a l c o n s t r a i n t s . While IQ as a p r e d i c t o r of problem f i n d i n g i s in the expected d i r e c t i o n , the p r o p o r t i o n of v a r i a n c e accounted f o r i s s l i g h t . R e s u l t s from backward e l i m i n a t i o n a l s o i n d i c a t e d that the r e s e a r c h hypothesis concerning order of entry of the p r e d i c t o r v a r i a b l e s was not supported. 4.3 Shrinkaqe Since the t e s t of the f u l l model was not s i g n i f i c a n t , a z. c r o s s - v a l i d a t i o n was not done. The shrinkage i n R was reported on the SPSS NEW REGRESSION output, however, and i s w i t h i n a c c e p t a b l e l i m i t s . Table VII r e p o r t s the a d j u s t e d R^ CR*) . 4.4 Test Of The Mediation Of I n s i g h t By Formal Operations The f o l l o w i n g F - s t a t i s t i c was d e r i v e d using r e s u l t s from the r e p l a c e m e n t - d e l e t i o n procedure w i t h i n the computer program *V/*->eV / A BMD: 03R Le,l980 : F = — ^ 3 . , , = 0.69. Formal reasoning was designated as v a r i a b l e 1; i n s i g h t as v a r i a b l e 2. A n o n - s i g n i f i c a n t F - s t a t i s t i c would make the n u l l h y pothesis that/? x=0 tenable and i n s i g h t does not, t h e r e f o r e , d i r e c t l y p r e d i c t problem f i n d i n g but i s mediated by formal reasoning. Since F( = 0.69) < ,fs 7* (= 3 . 97 ) , the n u l l hypothesis that fix =0 was found to be t e n a b l e . There i s thus not a d i r e c t p r e d i c t i v e r e l a t i o n s h i p between i n s i g h t and. problem f i n d i n g . The mediating e f f e c t of formal reasoning found i n t h i s a n a l y s i s supports the re s e a r c h hypothesis that c o g n i t i v e l e v e l w i l l 57 mediate the p r e d i c t i o n of problem f i n d i n g . That there i s , t h e r e f o r e , a r e l a t i o n s h i p between formal reasoning and i n s i g h t i s an important issue with i m p l i c a t i o n s both f o r d e f i n i t i o n of g i f t e d n e s s i n terms of i n s i g h t and f o r c u r r i c u l u m p l a n n i n g . These i m p l i c a t i o n s w i l l be taken up i n d e t a i l i n Chapter 5. R e s u l t s of the supplementary analyses w i l l now be looked at f o r t h e i r c o n t r i b u t i o n to the understanding of the v a r i a b l e s under study. 5. RESULTS OF THE SUPPLEMENTARY ANALYSES Two supplementary c o r r e l a t i o n a l analyses were c a r r i e d out as planned between the processes of i n s i g h t and problem f i n d i n g , and the processes of i n s i g h t and the formal reasoning schemata. In a d d i t i o n , s i n c e i n t e r c o r r e l a t i o n s among the v a r i a b l e s i n d i c a t e d r e l a t i o n s h i p s c o n s i d e r e d important to the study, another c o r r e l a t i o n a l a n a l y s i s was done to t e s t these r e l a t i o n s h i p s f o r s i g n i f i c a n c e . D i s c u s s i o n of the supplementary analyses w i l l , t h e r e f o r e , c o n s i s t of three p a r t s r e f l e c t i n g each of these r e l a t i o n s h i p s i n t u r n . 5.1 The R e l a t i o n s h i p Of Problem F i n d i n g Q u a l i t y To The Three  Processes Of I n s i g h t No s i g n i f i c a n t c o r r e l a t i o n s were found between i n s i g h t processes and problem f i n d i n g . R e s u l t s of the a n a l y s i s are found i n Table V I I I . Given the m a t u r a t i o n a l c o n s t r a i n t s o p e r a t i v e i n the sample which r e s u l t e d i n only lower order q u e s t i o n s being posed i n the problem f i n d i n g task and very few high i n s i g h t s c o r e s , i t i s to 58 Problem f i n d i n g q u a l i t y S e l e c t i v e encoding 0.02 S e l e c t i v e combination 0.12 S e l e c t i v e comparison 0.16 N=76 Table VIII - C o r r e l a t i o n matrix of problem f i n d i n g q u a l i t y with the three processes of i n s i g h t be expected that c o r r e l a t i o n s would be low, i n a l l p r o b a b i l i t y due to a " f l o o r e f f e c t . " An i n s u f f i c i e n t degree of a b s t r a c t i o n in responses and a t h e r e f o r e l i m i t e d range of scores r e s u l t e d in an inadequate t e s t of the hypothesized r e l a t i o n s h i p between i n s i g h t and problem f i n d i n g . 5.2 The R e l a t i o n s h i p Between The Three Processes Of I n s i g h t And  The Formal Reasoning Schemata I t was expected that the formal reasoning schemes of c o m b i n a t o r i a l reasoning and the c o o r d i n a t i o n of two or more systems or frames of r e f e r e n c e would c o r r e l a t e most s i g n i f i c a n t l y with the processes of i n s i g h t . In p a r t i c u l a r , the c o m b i n a t o r i a l reasoning scheme was seen as r e l e v a n t to the process of s e l e c t i v e combination f o r t h i s scheme " i n v o l v e s the concept of generating a l l p o s s i b l e combinations of a given number of v a r i a b l e s ... when a problem's s o l u t i o n r e q u i r e s that a l l p o s s i b i l i t i e s be accounted f o r " ( A r l i n , 1984a, p.10). The frames of r e f e r e n c e scheme was b e l i e v e d r e l e v a n t to the s e l e c t i v e comparison process of r e l a t i n g new to o l d i n f o r m a t i o n and to c e r t a i n i n s tances of s e l e c t i v e encoding where more than one frame of ref e r e n c e i s necessary to c o r r e c t l y encode 59 i n f o r m a t i o n r e l e v a n t to the problem. S i g n i f i c a n t c o r r e l a t i o n s were found between the i n s i g h t processes of s e l e c t i v e encoding and s e l e c t i v e combination and the c o m b i n a t o r i a l reasoning scheme. I t would appear that s e l e c t i v e encoding, as w e l l as s e l e c t i v e combination, i n v o l v e s some notion of c o m b i n a t o r i a l reasoning i n that r e l e v a n t f a c t s , once encoded, must be combined to a r r i v e at a s o l u t i o n . C o r r e l a t i o n s were a l s o s i g n i f i c a n t between both s e l e c t i v e encoding and s e l e c t i v e combination and frames of r e f e r e n c e . The c o r r e l a t i o n between s e l e c t i v e combination and frames of r e f e r e n c e may represent a r e l a t i o n s h i p s i m i l a r to the one which appears to e x i s t in the c o r r e l a t i o n of s e l e c t i v e encoding with frames of r e f e r e n c e ; that i s , more than one frame of ref e r e n c e may be necessary i n c e r t a i n i n s t a n c e s of combining seemingly " i s o l a t