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The effects of cognitive style, conceptual tempo and training on problem solving processes of fifth grade… Greer, Ruth Nancy Elizabeth 1974

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THE EFFECTS OF COGNITIVE STYLE, CONCEPTUAL TEMPO, AND TRAINING ON PROBLEM SOLVING PROCESSES OF FIFTH GRADE CHILDREN  by  RUTH NANCY ELIZABETH GREER B.A. Carleton University, 1973  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF • THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS < \i *  i n the Department of Educational  Psychology  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA December, 1974  -fi  In p r e s e n t i n g t h i s  thesis  in p a r t i a l  f u l f i l m e n t o f 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 the L i b r a r y s h a l l I  freely available  f u r t h e r agree t h a t p e r m i s s i o n  for  for  I agree  reference and  f o r e x t e n s i v e copying o f  this  that  study. thesis  s c h o l a r l y purposes may be granted by the Head of my Department or  by h i s of  make i t  Columbia,  this  representatives. thesis  It  is understood that copying o r p u b l i c a t i o n  f o r f i n a n c i a l gain s h a l l  not be allowed without my  written permission.  Department of  Educational  The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada  Psychology  Columbia  ii  ABSTRACT  The purpose of the present study was to explore the nature of the relationships between cognitive s t y l e , conceptual tempo, and processes employed by f i f t h grade children during verbal problem solving.  In addition, the effectiveness of programmed i n s t r u c t i o n to  t r a i n children i n the use of analytic and r e f l e c t i v e modes of problem solving was investigated. Cognitive s t y l e (analytic responses on Denney's Cognitive  Style  Test), conceptual tempo (errors and latency of response on Kagan's Marching Familiar Figures Test), verbal creative thinking a b i l i t y , and school achievement were determined for eighty-one children i n three f i f t h grade classes.  Verbal creative thinking a b i l i t y and school  achievement were treated .as covariates.. to three treatment conditions: programmed i n s t r u c t i o n ;  Classes were randomly assigned  1) problem solving t r a i n i n g v i a  2) programmed i n s t r u c t i o n of unrelated  content;  3) no programmed i n s t r u c t i o n . The  treatment, s t y l e , and tempo variables were evaluated i n  terms of their effects upon ten measures of problem solving which included time spent on four c r i t e r i o n problems, quantity and quality of questions asked, and number of solutions offered.  The data indicated  that t r a i n i n g was successful i n increasing time spent on the problems, and quantity and quality of questions asked, but had no e f f e c t on number of solutions offered.  However,  aptitude by treatment interactions  between t r a i n i n g and both s t y l e and tempo indicated that the performance  iii  of non-analytic untrained  and highly impulsive  children was  no better than  children of similar s t y l e and tempo.  While conceptual tempo was  found to account for a s i g n i f i c a n t  amount of the variance i n the three measures of time spent on  the  problems and one measure of question asking, cognitive s t y l e was an important contributor to measures.of problem solving. were repeatedly  Interactions  found between s t y l e and tempo which indicated that these  two variables tended to have a moderating e f f e c t on each other. a c h i l d who  was  highly impulsive performed r e f l e c t i v e l y i f he was  highly a n a l y t i c . i f he was  not  Likewise, a non-analytic  Thus, also  c h i l d performed a n a l y t i c a l l y  also highly r e f l e c t i v e .  While school achievement was creative thinking a b i l i t y was  not related to performance, verbal  found to be p o s i t i v e l y related to problem  solving performance, with verbal o r i g i n a l i t y being a better predictor than either verbal fluency or f l e x i b i l i t y . A l i m i t a t i o n of this study arose from differences i n teaching s t y l e to which the students had been exposed during the eight months preceding this study. As a r e s u l t of the analyses,  i t was  concluded that a reappraisal  of the e f f e c t s of s t y l e and tempo i s warranted, with attention given to the i n t e r a c t i o n between these two variables.  Assessment of the  effectiveness of modified versions of the present self-paced t r a i n i n g program with non-analytic  and highly impulsive  children was  recommended.  iv TABLE OF CONTENTS CHAPTER I. II.  P  A  G  INTRODUCTION  1  REVIEW OF THE LITERATURE  4  Problem Solving  4  Cognitive Style and Conceptual Tempo  22  Effects of Style and Tempo on Problem Solving  33  The Problem  3 5  Research Hypotheses  37  Rationale  III.  39  The Test Problems..  39  The Training Program  41  METHODOLOGICAL CONSIDERATIONS Subjects  44 • 44  Design  44  Description of Covariates  46  Achievement  • 46  Creativity  47  Stimulus Materials. . . .  48  Procedure;  50  P i l o t Testing  5  Pre-Testing  Post-Testing RESULTS S t a t i s t i c a l Procedures  0  Si-  Training  IV.  E  52 • •  5  3  •• •  5  5  55  V  CHAPTER  V.  PAGE  Tests of Hypotheses  58  Additional Findings  81  DISCUSSION  105  Cognitive Style and Problem Solving  105  Conceptual Tempo and Problem Solving  . . . 107  , Training Relationship Between Process and Product  110 . . . 113  Limitations  114  Recommendations f o r Further Research .  117  BIBLIOGRAPHY  120  APPENDICES  129  A.  The Test Problems and C l a s s i f i c a t i o n of Question Type  B.  The Conceptual Style Test and The Matching Familiar Figures Test  C.  The Training Program  D.  Results of Regression Analysis  E.  Tables of Mean Residuals f o r Trained and Untrained Groups with Style and Tempo Trichotomized.  vi  LIST OF TABLES TABLE I  TITLE  PAGE  COMPOSITION OF EXPERIMENTAL CLASSES.  45  SYMBOLS USED IN STATISTICAL ANALYSIS.  57  SUMMARY RESULTS (F-RATIOS) OF REGRESSION ANALYSES FOR ALL DEPENDENT VARIABLES.  59  GROUP MEANS FOR TEN MEASURES OF PROBLEM SOLVING.  60  V  CORRELATIONS BETWEEN ORGANISMIC VARIABLES AND MEASURES OF PROBLEM SOLVING.  64  VI  TESTS (FISHER'S Z) OF SIGNIFICANCE BETWEEN CORRELATIONS FOR TRAINED AND UNTRAINED GROUPS: COGNITIVE STYLE (CST), CONCEPTUAL TEMPO, (MFF ERRORS, MFF TIME) AND MEASURES OF PROBLEM SOLVING.  68  COMPOSITION OF NINE CELLS DERIVED VIA TRICHOTIMIZING RESPONSES ON THE CST AND ERRORS ON THE MFF.  83  MEAN RESIDUALS OF FIVE MEASURES OF PROBLEM SOLVING FOR LEVELS OF THE CST BY MFF ERRORS INTERACTION.  85  COMPOSITION OF NINE CELLS DERIVED VIA TRICHOTIMIZING LATENCY OF RESPONSE AND ERRORS ON THE MFF.  95  MEAN RESIDUALS OF TWO MEASURES OF PROBLEM SOLVING FOR LEVELS OF THE MFF ERRORS BY TIME INTERACTION.  96  II III IV  VII VIII IX  X XI  RESULTS OF REGRESSION ANALYSES FOR TORRANCE SUB-TEST SCORES AND PROBLEM SOLVING MEASURES.  103  vii LIST OF FIGURES FIGURE  TITLE  PAGE.  1  FACTORS IN PROBLEM SOLVING.  12  2  MEAN RESIDUALS OF MEAN TOTAL QUESTIONS FOR TRAINED (Tl) 7 0 AND UNTRAINED SUBJECTS AT THREE LEVELS OF ANALYTIC COGNITIVE STYLE (LOW, MEDIUM, HIGH CST).  3  MEAN RESIDUALS OF MEAN INFORMATION-SEEKING QUESTIONS ASKED BY TRAINED (Tl) AND UNTRAINED (T23) SUBJECTS AT THREE LEVELS OF ANALYTIC COGNITIVE STYLE (CST).  71  4  MEAN RESIDUALS OF MEAN RESIDUAL QUESTIONS FOR TRAINED (Tl) AND UNTRAINED (T23) SUBJECTS AT THREE LEVELS OF ANALYTIC COGNITIVE STYLE (CST).  72  5  TORRANCE SUB-TEST SCORES FOR TRAINED (Tl) AND UNTRAINED (T23) SUBJECTS AT THREE LEVELS OF ANALYTIC COGNITIVE STYLE (LOW, MEDIUM, HIGH).  75  6  MEAN RESIDUALS OF MEAN TOTAL TIME FOR TRAINED (Tl) AND UNTRAINED (T23) SUBJECTS AT THREE LEVELS OF IMPULSIVITY (LOW, MEDIUM, HIGH MFF ERRORS).  77  7  MEAN RESIDUALS OF MEAN RESIDUAL TIME FOR TRAINED (Tl) AND UNTRAINED (T23) SUBJECTS AT THREE LEVELS OF IMPULSIVITY (MFF ERRORS).  78  8  TORRANCE SUB-TEST SCORES FOR TRAINED (Tl) AND UNTRAINED (T23) SUBJECTS AT THREE LEVELS.OF IMPULSIVITY (LOW, MEDIUM HIGH).  80  9  MEAN RESIDUALS OF MEAN TOTAL TIME FOR SUBJECTS AT THREE LEVELS OF ANALYTIC STYLE (CST) AND THREE LEVELS OF IMPULSIVITY (MFF ERRORS).  86  10  MEAN RESIDUALS OF MEAN RESIDUAL TIME FOR SUBJECTS AT THREE LEVELS OF ANALYTIC STYLE (CST) AND THREE LEVELS OF IMPULSIVITY (MFF ERRORS).  87  11  MEAN RESIDUALS OF MEAN TOTAL QUESTIONS FOR SUBJECTS AT THREE LEVELS OF ANALYTIC STYLE (CST) AND THREE LEVELS OF IMPULSIVITY (MFF ERRORS).  88  12  MEAN RESIDUALS OF MEAN INFORMATION-SEEKING QUESTIONS FOR SUBJECTS AT THREE LEVELS OF ANALYTIC STYLE (CST) AND THREE LEVELS OF IMPULSIVITY (MFF ERRORS).  89  viii L i s t of Figures continued. FIGURE  TITLE  PAGE  13  MEAN RESIDUALS OF MEAN RESIDUAL QUESTIONS FOR SUBJECTS AT THREE LEVELS OF ANALYTIC STYLE (CST) AND THREE LEVELS OF IMPULSIVITY (MFF ERRORS).  90  14  MEANS FOR CTBS (A), FLUENCY (B), FLEXIBILITY (C), AND ORIGINALITY (D), FOR SUBJECTS AT THREE LEVELS OF ANALYTIC STYLE (CST) AND IMPULSIVITY (MFF ERRORS).  92  15  MEAN RESIDUALS OF MEAN PRIOR TIME FOR SUBJECTS AT THREE LEVELS OF ACCURACY (MFF ERRORS) AND THREE LEVELS OF REFLECTIVITY (MFF TIME).  97  16  MEAN RESIDUALS OF MEAN PRIOR QUESTIONS ASKED BY SUBJECTS AT THREE LEVELS OF ACCURACY (MFF ERRORS) AND THREE LEVELS OF REFLECTIVITY (MFF TIME).  98  17  MEANS FOR CTBS (A), FLUENCY (B), FLEXIBILITY (C), AND ORIGINALITY (D) FOR SUBJECTS AT THREE LEVELS OF ACCURACY (MFF ERRORS) AND REFLECTIVITY (MFF TIME).  100  ix  ACKNOWLEDGEMENTS  It i s with, pleasure that the writer acknowledges her gratitude to those who have contributed i n various ways to this work: To Dr. Stanley Blank, under whose supervision this work was completed.  Throughout the course of the investigation and i n the :  preparation of the training materials and manuscript, his advice, c r i t i c i s m s and encouragements have been most h e l p f u l . To Dr. Robert Conry, f o r d i r e c t i o n and advice during the data analysis and manuscript  preparation.  To Dr. Nancy Suzuki, whose h e l p f u l suggestions and continued interest i n the work i s g r a t e f u l l y acknowledged. To Darlene Harris, Joyce Fox, and J u l i a Litwintschik f o r t h e i r enthusiastic assistance during data c o l l e c t i o n . To Mr. M. Folkman, Mr. D. MacAulay, and the p a r t i c i p a t i n g p r i n c i p a l s , teachers, and students of the Chilliwack School System whose continued cooperation and interest made this study possible. F i n a l l y , to my husband Galen f o r empathy.  CHAPTER I INTRODUCTION  In the past, research i n both psychology and education has devoted considerable attention to i d e n t i f y i n g a variety of i n d i v i d u a l differences among children, and determining their effects on learning and achievement i n the educational setting.  Perhaps motivated by the apparently awesome  differences i n performance of lower and middle class children, recent i n t e r e s t has focused increasingly on i n d i v i d u a l variations i n cognitive processing. Expanding on the early work of Bruner (1961) , Gardner (1953), Witkin (1962, 1964) and others, Kagan and his associates 1966,  (1963, 1965 a,b;  a,b) have i d e n t i f i e d stable i n d i v i d u a l differences i n two dimensions  of cognition; " s t y l e " and "tempo".  Style refers to the degree to which  one attends to and analyzes stimulus components, while tempo involves the tendency to be r e f l e c t i v e or impulsive when processing information. What i s of p a r t i c u l a r importance i s the relationship that has been found to exist between these two response modes and a variety of cognitive processes such as attention, perception, memory, inductive reasoning, and decision-making.  In a l l of these areas impulsive, non-  analytic individuals have been found i n t e r i o r to t h e i r more r e f l e c t i v e a n a l y t i c peers (eg. Kagan and Moss, 1963; Kagan, et a l . , 1964; Kagan, 1965;  Seigelman, 1969; Drake, 1970; Odom, et a l . , Ault, et a l . , 1972).  In school children these differences result i n poorer performance i n a c t i v i t i e s such as reading, concept learning, and general problem solving (Meichenbaum and Goodman, 1969; Davis and Klausmeier, 1970; Davey, 1971;  2 Butler, 1972;  Mann, 1973).  In a recent review a r t i c l e concerning  i n d i v i d u a l differences i n cognitive processing, Kagan and Kogan (1970) present evidence to demonstrate that the impulsive and non-analytic modes of information processing a f f e c t the e f f i c i e n c y of problem solving at a l l stages i n the search, for solutions.  These individuals incompletely  perceive the subtleties of the stimulus array i n i t i a l l y , f a i l to questions that w i l l c l a r i f y the problem, and then continue to  ask  impulsively  offer solutions without adequate r e f l e c t i o n on their r e l a t i v e merits. In short, the impulsive, non—analytic c h i l d i s characterized by his  use  of Inadequate strategies. It has been demonstrated, however, that these individuals can trained to use  be  the more productive analytic and r e f l e c t i v e response  strategies i n some i s o l a t e d aspects of the problem solving process such as question-asking (eg. Ostfeld and Neimark, 1967; Messer, 1970;  Briggs and Weinberg, 1973;  Baird and Bee,  Denney, 1973).  I t has  1969; further  been demonstrated that children can be trained i n the use of e f f e c t i v e problem-solving strategies v i a programmed i n s t r u c t i o n (Covington and Crutchfield, 1965;  Blank and Covington, 1965;  Ripple and Dacey,  1967;  Stokes, 1968). The intent of the present study was  to explore the p o s s i b i l i t y  of training fifth-grade children i n the use of analytic and r e f l e c t i v e strategies when solving problems through the use of programmed i n s t r u c t i o n . This research addressed i t s e l f to providing  further insight into three  major issues: 1. jThe nature and d i r e c t i o n of the relationship that exists between cognitive s t y l e and processes used during verbal  problem solving. The nature and d i r e c t i o n of the relationship that exists Between conceptual tempo and processes used during verbal problem solving. The r e l a t i v e effectiveness of programmed i n s t r u c t i o n to t r a i n children at d i f f e r e n t points along the cognitive style and conceptual tempo continuums i n the use of analytic and r e f l e c t i v e strategies during verbal problem solving.  4 CHAPTER I I LITERATURE REVIEW  Problem Solving The d e f i n i t i o n of problem solving and the underlying processes thought to be involved vary according  to the t h e o r e t i c a l approach of the  researcher, whether Cognitive Gestalt, Behaviorist, or Information Processing.  Lti the l i t e r a t u r e review to follow, each of these t h e o r e t i c a l  approaches w i l l be de-Mt with.in turn.as Cognitive Gestalt;  they r e l a t e to problem solving.  From the viewpoint of Cognitive Gestalt  thinking, a problem i s a psychological state of discomfort or d i s e q u i l i brium as sensed by the i n d i v i d u a l and solving restores the "psychical balance" (Shulman, 1965).  As e a r l y as 1925 Kbhler referred to this state  of "psychic tension" as r e s u l t i n g when a d i r e c t route to a goal i s blocked. Kohler proposed that the problem solution requires i n s i g h t , a cognitive restructuring or reorganizing of thinking and perception.  For the  G e s t a l t i s t , problem solving i s not the running o f f of p r i o r habits but a process of restructuring and reorganizing.  Changes occur i n perception  rather than i n memory and what i s transferred from one s i t u a t i o n to another are common patterns and configurations, not s p e c i f i c elements. Other Cognitive Gestalt theorists have stressed the importance of a change or recentering of perception as important i n problem solving. Maier (1945) emphasized that the transfer of learning from one s i t u a t i o n to another i s dependent on the relations perceived.  For Maier, problem  solving i s not simply t r i a l and error but i s dependent on what the person has learned before that can be applied to the new s i t u a t i o n .  "Reasoning  5 w i l l not be limited to the way we have learned things, but w i l l depend upon the readiness with which the past learning i s subject to modification and reorganization.  Before o b j e c t i v e l y i d e n t i c a l elements can aid i n  solving the problem, i t i s necessary for the subject to change h i s perceptions or memories so as to make for subjective i d e n t i t y . " (Maier, 1945). Dunker (1945) spoke of the concept of "functional fixedness" as the i n a b i l i t y of the learner to perceive new relations or new uses for elements i n the s i t u a t i o n due to the fixedness of perception.  The process of  solution involves a productive reformulation of the problem and of the elements therein.  Solving problems such as the candle problem he  developed requires a change i n the perception of the possible uses of a box containing matches. More recent writing by cognitive theorists have continued to stress the importance of overcoming f i x a t i o n behavior by the recentering of perception of elements within the problem.  Sheerer (1963) has used his  "9-dot" problem to demonstrate the d i f f i c u l t i e s experienced by i n d i v i d u a l s when habits and conventions prevent recognition of the appropriate use of materials to solve problems. Asher (1963) has written that problem solving i s the process of disrupting previously established concepts, which he contends i s just the reverse of learning.  A s i m i l a r approach has been taken by Maier and  Burke (1966) with regard to the effect of previous learning and experience. The a b i l i t y to u t i l i z e experience  rather than merely to have had i t , i n  their view, becomes- the c r i t i c a l factor i n problem solving.  Generalization  i s a matter of s i m i l a r i t y among problem situations not the s i m i l a r i t y among solutions.  6 To the Cognitive Gestalt t h e o r i s t , behavior i n the problem solving s i t u a t i o n i s conscious, s t r a t e g i c and purposive. perceives,  "The  organism  thinks about, and analyzes his environment; he forms tenable  hypotheses, t r i e s plausible leads, follows rules, reasons, encodes, deduces, makes predictions, and calculates guesses."  (Davis, 1973).  This concept of an active organism i s further exemplified of Bruner (1961).  In Bruner's view, discovery  matter of rearranging y i e l d additional new to simplify the  i n the writings  and problem solving i s a  or transforming the evidence that i s assembled to insights.  Strategies are imposed by the  learner  problem, but ultimately human problem solving goes  beyond the information  given.  The p r i n c i p a l weakness of this theory l i e s i n the fact that i t does not specify what w i l l lead the learner to the reformulation problem i n a p a r t i c u l a r manner. perceptual  of a  While i t does emphasize the need for  acuity and thorough analysis of problem elements, for  r e f l e c t i o n on the implications of past situations to the present problem, and for f l e x i b i l i t y of thought processes, i t offers l i t t l e else of substantive  p r e s c r i p t i v e value to the educator interested i n t r a i n i n g  students to perform e f f e c t i v e l y i n the problem solving s i t u a t i o n . Behaviorist;  A second t h e o r e t i c a l approach to problem solving i s  that of the behavibrists.  An early proponent of the S-R  approach to  problem solving, Thorndike (1898) proposed that problem solving i s simply a complex.form of what i s currently referred.to as operant  conditioning.  The cats i n his puzzle box solved the escape problem by t r i a l and  error  through the gradual stamping.in of rewarded responses and.extinction unrewarded responses.  of  Skinner (1966) however, disagrees with Thorndike"s  concept of t r i a l and error learning.  The problem solving s i t u a t i o n  7 occurs, i t i s Skinner's .position, .when the r e l a t i o n s between a stimulus, a response, and the contingencies  are complex.  The solution involves  finding the response which s a t i s f i e s this complex set of Thus, to aid problem solving, the contingent-relevant  contingencies.  properties must  be made more discriminable. H u l l (1935) proposed the concept of habit-family hierarchies.  Any  given stimulus w i l l have associated with i t a series of responses which are arranged i n h i e r a r c h i c a l order.  The response at the top of the hierarchy  by d e f i n i t i o n has the greatest p r o b a b i l i t y of occuring and the shortest latency.  I f the strongest response i s i n c o r r e c t , then a problem e x i s t s .  