e d p i e c e s of i n f o r m a t i o n i n t o a u n i f i e d whole that may or may not resemble i t s p a r t s " (Sternberg & Davidson, 1983, p.53). The expected r e l a t i o n s h i p between frames of r e f e r e n c e and s e l e c t i v e comparison was not supported i n t h i s study. T h i s may be due, in p a r t , to a p o s s i b l y i n s u f f i c i e n t measure of s e l e c t i v e comparison, in that only one i n s i g h t p u z z l e emphasized t h i s p r o c e s s . A d d i t i o n a l s i g n i f i c a n t c o r r e l a t i o n s were obtained between s e l e c t i v e encoding and both p r o p o r t i o n and momentum, and between s e l e c t i v e combination and p r o p o r t i o n . These c o r r e l a t i o n s may r e l a t e to the " c o m b i n a t o r i a l system" thought to u n d e r l i e the p r o p o s i t i o n a l l o g i c of formal thought (Piaget & Inhelder, 1977). I t can be seen that a c o m b i n a t o r i a l system which would enable a 60 subject "to combine among themselves o b j e c t s with o b j e c t s or f a c t o r s with f a c t o r s ( p h y s i c a l , e t c . ) " or "to reason about a given r e a l i t y (a segment of p h y s i c a l r e a l i t y , an e x p l a n a t i o n based on f a c t o r s , or a theory i n the simple sense of a group of r e l a t e d p r o p o s i t i o n s " (Piaget & Inhelder, 1977, pp.398-399) as i s r e q u i r e d i n the t e s t items f o r momentum and p r o p o r t i o n i s a s e l e c t i v e form of thought r e l a t e d to the notion of s e l e c t i v e l y combining p i e c e s of in f o r m a t i o n i n t o a u n i f i e d whole (Sternberg & Davidson, 1983), and/or s e l e c t i v e l y encoding f a c t o r s or r e l a t e d p r o p o s i t i o n s i n a r e l e v a n t way. Table IX summarizes the c o r r e l a t i o n s between the three processes of i n s i g h t and the formal reasoning schemata. S e l e c t i v e Encoding S e l e c t ive Combinat ion S e l e c t i v e Comparison Volume 0.03 -0.04 0.08 P r o b a b i l i t y 0.13 0.05 -0.09 C o r r e l a t i o n s 0.22 0.15 0.13 Combinations 0.27* 0.49** 0.17 P r o p o r t i o n 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 of Reference 0.23* 0.32** 0.11 N=76; * p<0.05; ** p<0.0l Table IX - C o r r e l a t i o n matrix of the three processes of i n s i g h t with the formal reasoning schemata 61 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 C o r r e l a t i o n s among the v a r i a b l e s r e v e a l e d some s i g n i f i c a n t r e l a t i o n s h i p s which are r e l e v a n t to the re s e a r c h . These c o r r e l a t i o n s are presented i n Table X. In s i g h t IQ Problem F i n d i n g C o g n i t i v e L e v e l 0.43** 0.55** 0.09 In s i g h t 0.34** 0.13 IQ 0.22 N=76; ** p<0.0l Table X - C o r r e l a t i o n s among the p r e d i c t o r and c r i t e r i o n v a r i a b l e s The s i g n i f i c a n t c o r r e l a t i o n between c o g n i t i v e l e v e l and i n s i g h t supports the f i n d i n g that i n s i g h t i s mediated by formal o p e r a t i o n s . M a t u r a t i o n a l c o n s t r a i n t s are thus important i n any d i s c u s s i o n of i n s i g h t as a d i f f e r e n t i a l c o g n i t i v e a t t r i b u t e of the g i f t e d . The c o r r e l a t i o n between IQ and c o g n i t i v e l e v e l supports r e s e a r c h c i t e d in the review of the l i t e r a t u r e d e a l i n g with attainment of formal o p e r a t i o n s by g i f t e d c h i l d r e n . T h i s i s s u e w i l l be d i s c u s s e d f u r t h e r i n the subsequent s e c t i o n on q u a l i t a t i v e a n a l y s i s . That i n s i g h t c o r r e l a t e s with IQ appears to support the hypothesis that i n s i g h t may represent a d i f f e r e n t i a l i n f o r m a t i o n p r o c e s s i n g c h a r a c t e r i s t i c i n 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 (Davidson & Sternberg,1984; Sternberg & Davidson, 1982,1983). 62 In t h e i r study of c h i l d r e n i n grades fo u r , f i v e , and s i x , Davidson and Sternberg (1984) found a c o r r e l a t i o n of 0.55 between i n s i g h t and a group IQ measure. The c o r r e l a t i o n a l r e l a t i o n s h i p between IQ and problem f i n d i n g , while not s i g n i f i c a n t , i s i n the expected d i r e c t i o n and appears to support the d i r e c t i o n a l i t y found f o r IQ as a p r e d i c t o r of problem f i n d i n g . The weak c o r r e l a t i o n s between c o g n i t i v e l e v e l and problem f i n d i n g and i n s i g h t and problem f i n d i n g may r e f l e c t once more the m a t u r a t i o n a l c o n s t r a i n t s i n the sample. The hypothesized r e l a t i o n s h i p s between i n s i g h t and problem f i n d i n g need f u r t h e r t e s t i n g with a sample of more mature t h i n k e r s . Since problem f i n d i n g has been a s s o c i a t e d with post-formal thought ( A r l i n , 1984b) and t h i s study suggests m a t u r a t i o n a l c o n s t r a i n t s on i n s i g h t , an o l d e r sample would be a more a p p r o p r i a t e t e s t of the hypothesized r e l a t i o n s h i p s . T h i s issue w i l l be e x p l o r e d f u r t h e r i n Chapter 5 s i n c e there are i m p l i c a t i o n s a r i s i n g from these f i n d i n g s r e l e v a n t to the age-a p p r o p r i a t e d e f i n i t i o n of g i f t e d n e s s . R e s u l t s of a q u a l i t a t i v e a n a l y s i s w i l l now be presented for t h e i r c o n t r i b u t i o n to the r e s e a r c h f i n d i n g s . 6. QUALITATIVE ANALYSIS Re s u l t s of a q u a l i t a t i v e a n a l y s i s of h i g h scores on a l l v a r i a b l e s , while t e n t a t i v e due to the small number of high scores, do appear to c o n f i r m the m a t u r a t i o n a l c o n s t r a i n t s and s i g n i f i c a n t f i n d i n g s of the study. 63 Those s u b j e c t s with the highest IQ's were at the low formal or t r a n s i t i o n a l stage. Of p a r t i c u l a r i n t e r e s t were the two s u b j e c t s who scored highest on the IQ measure. Subject A (IQ 134) was the only low formal t h i n k e r i n the s i x t h grade; Subject B (IQ 136) the only low formal t h i n k e r i n the f i f t h grade. The remaining low formal t h i n k e r s were i n the seventh grade group. That these b r i g h t e r c h i l d r e n were at a more advanced c o g n i t i v e l e v e l than t h e i r peers has i m p l i c a t i o n s f o r i n s t r u c t i o n which w i l l be d e a l t with in the f o l l o w i n g chapter. The h i g h e s t i n s i g h t scores were obtained by those who were low formal t h i n k e r s and had average or above average IQ's. The one e x c e p t i o n was a subject who, while having an above average IQ, was a high concrete t h i n k e r . T h i s subject d i d , however, score a t the highest l i m i t f o r the high concrete c l a s s i f i c a t i o n and had the c o r r e l a t i o n s and frames of r e f e r e n c e schemes in p l a c e . T h i s may i n d i c a t e that t h i s subject was more of a t r a n s i t i o n a l t h i n k e r . A l t e r n a t i v e l y , s i n c e the frames of r e f e r e n c e scheme i s b e l i e v e d to be the l a s t of the formal schemes to emerge ( A r l i n , 1984b) and i t i s unusual f o r t h i s scheme to be i n place at a l e v e l below high formal, t h i s subject may have had some experience which enabled her to answer the frames of r e f e r e n c e q u e s t i o n s and to do w e l l on the i n s i g h t p u z z l e s . The seventh grade group had the smallest p r o p o r t i o n of low scores on the i n s i g h t p u z z l e s which would appear to support the suggested m a t u r a t i o n a l c o n s t r a i n t s on i n s i g h t . The p a t t e r n of high problem f i n d i n g scores was l e s s c o n c l u s i v e . 64 A high problem f i n d i n g score i n t h i s study r e f l e c t e d the frequent use of r e l a t i o n s and systems q u e s t i o n s s i n c e there were only two ins t a n c e s of higher order q u e s t i o n s i n the sample. R e l a t i o n s q u e s t i o n s are common i n samples of concre t e reasoners. Systems ques t i o n s u s u a l l y i n d i c a t e some evidence of a t r a n s i t i o n to formal o p e r a t i o n s ( A r l i n , 1977; A r l i n , 1984 i n press b ) . T h i s p a t t e r n was not i n d i c a t e d i n t h i s sample, however. Examination of systems que s t i o n s posed i n d i c a t e d two p o s s i b l e reasons f o r t h i s , s i n c e , i n g e n e r a l , systems q u e s t i o n s f e l l i n t o two c a t e g o r i e s . I t may be that the example given i n the i n s t r u c t i o n s , "Can you form four t r i a n g l e s out of these s i x match s t i c k s ? " p r ovided a " s e t " which the c h i l d r e n used i n f o r m u l a t i n g t h e i r q u e s t i o n s . The f o l l o w i n g are examples of systems que s t i o n s which appeared to match the example g i v e n : Can you make up a game using the s i x matches? Could you make a square out of f i v e matches? How many 3-sided t r i a n g l e s can you make out of 30 tacks? Could you make a 3-dimensional square out of s i x matches? A d d i t i o n a l l y , the q u e s t i o n , "Can they be math, q u e s t i o n s ? " was asked by s u b j e c t s i n response to the query, "Do you have any qu e s t i o n s f o r me before beginning?" T h i s , too, may have provided a d i r e c t i o n f o r responses to the task, f o r numerous systems q u e s t i o n s appeared to resemble mathematical 65 problems such as students encounter i n the mathematics c u r r i c u l u m . The f o l l o w i n g are some examples of t h i s type of q u e s t i o n : How many 20.5 cm p i e c e s can you cut from one of the cords? How long do you think i t would take f o r three candles to burn a 2-metre cor d i f i t takes one candle one hour? How many p i e c e s of cord would you have i f you cut i t i n h a l f and each h a l f i n q u a r t e r s ? If a box i s p e r f e c t l y square and the r i g h t s i d e i s 5 cm and the top i s 5 cm, what i s the measurement of the bottom and l e f t s i d e ? I t appears t h a t , s i n c e systems que s t i o n s g e n e r a l l y f e l l i n t o e i t h e r of the above c l a s s i f i c a t i o n s , higher problem f i n d i n g scores r e f l e c t i n g frequent use of systems q u e s t i o n s were r e l a t e d more to these " s e t s " than to evidence of a t r a n s i t i o n to formal o p e r a t i o n s . 7. SUMMARY OF CHAPTER FOUR Chapter 4 presented the r e s u l t s of the study. Regression a n a l y s i s of the f u l l model showed that c o g n i t i v e l e v e l and i n s i g h t were not s i g n i f i c a n t p r e d i c t o r s of problem f i n d i n g . T h i s r e s u l t , however, l e n t support to the developmental c o n s i d e r a t i o n s important to a study of problem f i n d i n g . The low c o g n i t i v e m a t u r i t y of the sample appeared to m i l i t a t e a g a i n s t 66 high l e v e l responses i n the i n s i g h t p u z z les and the problem f i n d i n g task. IQ as a p r e d i c t o r of problem f i n d i n g was i n the expected d i r e c t i o n , although the amount of v a r i a n c e accounted for was minimal. S i g n i f i c a n t c o r r e l a t i o n s were found among the p r e d i c t o r v a r i a b l e s which supplement the f i n d i n g s of the primary a n a l y s i s . Formal reasoning was found to mediate the p r e d i c t i o n of problem f i n d i n g by i n s i g h t . S i g n i f i c a n t c o r r e l a t i o n s between c e r t a i n of the formal reasoning schemata and the i n s i g h t processes of s e l e c t i v e encoding and s e l e c t i v e combination appeared to support t h i s mediating e f f e c t . C o n c l u s i o n s , i m p l i c a t i o n s , and suggestions f o r f u t u r e re s e a r c h stemming from the r e s u l t s of t h i s r e s e a r c h w i l l be presented i n the f o l l o w i n g chapter. 67 V. DISCUSSION AND CONCLUSIONS 1. OVERVIEW OF THE CHAPTER T h i s study was conducted to t e s t hypotheses r e l a t e d t o problem f i n d i n g as a d i f f e r e n t i a l 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 g i f t e d c h i l d r e n . The 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 l e v e l , IQ, and i n s i g h t were analyzed f o r t h e i r c o n t r i b u t i o n to the v a r i a n c e accounted f o r i n the c r i t e r i o n v a r i a b l e of problem f i n d i n g . The r e s u l t s of the a n a l y s i s r e v e a l e d that while c o g n i t i v e l e v e l d i d not emerge as a s t a t i s t i c a l l y s i g n i f i c a n t p r e d i c t o r , i t p r e d i c t e d lower order problem f i n d i n g a b i l i t y i n the sense that the low o v e r a l l concrete l e v e l of the sample appeared to preclude the asking of general q u e s t i o n s . The f i n d i n g t h a t i n s i g h t i s mediated by formal o p e r a t i o n a l t h i n k i n g and the developmental " f l o o r e f f e c t " o p e r a t i v e i n the sample l i k e w i s e worked a g a i n s t i n s i g h t emerging as a s t a t i s t i c a l l y s i g n i f i c a n t p r e d i c t o r . The r e g r e s s i o n procedure of backward e l i m i n a t i o n showed that IQ was i n the expected d i r e c t i o n as a p r e d i c t o r of problem f i n d i n g when i t alone appeared i n the r e g r e s s i o n equation. I t d i d , however, account f o r only 5% of the v a r i a n c e i n problem f i n d i n g . Chapter 5 i s devoted to d i s c u s s i o n of these r e s u l t s , with some suggestions f o r f u t u r e r e s e a r c h . L i m i t a t i o n s of the study w i l l be noted; some c o n c l u s i o n s drawn; and i m p l i c a t i o n s f o r the classroom presented. 