Problem solving i s completed when the order of the response hierarchy has so changed that the correct response i s now  dominant.  This change  i n h i e r a r c h i c a l arrangement takes place through t r i a l and error with s e l e c t i v e reinforcement  of correct responses and.extinction of the  incorrect ones. Maltzman (1955) and Kendler and Kendler (1961) have provided further elaboration of this concept.  Maltzman stresses that problem  solving involves both divergent and convergent mechanisms.  Productive  thinking and problem solving .is the consequence of the integration of previously unrelated experiences.  " A l l thinking involves mediated  generalization and hence compounding of previously i s o l a t e d habit segments"  (Maltzman, 1955).  Maltzman further states that "Thinking i n  general, and problem solving i n p a r t i c u l a r may  involve the s e l e c t i o n of  habit family hierarchies as well as the.selection of s p e c i f i c response sequences within the. hierarchy.  The entire habit hierarchy w i l l be  strengthened or weakened, not j u s t individual, responses."  Maltzman has  stressed the importance of c r e a t i v i t y , foriffpproblem solving i s the  8 combining of previously unassociated elements, then the more remote the elements i n the new combination the more creative the process of s o l u t i o n . To Hull's concept of habit family hierarchies, Kendler and Kendler (1961) have added the idea of horizontal and v e r t i c a l processes. While problem solving i s the consequence of combining previously independent  S-R units, these can involve chaining of responses over time  (horizontal) and the simultaneous operation of multiple associations at any one given time ( v e r t i c a l ) . Both Cofer (1957) and Staats (1966) stressed the role of verbal processes i n the f a c i l i t a t i o n of generalized mediation referred to by Maltzman.  Cofer contends  that verbal processes function to impose  r e s t r a i n t s on response systems, f a c i l i t a t e discrimination of elements, assist i n the formation of mediative or associative l i n k s , and are important tools for elaborating hypotheses solutions.  and judging v a l i d i t y of  Within Staats' mediational model, mediating verbal responses  serve to e l i c i t appropriate chains of motor behavior sequences. Harlow's (1949) concept of learning set has also been an important component of behaviorist theory.  I t i s h i s contention that a solution  to a problem does not result from a single learning experience but occurs over multiple learning problems.  "Learning to learn transforms the  organism from a creature that adapts to a changing environment by t r i a l and error to one that adapts by seeming hypothesis and i n s i g h t " .  Both  Luchin (1942) and Maier (1945) as G e s t a l t i s t s , have disagreed with Harlow on the value of sets. optimal performance.  Luchin contends that set interferes with  In his water-jar problems subjects who have  acquired a p a r t i c u l a r set f o r solution w i l l perseverate i n the use of  9 i t even when more e f f i c i e n t strategies are possible.  Maier stresses that  i t i s d i r e c t i o n and not set that i s important to e f f i c i e n t problem solving. new  "Mental set grows out of past experience and carry over into  s i t u a t i o n s , but directions i n thinking a r i s e under the stress of a  problem and when they are new  they cannot be traced to previously  situations."  Thus, while a behaviorist approach would  (Maier, 1945).  stress the importance of previously learned.responses.and their recombination, the cognitive Gestalt approach stresses the perception of s t i m u l i i n each problem s i t u a t i o n and the reorganization the solver imposes on them. Hilgard (1966) has offered a c l a r i f i c a t i o n of the differences between the i n s i g h t f u l versus t r i a l and error explanations solving.  of problem  He states that the difference between association theories  and Gestalt theories l i e s i n the implication of association theories that the possession the solution.  of the necessary past experience somehow guarantees  "While Gestalt theorists would agree that past experiences  w i l l f a c i l i t a t e solution, they object to explanations  i n terms of  previous experience without taking organization into account." G e s t a l t i s t insight i s used to exemplify  For the  the a p p l i c a b i l i t y of the laws of  organization but does not, i n and.of i t s e l f , explain a l l problem solving. As one considers more contemporary writings of  neo-behaviorists  and cognitive psychologists, the schism i n t h e o r e t i c a l approaches to problem solving become increasingly d i f f i c u l t to discriminate. Gagn£ (1966), as a neo-behaviorist,  defines problem, solving as "...an  inferred change, i n human c a p a b i l i t y that results i n the a c q u i s i t i o n of a generalizable rule which i s novel to the i n d i v i d u a l , which cannot have  10  been established by d i r e c t r e c a l l , and which can manifest i t s e l f i n a p p l i c a b i l i t y to the solution of a class of problems.". on the presence of certain previously learned r u l e s .  I t i s dependent  The role of the  problem solver i s to search through these rules to f i n d ones that are relevant to the s i t u a t i o n , and then combine these subrules to formulate an hypothesis which i s v e r i f i e d against r e a l i t y . Ausubel (1968) as a cognitive psychologist, defines problem solving as "...any a c t i v i t y i n which both the cognitive representation of p r i o r experience and the components of a current problem s i t u a t i o n are reorganized  i n order to achieve a designated  objective."  He  emphasizes that e x i s t i n g cognitive structure plays a key role i n problem solving and that.the solution of any given problem involves a reorganization of the residue of past experience so as to f i t the p a r t i cular  requirements of the current problem.  Ausubel further characterizes  problem solving as an organic process i n which the learner f i r s t  defines  the goal and then works backwards from i t i n endeavoring to discover means-ends relationships.  The increasing s i m i l a r i t y between these two  theoretical approaches as exemplified by Gagne and Ausubel i s marked i n comparison to the difference between e a r l i e r theorists such as Thorndike and KBhler. Information Processing:  The t h i r d p r i n c i p a l t h e o r e t i c a l approach  to problem solving i s the Information Processing model, which has evolved from attempts to simulate human cognitive a c t i v i t y with a computer.  In 1958 Newell, Simon, and Show stated that an adequate  theory of problem solving must provide the following:  11 1. 2. 3. 4. 5. 6. 7. 8.  Predict performance of i n s p e c i f i c tasks. Explain how human problem solving takes place. Define what processes are used. Specify the mechanisms used i n performing these processes. Predict i n c i d e n t a l phenomena that accompany problem solving. Show how changes, i n t e r n a l and external, change problem solving behavior. Explain how problem solving s k i l l s are learned. Define what a problem solver has when he has learned the s k i l l s necessary for problem solving.  The viewpoint of these writers was that computer simulation of human problem solving may shed further l i g h t on these issues. Within this f i e l d of research complex problem solving behavior Is b u i l t up of simple symbols manipulation.  An algorithmic  computer  program (Hunt, 1968) i s one which i s generated to examine a l l possible solution-combinations i n some pre-determined order.  Eventually and  inevitably, by pure t r i a l and error, i t locates the correct solution alternative.  Such_ a system, however, f a l l s far short of imitating the  shortcuts seen i n human problem solving.  This deficiency i s overcome  by the use of h e u r i s t i c s , which are rules of thumb which are b u i l t into the system to define hbw to search i n ways that are probably f r u i t f u l and e f f i c i e n t , thus cutting search time, as a l l p o s s i b i l i t i e s are not considered.  A h e u r i s t i c can be conceived of as s i m i l a r to a set or a  readiness to make a s p e c i f i c response to a s p e c i f i c stimulus. While these advances i n computer programming sophistication are of i n t e r e s t , i t i s questionable how much direct use they are i n c l a r i f y i n g human problem solving. particular deficiencies:  Reitman (1965) has c i t e d two  1. The sequence i s too r i g i d and does not  provide for human d i s t r a c t i b i l i t y ; 2. They assume a perfect memory, uncharacteristic of human problem solvers.  They are of value, however,  12 Functions, of Instructions  Internal Processes  Solution Rule  Individual Differences  Matching s p e c i f i c to retained general model -Retaining solution model  Provide solutionmodel  Verification  Provisional i i Rule  Guide Thinking-  Combining Subo r d i n a t e Rules 44*  o  Make cues d i s t i n c t i v e —  •—  o  Search and Selection ^  t t tit Stimulate Recall  Fluency i n making new combinations  -Distinguising r e l e vant and i r r e l e v a n t cues J  Recall of "* Subordinate*" Rules  .Recall of previously learned rules  illtU  Number of •previously rules  Figure 1 Factors i n Problem Solving  (Gagne, 1966)  learned  13  i n that such a study requires a precise and complete, statement of a sequentially organized set of problem solving processes  that w i l l  successfully complete the task, which no other theoretical approach has succeeded i n doing to date. While theoretical approaches to problem solving d i f f e r somewhat there has been considerable consistency over the years i n the stages thought to be involved. 1.  Dewey (1910) proposed a f i v e stage sequence:  recognition of the problem;  2.  location and d e f i n i t i o n of the  problem or the i s o l a t i o n of relevant features: possible alternative solutions;  4.  3.  formulation of  mulling over or reasoning through  the various p o s s i b i l i t i e s to determine the most l i k e l y one;  5.  testing  the selected s o l u t i o n . Wallas (1926) proposed the following four stages: 1.  preparation;  2.  incubation;  3.  i l l u m i n a t i o n ; 4.  verification.  Kingsley and Garry (1957) conceived of the following s i x steps: 1.  A  difficulty is felt;  3.  A search for clues i s made;  t r i e d out;  5.  2.  The problem i s c l a r i f i e d and defined; 4.  Various suggestions  A suggested solution i s accepted;  6.  appear and are  The s o l u t i o n i s  tested. Gagne i n 1966 developed the following model which allows for the examination of the functions of instructions and the e f f e c t of i n d i v i d u a l differences i n past experience, memory, perception, fluency, and evaluative s k i l l , (see Figure 1).  From the standpoint of the educator,  this model seems of p a r t i c u l a r p r e s c r i p t i v e value. I t can be seen from Gagne's model that instructions given to the learner have functional value at each stage of the process. has further a r t i c u l a t e d these functions as follows:  Gagne (1964)  14  1. 2. 3.  To i d e n t i f y terminal performance required To i d e n t i f y parts of the problem s i t u a t i o n To a s s i s t i n r e c a l l of relevant subordinate performance capabilities  4.  To channel thinking i n a given d i r e c t i o n  Colgrove (1970) has further demonstrated the e f f e c t s of i n s t r u c t i o n i n research with adults.  The subjects were told to assume the r o l e of  an i n d u s t r i a l time-study s p e c i a l i s t .  Half of the subjects were further  instructed that this s p e c i a l i s t was a very creative person.  The Control  group were simply given a description of the problem, which involved developing a worker rotation scheme that would maximize performance. The experimental  group given the "creative" instructions produced  s i g n i f i c a n t l y more o r i g i n a l and innovative solutions than did the Control group. Gagne and Smith (1962) gave school aged children the "pyramid problem" to solve, and one half of the subjects were instructed to give reasons f o r each move made, while the Control group was not required to do so.  Instructions to verbalize reasons had the e f f e c t of s i g n i f i c a n t l y  increasing the number of successful solutions over that of the Control group.  The authors conclude.that  such instructions serve.to force  children to analyze steps and to discover general p r i n c i p l e s involved. In a recentlstudy with both school aged children and adults, Robinson (1973) presented  a series of mathematical problems to subjects  In a verbal format and instructed one h a l f of the subjects to draw diagrams representing the relations'presented i n the .problems while T  trying to solve them.  A Control group received no such i n s t r u c t i o n s .  The results indicate superior performance f o r the experimental  group.  Robinson suggests that this superiority i s the r e s u l t of an increase i n  15  the concreteness of the problem, components: when such, drawing Instructions are given, and this aids solution. Other task variables have also been investigated as they affect performance.  Burke, Maier, and Hoffman (1966) examined the function  of hints to successful solution of the "Hat-Rack" problem.  One group of  subjects was given the hint at the onset of the problem while the second group was not given i t u n t i l twenty minutes of attempts at solving the problem.  The results indicate that a greater number of subjects i n the  former group solved the problem i n the ten-minute period following presentation of the hint than i n the l a t t e r group.  The authors conclude  that the hint serves to give d i r e c t i o n and to stop perseveration on inappropriate methods. Safren (1962) investigated the importance of establishing a set p r i o r to working on a problem.  His adults were given a verbal memory  task which served to establish a set for looking for words of a p a r t i c u l a r category p r i o r to solving anagrams.  The superior performance of this  group over a Control who only worked on the anagrams led Safren to conclude that such a set acts as a h e u r i s t i c to decrease the number of solutions that must be considered. Hoffman, Burke, and Maier (1963) designed a study to investigate the e f f e c t of solving a simpler but related problem on subsequent performance on a test problem.  One half of their subjects worked on  several versions of the "hat-rack" problem which allowed for the use of additional equipment than just the two sticks and clamp.  A Control  group had no such p r i o r experience. When performance was examined for both groups on the t r a d i t i o n a l version of this problem, those without previous experience solved the problem faster than those with such  16  experience.  The authors conclude that previous experience may i n h i b i t  productive problem solving by providing too many f a l s e s t a r t s . Attention has also been directed to the examination of i n d i v i d u a l differences within the problem solver as they effect.performance. trends have been examined i n a number of d i f f e r e n t tasks.  Age  Weir (1964) ,  using a p r o b a b i l i t y learning problem found children between seven and ten years of age, unlike adults, respond i n h i g h l y stereotype patterns and seem unable to discard a simple response pattern when i t does not pay o f f . He suggests that these young children may be unable to develop complex hypotheses, or cannot make f u l l use of them. B e i l i n (1967) examined performance i n anagram problems.  With  children from eight to fourteen years of age both solution time and number of problems solved increased with age.  I t i s to be expected that  vocabulary and verbal experience are strongly influentlaihlin such a task. A twenty-questions problem format was used (1968) with s i x to eight year olds.  by.VanHHdrne.aridBBartz  The use of a constraint-seeking  strategy i n information-seeking behavior was observed to increase with age.  Younger children tended to simply guess u n t i l the correct response  i s located by chance.  I t was the conclusion of the authors that the  younger c h i l d lacks the a b i l i t y to impose order on a perceptually disordered environment. Bruner (1961) noted s i m i l a r patterns of response as Van Horn and Bartz, but among d i f f e r e n t individuals of the same age. He found differences i n the degree to which children of the same age attempt to locate constraints before formulating an hypothesis. He c l a s s i f i e d children as using either "organized persistence" or "sheer doggedness".  17  In. Bruner's words, "...the c h i l d who has flooded himself with disorganized information from unconnected hypotheses w i l l Become discouraged and confused sooner than the c h i l d who has shown a certain cunning i n h i s strategy- of getting information - a cunning whose p r i n c i p a l component i s the recognition that the value of information i s not simply i n getting I t But i n Being aBle to use i t . " . A recent study conducted By Ault (19 73)  found similar trends.  F i r s t , t h i r d , and f i f t h grade children were f i r s t divided into two conceptual tempo groups, impulsive and r e f l e c t i v e , using Kagan's (1965) Matching Familiar Figures test.  These children were then oBserved i n a  twenty-questions game of proBlem solving.  The results indicate that  impulsive children at a l l grade l e v e l s ask less mature questions and use a constraint-seeking strategy to a much lesser extent than their r e f l e c t i v e peers.  Score on the twenty-question proBlems also was  correlated negatively with time measures from the Matching Familiar Figures test. Shulman (1965) examined differences i n strategies used By good and poor proBlem-solvers among adults using a "Teacher In-Basket Technique". It was his conclusion that good proBlem solvers were a s s o c i a t i v e l y fluent, cognitively complex, sound interpreters of written passages, r e f l e c t i v e , non—anxious, and spent more time than poor performers i n inquiry a c t i v i t y . There was no s i g n i f i c a n t r e l a t i o n Between grade point average of these college students and performance on h i s task. The relationship Between measured i n t e l l i g e n c e and proBlem-solving performance has also been examined.  French (1958) examined the performance  of adults on a switch-light problem i n which a pattern of l i g h t s must be  18  produced by the manipulation of switches, and found that performance positively- related to measured I.Q.  was  Mendelsohn, Griswold, and Anderson  (1966). also found that a p o s i t i v e r e l a t i o n existed between I.Q. and solving of anagram problems In children.  With the large verbal component  in both of these measures, this finding i s not surprising.  A problem  solving task was developed by Klausmeier and Laughlin (1961) which involved the manipulation of a s p e c i f i e d number of coins and b i l l s to produce a s p e c i f i e d sum.  They observed that as measured I.Q. increased,  a greater incidence i n noting and correcting mistakes independently, i n v a r i f y i n g solutions, and i n the use of a l o g i c a l approach was noted.  As  I.Q. decreased, nonpersistence, o f f e r i n g of incorrect solutions, and the use of  a random approach was noted.  Using the C a l i f o r n i a Test of Mental  Maturity as the measure of I.Q., Harootunian and Tate (1960) found a strong p o s i t i v e correlation with- this score and performance on the D i f f e r e n t i a l Aptitude Test of verbal and abstract reasoning, and on the Davis-Eells Game. Sex differences i n problem solving a b i l i t y indicate that this variable interacts with problem type.  While males tend to outperform  females i n the "two-string" problem (Duncan, .1961), and Maier's mathematical "Horse-trading"problem (Maier, 1970), no difference was found between the sexes i n anagram (Russell and Sarason, 1965) and inductive reasoning problems (Kagan, Pearson, Welch, 1966). One additional subject variable that has received considerable attention as i t relates to problem solving i s c r e a t i v i t y . Maier and Janzen (1970) found that those who  For example  gave a creative innovative  solution on the "Change Worker" problem referred to previously also solved  19  significantly-more objective problems i n which, only- one solution i s possible.  The authors suggest that good problem solvers are also  creative.  