68 2. LIMITATIONS OF THE STUDY The sample was l i m i t e d i n terms of number of s u b j e c t s . While the shrinkage of the m u l t i p l e c o r r e l a t i o n was w i t h i n a c c e p t a b l e l i m i t s , i t i s f e l t that a smaller r a t i o of the number of independent v a r i a b l e s to sample s i z e would have been a p p r o p r i a t e f o r more s t a b i l i t y i n r e s u l t s (Pedhazur, 1982). A l i m i t a t i o n a l s o e x i s t e d i n a " f l o o r e f f e c t " due to the low c o g n i t i v e maturity of the sample. While t h i s " f l o o r e f f e c t " l e d to n o n - s i g n i f i c a n t r e s u l t s i n the r e g r e s s i o n a n a l y s i s , i t d i d serve to h i g h l i g h t the m a t u r a t i o n a l issue i n both problem f i n d i n g and i n s i g h t , an i s s u e which i s l a r g e l y ignored i n the l i t e r a t u r e . R a t i o n a l e f o r using c h i l d r e n at the upper elementary l e v e l i n the study i n v o l v e d two c o n s i d e r a t i o n s . F i r s t l y , as s t a t e d i n Chapter 3, i n v e s t i g a t i o n s of g i f t e d n e s s done from a P i a g e t i a n p e r s p e c t i v e ( A r l i n , 1984, i n press a; C a r t e r & Ormrod, 1982; Keating, 1975; L o v e l l & S h i e l d s , 1967; Webb, 1974) were done with approximately the same age group. Secondly, Davidson and Sternberg's (1984) work with upper elementary school-aged c h i l d r e n suggested that there may be q u a l t 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 g i f t e d c h i l d r e n i n t h i s age group. 3. DISCUSSION OF THE RESULTS The e f f e c t s of the 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 l e v e l , i n s i g h t , and IQ w i l l be d i s c u s s e d s e p a r a t e l y . A f o u r t h s e c t i o n of the d i s c u s s i o n w i l l concern r e s u l t s from the supplementary analyses not covered under the above headings. 69 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 Problem F i n d i n g While the r e g r e s s i o n a n a l y s i s f a i l e d to co n f i r m the hypothesis that c o g n i t i v e l e v e l would be a s i g n i f i c a n t p r e d i c t o r of problem f i n d i n g , the r e l a t i o n s h i p between the mean c o g n i t i v e l e v e l of the sample and the lower order q u e s t i o n s posed i n the problem f i n d i n g task appears to con f i r m that c o g n i t i v e l e v e l i s a r e l e v a n t c o n s i d e r a t i o n when p r e d i c t i n g the a b i l i t y to f i n d problems. There appear to be developmental c o n s t r a i n t s on problem 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 c h i l d r e n . The f a i l u r e of c o g n i t i v e l e v e l to c o r r e l a t e h i g h l y with the c r i t e r i o n v a r i a b l e would appear to be due to the l i m i t e d range of c o g n i t i v e l e v e l , and, t h e r e f o r e , the l i m i t e d range of problem f i n d i n g scores i n the sample. T h i s l a c k of c o r r e l a t i o n may a l s o be due to the f a i l u r e of systems q u e s t i o n s to represent evidence of t r a n s i t i o n to formal o p e r a t i o n s . Systems qu e s t i o n s were f e l t to represent, r a t h e r , a " s e t " c r e a t e d by examples given p r i o r to completion of the problem f i n d i n g task, as d i s c u s s e d i n Chapter 4. 3.2 I n s i g h t As A P r e d i c t o r Of Problem F i n d i n g The h y p othesis concerning i n s i g h t as a " b e t t e r " p r e d i c t o r of problem f i n d i n g than IQ was not supported. Again, the mat u r a t i o n a l c o n s t r a i n t s that appeared to m i l i t a t e a g a i n s t the posing of gen e r a l q u e s t i o n s i n the problem f i n d i n g task seemed to r e s u l t i n l i m i t e d responses to the i n s i g h t task. These c o n s t r a i n t s appeared to be confirmed by the acceptance of the hypothesis that c o g n i t i v e l e v e l would mediate the p r e d i c t i o n of 70 problem f i n d i n g by i n s i g h t and by the s i g n i f i c a n t c o r r e l a t i o n between c o g n i t i v e l e v e l and i n s i g h t . Further r e s e a r c h should i n v e s t i g a t e p o s s i b l e r e l a t i o n s h i p s between the three i n s i g h t processes and problem f i n d i n g . Since problem f i n d i n g and i n s i g h t appear to bear a r e l a t i o n s h i p to formal o p e r a t i o n s and problem f i n d i n g has been f u r t h e r hypothesized to be c h a r a c t e r i s t i c of p o s t - f o r m a l , a d u l t thought ( A r l i n , 1984b), an o l d e r sample c o n s i s t i n g of more s o p h i s t i c a t e d t h i n k e r s would provide a more s u i t a b l e t e s t of a p o s s i b l e r e l a t i o n s h i p between i n s i g h t and problem f i n d i n g . 3.3 IQ As A P r e d i c t o r Of Problem F i n d i n g The h y p othesis concerning IQ as a r e l e v a n t p r e d i c t o r of problem f i n d i n g was supported to the extent t h a t , appearing alone in the p r e d i c t i o n equation generated by backward e l i m i n a t i o n , i t was seen to account f o r 5% of the v a r i a n c e i n problem f i n d i n g . While t h i s r e s u l t was i n the expected d i r e c t i o n , i t r e p r e s e n t s a very s m a l l p r o p o r t i o n of v a r i a n c e accounted f o r . The hypothesized r o l e of IQ as a weaker p r e d i c t o r than e i t h e r c o g n i t i v e l e v e l or i n s i g h t was not supported. Once again, e x p l o r a t i o n of the r e s e a r c h hypotheses d e a l i n g with the p r e d i c t i o n of problem f i n d i n g u s i n g an o l d e r sample would be f r u i t f u l . Given the s i g n i f i c a n t c o r r e l a t i o n s of IQ with both c o g n i t i v e l e v e l and i n s i g h t , i t may be t h a t , with o l d e r s u b j e c t s of high IQ, g r e a t e r c o g n i t i v e m a t u r i t y would r e s u l t i n c o g n i t i v e l e v e l and i n s i g h t being stronger p r e d i c t o r s than IQ. A d d i t i o n a l l y , such a sample may b e t t e r t e s t the 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 c o g n i t i v e a t t r i b u t e of the g i f t e d . 3.4 Furth e r D i s c u s s i o n Of The Supplementary A n a l y s i s I t has been noted that the c o r r e l a t i o n found between i n s i g h t and IQ (0.34; p< 0.01) appears to support research h y p o t h e s i z i n g i n s i g h t as a d i f f e r e n t i a l c o g n i t i v e a t t r i b u t e of the g i f t e d (Davidson & Sternberg, 1984; Sternberg & Davidson, 1982,1983). However, a c l o s e r look at one of these s t u d i e s r e v e a l s p o s s i b l e support f o r the ma t u r a t i o n a l c o n s t r a i n t s on i n s i g h t suggested i n t h i s r e s e a r c h . Of p a r t i c u l a r i n t e r e s t i s the Davidson and Sternberg (1984) work with c h i l d r e n i n grades fo u r , f i v e , and s i x . While g i f t e d c h i l d r e n c o n s i s t e n t l y outperformed t h e i r peers, scores are s t i l l low, with a mean score of 4.08 out of a p o s s i b l e 12 on s e l e c t i v e encoding problems and a mean score of 6.50 out of a p o s s i b l e 16 on s e l e c t i v e combination problems. The s e l e c t i v e comparison problems represented d i f f e r e n t t e s t i n g c o n d i t i o n s and w i l l be d e a l t with i n a subsequent s e c t i o n of the chapter f o r the i n s t r u c t i o n a l i m p l i c a t i o n s inherent i n the r e s u l t s . I t may be that c o g n i t i v e l e v e l i s a v a r i a b l e that should have been i n c l u d e d i n Davidson and Sternberg's r e s e a r c h . For example, one of the problems used to t e s t s e l e c t i v e combination was as f o l l o w s : 72 At a dinner p a r t y , there are f i v e people s i t t i n g in a row at a t a b l e . Scott i s seated at one end of the row. Ziggy i s seated next to Matt. Joshua i s not s i t t i n g next to Matt or S c o t t . Only 1 person i s s i t t i n g next to Walter. Who i s s i t t i n g next to Walter? (Davidson & Sternberg, 1984, p.61 ) Formal o p e r a t i o n a l t h i n k i n g i s c o n s i d e r e d necessary to reason with ideas only, as i n such a v e r b a l problem (Donaldson, 1978). P a r t i c u l a r l y r e l e v a n t would be the c o m b i n a t o r i a l reasoning scheme, as i n d i c a t e d by the s i g n i f i c a n t c o r r e l a t i o n found i n t h i s r esearch between t h i s scheme and s e l e c t i v e combination. . It would be r e l e v a n t in the Davidson and Sternberg (1984) resea r c h to c a r e f u l l y examine the responses to the i n s i g h t problems, with the f o l l o w i n g q u e s t i o n s i n mind. Are there problems that most of the sample are unable to answer? If so, what i s the nature of these problems? How does performance d i f f e r a cross grade l e v e l s ? Answers to such q u e s t i o n s may w e l l c o n f i r m that c o g n i t i v e m a t u r i t y i s r e l e v a n t to the d i s c u s s i o n of i n s i g h t as a d i f f e r e n t i a l c o g n i t i v e a t t r i b u t e of the g i f t e d . 4. CONCLUSIONS The developmental l e v e l of the c h i l d appears to be important i n terms of c o n s t r a i n t s on i n s i g h t and problem f i n d i n g . T h i s i s evident even among b r i g h t c h i l d r e n . There are i m p l i c a t i o n s f o r i n s t r u c t i o n and f o r age-appropriate d e f i n i t i o n s of g i f t e d n e s s inherent i n t h i s f i n d i n g . These i m p l i c a t i o n s are d e a l t with i n the f o l l o w i n g s e c t i o n of the chapter. 73 5. IMPLICATIONS I m p l i c a t i o n s from t h i s r e s e a r c h f a l l i n t o two general c a t e g o r i e s . The f i r s t category concerns i m p l i c a t i o n s for age-a p p r o p r i a t e d e f i n i t i o n s of g i f t e d n e s s . E d u c a t i o n a l i m p l i c a t i o n s concerning 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 and 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 form the second category. T h i s s e c t i o n of Chapter 5 w i l l , t h e r e f o r e , c o n s i s t of two p a r t s d e a l i n g with each of these i m p l i c a t i o n s i n t u r n . 5.1 D e f i n i t i o n Of G i f t e d n e s s F i r s t l y , t h i s r e s e a r c h suggests that d e s c r i p t i o n s of the g i f t e d as p o s s e s s i n g d i f f e r e n t i a l c o g n i t i v e a t t r i b u t e s such as the a b i l i t y to t h i n k i n a b s t r a c t terms ( C l a r k , 1983; E h r l i c h , 1982; H i l d r e t h , 1966; Kaplan, 1977; Newland, 1976) or to think with l o g i c a l systems (Rice, 1970) cannot be seen as a p p l i c a b l e to a l l age groups. The b r i g h t e s t c h i l d r e n i n t h i s sample, while more c o g n i t i v e l y mature than t h e i r average and below average peers, were s t i l l not f u l l y formal o p e r a t i o n a l t h i n k e r s . Some were low formal t h i n k e r s , with three to f i v e of the formal schemes present in t h e i r t h i n k i n g ( A r l i n , 1984a); others were t r a n s i t i o n a l , with two or three schemes p r e s e n t . These f i n d i n g s are c o n s i s t e n t with L o v e l l and S h i e l d s ' (1967) statement that "formal t h i n k i n g i s not a v a i l a b l e to the c h i l d in a l l s i t u a t i o n s at f i r s t " (p.206). It would seem that g i f t e d c h i l d r e n at the upper elementary l e v e l cannot thi n k a b s t r a c t l y or employ l o g i c to the extent i m p l i e d i n l i s t s of c h a r a c t e r i s t i c s of the g i f t e d . 