The use of such techniques as brainstorming  (Meadow and Parnes,  1959), a t t r i b u t e l i s t i n g (Crawford, 1954), synectics, and  Bionics  (Davis, 19.73) In problem solving situations outside of the purely educational sphere would attest to the popularity of the r e l a t i o n expressed by Maier and Janzen. Davis (1973) has recently proposed a "creative problem solving model" i n which he suggests that the following mental c a p a b i l i t i e s are necessary for both problem solving and c r e a t i v i t y :  abstracting, combining,  perceiving novel r e l a t i o n s h i p s , associating, imagining, f i l l i n g i n missing information,  transforming,  and taking an " i n t u i t i v e leap".  Whether one  views problem solving from a cognitive Gestalt, or a behaviorist approach t h e o r e t i c a l l y , i t seems d i f f i c u l t to argue with Davis that these s k i l l s are involved i n successful problem solving. of Davis that a creative attitude i s a voluntary  I t i s the  contention  act that can be  learned  i n a deliberate manner, and the more e f f o r t invested, the greater quantity of novel ideas. 1968;  To this end, Davis and h i s associates (Houtman,  Houtman, Warren and Roweton, 1969;  and Belcher,  the  Houtman, Warren, Roweton, Mari,  19 72) have developed workbooks for senior elementary and  junior high school students which seek to encourage creative problem solving behavior i n the following ways:  by instructions and  illustrations  dealing with creative attitudes and techniques; by student exercises allow him to f i n d new  that  ideas while p r a c t i c i n g the strategies; and by  example i n the s t o r i e s given. successful problem solving:  These programmes emphasize four steps i n 1.  Clearly understand the problem and  define  20  i t i n general terms; problem; approach;  3.  2.  Think, of d i f f e r e n t approaches to solving the  Think of d i f f e r e n t s p e c i f i c ideas for each problem  4.  Choose the best idea.  The authors report that these  i n s t r u c t i o n a l materials are markedly successful i n improving problem solving strategies and outcomes of the students who them.  have been exposed to  The present writer has not located any research, however, that has  evaluated the e f f e c t of these materials by an outside agent. Another set of similar i n s t r u c t i o n a l materials to those referred to above i s the Productive Thinking Program of Covington, Davies (19.66).  This material i s prepared  C r u t c h f i e l d and  i n i n d i v i d u a l lesson booklets  using a programmed i n s t r u c t i o n format that allows for i n d i v i d u a l student use.  Covington and Crutchfield (1965) report s i g n i f i c a n t gains for an  i n s t r u c t i o n a l group as compared with a non-instructional group of f i f t h and sixth—graders on three types of c r i t e r i a :  paper and p e n c i l problem-  solving tasks, paper and p e n c i l tests of divergent thinking, and attitude and s e l f evaluation measures.  These authors believe the the program acts  primarily to s e n s i t i z e the p u p i l to the use of s k i l l s he already possesses rather than to help him i n developing new  problem solving s k i l l s .  Further,  they note that their results support the notion that there i s a great degree of generalization of the s k i l l s strengthened other studies have confirmed  these findings.  employed these materials with eighth-grade  by the program.  A number of  Ripple and Dacey (1967)  students, and then tested  performance on Maier's "two-string" problem.  Their results indicate that  the subjects i n the i n s t r u c t i o n a l treatment solved this problem s i g n i f i c a n t l y faster than did those i n the noninstructional treatment. 0-968) adapted the Productive Thinking Programme to the format of  Stokes  21  computer assisted i n s t r u c t i o n and found that both, average and high a b i l i t y students receiving this: i n s t r u c t i o n a l outperformed s i m i l a r  non-  instructed children on three post-tests measuring problem-solving a b i l i t y . Contrary to the above findings, Treffinger and Ripple  (1968) found no  difference i n performance of an instructed and non-instructed  group on a  paper and p e n c i l test of problem solving a b i l i t y following exposure to the Productive Thinking Programme. Other forms of t r a i n i n g have also been investigated as they e f f e c t l a t e r performance.  Blank and Covington (1965) developed programmed  i n s t r u c t i o n a l materials during problem solving.  to induce grade s i x children to ask questions Those who  received  this t r a i n i n g improved i n  performance on an o r a l test of problem solving and on a written achievement t e s t , while a non-instructed  science  group did not.  An i n t e r e s t i n g project designed to improve problem solving s k i l l s of senior public school students has been reported by Robinson, T i c k l e and Brison (1972).  These authors have developed i n s t r u c t i o n a l materials  which t r a i n children i n the use of the various  c l a s s i c a l experimental  models; matched groups, randomization, c o r r e l a t i o n a l studies, case studies, and a " r e a l - l i f e " model, and have achieved promising results with children so instructed. Anderson (1965) was  Further evaluation i s s t i l l i n progress.  also successful i n teaching what he termed  "advanced problem solving s k i l l s " to f i r s t grade children through training.  The  task the children were required to learn were twenty-seven  different conjunctive requires  concepts using a selection paradigm.  This task  that the c h i l d be able to vary each factor i n the stimulus display  22  successively while holding a l l other factors constant, a technique normally very d i f f i c u l t f o r young children.  The t r a i n i n g took a  programmed i n s t r u c t i o n format, But functioned as a s c r i p t used By a trainer i n i n d i v i d u a l sessions with each c h i l d .  Results indicate that on  t r a i n i n g tasks presented l a t e r , the trained group solved more problems with fewer unnecessary t r i a l s than the control group.  The trained group  also solved more transfer problems and solved these more e f f i c i e n t l y than did  the control group.  Cognitive Style and Conceptual Tempo Over the past several decades a number of investigators have directed t h e i r ' e f f o r t s toward the i d e n t i f i c a t i o n of i n d i v i d u a l differences i n mode of cognitive functioning.  Gardner, i n 1953 used the terms  " l e v e l e r s " and "sharpeners" as i n d i c a t i v e of contrasting cognitive attitudes, p a r t i c u l a r l y at the perceptual l e v e l .  He suggested that these  attitudes r e f l e c t i n d i v i d u a l differences i n adaptive modes or the method of organizing and experiencing the stimulus world.  Sharpeners "analyze  out" suBtle differences i n a stimulus array, their perception of the world Being geared toward "oBjective v e r i t y " .  Levelers, on the other hand,  appear not to act upon their awareness of differences, and adopt a more relaxed approach to perception which Gardner terms "adaptive economy". In a suBsequent research report i n 1960, Holtzman and Gardner again used the terms " l e v e l e r s " and "sharpeners" to descriBe differences i n memory- organization.  systematic  They contend that the l e v e l i n g -  sharpening dimension r e f l e c t s " . . . s t r u c t u r a l p r i n c i p l e s of personality organization that give a p a r t i c u l a r cast to an individual's cognitive  23  behavior..." and describe opposite poles- of a dimensional p r i n c i p l e of cognitive control concerning  the degree of assimilation between  perceptual processes and memory traces.  L e v e l l i n g leads to omission of  inconsistencies, condensation of elements, and general s i m p l i f i c a t i o n of r e c a l l of material due to undifferentiated memory organization. contrast, sharpening brings about r e c a l l dominated by accurate  In reporting  of d e t a i l i n the o r i g i n a l perception brought about by a highly d i f f e r e n t iated memory- organization.  This difference was further substantiated  i n a recent study (Ausubel and Schwartz, 1972) which examined retention of prose material for levelers and sharpeners.  Sharpeners r e c a l l e d more  s p e c i f i c d e t a i l and made fewer errors and misinterpretations of content than did l e v e l e r s . The work of Witkin and h i s associates (1962) with reference to field-dependent  and field-independent  cognitive styles follows l o g i c a l l y  from this early work of Gardner and Holtzman.  Witkin contends that this  dichotomy r e f l e c t s a global versus a n a l y t i c or highly d i f f e r e n t i a t e d way of experiencing  and perceiving.  Cognitive s t y l e refers to "...the s p e c i f i c  class of structures comprised of enduring arrangements of cognitive processes that shape the expression of environmental conditions."  of intentions under p a r t i c u l a r types  (Witkin, 1964).  These structures include  cognitive controls, defense mechanisms and i n t e l l e c t u a l structures. While the fieId-dependent i n d i v i d u a l makes use of less d i f f e r e n t i a t e d processing of information t y p i c a l of a more rudimentary form of responding of the system as a whole, the field-independent,  a n a l y t i c s t y l e brings  about greater d i f f e r e n t i a t i o n and highly s p e c i f i c responding c h a r a c t e r i s t i c of a more advanced l e v e l of functioning.  These two modes of functioning  24  are particularly- important i n situations whicfL require the i n d i v i d u a l to s e l e c t i v e l y attend to relevant s t i m u l i i n the face of other i r r e l e v a n t features.  Witkin further suggests that s t y l e of cognitive functioning  employed w i l l have far-reaching  Implications:  " I n t e l l e c t u a l problems that c a l l for a high degree of creative a c t i v i t y but do not involve perception d i r e c t l y , often also require that 'parts' be separated from the context i n which they are imbedded and brought into new relationships. I t i s l i k e l y that i f a person has this basic a b i l i t y to 'break up' a configuration i t w i l l be manifest not only i n straight-forward perceptual s i t u a t i o n s , but i n problem solving situations as w e l l . " (Witkin, Dyk, Faterson, Goodenough, Karp, 1962) In a recent .study conducted by J . K. Davis (1973) the e f f e c t of global versus analytic cognitive s t y l e was assessed with regard to hypothesis testing strategies employed.  Witkin's Hidden Figures Test was  used to determine cognitive s t y l e of university students. formation  In a concept  task which involved the simultaneous presence of four  dimensions, the analytic subjects gave evidence of more p r o f i c i e n t hypothesis testing behavior. of errors:  1.  The global subjects frequently made two types  Switching hypotheses i n absence of feedback which would  indicate one should do so, and 2.  Responding with a hypothesis that did  not f i t the relevant dimensions given.  The author concluded that this  could be due to either faulty memory, inadequate attention, or f a u l t y u t i l i z a t i o n of feedback. Kagan, as a developmentalist,  began to investigate differences i n  cognitive s t y l e i n young children i n 1963.  In an early study with Lee  and Rabson (1963) Kagan operationalized a n a l y t i c versus non-analytic mode of information processing i n terms of the classes of responses given i n a  25 categorization task.  These response categories were " a n a l y t i c " :  on objective elements of s i m i l a r i t y that were part of the t o t a l "relational":  stimulus;  involving p a i r i n g based on a functional relationship  between obvious aspects of the t o t a l stimulus; cal":  based  and " i n f e r e n t i a l - c a t e g o r i -  including conceptual pairings that are based on some i n f e r r e d  quality or language convention.  He found that children classed as analytic  learned an analytic concept i n a paired-associate faster than non-analytic  task s i g n i f i c a n t l y  children, and that these non-analytic  learned a r e l a t i o n a l concept faster.  children  Kagan suggests that i t i s the  children's d i f f e r i n g a b i l i t y to v i s u a l l y analyze presented material into component parts that resulted i n these findings. A paper by Kagan and Moss i n 1963  added further to the developmental  components of this difference between analytic and non-analytic information  processing.  modes of  While these authors noted that there are general  developmental trends toward l e s s - g l o b a l perceptions of the world to more a r t i c u l a t e d and greater d i f f e r e n t i a t i o n of perception,  they found  evidence for stable i n d i v i d u a l differences i n this capacity to analyze which was  independent of a l l sub-test  picture arrangement section.  scores on the W.I.S.C. except the  There was  also marked difference i n the  willingness to persevere at a d i f f i c u l t task among these two  groups of  children. Kagan, Rosman, Day, an additional behavioral  Albert and P h i l l i p s (1964) began to look at  component of the analytic-non-analytic  dimension.  In addition to the i n c l i n a t i o n to v i s u a l l y analyze and to d i f f e r e n t i a t e s t i m u l i , they added the component of r e f l e c t i o n versus impulsivity of response mode.  They found s i g n i f i c a n t negative correlations between the  26 impulsive reporting of a response and the degree of d i f f e r e n t i a t i o n or v i s u a l analysis imposed on the s t i m u l i presented to the children. In addition, by structuring the experimental s i t u a t i o n i n such a way that a r e f l e c t i v e attitude was encouraged, they found an increase i n a n a l y t i c responses.  In 1966 Kagan operationalized the dimension of r e f l e c t i o n -  impulsivity as the decision time to solution i n situations of high response uncertainty.  He contends that this mode of responding i s linked  tosome fundamental aspect of the child's personality, not unlike the thinking of Gardner with respect to "levelling-sharpening". "A r e f l e c t i v e d i s p o s i t i o n displays a s t a b i l i t y over time and a generalltyaacross tasks that i s unusual for psychological attributes, and tempts one to conclude that this response tendency must be a basic component of the individual's behavioral organization." (Kagan, 1966). What i s of considerable  importance i n educational  relationship between the impulsive  terms i s the  "conceptual tempo" and high error rate  i n a v a r i e t y of cognitive tasks, independent of scores on the verbal subtest of the WISC (Kagan, 1965).  For example, Kagan found that  impulsive  f i r s t and second grade children made more errors i n reading both i n d i v i d u a l words and short passages (Kagan, 1965), had higher error  scores  on inductive reasoning tests (Kagan, Pearson, and Welch, 1966), reported more errors of commission i n a s e r i a l learning task (Kagan, 1966), and showed autonomic patterns  (cardiac and respiratory measures) c h a r a c t e r i s t i c  of less attention than children who were r e f l e c t i v e and preferred an analytic conceptual s t y l e (Kagan and Rosman, 1964). this higher error rate demonstrated by impulsive  Kagan suggests that  children i s due to t h e i r  f a i l u r e to take time to r e f l e c t on possible a l t e r n a t i v e hypotheses and to welgh_ each before responding, being more concerned with providing a quick,  but not n e c e s s a r i l y correct response. avoidance c o n f l i c t s i t u a t i o n .  "Each, c h i l d i s i n an approach-  If the strength of the approach, gradient  i s stronger (seek quick success) he w i l l be impulsive; i f the strength of  the avoidance gradient i s stronger (anxiety over making a mistake),  he w i l l be r e f l e c t i v e . "  (Kagan, 1966, p.  155).  In summary, the difference between analytic and non-analytic i n d i v i d u a l s , as seen by Kagan i s determined by two behavioral components: 1. 2.  The tendency to v i s u a l l y analyze stimulus arrays into d i f f e r e n t i a t e d components The tendency to be impulsive or r e f l e c t i v e i n response mode when solving a problem.  Since these e a r l i e r investigations by Kagan and h i s associates a considerable number of further studies have been reported by other researchers which are i n general agreement with the i n i t i a l proposals of Kagan.  Perceptual s k i l l s were examined i n four studies (Siegelman,  Drake, 1970;  Odom, Mclntyre and Neale, 1971;  1969;  Ault, Crawford, J e f f r e y ,  1972)  comparing the performance of r e f l e c t i v e and impulsive school children using an eye marker apparatus, videotapes of eye movement, or an apparatus that required the c h i l d to manipulate a d i a l to bring s t i m u l i into focus. In a l l cases performance was Familiar Figures Test (MFF) conclusion.  examined using versions of Kagan's Matching items.  A l l the above authors came to the same  Reflective children look longer at each item, and make  s i g n i f i c a n t l y more comparisons with the standard item before making decisions.  Impulsives  ignore s i g n i f i c a n t l y more alternatives than  r e f l e c t i v e s and make a decision before a l l alternatives have been considered.  Siegelman suggested  that impulsives may  u t i l i z e an  impoverished  input such that the f i r s t p l a u s i b l e alternative becomes the preferred  28  candidate while r e f l e c t i v e s canvass the array more extensively, sample from i t more i m p a r t i a l l y and spend longer per look at a l t e r n a t i v e s . Odom, Mclntyre and Neale also noted that r e f l e c t i v e s process d i s t i n c t i v e features to a greater extent than  impulslves.  The relationship between tempo and measures- of academic achievement and a b i l i t y have also been further examined.  Ault (1972) found no  r e l a t i o n between cognitive tempo and achievement motivation  i n school.  Christos (1972) found tempo was not meaningfully related to standardized school measures of achievement, academic aptitude, age, sex, or s o c i a l class.  Ward (1968) compared scores on theePeabody Picture Vocabulary  Test and tempo and found no s i g n i f i c a n t c o r r e l a t i o n . compared performance of r e f l e c t i v e and impulsive  Bierbryer (1972)  children on the Torrance  test of f i g u r a l c r e a t i v i t y and found that the two tempo groups did not significantly differ. impulsives  Kopfstein  (1973) also found no difference between  and r e f l e c t i v e s i n an experimental s i t u a t i o n that allowed him  to assess r i s k - t a k i n g behavior. In spite of the i n s i g n i f i c a n t differences between the two groups on the variety of measures mentioned above, impulsive  and r e f l e c t i v e  children continue to be found to d i f f e r on a number of cognitive tasks. Both Davey (1971) and Butler (1972) found impulsive  children to be  markedly i n f e r i o r to r e f l e c t i v e children on measured reading achievement. Meichenbaum and Goodman (1969) found impulsive kindergarten  children  demonstrated less a b i l i t y to i n h i b i t motor behavior by covert instruction than r e f l e c t i v e peers.  self-  Mann (1973) examined the latency i n  making decisions of r e f l e c t i v e and impulsive  children i n four settings:  toy choice, Mischel decisions, a goal-setting game, and s p e l l i n g decisions,  29  and found that r e f l e c t i v e children took s i g n i f i c a n t l y longer i n making decisions but no difference existed i n the quality of decisions made by the two groups.  Ault (1973), as- previously noted, found impulsive  children used a less mature and less e f f i c i e n t strategy i n solving problems than their r e f l e c t i v e peers-. A variety of procedures have been employed to attempt to modify both the analytic-non-analytic cognitive s t y l e and the reflective-impulsive conceptual temp.  In 1967 Ostfeld and Neimark administered one version of  Kagan's Conceptual Style Test (CST) to seven and eight year olds and divided them into analytic and non-analytic groups on this basis.  These  children were then retested on a second version of the CST, but one h a l f of each cognitive s t y l e group was required to delay their response.  The  authors found that by forcing an i n c r e a s e i i n response latency, an increase i n the proportion of analytic responses was seen. in the Control groups.  No such change occurred  Baird and Bee (1969) examined the effects of  reinforcement i n the form of candy on the production of analytic or nonanalytic responses on the CST. Not unexpected, they found that the category of response that was reinforced occurred to a greater extent than the non-reinforced response mode for these f i r s t and second grade children. Davis and Klausmeier (1970) examined the performance of a n a l y t i c and nonanalytic children i n a concept learning task.  