74 Q u a l i f i c a t i o n i s needed on these l i s t s i n terms of age and extent of " a b s t r a c t i o n " and " l o g i c a l t h i n k i n g . " I m p l i c a t i o n s for i n s t r u c t i o n a l s o stem from t h i s issue and w i l l be presented l a t e r i n the chapter. Secondly, i t has been seen that more resea r c h i s necessary i n t o the h y p othesis that problem f i n d i n g may be a d i f f e r e n t i a l c o g n i t i v e a t t r i b u t e of the g i f t e d . If such a hypothesis i s supported, t h i s research and that of A r l i n (1975-76, 1977) appear to i n d i c a t e that g i f t e d n e s s d e f i n e d i n terms of problem f i n d i n g would a l s o need to be a g e - a p p r o p r iate. T h i r d l y , d e f i n i t i o n s of g i f t e d n e s s i n terms of s u p e r i o r i n s i g h t s k i l l s a l s o need to recognize the p o s s i b l e developmental c o n s t r a i n t s on i n s i g h t . While the c o r r e l a t i o n s between i n s i g h t and IQ o b tained in t h i s r e s e a r c h and that of Davidson and Sternberg (1984) i n d i c a t e a s i g n i f i c a n t p o s i t i v e r e l a t i o n s h i p between IQ and i n s i g h t i n c h i l d r e n at the upper elementary l e v e l , both s t u d i e s i n d i c a t e that there are c o n s t r a i n t s on t h i s s u p e r i o r i t y . Even the b r i g h t e s t c h i l d r e n , i n g e n e r a l , are unable to answer a s i g n i f i c a n t number of i n s i g h t problems. C o g n i t i v e m a t u r i t y may w e l l be germane to the d e f i n i t i o n of g i f t e d n e s s i n terms of s u p e r i o r i n s i g h t . E d u c a t i o n a l i m p l i c a t i o n s stemming from the i s s u e s r a i s e d concerning the age-appropriate d e f i n i t i o n of g i f t e d n e s s w i l l now be presented. 75 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 Two i s s u e s concerning e d u c a t i o n of the g i f t e d a r i s e from t h i s r e s e a r c h . Appropriateness of c u r r i c u l u m i s c l o s e l y t i e d to the i s s u e s presented i n v o l v i n g d e f i n i t i o n of g i f t e d n e s s and w i l l be d i s c u s s e d f i r s t . Secondly, the i s s u e of 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 i s important to a developmental p e r s p e c t i v e on g i f t e d n e s s . T h i s w i l l be d i s c u s s e d with r e f e r e n c e to formal reasoning, i n s i g h t , and problem f i n d i n g . 5.2.1 Age-appropriateness Of C u r r i c u l u m For The G i f t e d Age-appropriateness of c u r r i c u l u m f o r the g i f t e d i n v o l v e s two c o n s i d e r a t i o n s . F i r s t l y , s i n c e g i f t e d c h i l d r e n appear to be developmentally c o n s t r a i n e d i n t h e i r a c q u i s i t i o n of formal o p e r a t i o n s , and i n t h e i r a b i l i t y to d i s c o v e r problems (that i s , to formulate general q u e s t i o n s ) and use the processes of i n s i g h t , c u r r i c u l u m m a t e r i a l s f o r elementary school-aged g i f t e d c h i l d r e n should take i n t o account these c o n s t r a i n t s on a b s t r a c t and l o g i c a l reasoning. Secondly, c u r r i c u l u m needs to be s u f f i c i e n t l y c h a l l e n g i n g for the g i f t e d c h i l d who i s e n t e r i n g formal o p e r a t i o n s and i s becoming more of a p r o p o s i t i o n a l t h i n k e r . C a r t e r and Ormrod (1982) and A r l i n (1984a) suggest that P i a g e t i a n assessment can be u s e f u l f o r determining c o g n i t i v e l e v e l and p l a n n i n g c u r r i c u l u m a c c o r d i n g l y . 76 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 Formal Reasoning Inhelder and Piaget (1958) d e f i n e formal o p e r a t i o n a l schemata as "the concepts which the s u b j e c t p o t e n t i a l l y can organize from the beginning of the formal l e v e l when faced with c e r t a i n kinds of data, but which are not manifest o u t s i d e these c o n d i t i o n s " (p.308). T h i s p o t e n t i a l , v i s - a - v i s the " c o g n i t i v e nourishment" and " i n t e l l e c t u a l s t i m u l a t i o n " seen by Piaget (1972) as necessary f o r the c o n s t r u c t i o n of formal thought, may i n d i c a t e the a p p r o p r i a t e n e s s of i n c o r p o r a t i n g the p r i n c i p l e s of formal o p e r a t i o n s i n the c u r r i c u l u m f o r those students at the t r a n s i t i o n a l l e v e l showing some evidence of formal reasoning or those students who are low formal t h i n k e r s . 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 In Davidson and Sternberg's (1984) study of the r o l e of i n s i g h t i n i n t e l l e c t u a l g i f t e d n e s s , the g i f t e d appeared to b e n e f i t from the r e c e i p t of examples i n t h e i r s o l v i n g of s e l e c t i v e comparison problems. A subsequent i n s i g h t t r a i n i n g experiment r e v e a l e d that " i n s i g h t s k i l l s are at l e a s t somewhat t r a i n a b l e " (p.63). I t does, however, seem necessary to s p e c i f y at what stage t h i s t r a i n i n g may be most e f f e c t i v e . The r e l a t i o n s h i p between i n s i g h t and formal reasoning suggested by t h i s r e s e a r c h and the r o l e of 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 i n promoting formal o p e r a t i o n a l thought as d i s c u s s e d above appear to i n d i c a t e that i n s i g h t t r a i n i n g may w e l l be most e f f e c t i v e when introduced at the t r a n s i t i o n a l or low formal stage. 77 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 Problem F i n d i n g The connection between formal reasoning and problem f i n d i n g ( A r l i n , 1975-76, 1977) may i n d i c a t e that problem f i n d i n g e x p e r i ences, too, may best be introduced i n t o the c u r r i c u l u m when a c h i l d i s becoming a formal t h i n k e r . These experiences should c o n s i s t 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 to r a i s e q u e s t i o n s from problematic s i t u a t i o n s i n which there i s no known fo r m u l a t i o n , method of s o l u t i o n , or s o l u t i o n ( G e t z e l s & C s i k s z e n t m i h a l y i , 1975). Support f o r i n c l u d i n g these types of experiences becomes apparent when the t r a d i t i o n a l focus of education on presented problem s i t u a t i o n s i s c o n s i d e r e d . D i l l o n (1982) and G e t z e l s and D i l l o n (1973) emphasize that d i s c o v e r e d problem s i t u a t i o n s are e i t h e r avoided or ignored i n educa t i o n . G e t z e l s (1964) p o i n t s out that Bloom's taxonomy, which i s used as the 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 f o r the g i f t e d , "omits from c o n s i d e r a t i o n and seems not to recognize i n the classroom a s i g n i f i c a n t group of problems we may c a l l d i s c o v e r e d problems" (p.241). In Chapter 1 i t was seen that s u p e r i o r problem f i n d e r s are b e l i e v e d to be c r u c i a l to the fo r m u l a t i o n of resea r c h problems and the genera t i o n of ideas i n many d i s c i p l i n e s ( G e t z e l s & D i l l o n , 1973; Helvey, 1971; Mackworth, 1965). I t would seem important, t h e r e f o r e , to i n c l u d e problem f i n d i n g experiences at the a p p r o p r i a t e time in c u r r i c u l u m f o r the g i f t e d . 