He then required one h a l f  of the children from each cognitive s t y l e group to verbalize a l l attributes of each stimulus that was presented to them before responding.  The results  indicate that this procedure resulted i n s i g n i f i c a n t l y better performance of the non-analytic experimental children over their l i k e Control group. The authors suggest that this procedure forces the c h i l d to d i f f e r e n t i a t e  30  the relevant variable, something that these non-analytic children tend to do inadequately. Denney 0-972) exposed.non-analytic and impulsive second grade children to a female model who displayed an analytic and r e f l e c t i v e pattern of behavior on the CST.  The r e s u l t of this exposure  was an increase i n both latency of response and i n number of analytic responses by these children when exposed to a version of the CST.  This  difference lasted for fourteen days, as delayed post-testing indicated. Attempts to change tempo are also numerous.  Messer (1970) induced  anxiety over adequacy of i n t e l l e c t u a l performance i n young school children and found that this treatment resulted i n an increase i n response latency for both r e f l e c t i v e and impulsive children.  Briggs and Weinberg (1973)  found that by t r a i n i n g children to delay responses on items similar to the match to standard items on the MFF resulted i n an increase i n response latency and a decrease i n errors on subsequent testing on MFF items.  No such change was noted i n a Control group not given training. In an interesting cross-modal study conducted by Butter (1971)  children were trained to delay responses i n match to standard items presented i n either the v i s u a l or haptic mode.  This training resulted  i n a s i g n i f i c a n t increase i n response latency and decrease i n errors for both training groups over that of a control group when tested on the v i s u a l l y presented MFF  test.  It has been noted previously that impulsive children d i f f e r from t h e i r r e f l e c t i v e counterparts i n the use of constraint-seeking strategies i n a twenty-questions problem format.  Denney (1973) d i f f e r e n t i a t e s two  types of questions used by children i n such a task. Hypothesis-seeking questions are those which test s p e c i f i c s e l f - s u f f i c i e n t hypotheses that  31 have no r e l a t i o n to previous questions asked, and result i n pure guessing behavior.  This type of question i s found to be more t y p i c a l of impulsive  children.  Constraint-seeking questions are more general questions  r e l a t i n g to previous questions and seek an answer which would eliminate a number of alternatives.  These are more t y p i c a l of the r e f l e c t i v e c h i l d .  Denney found that by i n s t r u c t i n g seven— and eight-year—olds to delay t h e i r responses i n this twenty-questions problem, more constraint-seeking questions occur than i n a control group not so instructed. Modelling has been used i n a number of studies to bring about changes i n conceptual tempo.  Debus (1970) using a l i v e model with  t h i r d graders and Ridberg, Parke, and Hetherington (19 71) using a filmed model with, fourth graders found that the observation of a r e f l e c t i v e model resulted i n more r e f l e c t i v e patterns of behavior of these children on subsequent tests groups who  with the MPF.  No difference occurred i n control  did not observe a model i n either of these studies.  An investigation conducted by Yando and Kagan (1968) would suggest that young children are susceptible to very subtle cues concerning tempo i n the classroom s e t t i n g . children was determined  In this study the tempo of both teachers and  at the beginning of the school year.  of the school year children were again tested to determine  At the end  their tempo.  Results indicate that exposure to an experienced r e f l e c t i v e teacher resulted i n an increase i n r e f l e c t i v i t y i n the children, while such a difference did not occur for children taught by an impulsive teacher. Meichenbaum and Goodman 0-971) trained impulsive second grade children to t a l k to themselves on items similar to those used i n the MFF test.  Retesting on the MFF following training indicated an increase i n  32  response latency- and a decrease i n errors.  The authors report that t h i s  difference i n response mode also transferred to performance on the Porteus Maze test and on performance scores- on the WISC.  Retesting on the MFF one  month l a t e r indicated that the change i n behavior continued to be seen. The deficiencies noted e a r l i e r i n the perceptual  s k i l l s of  impulsive children led several investigators to attempt to t r a i n such children i n more systematic strategies.  Egeland (1973) used items  s i m i l a r to those employed i n the MFF to t r a i n children.  During t r a i n i n g  the c h i l d was required to look at each a l t e r n a t i v e , to break each a l t e r native down into parts, then to compare each part successively over alternatives, and f i n a l l y to compare each alternative with the standard. The results of performance on the MFF following t r a i n i n g indicate s i g n i f i c a n t l y longer latencies and lower error scores than a non-trained group of controls.  The authors also note that the trained group showed  improvement on the vocabulary and comprehension  subtests  of the Gates-  MacGinitie-Reading Test. Roettger (1970) trained a group of impulsive kindergarden children in e f f i c i e n t scanning strategies using items from the Word Discrimination Test.  The children were taught to compare each word l e t t e r by l e t t e r to  make the necessary discrimination.  An increase i n response time and a  decrease i n errors over that of an untrained  control group on MFF items  was found. It would appear from the above that both dimensions of the cognitive s t y l e variable; degree of analytic responding, and tempooof response are modifiable  and that changing a child's s t y l e as measured by  the CST or the MFF can transfer to a variety of other tasks.  33  Effects of Cognitive Style and Conceptual Tempo on Problem Solving In a recent comprehensive review of the l i t e r a t u r e  concerning  individual differences i n cognitive processing Kagan and Kogan (1970) have suggested that the analytic-non-analytic and the impulsive-reflective dimensions affect the e f f i c i e n c y of problem-solving process.  at a l l stages i n the  In the f i r s t phase when the problem i s being decoded, the  thoroughness of the i n i t i a l discrimination of the stimulus  array  constituting the problem, and the i d e n t i f i c a t i o n of relevant components w i l l effect  a l l subsequent stages of the problem solving sequence.  Gardner, Holtzman, Witkin, and Kagan have a l l noted stable i n d i v i d u a l differences i n the degree to which subtle differences insstimulus are discriminated and attended to.  arrays  This finding has further been  substantiated by the research studies of Siegelman, Drake, Odom, and Ault concerning  differences i n perceptual s k i l l s of children d i f f e r i n g on  cognitive s t y l e and conceptual  tempo dimensions.  Children who  are high i n  this a b i l i t y to "attend and discriminate" should demonstrate more e f f i c i e n t problem solving than impulsive non-analyzers, and such would appear to be the case from the research evidence of Bruner (1961), Ault (1973), and Shulman (1967). The next important step i n problem solving i s information  gathering,  either by the r e c a l l of previously learned r u l e s , as suggested by Gagne's model, and/or by asking questions whose answers w i l l f i l l i n missing or impose further organization on e x i s t i n g information.  data  It would appear  j u s t i f i e d to conclude, on the basis of the writing of Holtzman and Gardner with regard to memory organization, and the research of Kagan (1965, 1966), Davey (1971), and Butler (1972) that children at the  non-  34  a n a l y t i c and  i m p u l s i v e ends, o f the s t y l e and  tempo continuums are  a b l e to r e c a l l and u t i l i z e p r e v i o u s l y e x p e r i e n c e d a d d i t i o n , the demonstrated i n f e r i o r i t y o f these asking s k i l l s  In  children i n question-  i n a number of s t u d i e s reviewed above would a l s o l e a d one  p r e d i c t i n f e r i o r performance at t h i s stage In the next g e n e r a l stage use  information.  of problem s o l v i n g when the c h i l d must  n o n - a n a l y t i c c h i l d i s a g a i n at a disadvantage. data base, f a i l s  The  He  impulsive  i s working from a more  to r e f l e c t s u f f i c i e n t l y on the i m p l i c a t i o n s  o f the i n f o r m a t i o n d e r i v e d , and a wrong i n f e r e n c e .  to  i n the problem s o l v i n g p r o c e s s .  the i n f o r m a t i o n a v a i l a b l e to d i s c o v e r p o s s i b l e s o l u t i o n s , the  impoverished  less  evidence  as a consequence i s more l i k e l y to choose r e p o r t e d by Kagan (1966) that  c h i l d r e n make more e r r o r s o f i n d u c t i v e r e a s o n i n g would support  impulsive this  contention. In the f i n a l stage of the problem s o l v i n g p r o c e s s v e r i f i c a t i o n against r e a l i t y occurs, a g a i n at a disadvantage. "adaptive  i n which  hypothesis  the i m p u l s i v e n o n - a n a l y t i c c h i l d i s  H i s p e r c e p t i o n of r e a l i t y i s geared toward  economy" as opposed to " o b j e c t i v e v e r i t y "  (Gardner, 1953)  which  can be expected to l e a d to l e s s s t r i n g e n t t e s t i n g o f p o s s i b l e hypotheses. In a d d i t i o n , the i m p u l s i v e q u a l i t y o f h i s response tempo would r e s u l t i n the r e p o r t i n g of a q u i c k but not n e c e s s a r i l y c o r r e c t response w i l l l e a d to sub-optimal  performance.  t y p i c a l of the i m p u l s i v e  Kagan has  suggested t h a t the p a t t e r n o f  c h i l d when f a c e d w i t h a problem to s o l v e i s as  follows: Problem  behavior  ^ Inadequate d i s c r i m i n a t i o n of components  Impulsive  s e l e c t i o n of a solution,  Impulsive  s e l e c t i o n of a second s o l u t i o n  Failure,  •> A n x i e t y  + Failure  35 Anxiety  > Withdrawal from the problem s i t u a t i o n .  Thus, the c h i l d perseverates i n the use of an inadequate strategy brought about by his f a i l u r e to thoroughly analyze the elements i n the problem, his f a i l u r e to ask questions that w i l l c l a r i f y the problem, and by continuing to impulsively o f f e r solutions without adequate r e f l e c t i o n on their r e l a t i v e merits. Considerable research evidence exists to suggest, however, that the tendency of the c h i l d to employ these inadequate strategies i s modifiable.  In the l i t e r a t u r e reviewed, i t was  demonstrated that problem  solving s k i l l s , cognitive s t y l e , and conceptual tempo can be changed, given appropriate t r a i n i n g procedures.  independently  I t has also been  demonstrated that changing cognitive s t y l e and conceptual tempo w i l l result i n changes i n some isolated aspects of problem solving behavior. For example, i t w i l l be r e c a l l e d that Denney (1973) increased the l e v e l of maturity of question-asking s k i l l s i n impulsive children by  imposing  a r e f l e c t i v e response mode on them.  The Problem The purpose of the present study was nature of the relationships that may  to further investigate the  exist between cognitive s t y l e ,  conceptual tempo, and processes used during problem solving.  In addition,  this study sought to explore the p o s s i b i l i t y of improving the problem solving s k i l l s of impulsive, non-analytic children through exposure to t r a i n i n g materials i n the programmed instruction format which were designed to teach, r e f l e c t i v e and analytic modes of responding at a l l stages of the problem solving process.  Furthermore, the research sought to  36 determine the r e l a t i v e effectiveness of these techniques with children at d i f f e r i n g points: along the analytic-non-analyttc and the impulsiver e f l e c t i n g continuums.  These p o s s i b i l i t i e s were explored by- adapting to  a printed programmed i n s t r u c t i o n format materials from several sources. These included a combination of various training techniques  found to be  successful i n previous research designed to change problem solving and/or cognitive s t y l e and conceptual tempo, as w e l l as materials developed by the present  researcher.  To provide an adequate measure of the v a r i e t y of s k i l l s involved i n problem solving, each c h i l d was administered the form of short mysteries following experimental  a set of four problems i n  to be solved i n i n d i v i d u a l testing sessions  treatment (see Appendix A).  These problems were  presented with a paucity of information so that the c h i l d must have asked questions  f o r solution to occur.  In addition, a l l problems were structured  i n such a manner that more than one solution was possible. were employed to assess problem solving performance.  Ten measures  These were as  follows: A.  Time Factors 1.  Mean Total Time - Time from presentation of a problem to when the subject indicates by turning over the "Finished" card that he has no further questions to ask or solutions to o f f e r , to a maximum of f i v e minutes.  2.  Mean P r i o r Time - Time from presentation of a problem to when the subject indicates by turning over the "Ready" card to indicate that he i s prepared to o f f e r h i s f i r s t s o l u t i o n . (Did not include those solutions phrased as hypothesis-seeking questions).  3.  Mean Residual Time - Time from o f f e r i n g of f i r s t solution u n t i l the subject indicates that he has no further questions to ask or solutions to o f f e r , by turning over the "Finished" card.  37  B.  C.  , Ques t ion-Askin g.; B ehavio r: 4.  Mean. Information-Seeking Questions Asked .-, Those questions which seek factual information about some parameter of a stimulus element i n thepproblem.  5.  Mean Constraint-Seeking Questions Asked - Those questions which relate to previously asked questions and seek an answer which would eliminate a number of alternative solutions (Denney, 1973).  6.  Mean Hypothesis-Seeking Questions Asked - Those questions which test s p e c i f i c s e l f - s u f f i c i e n t hypotheses that have no r e l a t i o n to previously asked questions (Denney, 1973).  7.  Mean Total Questions Asked - The mean number of questions asked over four problems, regardless of type of question.  8.  Mean P r i o r Questions Asked - Those questions asked, regardless of type, from the i n i t i a l presentation of a problem u n t i l the subject indicates by turning over the "Ready" card that he i s prepared to o f f e r h i s f i r s t solution.  9.  Mean Residual Questions Asked - Those questions asked a f t e r the f i r s t solution i s offered, u n t i l the subject indicates that he has no further questions to ask or solutions to o f f e r , by turning over the "Finished" card.  Solutions: 10.  Total Solutions: The t o t a l number of solutions offered by the subject as indicated by h i s turning over the "Ready" card. (Did not include those stated as Hypothesis-seeking questions.) The performance of three separate groups of fifth-grade children  were assessed: those that had received the problem solving t r a i n i n g program (TI);  those that had received programmed i n s t r u c t i o n whose content  was unrelated to problem solving (T2); those that had received no programmed i n s t r u c t i o n (T3).  The i n c l u s i o n of the T2 group acted as a  control for any influence which might r e s u l t from exposure to programmed i n s t r u c t i o n a l materials, independent of content. The three major substantive hypotheses that were explored were: 1.  Problem solving performance of children at d i f f e r i n g points along the cognitive s t y l e continuum w i l l increase as measured a n a l y t i c a b i l i t y increases.  38 2.  Problem solving performance of children at d i f f e r i n g points along the conceptual tempo continuum w i l l increase as measured r e f l e c t i v i t y increases.  3.  Training i n problem solving w i l l be equally e f f e c t i v e for children at a l l points along the cognitive s t y l e and conceptual tempo continuum and with result i n the trained group being superior i n problem solving as measured by the ten dependent variables.  While this study was p r i n c i p a l l y intended to be exploratory i n nature, a number of s p e c i f i c research hypotheses were tested, based on the findings of previous research i n this area.  These were as follows:  1.  In terms of a l l measures of problem solving except Mean Hypothesis-seeking Questions Asked, the trained group (Tl) w i l l spend more time, ask more questions, and provide more solutions than the untrained groups (T2, T3).  2.  The two untrained groups (T2, T3) w i l l ask more Hypothesisseeking Questions than the trained group ( T l ) .  3.  No difference w i l l exist between the two untrained groups (T2, T3) on any of the ten measures of problem solving.  4.  The number of analytic responses on the CST w i l l be p o s i t i v e l y related to the scores on a l l measures of problem solving except mean hypothesis-seeking questions asked f o r a l l experimental groups combined.  5.  The number of analytic responses on the CST w i l l be negatively related to the mean number of hypothesis-seeking questions asked for a l l experimental groups combined.  6.  The t o t a l number of errors on the MFF w i l l be negatively related to the scores on a l l measures of problem solving except mean hypothesis-seeking questions asked f o r a l l experimental groups combined. T The t o t a l number of errors on the MFF w i l l be p o s i t i v e l y related to the mean number of hypothesis-seeking questions asked for a l l experimental groups combined.  7. 7.  8.  The mean latency of response on the MFF w i l l be p o s i t i v e l y related to the scores on a l l measures of problem solving except mean hypothesis-seeking questions asked f o r a l l experimental groups combined.  9.  The mean latency of response of the MFF w i l l be negatively related to the mean number of hypothesis-seeking questions asked for a l l experimental groups combined.  39 10.  An i n t e r a c t i o n w i l l exist between training and cognitive s t y l e such that the relationship between the number of analytic responses on the CST and a l l measures of problem-solving w i l l be p o s i t i v e and greater for the untrained groups (T2, T3) than for the trained group ( T l ) .  11.  An i n t e r a c t i o n w i l l exist between t r a i n i n g and conceptual tempo such that the relationship between the number of errors on the MFF and a l l measures of problem solving w i l l be negative and greater for the untrained groups (T2, T3) than for the trained group ( T l ) .  12.  An i n t e r a c t i o n w i l l e x i s t between t r a i n i n g and conceptual tempo such that the relationship between the mean latency of response on the MFF and a l l measures of problem-solving w i l l be p o s i t i v e and greater for the untrained groups (T2, T3) than for the trained group ( T l ) .  Rationale The  rationale for the predictions made were based on  p r i n c i p a l assumptions.  F i r s t , i t was  two  assumed that an analytic  and  r e f l e c t i v e c h i l d w i l l be better equipped to carry out the processes necessary to solve the four problems given to him.  These problems were  selected from The Productive Thinking Program developed by Covington, Crutchfield, and Davies (1966), as being p a r t i c u l a r l y suited to assessment of the differences i n problem solving behavior expected of children who  d i f f e r i n analytic and r e f l e c t i v e response modes.  i l l u s t r a t i o n , one of the problems, t i t l e d "The Jewel" w i l l be described  in detail.  For purposes of  Mystery of the Missing  The problem facing the subject i n  this mystery story i s to determine how  a jewel was  stolen from a r i c h  widow during a black-out which occurred during a dinner party given by herself for three other guests. the rooms, but the jewel was  The policessearched  nowhere to be found.  a l l the guests and A window was  however no footprints were to be seen on the muddy ground below.  