78 5.2.5 D i r e c t i o n s For Research The e d u c a t i o n a l i m p l i c a t i o n s stemming from t h i s r e s e a r c h are seen as important i s s u e s to be pursued. In p a r t i c u l a r , the n o t i o n of 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 suggests q u e s t i o n s f o r r e s e a r c h which are a p p l i c a b l e to the p l a n n i n g of c u r r i c u l u m f o r the g i f t e d . How might the p r o v i s i o n of " i n t e l l e c t u a l s t i m u l a t i o n " ( P i a g e t , 1972) i n the form of i n s t r u c t i o n a l experiences i n c o r p o r a t i n g formal o p e r a t i o n a l p r i n c i p l e s a f f e c t the r a t e of 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 the concepts and o p e r a t i o n s a s s o c i a t e d with formal thought? H o r i z o n t a l decalage i s seen as a f u n c t i o n of i n t e l l i g e n c e ( A r l i n , 1984, i n press a; Webb, 1974), but 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 may w e l l be an a d d i t i o n a l important component in the a c q u i s i t i o n and mastery of the formal schemes. 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 may w e l l be v i t a l to the f a c i l i t a t i o n of problem f i n d i n g c a p a b i l i t y and i n s i g h t s k i l l s as w e l l . How might the i n c o r p o r a t i o n of problem f i n d i n g and i n s i g h t tasks i n t o c u r r i c u l u m f o r the g i f t e d a f f e c t t h e i r a b i l i t y to pose general q u e s t i o n s and/or demonstrate s i g n i f i c a n t i n s i g h t i n t o problems? A d d i t i o n a l l y , what i s the most e f f e c t i v e way of p r e s e n t i n g these experiences? Questions concerning the optimum time f o r 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 , the nature of the i n t e r v e n t i o n , and the design of a p p r o p r i a t e tasks to encourage the development and i n t e g r a t i o n of formal o p e r a t i o n a l thought, problem f i n d i n g a b i l i t y , and i n s i g h t p rovide a f u l l agenda for f u t u r e r e s e a r c h . 79 6. SUMMARY OF CHAPTER 5 T h i s chapter d i s c u s s e d the m a t u r a t i o n a l c o n s t r a i n t s on i n s i g h t and problem f i n d i n g and the i m p l i c a t i o n s inherent i n these c o n s t r a i n t s f o r age-appropriate d e f i n i t i o n s of g i f t e d n e s s . D e f i n i t i o n i n terms of problem 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 the i n t e l l e c t u a l l y g i f t e d was found to need f u r t h e r i n v e s t i g a t i o n with an o l d e r sample to determine the a p p r o p r i a t e n e s s of such a d e f i n i t i o n . S i m i l a r l y , developmental c o n s i d e r a t i o n s were found to be important i n the d e f i n i t i o n of g i f t e d n e s s in terms of s u p e r i o r i n s i g h t . Optimal times f o r e f f e c t i v e 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 were d i s c u s s e d . I t was suggested that P i a g e t i a n assessment be employed to determine a g i f t e d c h i l d ' s r e a diness f o r problem f i n d i n g experiences and i n s t r u c t i o n i n the p r i n c i p l e s of formal o p e r a t i o n s and i n s i g h t s k i l l s . 80 BIBLIOGRAPHY A l v i n o , J . (1981) Do g i f t e d and n o n g i f t e d c h i l d r e n l e a r n d i f f e r e n t l y ? P r i n c i p a l , 60 (5), 39-40. A r l i n , P . K . (1975-76) A c o g n i t i v e process model of problem r i n d i n g . E d u c a t i o n a l Horizons, 54 (2), 99-106. A r l i n , P . K . (1977) P i a g e t i a n o p e r a t i o n s i n problem f i n d i n g . Developmental Psychology, 13 (4),297-298. 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 study of a t e s t of formal reasoning. 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 A r l i n t e s t of  formal reasoning. East Aurora, NY: Slosson E d u c a t i o n a l P u b l i c a t i o n s , Inc. A r l i n , P.K.(1984b) Adolescent and a d u l t thought: A s t r u c t u r a l i n t e r p r e t a t i o n . In M.L. Commons, F.A.Richards, & C. Armon (Eds.), Beyond formal o p e r a t i o n s . Late adolescent  and a d u l t c o g n i t i v e development. New York, Praeger. A r l i n , P.K. (1984c) A r l i n t e s t of formal reasoning. East Aurora, NY: Slosson E d u c a t i o n a l P u b l i c a t i o n s , Inc. A r l i n , P . K . (1984, in press a) Developmental c o n s t r a i n t s on d e f i n i t i o n s of the a c a d e m i c a l l y t a l e n t e d and c r e a t i v e l y g i f t e d . A r l i n , P.K. (1984, in press b) Problem f i n d i n g and young a d u l t c o g n i t i o n . In R. Mines and K.S. 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(1974) Concrete and formal o p e r a t i o n s i n very b r i g h t 6- to 11-year o l d s . Human Development, 17, 292-300. Wertheimer, M. (1945) P r o d u c t i v e t h i n k i n g . New York: Harper and Brothers P u b l i s h e r s . 85 APPENDIX A - DATA USED IN THE REGRESSION ANALYSES The f i r s t two columns represent scores on the A r l i n Test Formal Reasoning ( A r l i n , 1984c). The maximum p o s s i b l e score 32. Subsequent columns l i s t scores on the i n s i g h t p u z zles (maximum p o s s i b l e , 8), the IQ t e s t , and the problem f i n d i n g task. 10 1 078 3. 20 11 1 1 22 0. 00 1 6 3 1 28 4. 00 1 6 1 1 05 3. 1 4 10 0 098 3. 20 05 0 086 3. 00 15 1 1 16 3. 00 10 1 1 02 3. 67 1 1 3 1 1 5 3. 00 1 2 0 1 07 3. 38 06 1 082 3. 00 1 2 1 097 3. 00 21 7 121 3. 67 07 1 095 2. 38 1 3 0 085 3. 1 3 09 0 105 3. 75 21 6 090 2. 44 08 1 094 3. 10 1 5 2 101 4. 00 07 2 098 2. 00 21 1 093 2. 83 1 3 2 121 3. 60 1 3 0 096 2. 71 10 4 086 1 . 40 1 4 1 090 4. 00 08 2 088 4. 00 1 2 0 082 1 . 75 1 1 2 101 4. 00 1 1 2 097 0. 00 1 2 2 109 3. 25 1 3 1 1 04 3. 33 08 1 085 4. 00 1 1 1 089 3. 00 1 1 2 093 4. 00 04 0 068 3. 00 1 2 0 076 0. 00 08 0 075 1 . 60 19 2 1 34 4. 00 1 4 1 1 1 0 3. 50 1 3 1 100 3. 20 06 1 086 0. 00 1 4 0 109 4. 00 1 4 7 1 1 7 4. 33 13 2 093 2. 83 07 1 072 2 .50 05 0 072 1 .00 14 0 077 2 .00 06 0 097 4 .00 05 0 089 3 .00 08 1 065 4 .00 1 3 1 099 1 .67 08 0 095 2 .50 09 0 099 3 .40 1 1 0 071 3 .50 08 2 097 3 .67 07 1 088 4 .00 1 1 0 1 05 3 .50 05 1 090 3 .33 1 7 2 1 24 2 .63 1 4 1 1 12 4 .00 1 2 0 1 03 1 .75 18 1 1 36 3 .50 10 2 1 06 4 .00 1 6 2 099 4 .00 04 1 091 4 .00 1 2 2 118 3 .75 08 1 098 3 .00 04 0 083 4 .00 1 4 1 1 10 4 .00 04 1 092 3 .25 09 0 1 10 1 .88 1 2 0 1 1 1 3 .00 13 2 102 0 .00 08 2 091 2 .67 1 3 1 093 4 .00 10 2 1 05 4 .00 87 APPENDIX B - DATA USED IN THE SUPPLEMENTARY ANALYSIS Reading from l e f t to r i g h t , the f i r s t e i g h t scores are the sub-test s c o r e s , 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 reasoning schemata: volume, p r o b a b i l i t y , c o r r e l a t i o n s , combinations, p r o p o r t i o n a l reasoning, forms of 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), mechanical e q u i l i b r i u m , and frames of r e f e r e n c e . The next three scores are scores f o r the three i n s i g h t processes: s e l e c t i v e encoding, s e l e c t i v e combination, and s e l e c t i v e comparison. The f i n a l score i s the problem f i n d i n g score. T h i s data was used i n the supplementary c o r r e l a t i o n a l a n a l y s i s . 1 0 3 0 2 1 3 0 0 0 1 3.20 0 4 3 0 1 1 1 1 1 0 0 0.00 4 2 3 1 2 0 2 2 1 1 1 4.00 4 1 3 1 1 2 1 3 0 0 1 3.14 2 2 2 0 2 0 2 0 0 0 0 3.20 0 1 1 0 0 1 1 1 0 0 0 3.00 1 2 4 1 2 2 1 2 1 0 0 3.00 1 2 3 1 1 0 0 2 1 0 0 3.67 2 1 4 0 0 3 1 0 2 0 1 3.00 3 2 4 0 1 0 1 1 0 0 0 3.38 0 2 1 1 0 0 1 1 0 0 1 3.00 1 3 4 0 1 1 2 0 0 0 1 3.00 1 2 3 4 4 2 2 3 3 3 1 3.67 2 1 1 0 1 0 0 2 0 1 0 2.38 0 1 3 0 2 2 4 1 0 0 0 3.13 4 2 1 0 0 1 1 0 0 0 0 3.75 2 4 4 2 4 0 3 2 2 3 1 2.44 0 2 4 0 1 1 0 0 0 0 1 3.10 4 1 4 0 2 0 2 2 1 0 1 4.00 0 1 4 0 1 0 1 0 1 0 1 2.00 2 4 4 2 4 0 2 3 1 0 0 2.83 2 2 4 0 2 0 1 2 2 0 0 3.60 2 3 4 2 0 1 1 0 0 0 0 2.71 2 2 1 1 2 1 1 0 3 0 1 1 . 40 2 2 2 0 2 0 3 3 0 0 1 4.00 0 1 1 0 2 1 0 3 1 0 1 4.00 2 2 4 0 1 0 1 2 0 0 0 1 .75 2 3 2 0 1 0 1 2 1 0 1 4.00 1 2 3 1 1 1 1 1 2 0 0 0.00 0 1 3 1 1 3 2 1 1 0 1 3.25 2 2 2 1 1 1 2 2 0 1 0 3.33 1 1 3 0 1 1 0 1 1 0 0 4.00 1 2 3 2 0 0 2 1 0 0 1 3.00 2 1 2 1 2 1 3 0 1 0 1 4.00 1 0 1 1 1 0 0 0 0 0 0 3.00 2 2 0 1 3 1 2 1 0 0 0 0.00 1 2 2 0 2 1 0 0 0 0 0 1 .60 4 2 4 2 2 1 1 3 1 0 1 4.00 4 2 4 0 0 1 1 2 0 0 1 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 ) ( ^ ^ r s i < N C N C N 0 0 - - C \ l ( N ' - " - ^ ' - r \ l ' - C N O < 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 ' - ' - O C N l — * - 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 *— •— '— <— *— 1— '— <— CN o 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 89 APPENDIX C - ARLIN PROBLEM FINDING TASK ( A r l i n 1975-76,1977) I n s t r u c t i o n s : In f i v e minutes please make up as few or as many qu e s t i o n s as you can about any obj e c t or o b j e c t s i n f r o n t of you. Your q u e s t i o n s can take any form that you wish them to take. They can be b r a i n t e a s e r s , p u z z l e s to s o l v e , novel q u e s t i o n s . An example i s , "Can you form four t r i a n g l e s out of these s i x match s t i c k s ? " Your q u e s t i o n s can be any type that you wish them to be. The only t h i n g that you have to be sure to do i s to r e f e r to one or more of the o b j e c t s before you i n each of your q u e s t i o n s . Do you have any qu e s t i o n s f o r me before beginning? 90 A r l i n Problem F i n d i n g Task ( A r l i n , 1975-76, 1977) SOME OBJECTS 1 C-clamp 1 black wooden block f2cm X 2 cm.) 1 plain wooden block (1cm x 1 cm.) 1 small index card (3" X 5") with a dime-s ized hole in the center 1 25 cent piece 1 small box top T small box bottom 3 small colored candles 6 wooden matches 10 thumb tacks 2 2-meter long cords 1 pair of scissors 1. 2. 3. 4. 5. 6 8 91 APPENDIX D - SAMPLE PAGE FROM THE ARLIN TEST OF FORMAL REASONING 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. ( A r l i n , 1984c) 92 APPENDIX E - THE INSIGHT PUZZLES On the f o l l o w i n g three pages are some " b r a i n - t e a s e r " p u z z l e s for you to s o l v e . You may take as much time as you need to work out your answers. You may use the s c r a t c h paper p r o v i d e d to f i g u r e out your answers i f you wish. Do you have any q u e s t i o n s before you begin? 93 Name School Grade 1. Suppose you and I have the same amount of money. How much must I give you so that you have ten d o l l a r s more than I? 2. Water l i l i e s double in area every 24 hours. At the beginning of the summer there i s one water l i l y on a l a k e . I t takes 60 days f o r the lake to become covered with water l i l i e s . On what day i s the lake h a l f covered? 3. With a seven-minute hourglass and an 11-minute h o u r g l a s s , what i s the simplest way to time the b o i l i n g of an egg f o r 15 minutes? 4. How c o u l d two men play f i v e games of checkers and each win the same number of games without any t i e s ? 5. If on the l a s t day of February 1980 - and remember, 1980 was a Leap Year - you had gone to bed at seven o ' c l o c k , having set your alarm c l o c k to wake you up at 8:15 i n the morning, how much sl e e p would you have had? 6. In h i s cozy l i t t l e i g l o o near the North Pole, Santa Claus keeps a l a r g e chest of drawers. In the bottom drawer Santa keeps h i s socks. Santa Claus has c o l d feet so he needs a l o t of socks. He has 36 socks i n a l l , and 18 of them are red and 18 of them are green. Since i t ' s very dark at the North Pole, Santa Claus can never see what he's doing, so when he opens h i s bottom drawer to f i s h out a p a i r of socks he i s n ' t a ble to t e l l which c o l o u r he has p i c k e d . To make sure of having one matching p a i r of socks, how many socks must Santa take out of h i s bottom drawer? 7. With nothing at hand except a t h r e e - l i t r e jug and a f i v e -l i t r e jug, how can you measure out e x a c t l y one l i t r e of water? 94 8. I have two c l o c k s . One of them has stopped completely. The other one gains h a l f a minute every 24 hours. Which of the two c l o c k s t e l l s the exact time more often? 95 Process emphasized Puzzle number S e l e c t i v e encoding S e l e c t i v e combination S e l e c t i v e comparison 4,5,6 1,2,3,7 8 Source Puzzle number Sternberg & Davidson (1982,1983) Brandreth (1979) 1,2,3,4 5,6,7,8 * Puzzle 6 i s very s i m i l a r to the f o l l o w i n g problem from Sternberg and Davidson: " I f you have black socks and brown socks in your drawer, mixed i n the r a t i o of 4 to 5, how many socks w i l l you have to take out to make sure of having a p a i r the same c o l o r ? " (1982, p.42). 

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