open, Key  40 clues for the subject to solve this problem are a feather found on the f l o o r and an opened box with perforations which one of the guests had brought with him.  The correct solution of the mystery i s that one of the  guests brought a trained b i r d i n the perforated box into the room which he released after blacking out the l i g h t s and opening the window.  This  guest stole the jewel, attached i t to the trained b i r d which flew out the window, where i t presumably waited for i t s master, the guest. The strategies needed for the solution to this mystery problem appear related to the cognitive processes assessed by the Style Test and the Matching Familiar Figures Test.  Conceptual  The s i t u a t i o n facing  the subject i n this problem i s to combine the various clues presented to him i n such a way  that he arrives at the solution: who  stole the jewel.  At the beginning of the problem he i s given the s i t u a t i o n a l context where any of the three guests could have a l o g i c a l motive for s t e a l i n g the jewel, and must r e s i s t the impulse to designate any one of the three as the thief before careful attention i s given to the details of the problem.  In addition, he must be able to perceive some facts as relevant  clues and other facts as irrelevant to the solution.  Success i n perceiving  the relevant facts or clues by asking information and constraint-rseeking questions p r i o r to o f f e r i n g a solution would seem to indicate an a n a l y t i c and r e f l e c t i v e approach to the elements of the problem.  Insufficient  attention of the details of the s i t u a t i o n i n which the theft occurred would result i n the various relevant and i r r e l e v a n t clues appearing together', thereby hampering solution of the problem.  'fused  Where such an  approach to the problem seemed to occur, as indicated by f a i l u r e to ask questions p r i o r to o f f e r i n g a solution, one might suspect the subject  41 to be r e l a t i v e l y non-analytic and impulsive.  He would be unable to  separate the elements of the problem and recombine them into  new  configurations which would have l e d him to the correct solution.  While  no research exists to date which tests children on this type of problem material, the wealth of data that does exist suggesting that non-analytic and impulsive children use less e f f i c i e n t strategies at a l l i n d i v i d u a l stages i n the problem solving process would give support to the  assumption  that s i m i l a r trends would be found i n the present study. The second assumption  on which the predictions were based was that  the programmed i n s t r u c t i o n a l materials to be used for t r a i n i n g w i l l teach children analytic and r e f l e c t i v e strategies for coping with problems. These materials evolved from a task analysis of problem solving (see Appendix C), and drew heavily on t r a i n i n g materials developed by other researchers.  The materials were prepared into s i x separate booklets, each  including a number of exercises and a c t i v i t i e s thought to be necessary to achieve the behavioral objectives to which each task i n the analysis aimed. The materials used i n the f i r s t booklet were designed to develop s k i l l s i n v i s u a l analysis and i n i i d e n t i f i c a t i o n and discrimination of problem elements.  These exercises included the following:  1.  Mazes: French, Ekstrom, and Price (1963) suggest that mazes require a b i l i t y to scan the f i e l d and reject f a l s e leads; willingness to f i n d a correct path v i s u a l l y before wasting time i n marking the paper. By gradually increasing the d i f f i c u l t y of these items, i t i s the contention of the writer that these can serve as appropriate materials f o r teaching r e f l e c t i v e and analytic perceptual s k i l l s .  2.  Ambiguous Figures: These items are designed to a l e r t the c h i l d to the fact that things are not always what they seem on f i r s t inspection. The intent i s to encourage children to go back and take another careful look when presented with  42 p i c t o r i a l or written material. 3.  Match to Standard Items: These include the training items used by Briggs and Weinberg (1973) to develop s k i l l s i n making successive comparisons between v i s u a l s t i m u l i that are highly s i m i l a r ; i n varying only one element at a time to i d e n t i f y subtle differences.  4.  Verbal to V i s u a l I d e n t i f i c a t i o n : Several highly s i m i l a r v i s u a l s t i m u l i are given along with a verbal d i s c r i p t i o n that i d e n t i f i e s only one. The c h i l d must coordinate two sets of information and attend to fine d e t a i l to make the necessary identification.  The exercises i n the second booklet were designed to promote the a b i l i t y to select relevant cues from a stimulus display i n the presence of d i s t r a c t i n g information, and to use constraint-seeking questions to impose organization on the problem elements. These exercises included: 1.  Witkin Embedded Figures Items: These items are proported to test the a b i l i t y to keep one or more d e f i n i t e configurations in mind i n spite of perceptual d i s t r a c t i o n ; to search a perceptual f i e l d containing irrelevant materials (French, Ekstrom, and Price, 1963). By gradually increasing the d i f f i c u l t y of a series of such items, i t i s the contention of the writer that these items can also be used as appropriate training devices for this a b i l i t y .  2.  Twenty-Questions Items: These exercises are s i m i l a r to those used by Ault (1973) and others, and present the c h i l d with a number of items that f a l l into d i f f e r e n t general categories. The use of constraint-seeking questions i s demonstrated and developed as a device i n f a c i l i t a t i n g i d e n t i f i c a t i o n , and the a b i l i t y to vary one component while holding a l l others constant.  The t h i r d booklet contained problems from both the Blank and Covington programme on question-asking (1965) and from the Productive Thinking Programme (Covington, Crutchfield, Davies 1965).  These  exercises presented problems to a c h i l d with inadequatelinformation for solution and guided him i n the i d e n t i f i c a t i o n of points where information was  lacking, and i n the use of information-seeking questions.  4 3  The remaining three booklets were comprised of material taken from the Productive Thinking Programme.  These items were designed to promote  hypothesis generation i n the form of "general p o s s i b i l i t i e s " and " p a r t i c u l a r ideas".  They encouraged the generation of more than on  hypothesis and provided guidelines to the c h i l d for using the information he had collected to evaluate each solution he generated.  Reports by  Covington and Crutchfield (1965), Ripple and Dacey (1976), and Stokes (1968)1 would attest to the success of these materials i n achieving these goals.  Sample exercises from each booklet are provided i n Appendix C. The program was of a l i n e a r format which provided consistent feed-  back of correctness of response, where applicable.. When more than  one  response was possible, a number of alternatives were provided against which the student could compare h i s own.  The sequence of exercises of  any one type showed a gradual increment i n d i f f i c u l t y and dimunision of explicitness of prompts.  This was  done to maximize the p o s s i b i l i t y of  correct responding and thereby attempted to avoid the experiencing of f a i l u r e that Kagan has suggested  i s a l l too frequent and i n h i b i t i n g for  the non-analytic impulsive c h i l d . Given the previous research data that reports success i n the use of i s o l a t e d components of these materials i n promoting e f f i c i e n t problem solving s k i l l s , i t seemed l o g i c a l to assume that similar f a c i l i t a t i o n would result from a combination  of these materials.  44  CHAPTER I I I METHODOLOGICAL CONSIDERATIONS  Subjects Ninety-two f i f t h , grade children enrolled i n three elementary schools within the Chilliwack School System which were not s p e c i f i c a l l y designed for the " g i f t e d " or the "learning disabled" served as the i n i t i a l pool of subjects.  Three schools serving comparable lower-middle  to middle class r e s i d e n t i a l areas were selected i n consultation with the central administrative s t a f f of the Chilliwack School Board.  A l l three  classes were taught i n a t r a d i t i o n a l non-rotation system, s o l e l y by their respective female teachers.  None of the subjects had had previous  exposure to the Productive Thinking Program. Subject a t t r i t i o n due to repeated absenteeism during the course of  the research program (five subjects), technical f a i l u r e of recording  equipment during post-testing (three subjects), or procedural error by the experimenter during post-testing (three subjects) resulted i n a f i n a l sample of eighty-one subjects for whom a l l experimental measures were available.  The f i n a l composition of each class by sex can be seen i n  Table I.  Design The design involved three between-subjects experimental conditions; a training class (TI) which was  exposed to the problem solving programmed  materials, a Control class (T2) which worked through programmed  45 TABLE I COMPOSITION OF EXPERIMENTAL  CHARACTERISTICS  CLASSES  Tl  T2  T3  MALES  13  12  15  FEMALES  12  14  15  TOTAL  25  26  30  F  p  FREQUENCY  MEAN CST  7.60  5 . 96  6 . 13  MEAN MFF ERRORS  8.00  8 • 19  6.93  11.74  13 . 06  5.21  5 . 28  MEAN MFF TIME MEAN CTBS  14.64 • 4 . 94  1 . 0759  . 34  .8881  . 41  1 .3526  . 26  .8849  .41  MEAN FLUENCY  36.64  39 .31  42.77  5 .8385  .004  MEAN F L E X I B I L I T Y  43.86  44 . 19  49 . 63  2 . 7825  .07  MEAN ORIGINALITY  45.96  42 .62  49 . 03  5 . 1497  . 008  46  i n s t r u c t i o n a l materials not s p e c i f i c a l l y designed to f a c i l i t a t e problem solving, and a second Control class ( T 3 ) which received no programmed instruction.  Classes were randomly assigned to the treatment  and  control conditions. Three pre-treatment  measures were obtained for each subject 'as  measures of cognitive s t y l e and conceptual tempo.  These included the  t o t a l number of analytic responses on Denny's Conceptual Style Test t o t a l number of errors on Kagan's Matching Familiar Figure Test errors) , and mean latency of response on the MFF items are presented i n Appendix B.  (MFF time).  (CST),  (MFF  Sample test  To determine that the three classes  did not d i f f e r s i g n i f i c a n t l y on these measures of cognitive s t y l e and conceptual tempo, a simple analysis of variance was scores.  carried out on these  As can be seen from Table I, no s i g n i f i c a n t differences existed  between the classes on these measures.  Description of the Covariates The intent of this study was  to examine processes used i n problem-  solving c o n t r o l l i n g for the effects of general a b i l i t y and statistically.  creativity  Therefore, these measures were treated as covariates.  As a measure of general a b i l i t y , the o v e r a l l score on the Canadian Tests of Basic S k i l l s was  employed.  This test i s a Canadian  adaptation of the Iowa Tests of Basic S k i l l s and includes sub-scores for vocabulary, reading comprehension, language ( s p e l l i n g , c a p i t a l i z a t i o n , punctuation, usage), work-study s k i l l s (maps, graphs, and tables, reference materials), and mathematics s k i l l s (concepts, problem-solving). "This battery aims at the evaluation of generalized educational s k i l l s  and a b i l i t i e s , not content achievement" (Birch, 1972).  A l l norms are  expressed as grade equivalents and the o v e r a l l scores used i n this study represent the mean of t h e " f i f t e e n sub-test scores for each c h i l d . treatment  The  group means for this measure of a b i l i t y are presented i n Table I.  No s i g n i f i c a n t difference existed between the three classes on this measure (F_  j, /y  = .8849, p < .41).  Three measures of c r e a t i v i t y ; fluency, f l e x i b i l i t y , and o r i g i n a l i t y were obtained by administering the Torrance Test of Creative Thinking, Verbal Form A to each class p r i o r to conducting this research.  In this  test "fluency" i s defined as the t o t a l number of relevant responses given, relevancy, being defined i n terms of the requirements as set f o r t h i n the instructions.  of the tasks  " F l e x i b i l i t y " i s the number of  d i f f e r e n t categories of responses, as given i n the scoring manual. " O r i g i n a l i t y " i s the sum of credits where routine responses count zero, less common responses get a score of one, and responses too infrequent to be on the l i s t i n the scoring manual (given by less than two of the sample on whom the test was  percent  standardized) are given a credit of  two.  Thus, the o r i g i n a l i t y score i s based on the s t a t i s t i c a l r a r i t y of the responses.  The sum of the raw scores on these measures are converted  into T-scores, using the norms given i n the scoring manual for f i f t h grade students. The Verbal Test consists of seven tasks, each battery requiring a t o t a l of f o r t y - f i v e minutes i n addition to the time necessary for giving an orientation, passing out booklets, and giving i n s t r u c t i o n s . a c t i v i t i e s involve:  The  asking questions about a drawing, making guesses  about the causeslaf the event pictured, making guesses about the possible  48 consequences of the event, producing ideas f o r improving a toy so that i t w i l l be more fun f o r children to play with, thinking of unusual uses of cardboard boxes, asking provocative questions, and thinking of the varied possible ramifications of an improbable event.  This test battery  was designed to provide a measure of c r e a t i v i t y defined by Torrance as "...a process of becoming sensitive to problems, d e f i c i e n c i e s , gaps i n knowledge, missing elements, disharmonies, and so on:  i d e n t i f y i n g the  d i f f i c u l t y ; searching f o r solutions; making guesses; or formulating hypotheses  about these d e f i c i e n c i e s ; testing and retesting these hypo-  theses and possibly modifying and retesting.them; and f i n a l l y the r e s u l t s . "  communicating  (Torrance, 1966, p. 6). The s i m i l a r i t y of this description  to the problem-solving measures selected for examination i n the present research makes the Torrance Test scores p a r t i c u l a r l y suited as covariates. The means for each treatment group on these c r e a t i v i t y scores are presented on Table I. While no s i g n i f i c a n t difference existed between the three groups on mean f l e x i b i l i t y , this was not the case for mean fluency and o r i g i n a l i t y .  Using Dunn's test for pairwise.comparisons  among the means f o r fluency showed that this s i g n i f i c a n t difference was accounted for by the superiority of T3 over T l (d=6.1267, exceeding c r i t i c a l value of d=4.6146 with alpha .05).  For o r i g i n a l i t y the difference  was accounted f o r by the superiority of T3 over T2 (d=4180, exceeding c r i t i c a l value of d=5.1623 with alpha .05). as covariates, however, s t a t i s t i c a l l y  Treatment of these variables  controlled f o r any systematic e f f e c t .  Stimulus Materials The f i f t e e n items constituting Form N of Denny's CST were mimeo-  49  graphed and prepared i n booklet form f o r each subject. items was randomized  f o r each subject.  The order of  One item from Form M of the CST  served as a sample item. Each of the twelve items of the MFF were presented i n black ink on two sheets of white paper covered by protective p l a s t i c .  The standard  item was drawn i n the center of one sheet, and the f i v e variants and one i d e n t i c a l item were arranged i n two rows of three items on the second sheet.  The position of the correct item within these s i x positions was  arranged such that each position was occupied by the correct item twice. Two additional sample items were provided f o r practice.  One set of these  items was prepared f o r each of two female experimenters.  Each experimenter  was equipped with a stopwatch and a score sheet f o r recording latency of response, and errors. The four items to be used i n the test of problem-solving a b i l i t y were prepared on a single sheet of paper covered i n protective p l a s t i c . This included the verbal description of the problem and a p i c t o r i a l representation.  Each experimenter was provided with a l i s t of standard  responses to be given to questions asked by the c h i l d (see Appendix A). Two cards were provided f o r use by the c h i l d , one with the word "READY" printed i n large black l e t t e r s , and.one marked "FINISHED". The problem-solving training program has been described f u l l y i n Chapter I I .  Each booklet was bound i n a d i f f e r e n t colored cover, c l e a r l y  i n d i c a t i n g the number of the booklet.  The f i r s t of the s i x booklets was  placed i n an envelope marked with each child's name. supplied .with the f i v e remaining booklets.  The teacher was  On the face of the envelope  a chart was provided so that the c h i l d could record the page at which he  50 stopped work each day. The control group program was Seasons:  e n t i t l e d Day and Night and the Four  A Study of Earth-Sun Relationships published by the American  Institute for Research i n the Behavioral Sciences.  This program was  of a  l i n e a r , small step format which provided one hundred per cent knowledge of results.  Concepts dealt with by the content of the program included  rotation, revolution, the significance of certain l a t i t u d e s , causes of the four seasons, etc.  The material i n the program had not to this point  been e x p l i c i t l y covered i n the students' regular curriculum.  The lesson  booklet and accompanying answer booklet were provided to each c h i l d i n T2 i n a large envelope.  A chart was provided on the face of the envelope  so that the c h i l d could record the page at which he stopped work each day.  Procedure P i l o t Testing: was  Formative  testing of the problem-solving program  carried out with t h i r t y - s i x f i f t h grade children within the  Chilliwack School System who were not subsequently research.  This p i l o t testing was  involved i n this  undertaken to ensure that the content  and instructions i n the program were s u f f i c i e n t l y unambiguous, and to obtain time measures for completion of each booklet.  Each c h i l d  given one of the s i x booklets which constituted the program.  was  Children  were requested to work through the booklet without interruption, and to n o t i f y the researcher i f there were any instructions which they did not understand.  Total time to completion was  recorded for each c h i l d .  No c h i l d reported d i f f i c u l t y i n understanding completing any exercise i n the booklets. booklets one through s i x were as follows:  instructions or i n  The mean time to complete thirty-seven minutes, t h i r t y -  seven minutes, f i f t y - f i v e minutes, f i f t y - s i x minutes, f i f t y - f o u r minutes, sixty-three minutes.  On the basis of this data i t was  decided that  fourteen thirty-minute periods would allow ample time for a l l children i n the training class to complete a l l s i x booklets. Following completion of the booklets, each c h i l d involved i n p i l o t t e s t i n g was  given the four post-test problems intended for use i n this  research i n mimeograph form.. Instructions were given to examine the problem c a r e f u l l y and write down a l l the questions that they would ask i f they were trying to solve the problem.  This procedure provided a pool  of questions for which standardized answers could be constructed p r i o r to undertaking the testing of the experimental subjects. Pre-testing:  Two weeks p r i o r to beginning t r a i n i n g , group  administration of the CST was undertaken within each experimental  class-  room. . One week l a t e r the Torrance Test of Creative Thinking, Verbal Form A was  administered i n the same manner.  The School Board had  administered the Canadian Tests of Basic S k i l l s (CTBS) to a l l fifth-grade children at the beginning of the school year and these scores were collected from the school f i l e s for each c h i l d involved i n this research. The administration of the MFF was i n d i v i d u a l l y by two female experimenters.  carried out with each c h i l d Each experimenter  tested an  equal number of subjects of each sex from each class.  The c h i l d was  taken  to a quiet room outside of his classroom for testing.  The f i r s t sample  item was placed on the desk with the standard item above the picture of s i x variants.  The following instructions were read to the c h i l d :  "I am going to show you some pictures, l i k e these (points to sample). I want you to look at this picture c a r e f u l l y (points to standard). Then look at each of these pictures (points to variants). One of these pictures i s exactly the  52  same as that i s take as the one  the one exactly long as that i s  at the top. Your job i s to fine the one the same as the one at the top. You may you need to make your choice. Point to exactly the same when you find i t . "  If the subject made an incorrect s e l e c t i o n , the directed the c h i l d to look again.  experimenter  Following successful completion of the  sample items, the f i r s t test item was presented.  The experimenter  started  the watch as soon as the item was placed .in .front of the subject and stopped i t when the subject indicated h i s f i r s t s e l e c t i o n . selection was  incorrect, the experimenter  directed the c h i l d to look again.  I f the  recorded"the error and  This procedure  continued u n t i l a l l  twelve items had been presented. Training:  P r i o r to the commencement of t r a i n i n g , the teacher  of T l was v i s i t e d by the researcher and given a f u l l description of the intent of the study and the importance of her not providing aid to the students while they worked on the materials beyond making available the booklets.  She was  cautioned to r e f r a i n from discussing the children's  progress with the material and was  requested to act as a "watch-dog" to  ensure that children did not talk among themselves during work sessions. On the f i r s t day of''training the researcher introduced the program to both T l and T2 with the explanation that these were new books that had been written for f i f t h grade ' students, and they were being asked to use them so that the researcher could see i f students would complete a l l the exercises i n the booklets with no help from anyone else.  The  children were then provided with general instructions on the use of the materials, and on the importance of keeping an accurate record of how many, pages they completed each day.  53  It was arranged with the two teachers that the t h i r t y minute period immediately  following lunch would be set aside for work on the  materials for.the following fourteen days.  The teachers were instructed  to c o l l e c t the envelopes at the end of each work session.  I f any c h i l d  completed the program before the alotted time, he was instructed to work on other reading or school projects. Post-Testing:  The administration of the tests of problem-solving  a b i l i t y were conducted during the week following t r a i n i n g .  The test was  administered i n d i v i d u a l l y to each c h i l d by four female experimenters had received training i n administering these materials.  who  The assignment  of subjects to experimenters was such that each experimenter  tested as  equal a number of children of each sex i n each.class ast-thettotal number would allow.  A l l test sessions were recorded on audio tape.  was tested i n a quiet room separate from the classroom. seated across the table from the experimenter  Each c h i l d  The c h i l d was  and read theffollowing  instructions: "I am going to.give you some mystery stories to solve. I w i l l show you a picture and read you the story about the mystery. You can follow along on your own copy while I read. Your job i s to t r y to guess at some solutions. You may ask me any questions that you think w i l l help you to find a solution. When you think you are ready to take a guess, turn over this card and say "READY". Then you can t e l l me your guess. I f you want to ask me some more questions after you have made your f i r s t guess, you can. Try to think of as many guesses as you can. When you can't think of any more guesses or questions, turn over this card and say "FINISHED" and we w i l l go on to the next mystery." The experimenter  then placed the sheet containing the f i r s t problem  before the c h i l d and read the description. subject had said nothing, the experimenter you would l i k e to ask me?".  I f after two minutes the asked "Are there any questions  I f after three minutes the c h i l d had not  54  said anything he was asked i f he was f i n i s h e d , and instructed to turn over the FINISK card. determined manner. experimenter  A l l questions were answered according to the pre-  Each'time the subject offered a solution the  said "Yes, that could be what happened.  questions or guesses?". problem, the experimenter  Do you have any more  I f a subject spent more than f i v e minutes on a allowed the c h i l d one further opportunity to  provide a solution and then said "We had better move on to the next one now: or there won't be time to look at a l l of them." This procedure  continued u n t i l a l l four problems has been presented.  Order of presentation of problems was randomly determined  f o r each c h i l d .  Transcriptions of a l l test sessions were made and responses according to the ten dependent measures.  scored  The procedure employed for  c l a s s i f i c a t i o n of questions into the three types, information-, constraint-, and hypothesis-seeking, was as follows.  A l l questions were collected and  c l a s s i f i e d into the three types by the experimenter. independent judge c l a s s i f i e d a l l questions.  Following t h i s , an  Those questions on which  there was not i n i t i a l agreement were then discussed u n t i l a concensus was  reached.  Examples of questions of the three types are presented i n  Appendix A for each problem.  55  CHAPTER IV RESULTS  Mean scores for each subject for the four problems were determined for each dependent variable. questions, p r i o r questions, seeking questions,  These were t o t a l time, p r i o r time, t o t a l information-,  constraint-, and  residual time, r e s i d u a l questions,  number of solutions offered.  hypothesis-  and the t o t a l  These data were then analyzed using a  regression analysis procedure designed to v e r i f y the research hypotheses stated i n Chapter I I . The regression analysis approach employed for this analysis has been described by several writers (Bottenberg and Ward, 1963; Overall and Spiegal, 1969;  Walberg, 1971;  Cohen,  Draper and Smith, 1966).  advantages o f . t h i s method of data analysis over the conventional approach have been discussed  i n d e t a i l by these writers.  1968; The  ANOVA  In the present  study the use of regression analysis allowed for the effects of the continuous variables Cognitive Style and Conceptual Tempo to be  tested  without having to a r b i t r a r i l y l e v e l the variables as i n ANOVA.  In  addition, Cronbach and Snow (1969) and Bracht (1970) have recommended the use of the regression analysis method for testing i n t e r a c t i o n terms i n . A.T.I. (Aptitude by Treatment Interaction) studies.  In.the present  study the i n i t i a l i d e n t i f i c a t i o n of these interactions was a regression analysis procedure.  Following  undertaken by  t h i s , categorization of the  continuous organismic variables then allowed for closer examination of those interactions which the regression analysis found to be s i g n i f i c a n t .  56 Separate stepwise regression analyses were performed f o r each of the ten dependent variables i n order to test the hypotheses of this study. These analyses were performed and correlations generated using the BMD02R Stepwise Regression Program (Halm, 1972).  Major hypotheses were  tested at alpha .05. The hypotheses given at the end of Chapter II were t r a n s l a t e r into s t a t i s t i c a l terms.  The symbols used to represent the variables i n this  study are given i n Table I I .  An ordering l o g i c was defined i n t e s t i n g  the terms i n the equation i n a stepwise manner, as suggested by Overall and Spiegal (1970).  The ordering model was as follows:  Y = Covariates + Organismic Variables + Treatment + Interactions The r e s u l t i n g regression equation took the following general form: Y  l  10  =  l 2  X  +  + X  X  5  +  3  X  + X  + Xg + X  +  X  4  (  + X  6  C o v a r i a t e s  + Xg  7  )  (Organismic Variables)  (Treatment)  1 Q  + XgX^ + XgXg + X^Xg (Organismic Interactions) +  X  X 5  9 +  x  x 5  io  +  X  69 X  +  X  6 10 X  +  X  7 9 X  +  X  7 10 X  +  X  8 9 X  +  X  8 10 X  (Organismic by Treatment Interactions) + e  (Error)  Thus, the order used involved entering the covariates (School Achievement and Creativity) f i r s t into the regression equation, followed by organismic variables (Sex, Cognitive Style, Conceptual Tempo), i n turn followed by treatment terms and then organismic organismic  interactions terms l a s t .  interactions and treatment by This means that the e f f e c t s of  organismic variables were tested with the e f f e c t s of the covariates being controlled s t a t i s t i c a l l y .  Likewise, treatment and i n t e r a c t i o n e f f e c t s  were tested with the e f f e c t s of the covariates and organismic variables  57  TABLE I I SYMBOLS USED IN STATISTICAL SYMBOL  ANALYSIS  VARIABLE  Y  Mean T o t a l Time  Y^  Mean P r i o r  Y^  Mean T o t a l  Questions  Y^  Mean P r i o r  Questions  Y^  Mean I n f o r m a t i o n - S e e k i n g  Y  Time  Questions  o Y^  Mean C o n s t r a i n t - S e e k i n g  Questions  Mean H y p o t h e s i s - S e e k i n g  Questions  Y  Total  o  Q  Solutions  Yg  Mean R e s i d u a l  Y^Q  Mean R e s i d u a l  X  Canadian Test  1  Time Questions of B a s i c  Skills  Torrance  Verbal  Fluency  Torrance  Verbal  Flexibility  X^  Torrance  Verbal  Originality  X  Sex  5  (CTBS)  X, o X^  A n a l y t i c R e s p o n s e s on C o g n i t i v e  X  0  Mean L a t e n c y  g  First  X X  o  1 Q  E r r o r s on M a t c h i n g  Second  S t y l e T e s t (CST)  Familiar Figures  Test  of Response on MFF T e s t  Treatment Treatment  Contrast Contrast  - TI versus - T2 v e r s u s  (MFF e r r o r s )  (MFF t i m e ) T2 + T3 T3  58 controlled s t a t i s t i c a l l y .  Hypothesis  Testing  In order to test Hypotheses 1, 2, and 3 concerning the e f f e c t s of the treatment, a series of regression analyses were run, one f o r each of the ten dependent variables. i s presented i n Table I I I .  A summary of the results of these analyses A more detailed report of the results of  these analyses can be found i n Appendix D. The results f o r Treatment DV1 ( T l vs T23) i n Table I I I indicate that t r a i n i n g accounted Ipraa s i g n i f i c a n t * amount of the variance i n the scores of four of the dependent variables when the trained group (Tl) i s compared to the combined control groups (T23). t o t a l time (F  C Q  These measures were mean  = 7.2439, p..<.009), mean p r i o r time (F  p.<.002), mean t o t a l questions (F-  = 10.3918,  = 4.8119, p< .03) and mean constraint-  l ,oy  seeking questions ( F  15 g  = 8.3301, p< .005).  The means f o r T l and T23  are presented i n Table IV. From this table i t i s apparent that while mean t o t a l time spent on the problems by the trained group was 227.13 seconds, that f o r the combined control groups was 201.45.  The difference  between T l and T23 i n terms of mean p r i o r time was also highly s i g n i f i c a n t , with means of 72.75 and 46.70 seconds respectively.  The trained group  also exceeded the control groups on mean t o t a l questions asked, the means being 4.82 and 3.28 respectively.  In terms of mean number of constraint-  seeking questions asked, the mean f o r T l of 1.16 also exceeded that of T23 with a mean of .44.  throughout this Chapter, the term " s i g n i f i c a n t " denotes " s t a t i s t i c a l l y significant."  TABLE SUMMARY  OF RESULTS  OF REGRESSION ANALYSES  III ( F - R A T I O S ) FOR  TEN DEPENDENT VARIABLES MEAN H. S . QUES .  MEAN RES . TIME  MEAN RES . QUES .  2 ,9696 .  1.. 4953  1.. 1481  2. , 2585  2 . 0078  . 0000  . 0000  1..3307  . 6363  2 .0747 ,  .6535  . 0808  .7570  6 .3030* ,  .3738  MEAN TOTAL TIME  MEAN PRIOR TIME  MEAN TOTAL QUES .  MEAN PRIOR QUES .  MEAN I . S . QUES .  MEAN C. S . QUES .  6. 5 0 0 0 *  1. 7010  2 .5940  1.,8269  2 .9807  2 .2162  3. 5 8 1 3 *  3. 0 2 0 6 *  4. 1 8 8 1 *  4., 2532*  2. 7 7 5 6 *  3, . 3851*  6.,7115*  1..2047  SEX  .0244  .0412  , 0990  ,8543  ,2095  CST  .0365  7319  1., 6831  2 ,7087 .  .5428  SOURCE OF  VARIATION  CTBS TORRANCE  TESTS  MFF  ERRORS  3 .7 5 6 0 *  MFF  TIME  3. 4024 7. 2 4 3 9 *  TREATMENT DV1 ( T l v s T23) TREATMENT DV2 (T2 v s T 3 ) CST x MFF ERRORS CST  x MFF  MFF  ERRORS x MFF  SEX  x TREATMENT  CST  1463 15. 8048* 1097  TIME  .2884 . 2115  5576 1., 9613  ,0097  . 0097  3,.5000  ,3942  . 0097  1.. 5544  2 .2692 .  ,4134  3 . 9611*  1..3142  10. 3 9 1 8 *  4..8119*  2 .7500 ,  2 ,9135 .  8..3301*  1,.6952  1. 8454  .8218  5,.4615*  1.. 0480  .8738  1.,7113  5..8316*  .5384  5,.5576*  2 ., 1165  1,.1980  . 6442  .7403  1,.5048  5. 8 9 6 9 * 7010  ,2164  ,1287  . 1612 3,.4095  3 .2243  .2126  1,.8586  .2056  . 0393  10..2727*  7 .6728* .8317  . 0190  .4409  . 0000  .1401  2 . 0285  1 .3070  . 1809 1 .8190  1 . 0961  . 0485  2683  .7268  . 8713  . 2788  1 . 0288  ,.7 67 0  x DV1  .2926  1..0103  3 .7425*  .3942  6 .4711*  .7184  CST  x DV2  2..8048  .0309  .4257  . 0384  1 . 0384  . 3592  MFF  ERRORS x DV1  5..2682*  .4226  .0297  .2019  . 1250  . 1165  . 3238  MFF  ERRORS x DV2  .0121  .4432  . 0990  . 0576  .1057  . 0097  .0285  MFF  TIME  x DV1  1,. 9756  . 0412  . 3465  . 1153  . 1442  1 .2524  MFF  TIME  X DV2  , 0000  1 . 0309  .1188  .0096  .1442  .0873  p < . 05  .2626  . 0078  . 0000  4 .3750*  *  1,.0629  .1338  . 6930  2. 7805  ,5275  .5333  6..2164*  TIME  TOTAL SOL.  1,.2576  1,.1916  .1968  1,. 6962  4,. 7 9 4 3 *  .1732  3,.4747  . 5420  3,. 6 9 6 9 *  .3364  .1574  .1212  .3551  . 0476  .3543  2 .5858 ,  . 6476  1,.1259  .5959  1 .6535  1.. 1121 .1588  60 TABLE IV GROUP MEANS FOR TEN MEASURES  VARIABLE  OF PROBLEM  T123* ' T l  T2  SOLVING  T23**  T3  MEAN TOTAL TIME  209.94  227 . 13  109 . 09  212 .82  201. 45  MEAN PRIOR TIME  54.59  72 .75  49 . 75  43 .65  46 . 70  MEAN TOTAL QUESTIONS  3.76  4 .82  3 .19  3 . 38  3 .28  MEAN PRIOR  1.66  2 .11  1. 72  1 . 24  1. 48  MEAN INFORMATIONSEEKING QUESTIONS  2 . 64  3 .16  2 .39  2 . 43  2 .41  MEAN CONSTRAINTSEEKING QUESTIONS  . 66  1. 16  • 46  .43  • 44  MEAN HYPOTHESISSEEKING QUESTIONS  .46  • 52  • 34  . 53  • 43  10.85  11. 04  9 .96  155.34  154. 38  140. 33  169 . 16  154. 74  2 .72  1. 47  2 . 13  1. 80  TOTAL  QUESTIONS  SOLUTIONS  MEAN RESIDUAL TIME MEAN RESIDUAL QUESTIONS  2 . 10  *T123=ALL EXPERIMENTAL GROUPS **T2-3= TWO  CONTROL GROUPS  POOLED  POOLED  11 .47  10 .71  61 There was further evidence of superiority of the trained group over that of the combined control groups which was marginally r e l i a b l e f o r three additional measures. T23 = 1.48; F^ ^  These were mean p r i o r questions ( T l = 2.11,  = 2.7500, p< .09), mean information-seeking questions  ( T l = 3.16, T23 = 2.41; F  c  _ = 2.9135, p< .08), and mean residual  x,  questions ( T l = 2.72, T23 = 1.80; F..  = 3.2243, p< .07).  J->->9  The results for Hypothesis 1 stated i n Chapter I I can be summarized as follows: Hypothesis 1:  In terms of mean t o t a l time, mean p r i o r time, mean t o t a l questions, and mean constraint-seeking questions, there was a s i g n i f i c a n t difference between scores of T l and T23 with the scores of T l being greater.  The difference between the scores  of trained and control groups approaches s i g n i f i cance f o r mean p r i o r questions, mean informationseeking questions, and mean r e s i d u a l questions. No s i g n i f i c a n t difference existed between the scores of the trained and the control groups f o r t o t a l solutions and mean residual time. It was predicted i n Hypothesis 2 that the combined control groups would ask more hypothesis-seeking questions than the trained group.  An  examination of the variance accounted f o r by Treatment DV1 ( T l vs T23) in Table I I I f o r this type of question indicates that this difference was not s i g n i f i c a n t (F.,  c o  = 1.6952, p< .19).  In fact, as shown on Table IV,  the trend was i n the reverse d i r e c t i o n with the mean for T l being .52 and for T23 .43. The results f o r Hypothesis 2 can be stated as follows:  62 Hypothesis 2:  No s i g n i f i c a n t difference existed between the mean number of hypothesis-seeking questions asked by the trained and the control groups.  Hypothesis 3 was designed to test for any s i g n i f i c a n t differences in the scores of the two control groups.  As can be seen by examining the  results for Treatment DV2 (T2 vs T3) on Table I I I , the scores of these groups d i f f e r e d s i g n i f i c a n t l y on only one of the ten dependent measures, mean p r i o r questions (F^ ^  = 5.4615, p<.02).  The mean for T2 exceeded  that of T3 on this measure (T2 = 1.72, T3 = 1.24), as shown on Table IV. The results for Hypothesis 3 can be stated as follows: Hypothesis 3:  No s i g n i f i c a n t difference existed between the scores of the two control groups on any of the ten measures of problem solving except mean p r i o r questions asked, where T2 exceeded T3.  Hypotheses 4 and 5 predicted that a p o s i t i v e relationship would exist between the organismic variable "cognitive s t y l e " and a l l measures of problem solving, except mean hypothesis-seeking questions asked, f o r which a negative relationship was predicted.  Examination of the values  for CST (mean number of analytic responses on the CST) on Table I I I indicate that no such relationship was found between this variable and any of the ten measures of problem solving.  The results for Hypotheses  4 and 5 can be summarized as follows: Hypothesis 4:  No s i g n i f i c a n t relationship exists between the number of analytic responses on the CST and measures of problem solving for a l l experimental groups combined.  63 Hypothesis 5:  No s i g n i f i c a n t relationship exists between the number of a n a l y t i c responses on the CST and mean hypothesis-seeking questions asked for a l l experimental groups combined.  Hypotheses 6 and 7 predicted that a negative relationship would exist between the organismic variable "conceptual tempo" as measured by the errors on the MFF test, and a l l measures of problem solving except mean hypothesis-seeking questions asked, for which a p o s i t i v e relationship was predicted.  Examination of the results f o r the variable MFF errors on  Table III indicate that a s i g n i f i c a n t amount of the variance i n two problem solving measures, mean t o t a l time (F^ ^  = 3.7560, p<.05) and  mean p r i o r time (F.. = 5.8969, p <.01) was accounted for by this l,oy measure of conceptual tempo. I t should further be noted that the C Q  influence of this variable approaches significance f o r mean p r i o r questions (F.. = 3.5000, p< .06). ±,->y C Q  In order to determine  the d i r e c t i o n of the relationship between  this measure of conceptual tempo and the three measures of problem solving, the correlations presented i n Table V were examined.  From this  table i t can be seen that the correlation between MFF errors and mean t o t a l time was -.24, between MFF errors .and mean p r i o r time was -.25, and between MFF errors and mean p r i o r questions was -.21.  The results f o r  Hypothesis 6 can be summarized as follows: Hypothesis 6:  A s i g n i f i c a n t negative relationship exists between t o t a l errors on the MFF and mean t o t a l time and mean p r i o r time.  The relationship approaches  significance f o r mean p r i o r questions.  No  H H  TI TI  S  Tl M pd  n H H Tl CO S Tl H M X  pa  td s pd pd Tl O pd CO  n CO H  o < pel M pd  X  •  o  Tl < f W W Pd W •  >  tr  1  tn w a  >  Pd Pd  1—I  ?d  S  n  CO  H w  H  o  W  > n f  n CO  PI  H g  <  W X  CO  pd  > pa pa o  M f>  CO  K!  <! O >  3  w  s  W H f CO  n  CO M  o  O  pa-  H H M ho M NO U) U) 1 o NO NO Ui Ul 0 0 1-3  H H H No M to LO LO h- I— O to -J 1  1  H H H H LO to 1— to LO 1 O o LO NO NO 1  H H h- NO I— NO LO U) LO LO to o to to 1  1  rtH H  H H H h- to to LO LO M M -p- 0 0 O N  t— to M ho LO LO to to Lo h- -p- Lo  1  1  1  H H H M to hto LO LO to LO l-P-P-  1  1  H H H h- to M to LO LO 1 1 1 to 0O0 -p1  H H H 1— to I— to LO LO O 1 O LO O -o 1  1  H H H h- NO hNO LO LO NO NO NO LO O O N 1  1  H H H GROUPING t— NO H NO LO LO TOTAL M hNO NJ TIME 1  1 1 o H* I-  1 1 1 Ul •^J O LO  O -p-  1 1 O O OhLO 4>  O o Ul -P-  O h- O Ui O N O N  1 1 1 LO to Ul O -O  1 1 1 O o to ~~J to ~-J  hO LO Ul NO  O O NO PRIOR Ul O TIME  1  1 o hLO M VO  1 1 O o o LO LO Lo  1 O to M h-' O  LO •P- to NO Ul O  M to O to -P-  to LO to O O N to  1 1 o O 00 LO to  o M hVO  1  LO  1 o to LO to 0 0  M NO o ON LO NO  O O H- TOTAL vo •P- LO QUESTIONS  1 1 1 h- o o 00 O  1 1 o O o o Ui Ul  1 1 1 O O M ON 0 0  LO to LO h- vo  1 O O O h- LO to  I-  Lo M  1 o O O Lo I— Lo  1 1 1 to to to M -P- O N  i O o o Ui LO o  1 to 00 0 0 4>  O O I- PRIOR -P- 1— Lo QUESTIONS  1 o o to O N O N NO  o O hNO to LO  1 M o NO O to NO  •P- M vo M Ul  M to M -P- Ul O  to LO to h- LO Lo  1 o O O t— h-  M h- 10—0'  1 1 1  1 h- o -pUl o  t— NO o 00 NO  O o O I . S . • 4> h- Ui QUESTIONS  1 1 1 I- o Ivo LO  1 1 ho NO Ul Ul  LO to to LO Ul  O M O O LO Lo  O h- to LO VO Ul  1 t— O to Ul to to  1 1 1 O h- o Lo Ui 1—'  M  h-'  1 I— LO o Ul  M o NO C . S . VO -O QUESTIONS  1  1 1 1 o M LO vo - O Ul  1 1 1 M o O VO •p- Ul  LO •P- O Ul VO  1 LO to O to LO  1 to •e- o 00 Lo -p~  1 1 1 M o to to O N -o  1 1 O o o LO LO  1 1 1 I- VoO NO t— NO  1 o O o hNO  M O o H.S . vo -p- QUESTIONS  M h- LO 0 0 Ui Ul  1 O o o 00  h-> LO  to N) o ON O to  M to  LO  1 i 1 h- O to ON ON VO  M M NO Lo O LO  I- tNO O 00 vo  1 1 h- o NO TOTAL O Ui LO SOLUTIONS  O  M h- 1— 00 LO to  h- to o VO O LO  ho to -P- 0 0 Ul  1 1 o o Lo VO O Ul  1 O o LO 00 Ul O N  M H* LO -o LO O N  IO -p- O to 0 0  M LO O 00 LO  to LO I— O VO o  1 1 o O M VO to VO  O o O to Ui to  1 h- o LO -P- -p> V O  OO 1— N LO NO LO  1  1  1  1  o o  1— LO 1  Ui Ul  1 1 o NO O 00 -f> Ul NO  NO  ON  1 LO o  1 1 o hto NO o 1  1  1  1  hUi  NO  1  NO  ON  1 1 O o O 4> NO h1  ON  o H Ul 0 0  O o VO O N  00  NO  1  NO  NO  00  NO ON  M o LO O 0 0 Ul  to 00  to ON  VO 1  1  1  1  1  00  1  1  1  1 ho 1  00  1  1  1  1  1  1  1  1— 1  Ul to  O  1  1  NO t-  1  1  1  1  h-  1  VO  00  1  1  1  1  >  S  M  >  1  1  1  1  1  1  1  po  1  w a  Pd o  w f M s  CO o  1  O  1  1 O H" O RESIDUAL LO Lo TIME  VO  h- O M RESIDUAL O •P- O QUESTIONS 1  w  M M CO H s: o  1  1  H M O  CO CO <=!  1 1 O o O 00 -P-  1  pa w t-  1  < 1—1 o  o pa o  > M CO  > f  <  s  H n  < > pa M  > c-  1  M CO  > o  ON  65 s i g n i f i c a n t relationship exists between t o t a l errors on the MFF and the remaining measures of problem solving, for a l l experimental groups combined. MFF errors did not account for a s i g n i f i c a n t amount of the variance i n mean hypothesis-seeking questions asked ( F , ,  C Q  = .0097, p < .88), as  shown on Table I I I , i n d i c a t i n g that no support was found for Hypothesis 7.  In addition, the correlation between mean hypothesis-seeking questions  asked of -.03 demonstrates that the relationship was not i n the p o s i t i v e d i r e c t i o n that had been predicted.  The results for Hypothesis 7 can be  stated as follows: Hypothesis 7:  No s i g n i f i c a n t relationship exists between t o t a l errors on the MFF and mean hypothesis-seeking questions asked, for a l l experimental groups combined.  Hypotheses 8 and 9 predicted  that a p o s i t i v e relationship would  exist between the organismic variable "conceptual tempo" as measured by mean latency of response on the MFF test and a l l measures of problem solving except mean hypothesis-seeking questions asked, for which a negative relationship was predicted. An examination of the results of the variable MFF time on Table I I I indicate that this measure of conceptual tempo accounted for a s i g n i f i c a n t amount of the variance i n two measures of problem solving, mean constraintseeking questions asked (F, ,- = 3.9611, p<.04) and mean residual time Q  i,Dy  (F^  = 6.3030, p< .01).  A marginally r e l i a b l e relationship was found  between this organismic variable and mean t o t a l time (F  1 c o  = 3.4024, p< .06).  i , jy The correlations presented i n Table V indicate that the d i r e c t i o n of the  relationship between mean latency of response on the MFF and mean t o t a l time (r = +.24), and mean residual time (v ~ +.24) was i n the p o s i t i v e direction predicted, but that the reserve was found for mean constraintseeking questions asked (r = -.15). It can be seen from the data on Table I I I that the mean latency of response on the MFF did not account for a s i g n i f i c a n t amount of the variance i n the mean hypothesis-seeking questions asked (F  _ = 1.3142,  1,39  p <.25), as predicted by Hypothesis 9.  From Table V i t can be seen,  however, that the relationship between these two variables was i n the negative d i r e c t i o n predicted with r = -.12. The results for Hypotheses 8 and 9 can be summarized as follows: Hypothesis 8:  A p o s i t i v e relationship exists between mean latency of response on the MFF and mean residual time, and a marginally r e l i a b l e p o s i t i v e relationship exists between mean latency of response on the MFF and mean t o t a l time.  A negative relationship exists  between MFF time and mean questions asked.  constraint-seeking  No s i g n i f i c a n t relationship exists  between t h i s measure of conceptual tempo and mean p r i o r time, mean t o t a l questions, mean p r i o r questions, mean information-seeking questions, t o t a l solutions, and mean residual questions f o r a l l experimental groups combined. Hypothesis 9:  No s i g n i f i c a n t relationship exists between the mean latency of response on the MFF and mean hypothesisseeking questions asked f o r a l l experimental groups combined.  In Hypothesis: 10 i t was predicted  that a s i g n i f i c a n t i n t e r a c t i o n  would exist Between t r a i n i n g and cognitive s t y l e such that the r e l a t i o n ship Between the numBer of analytic responses on the CST and a l l measures of proBlem-solving would Be p o s i t i v e and greater f o r the untrained groups (T23) than for the trained group ( T l ) . Examination of the results f o r the interaction term "CST x DV1" on Table III indicate that this i n t e r action of treatment with cognitive s t y l e accounted for a s i g n i f i c a n t amount of the variance i n three of the ten dependent variables. were mean t o t a l questions (F  These  = 3.7425, p<.05), mean information-  l,oy  seeking questions (F^ ^ (F  = 6.4711, p< .01), and mean residual questions  = 4.7943, p< .03). In order to determine  the d i r e c t i o n of these relationships, the  correlations between mean analytic responses on the CST and these three dependent variables were examined for T l and T23. From Table V i t can be seen that the correlation between the CST score and mean t o t a l questions for T l i s +.28 and for T23 i s -.02; for mean informationseeking questions T l = +.40 and T23 = -.05; for mean residual questions T l = +.39 and T23 = -.05.  Fisher's r to Z transformation was used to  test for significance of differences between these pairs of correlation coefficients.  These values are presented on Table VI.  None of the  differences between the pairs of correlation c o e f f i c i e n t s reached the c r i t i c a l Z value of 1.96 to be s i g n i f i c a n t at .05 alpha.  I t should be  noted, however, that the d i r e c t i o n of these relationships was i n the reverse of what had been predicted.  I t was expected that training would  decrease the e f f e c t of cognitive s t y l e on the problem-solving measures. Hence, the correlations for T l were predicted  to be lower than those f o r  68  TABLE VI TESTS  (FISHER'S Z) OF SIGNIFICANCE BETWEEN CORRELATIONS  TRAINED  AND UNTRAINED GROUPS: COGNITIVE STYLE  CEPTUAL TEMPO  FOR  ( C S T ) , CON-  (MFF ERRORS, MFF TIME) AND MEASURES OF PROBLEM SOLVING.  PROBLEM SOLVING MEASURES  CST  MEAN TOTAL TIME  . 5507  MEAN PRIOR  TIME  . 9861  . 6706  . 3944  MEAN TOTAL  QUESTIONS  1 . 1834  . 0788  .5917  MEAN PRIOR  QUESTIONS  . 1183  . 0788  . 0708  MEAN I . S . QUESTIONS  1 .7751  .2761  . 1183  MEAN C.S. QUESTIONS  .2761  . 5522  . 9467  MEAN H.S.  .5128  . 1577  . 8284  . 5128  . 9072  .7100  TOTAL  QUESTIONS  SOLUTIONS  MFF ERRORS  1.3889  MFF  TIME  . 7889  MEAN RESIDUAL  TIME  1 . 6173  1. 3806  .5128  MEAN RESIDUAL  QUESTIONS  1 .7357  . 1183  .8284  69 T23, between cognitive s t y l e and measures of problem-solving.  In the  three cases c i t e d above the correlations between these measures were consistently p o s i t i v e and i n the d i r e c t i o n of being higher for T l than f o r T23, although the Z transformation test indicates that no s i g n i f i c a n t differences e x i s t . To allow for a further examination  of these interactions, scores  on the CST were trichotimized so that the lowest t h i r d of the t o t a l sample whose scores were between 0 and 3 were designated as LOW,  the  middle t h i r d whose scores were between 4 and 8 were designated as MEDIUM, and the top third whose scores were between 9 and 15 were designated as HIGH analytic.  For each of the three interactions which were s i g n i f i c a n t  i n the regression analysis, the residuals remaining for each subject after the effect of the covariates, organismic main e f f e c t s ,  treatment,  and organismic interactions had been removed were collected, and the means calculated for the LOW, T23.  MEDIUM, and HIGH analytic subjects within T l and  Hence, the residuals represent the raw scores adjusted for the  effects of the terms which entered the regression model p r i o r to the interaction terms of i n t e r e s t , and are therefore the appropriate values to use i n this type of detailed examination the interactions.  into the s p e c i f i c nature of  These group means are presented i n Figures 2, 3, and 4.  CA table of the means can be found i n Appendix E).  In Figure 2 the  relationship between training and cognitive s t y l e can be seen for mean t o t a l questions.  The trained group asked more questions than the control  groups i f they were classed as MEDIUM or HIGH analytic.  The control  groups, however, asked more questions than the trained group i f they were classed as LOW  analytic.  A similar trend can be seen i n Figure 3  70  Tl .  . T23  + 1.20  I MEDIUM 4  i  GROUP LOWER LIMIT UPPER LIMIT  LOW 0 3 COGNITIVE  HIGH 9 15  STYLE GROUPING  FIGURE 2 MEAN RESIDUALS AND  UNTRAINED  OF MEAN TOTAL QUESTIONS FOR  TRAINED ( T l )  (T23) SUBJECTS AT THREE LEVELS OF  COGNITIVE  STYLE (LOW,  ANALYTIC  MEDIUM, HIGH C S T ) .  71 ,T1 T23  + .75 + .50  + .25L  1-5  < P  - . 25L  H W -  !3  .50  - -75L  w  -1. 00 -1.25-1.50.  GROUP LOWER LIMIT UPPER LIMIT  MEDIUM 4 8  LOW 0 3  HIGH 9 15  COGNITIVE STYLE GROUPING FIGURE 3 MEAN RESIDUALS OF MEAN INFORMATION-SEEKING ASKED BY TRAINED AT THREE LEVELS  ( T l ) AND  UNTRAINED  QUESTIONS  (T23) SUBJECTS  OF ANALYTIC COGNITIVE STYLE  (CST) .  t  Tl  _ _. T23  +1.00  P  +  . 75  +  .50 1"  +  . 25  V  C/3 < P  H w  25  53  <« - .50 w  75 -1. 00 -1. 25  GROUP LOWER LIMIT UPPER LIMIT  HIGH 9 15  MEDIUM 4 8  LOW 0 3 COGNITIVE  STYLE GROUPING  FIGURE 4 MEAN RESIDUALS TRAINED  OF MEAN RESIDUAL  ( T l ) AND  UNTRAINED  THREE LEVELS OF ANALYTIC  QUESTIONS  FOR  (T23) SUBJECTS  AT  COGNITIVE  STYLE (CST)  for mean, number of information-seeking questions asked.  With, regard to  mean residual questions asked (Figure 4), the trained group exceeded the untrained  group only i f they were highly analytic.  If they were moderately  analytic, the scores were v i r t u a l l y the same for the two Consistent with the other two groups who LOW  were LOW  treatment groups.  dependent variables of concern, the control  analytic asked more residual questions than did the  analytic trained group. To gain further insight Into the question of why  the LOW  analytic  trained group did not appear to benefit from t r a i n i n g , unlike their MEDIUM and HIGH analytic classmates, a further comparison was As the t r a i n i n g program was  completely self-paced, the student was  to work through the materials  free  as quickly or as slowly as they wished  (to a maximum of 14 30-minute sessions). possible that the LOW  performed.  For this reason i t seemed  analytic c h i l d would work through the  materials  quickly, and hence l i k e l y derive l i t t l e benefit from t h e i i n s t r u c t i o n provided therein.  To test for this p o s s i b i l i t y , a correlation was  calculated between the child's score on the CST which he spent on the t r a i n i n g materials. .45 with a Z of 2.3247 (p< .05). the explanation  and the number of days  The r e s u l t i n g c o e f f i c i e n t was  This finding would o f f e r support for  offered above as to why  LOW  analytic trained children did  not appear to benefit from the t r a i n i n g . S t i l l unexplained, however, was analytic untrained  the consistent finding that  low  children not only exceeded the trained children of  l i k e cognitive s t y l e , but also exceeded their moderately and  highly  analytic classmates on the three dependent variables shown i n Figures 3, and 4.  2,  From Table V i t can be seen that the correlations between the  Torrance measures of c r e a t i v i t y and mean t o t a l questions, mean  information-  74 seeking questions, and mean residual questions were p o s i t i v e and consistently higher f o r the untrained than for the trained group. Because of t h i s trend, i t was f e l t that an examination of the r e l a t i o n ship between conceptual s t y l e and Torrance sub-test scores within T l and T23 might shed some further l i g h t on the unexpected finding for the LOW analytic untrained group.  To this end, the mean fluency,  flexibility,  and o r i g i n a l i t y scores were calculated for each of the three conceptual style groups within T l and T23. These means are shown graphically i n Figure 5: A, B, and C.  As can be seen from these figures, the untrained  group consistently exceeded t h e i r trained peers i n terms of both fluency and f l e x i b i l i t y , but notcon o r i g i n a l i t y .  Moreover, the low  analytic untrained children proved to be more fluent and f l e x i b l e than their MEDIUM and HIGH analytic classmates.  Given these additional facts  concerning the nature of the children who f a l l into this untrained LOW analytic c l a s s i f i c a t i o n , a possible explanation for t h e i r unexpectedly high performance on the three dependent variables of concern might be their higher measured verbal fluency and f l e x i b i l i t y . In summary, the results for Hypothesis 10 can be stated as follows: Hypothesis 10: A s i g n i f i c a n t i n t e r a c t i o n exists between t r a i n i n g and cognitive s t y l e such that the relationship between number of analytic responses on the CST and mean t o t a l questions, mean information-seeking questions, and mean residual questions i s positive and greater for the trained than for the untrained subjects.  No s i g n i f i c a n t interaction exists between  cognitive s t y l e and training for the remaining seven dependent measures.  FLUENCY H O  i\  CO On  CO  •PCO  CO  1—  C/1  > o W CO  w  o  H W  CO  H  CO  H CO  o  > > f  i-< H  n o  pa M CO  o pa  FLEXIBILITY  H  n o o o  - M  H  H ps  •pCO  > M  •O  C/i  Cn Co  1  a w o  -p-  -I  1  M  < M  H M  S  '  CO  H f  >  a a a  1—1  CD  n  /  CO  /  /  /  H  H  CO  —s  H O • PS s: ' > M  S  M  21 W a  a M  a  ^—,  H  N J  C O  H  CO  tu  w  ORIGINALITY  J> CO  M H CO  > H H a  pd w w  r<  < m f CO  -P"  -PLn  4*On  -r  Ch  •  4>-  n CO  H  -P-  4> 00  76 In Hypothesis 11 i t was predicted that a s i g n i f i c a n t interaction would e x i s t between t r a i n i n g and conceptual tempo (as measured by errors on the MFF),  such that the relationship between the number of errors on  the MFF and a l l measures of problem-solving would be negative and greater for the untrained  groups (T23) than for the trained group ( T l ) .  Examination of the values for the i n t e r a c t i o n of MFF errors with Training DV1 ( T l vs T23) on Table III indicate that the variance  accounted f o r  by this term was s i g n i f i c a n t i n two of the ten dependent variables. These were mean t o t a l time (F^ ^ time (F __ = 3.6969, p< .05). i ,i>y  = 5.2685, p < .02)  and mean residual  To determine the d i r e c t i o n of these  relationships, the correlations between errors on the MFF and these two dependent variables for T l and T23 were examined (see Table V). to expectation,  Contrary  the negative relationship between these variables was  greater for the trained than for the untrained  group; for mean t o t a l time  they were T l = -.47, T23 = -.08; for mean residual time T l = -.30 and ..i  T23 = +.05.  The differences between these pairs of c o e f f i c i e n t s were  not s t a t i s t i c a l l y s i g n i f i c a n t , however (see Table VI). To allow for further examination of these interactions, trichotimization of the continuous variable "MFF errors" was undertaken i n a manner s i m i l a r to that used to trichotimize CST. to 5 erros were c l a s s i f i e d as LOW impulsive, impulsive,  Subjects with 0  6 to 9 errors as MEDIUM  and 10-16 errors were considered HIGH impulsive.  The means  of the residuals for mean t o t a l time and for mean residual time for each l e v e l of impulsivity within T l and T23 were then calculated by the same procedure used i n the previous section.  These mean are shown graphically  i n Figures 6 and 7 (the means are presented i n table form i n Appendix E ) .  Tl •  • T23  + 20,  +  151  + 10fr + 5 CO  Q M  erf -10  -15 -20 -25 -30  GROUP LOWER LIMIT UPPER LIMIT  LOW 0 5  MEDIUM 6 9  HIGH 10 16  IMPULSIVITY GROUPING FIGURE 6 MEAN RESIDUALS UNTRAINED  OF MEAN TOTAL  (T23) SUBJECTS (LOW,  TIME  FOR TRAINED  ( T l ) AND  AT THREE LEVELS OF IMPULSIVITY  MEDIUM, HIGH MFF  ERRORS).  78 Tl T23  + 25 r+ 20 U + 15 + 10  <  + 5  o M  C O  w - 5 -10 -15 -20 _1_  JL.  GROUP LOWER LIMIT UPPER LIMIT  MEDIUM  LOW 0 5  6 9 IMPULSIVITY  HIGH 10 16  GROUPING  FIGURE 7 MEAN RESIDUALS AND  UNTRAINED  OF MEAN RESIDUAL TIME FOR TRAINED ( T l ) (T23) SUBJECTS AT THREE LEVELS OF IMPULSIVITY  (MFF ERRORS).  79 In both, figures i t can be seen that LOW and MEDIUM impulsive children i n the trained group exceeded the untrained  group on both of these  dependent measures, but that the reverse was true for HIGH impulsive children. Because i t was suspected that HIGH impulsive children may have worked through the t r a i n i n g materials  quickly, as had occurred with LOW  analytics, the c o r r e l a t i o n between days spent on the programme and errors on the MFF was calculated. p< .05.  The r e s u l t i n g c o e f f i c i e n t wass-,40, Z = 1.986,  This finding would support the contention  that HIGH impulsive  children do not benefit from the t r a i n i n g because they do not take the time necessary for benefit to derive while working through the materials. Because the correlations between the c r e a t i v i t y sub-test  scores  and mean t o t a l time and mean residual time tended to be higher for the untrained  than for the trained subjects  (see Table V), the means f o r the  three impulsivity groups on these c r e a t i v i t y measures were calculated for each treatment group.  The r e s u l t i n g means are presented graphically i n  Figure 8: A, B, and C.  I t w i l l be noted that HIGH impulsive subjects i n  T23 achieved higher scores on the fluency and f l e x i b i l i t y sub-tests did HIGH impulsive subjects i n the trained group.  This o r i g i n a l  difference between these two groups may have contributed i t y of the untrained  than  to the superior-  group on the two problem-solving measures of concern.  The results for Hypothesis 11 can be summarized as follows: Hypothesis 11: A s i g n i f i c a n t i n t e r a c t i o n exists between training and  conceptual tempo such that the relationship  between the number of errors on the MFF and mean t o t a l time and mean residual time i s negative and  F L U E N C Y CO  CO  CO  U l  H o pd PC) > a o w  4>» M  4>  CO  1  1  U l  4> 1  i  CO  <=! td  f  I  CO  W  pd i—i pd < O H pd H  H M  CO  H  CO K | CO  o  O pd M o  CO  M  o Pd  S hd a tr CO 1  M  < H H K!  EC F L E X I B I L I T Y  4>-  H Pd  >  4> -P-  ON  •poo  U l  O  U l  K5  rN*—r  M  a w u  .-—s '  N  r o s: » 1  sw et 1—1  a  a •  H  S  1  M  •—'  o  > a o  a H pd  in  pd M 00  N  i—i  s t" CO 1  td  M pd Pd o Pd CO  l-H  < H  s  T " l  I. •  H K!  — '  H  Al  s  **  H 1—  CO  a M o  a  a H  N3  O R I G I N A L I T Y  CO  •P-  •P-  •P>  -P~  U l  ON  CO  .V-r  a w  tr" L  C-4  M  n H  CO  /-N  |—I  •> H  tr  1  H a Pd W  M  CO  pO H  Pd  O  pd  <  H  H co K !  < M CO  08  a  -P-  -P~  00  •p-  o  H  81  greater for the trained than for the group.  untrained  No s i g n i f i c a n t interaction exists for the  remaining eight measures of problem-solving. In Hypothesis 12 i t was  predicted that a s i g n i f i c a n t i n t e r a c t i o n  would e x i s t between t r a i n i n g and conceptual tempo such that the r e l a t i o n ship between mean latency of response on the MFF  and the ten measures of  problem-solving w i l l be p o s i t i v e and greater for the untrained  than for  the trained group.  time and  Training DV1  Examination of the interaction between MFF  ( T l vs T23)  on Table III reveal that this i n t e r a c t i o n term  did not account for a s i g n i f i c a n t amount of the variance ten dependent variables. between MFF  i n any of the  I t w i l l further be noted that the correlations  time and measures of problem solving (see Table V) for T l  and T23 show no consistent pattern. be summarized as  The results for Hypothesis 12  can  follows:  Hypothesis 12: No s i g n i f i c a n t interaction exists between t r a i n i n g and conceptual tempo as measured by mean latency of response on the MFF  for any of the ten dependent  variables. Additional  Findings  It w i l l be r e c a l l e d that the present study was p r i n c i p a l l y intended to be exploratory  i n nature.  While a number of s p e c i f i c  hypotheses were put forward for examination concerning the e f f e c t s of cognitive s t y l e , conceptual tempo, and  t r a i n i n g upon problem-solving  processes, of equal i n t e r e s t were any additional s i g n i f i c a n t findings which were uncovered by the regression analysis.  In the following section  these additional findings w i l l be presented and summarized.  82  To allow for the examination of the interaction between cognitive style and conceptual tempo, the following three terms were generated and entered into the regression equations for each dependent v a r i a b l e : XgX^ - Analytic responses on CST x Total errors on MFF XgXg - Analytic responses on CST x Mean latency of response on MFF X.,X - Total errors on MFF x Mean latency of response on MFF / o 0  Interaction of CST with MFF errors: The results presented i n Table I I I indicate that the i n t e r a c t i o n between CST and MFF errors accounted for a s i g n i f i c a n t amount of the variance i n f i v e of the measures of problem-solving. t o t a l time (F-j^  5 g  There were mean  = 15.80, p«i .0003), mean t o t a l questions ( F  15 g  = 5.8316,  p< .01), mean information-seeking questions (F^ ,_ - 5.5576, p < .02) , g  mean residual time (F.. = 10.2727, p < .002) and mean residual questions i,oy (F. _ = 7.6728, p < .007). i,jy C Q  In order to examine further the e f f e c t of the i n t e r a c t i o n between s t y l e and tempo on each of these f i v e problem-solving measures, the two continuous organismic variables (CST and MFF errors) were treated as trichotomous variables, as defined i n the reporting of Hypotheses 10 and 11 i n the preceding section.  Each subject within the t o t a l sample of  81 was then assigned to one of the c e l l s of the r e s u l t i n g 3 x 3 matrix. The composition of each of these nine c e l l s i n terms of school achievement, c r e a t i v i t y , and treatment group membership are presented i n Table VII. For each of the f i v e dependent variables for which this i n t e r a c t i o n was s i g n i f i c a n t , the residuals which remained for each subject when the effects of the covariates, organismic, and treatment main effects had  TABLE V I I COMPOSITION OF NINE  CELLS DERIVED VIA TRICHOTIMIZING  RESPONSES ON THE CST AND ERRORS ON THE MFF  M F F  LOW  L 0  w  C .  S .  M E D I U M  TT  a  I H  E R R O R S  MEDIUM  HIGH 4 .73 41.16 47.33 47.66 3 1 2 6  CTBS FLUENCY FLEXIBILITY ORIGINALITY T l n: T2 n: T3 n: Total  5 .66 45 . 66 55 .83 49 . 50 1 3 2 6  4 .62 39 . 00 45.75 46.58 4  CTBS FLUENCY FLEXIBILITY ORIGINALITY T l n: T2 n: T3 n: Total  5 . 45 40.70 48 . 30 47 . 90 2 2 6 10  5. 38 . 45 . 43 . 1 4 4 9  38 88 11 55  4.80 39 . 80 42 .80 43.80 1 5 4 10  CTBS FLUENCY FLEXIBILITY ORIGINALITY Tl n : T2 n: T3 n: Total  5 . 40 41.81 48 . 90 49.18 6 2 3 11  4.82 36.00 41. 85 44 . 00 2 1 4 7  5 .36 36.50 41.70 42 . 80 5 4 1 10  %  4 12  84 been s t a t i s t i c a l l y removed were obtained.  The means of these residuals  were then calculated for each of the nine c e l l s i n the matrix.  These  means are presented i n Table VIII and are plotted graphically i n Figures 9, 10, 11, 12, and 13.  For the two dependent measures which deal with  time, mean t o t a l time (Figure 9) and mean residual time (Figure 10), a number of consistent  trends w i l l be noted.  These can be summarized as  follows: 1. For low analytic children, time spent on the problem generally decreases as impulsivity increases. 2. For moderately analytic children time spent on the problem generally remains constant as impulsivity increases. 3. For highly analytic children time spent on a problem decreases for moderately impulsives, and then increases for highly impulsive children. 4. For low impulsive children, time spent on a problem as analytic a b i l i t y decreases.  increases  5. For moderately impulsive children, highly analytic children spend less time on the problem than either moderately or low analytic children, who differ?very l i t t l e from one another. 6. For highly impulsive children, time spent on a problem as analytic a b i l i t y increases.  increases  For the three measures of question-asking behavior, t o t a l questions (Figure 11), mean information-seeking questions (Figure 12), and mean residual questions (Figure 13), very s i m i l a r trends were found to those concerning time.  These can be summarized as follows:  1. For low analytic children, questions asked during problem-solving decreases as impulsivity increases. 2. For moderately analytic children, questions asked during problem-solving increases for moderately impulsives and then decreases again for the highly impulsives to a l e v e l s i m i l a r to the low impulsives. 3. For the highly analytic children, the number of questions asked during problem-solving decreases s l i g h t l y from low to moderately  85  TABLE  VIII  MEAN RESIDUALS OF FIVE MEASURES OF PROBLEM SOLVING FOR LEVELS OF THE CST BY MFF ERRORS  MFF DEPENDENT VARIABLE  LOW  INTERACTION  ERRORS MEDIUM  HIGH  TOT . TIME TOT . QUES . I . S .: QUES. RES . TIME RES . QUES .  + 13 .9666 + 1. 7987 + 1. 3231 + 20 .2134 + 1. 7278  + 24 . 8500 .3902 .4703 + 8 .7527 . 1270 —  -65 .5205 - 1. 8714 - 1 .1990 -44 . 6417 - 1. 3152  X TOT . TIME M X .TOT . QUES . E X I . S . QUES . D . X RES . TIME X RES . QUES .  - 6. 7803 4186 0854 + 6. 5034 4240  + 6 . 0550 + .8402 + . 6012 + 8 .2976 + .4211  + 12 ••2045 1070 0567 + + 4. 0467 0815  X TOT . TIME X TOT . QUES . X I . S .QUES . X • RES .TIME X RES . QUES .  -15 .9156 4943 2942 -14. 0976 5985  -40 .7877 .8757 .6690 -48 . 2757 .7211  +36 .2921 + 1. 1380 7693 + +39 .9105 + 1. 1947  L 0 w  X X X X X  C.  H I G H  —  LOW GST MEDIUM CST HIGH CST + 40 _  + 30 + 20 + 10  CO  i—* Q  S -20 Pi  <!  w -30 S  -40 -50  -60 -70  GROUP LOWER LIMIT UPPER LIMIT  •I  HIGH 10 16  MEDIUM 6 9  LOW 0 5  IMPULSIVITY  GROUPING  FIGURE 9 MEAN RESIDUALS OF MEAN TOTAL TIME FOR SUBJECTS THREE LEVELS  OF ANALYTIC  LEVELS  STYLE  OF IMPULSIVITY  (CST) AND THREE (MFF ERRORS).  AT  87 _a LOW CST MEDIUM CST ^ HIGH CST  ^  GROUP LOWER LIMIT UPPER LIMIT  L  0  MEDIUM 6  W  0 5  HIGH 10 16  . 9  IMPULSIVITY  GROUPING  FIGURE 10 MEAN RESIDUALS OF MEAN RESIDUAL TIME FOR SUBJECTS THREE LEVELS LEVELS  OF ANALYTIC  STYLE  OF IMPULSIVITY  (CST) AND THREE  (MFF ERRORS).  AT  88  . LOW l  CST  MEDIUM  A HIGH  CST  CST  +2.0. •  +1.5  L  + 1. 0  +  . 5  -  . 5  CO  <  !=> Q  I—I CO  W  Pi  <! W  a  -1.0 -1.5 r-2 . 0  GROUP LOWER LIMIT UPPER LIMIT  HIGH 10 16  MEDIUM 6 9  LOW 0 5  IMPULSIVITY  FIGURE  GROUPING  11  MEAN RESIDUALS OF MEAN TOTAL QUESTIONS FOR AT THREE LEVELS LEVELS  OF ANALYTIC OF  STYLE  IMPULSIVITY  (MFF  (CST) AND ERRORS).  SUBJECTS THREE  89  +1.40 _  • H.  • LOW CST | MEDIUM CST HIGH CST A  + 1.20 + 1. 00 + .80 + .60 + .40 co ^+ n C O  w  -20 0  Pi  53  3 - .20 40 60 - .80 -1. 00 -1.20  I GROUP LOWER LIMIT UPPER LIMIT  I LOW 0 5  I MEDIUM 6 9  • HIGH 10 16  IMPULSIVITY GROUPING FIGURE 12 MEAN RESIDUALS OF MEAN INFORMATION-SEEKING  QUESTIONS  FOR SUBJECTS AT THREE LEVELS OF ANALYTIC STYLE (CST) AND THREE LEVELS  OF IMPULSIVITY  (MFF ERRORS).  LOW CST -a MEDIUM CST •A HIGH CST  + 1.75  90  +1.50 + 1.25  + 1. 00 +  .75  +  .50  S+  .25  P 0 aw  .25  a  -  .50  -  .75  -1. 00 -1.25 -1.50  GROUP LOWER LIMIT UPPER LIMIT  I LOW 0 5  MEDIUM 6 9 IMPULSIVITY  HIGH 10 16  GROUPING  FIGURE 13 MEAN RESIDUALS OF MEAN RESIDUAL QUESTIONS FOR AT THREE LEVELS LEVELS  OF  OF ANALYTIC IMPULSIVITY  STYLE (MFF  (CST) AND ERRORS).  SUBJECTS THREE  91  impulsive, but increases for the highly impulsives. 4. For low impulsive children the number of questions asked during problem-solving increases as analytic a b i l i t y decreases. 5. For moderately impulsive children, those who are also moderately analytic ask most questions, and those who are highly analytic ask fewest questions, with the low analytics f a l l i n g i n between. 6. For highly impulsive children, the number of questions asked during problem-solving increases as analytic a b i l i t y increases. Because the c l a s s i f i c a t i o n of the eighty-one subjects into nine c e l l s v i a trichotomization of the two continuous organismic variables had been performed on a post hoc b a s i s , i t appeared b e n e f i c i a l to analyze the composition of the c e l l s i n terms of school achievement, c r e a t i v i t y , and training group, as presented i n Table VII.  From Figure 14 i t can be  seen that school achievement, as measured by the CTBS generally decreases as impulsivity increases.  For highly analytic subjects, however, more  impulsive children score only s l i g h t l y lower than r e f l e c t i v e impulsive) children on this measure of school achievement. the general superiority of this group on the time and  (LOW  Recalling  question-asking  measures that were presented above, this a d d i t i o n a l information provides further explanation for this finding. In terms of the c r e a t i v i t y measures (Figure 14: B, C, and D), general trends emerge:  two  1. Low impulsive children tend to score higher on  these c r e a t i v i t y measures while moderately and highly impulsive children d i f f e r very l i t t l e ;  2. Low  analytic children tend to score higher on  measured verbal fluency, f l e x i b i l i t y and o r i g i n a l i t y than moderately or highly a n a l y t i c , p a r t i c u l a r l y at the two extremes of the impulsivity scale.  I t w i l l be r e c a l l e d that low analytic-low impulsive children  consistently exceeded moderately and highly analytic children of low  92  LOW CST 5.8  ^ MEDIUM CST  r-  ^ HIGH CST 5.6  46  \-  44  5.4  £  co5.2  m  w  H  u  1-1  ^5.0  *  a  w  <! w  a  4.8  42  40  38  U  \ \  36  4.6  LOW  MEDIUM  HIGH  LOW.  IMPULSIVITY  MEDIUM IMPULSIVITY  A. 56  H  B. 50  «.  52  H  H  H CQ M  XI  HIGH  „  48  <U 48  L  M 46 O I—I Pi  44  L  o  w <i W  44  W a  40  LOW  MEDIUM  42  HIGH  LOW  IMPULSIVITY  MEDIUM IMPULSIVITY  C .  D. FIGURE 14  MEANS FOR CTBS ORIGINALITY ANALYTIC  ( A ) , FLUENCY  ( B ) , FLEXIBILITY  (D) FOR SUBJECTS  STYLE  (CST) AND  ( C ) , AND  AT THREE LEVELS OF  IMPULSIVITY  (MFF ERRORS).  HIGH  impulsivity on the f i v e measures of time and question-asking behavior reported above.  The demonstrated s u p e r i o r i t y of this low analytic group,  i n terms of Fluency and F l e x i b i l i t y , may  p a r t i a l l y account for t h e i r out-  performing moderately and highly analytic peers on these problem-solving measures. Figures 9 through 13 consistently show a U-shaped pattern i n both time spent and questions asked during problem-solving for the highly analytic children over the three levels of impulsivity. i n Table VII that s i x of the eleven children i n the low analytic group were from the trained class ( T l ) .  It w i l l be noted impulsive-high  Five of the  ten  children i n the high impulsive-high analytic group were trained.  Only  two of the seven children i n the moderately impulsive-high a n a l y t i c group (who  consistently scored lowest of the three groups) were trained.  This difference i n c e l l composition could, i n part, account f o r the poorer performance of this moderately impulsive group, p a r t i c u l a r l y i n l i g h t of the fact that t r a i n i n g had increasing a l l but one  the e f f e c t of s i g n i f i c a n t l y  (mean residual time) of the f i v e dependent  variables under consideration  Interaction of CST with MFF  at t h i s point.  Time  Table III indicates that this i n t e r a c t i o n term did not account for a s i g n i f i c a n t amount of the variance i n any of the ten dependent variables.  94  Interaction of MFF errors with MFF Time The interaction of these two measures of conceptual tempo accounted f o r a s i g n i f i c a n t amount of the variance i n two measures of problem-solving (see Table I I I ) . These were mean p r i o r time (F. 6.2164, p< .01) and mean p r i o r questions (F.^ ^  _ =  = 4.3750, p * . 0 3 ) .  To  allow for a closer examination of these interactions, a s i m i l a r procedure of trichotomization was used f o r the two continuous organismic variables as had been done f o r the interactions between CST and MFF errors, placing each of the eighty-one subjects i n one of the c e l l s of the r e s u l t i n g 3 x 3 matrix.  The composition of each of the r e s u l t i n g nine c e l l s i n  terms of school achievement, c r e a t i v i t y , and treatment group membership i s presented i n Table IX.  I t should be r e c a l l e d by the reader at this  point that a high score on the MFF errors measure implies impulsivity while a high schore on the MFF time measure implies the opposite, reflectivity.  For the purpose of simplifying the following presentation,  differences on the MFF errors w i l l be referred to as "accurate" versus "inaccurate", and differences on the MFF time measure w i l l be referred to as "slowness" versus "fastness". Mean residuals were calculated f o r each of the nine c e l l s , using the same procedure described i n the preceding section.  These data are  presented i n Table X and are plotted graphically i n Figures 15 and 16. Inspection of these two figures reveals s l i g h t l y d i f f e r e n t trends.  For  the measure of p r i o r time, the following s i x trends are noted: 1. For accurate children, as "fastness" increases, time spent p r i o r to o f f e r i n g a solution increases. 2. For moderately accurate children, as "fastness" increases, time spent p r i o r to o f f e r i n g a solution decreases.  95 TABLE IX COMPOSITION OF NINE CELLS DERIVED VIA TRICHOTIMIZING LATENCY  OF RESPONSE AND ERRORS ON THE MFF  MFF HIGH  MEDIUM  LOW  H I G H  CTBS FLUENCY FLEXIBILITY ORIGINALITY T i n : T2 n: T3 n: Total  4 . 98 36 . 00 39.60 41.20 0 3 2 5  5 . 09 40.30 45 .40 47.10 3 3 4 10  4 .92 3 8.81 43.36 43 . 18 6 4 1 11  M E D I U M  CTBS FLUENCY FLEXIBILITY ORIGINALITY T l n: T2 n: T3 n: Total  4.81 36 . 85 42.57 44. 57 1 3 3 7  5. 38 . 44 . 45 . 4 3 5 12  96 08 00 66  4 .81 39 . 44 46.88 44 . 33 2 3 4 9  CTBS FLUENCY FLEXIBILITY ORIGINALITY T l n: T2 n: T3 n: Total  5 .43 41.50 46.92 47 ,50 4 3 7 14  5 .60 41.36 48 . 90 48 .71 5 3 3 11  5 . 05 52.50 67 . 00 57.50 0 1 1 2  M F F E R R 0 R S  TIME  L 0 W  c 96  TABLE X MEAN RESIDUALS OF TWO  MEASURES OF PROBLEM SOLVING  FOR LEVELS OF THE MFF  ERRORS BY TIME INTERACTION  MFF  DEPENDENT VARIABLE  M F F E R R 0 R S  H I G H  MEDIUM  LOW  X PRIOR  TIME  +15.6890  -14 .5244  - 9.9 34 7  X PRIOR  QUES.  +  -  .4555  -  .4140  TIME  +14.0285  +10.6112  +  .2238  QUES.  -  +  +  .2530  X PRIOR  TIME  -11.3392  + 2.1857  +41.6172  X PRIOR  QUES.  -  +  + 1.3235  M X PRIOR E D. X PRIOR L 0 W  HIGH  TIME  .9627  .3895  .1653  .2291  .1271  + 45  97  LOW MFF ERRORS  + 40  I  MEDIUM MFF ERRORS  A  HIGH MFF ERRORS  + 35 + 30 + 25 + 20 w +15 <!  S3  o  M  CO  +10  w  Pi  a + 5 w a  o - 5 -10 -15 -20  GROUP LOWER LIMIT UPPER LIMIT  X MEDIUM 9 15  HIGH 16 37  LOW 1 8  REFLECTIVITY GROUPING FIGURE 15 MEAN RESIDUALS OF MEAN PRIOR TIME FOR SUBJECTS AT THREE LEVELS  OF ACCURACY  LEVELS  (MFF ERRORS) AND THREE  OF REFLECTIVITY  (MFF T I M E ) .  98 LOW MFF ERRORS MEDIUM MFF ERRORS HIGH MFF ERRORS  + 1.2 + 1. 0  + w + . 6 <3 !=> P H + . 4 CO  w erf  a  <u w s  + . 2 0  -  . 2  - .4  GROUP LOWER LIMIT UPPER LIMIT  MEDIUM 9 15  HIGH 16 37  REFLECTIVITY  Jl  LOW 1  GROUPING  FIGURE 16 MEAN RESIDUALS OF MEAN THREE LEVELS  PRIOR QUESTIONS ASKED BY SUBJECTS AT  OF ACCURACY  (MFF ERRORS) AND THREE LEVELS OF  REFLECTIVITY  (MFF T I M E ) .  99  3. For inaccurate children, as "fastness" increases, time spent p r i o r to offering a solution decreases and then increases slightly. 4. For slow children, as accuracy decreases, time spent p r i o r to o f f e r i n g a solution Increases. 5. For moderately slow children time spent p r i o r to o f f e r i n g a solution i s lowest for the inaccurate, highest f o r the moderately accurate, with the highly accurate f a l l i n g midway. 6. For fast children, as accuracy increases, time spent p r i o r to o f f e r i n g a solution increases. A number of s l i g h t l y d i f f e r e n t trends can be seen i n Figure 16 with regard to question-asking behavior: 1. For accurate children, as "fastness" increases, number of questions asked p r i o r to o f f e r i n g a solution increases. 2. For the moderately accurate children, as "fastness" increases, number of questions asked p r i o r to o f f e r i n g a solution increases. 3. For highly inaccurate children, as "fastness" increases, the number of questions asked p r i o r to o f f e r i n g a solution decreases. 4. For slow children, number of questions asked p r i o r to o f f e r i n g a solution i s highest for the inaccurate, with the moderately and highly accurate d i f f e r i n g very l i t t l e . 5. For moderately slow children, the inaccurate ask fewest questions p r i o r to o f f e r i n g a solution, with the moderately and highly accurate d i f f e r i n g very l i t t l e . 6. For fast children, as accuracy increases, the number of questions asked p r i o r to o f f e r i n g a solution increases. To gain additional insight into the composition of each of the nine c e l l s , the data presented i n Table IX was examined further.  As can be  seen from Figure 17A children who were c l a s s i f i e d as accurate by their number of MFF errors tend also to be high scorers on measures of school achievement, p a r t i c u l a r l y i f they were assessed as being highly or moderately r e f l e c t i v e on the MFF time measure.  I t w i l l be further noted  from Figure 17B, C, and D that the highly accurate children tended to  LOW MFF ERRORS  100  MEDIUM MFF ERRORS HIGH MFF ERRORS 56 5 . 6r  52  5.4  48  5. 2  era PQ H U  U  44  55  W PJ  5. 0  40  S3 <!  w S  K  4.8  s  HIGH  MEDIUM  36 X HIGH  LOW  MEDIUM  LOW  REFLECTIVITY (MFF TIME)  REFLECTIVITY (MFF TIME)  B . 6157  68 >*  EH  H  60  H  531.  >J <! is i—i  M  X 52  o 49  w  H O  5s 44 «3 W S 36  a 45 < w  a  HIGH  MEDIUM  41 L  HIGH  LOW  MEDIUM  REFLECTIVITY (MFF TIME)  REFLECTIVITY (MFF TIME)  C  D. FIGURE 17  MEANS FOR CTBS ORIGINALITY  ( A ) , FLUENCY  ( B ) , FLEXIBILITY  ( C ) , AND  (D) FOR SUBJECTS AT THREE LEVELS OF ACCURACY  (MFF ERRORS) AND REFLECTIVITY  (MFF T I M E ) .  LOW  1 0 1  score higher on the Torrance measures of c r e a t i v i t y , p a r t i c u l a r i t y at the fast end of the MFF time scale.  The consistent superiority of this  quick-accurate group on both p r i o r time and p r i o r questions could be j u s t i f i e d i n part by this superiority i n c r e a t i v i t y .  I t should be noted,  however, that only two subjects f e l l into this quick—accurate c l a s s i f i cation, neither of whom were from the training group.  The very small  size of this p a r t i c u l a r group, of necessity, places severe r e s t r i c t i o n s on the g e n e r a l i z a b i l i t y of the performance of this group.  Summary of Effects of Organismic Interactions* In summary, i t would appear that the effects of the organismic variables discussed above tend to modify each other.  If a child i s  highly impulsive but a n a l y t i c , he w i l l spend a longer time on the problem and ask more questions than would normally be predicted on the basis of impulsivity alone.  Likewise, i f he i s not analytic but  r e f l e c t i v e , he w i l l spend a longer time i n problem solving and ask more questions than would be expected on the basis of being non-analytic alone. I f a c h i l d i s highly impulsive but accurate, he w i l l spend a longer time and ask more questions p r i o r to o f f e r i n g a solution than would be expected on the basis of impulsivity only, and i f he i s highly inaccurate but r e f l e c t i v e , he w i l l also spend more time and ask more questions than his l e v e l of inaccuracy alone would lead one to predict.  Creativity and Problem-Solving The p r i n c i p a l purpose foroobtaining the three Torrance sub-test scores f o r the eighty-one children who participated i n this study was to allow for the examination  of problem-solving with the effects of  102 c r e a t i v i t y s t a t i s t i c a l l y controlled.  The rationale for this decision,  based on the research l i t e r a t u r e i n the area of c r e a t i v i t y , has been a d d i t i o n a l l y j u s t i f i e d i n the present study.  As demonstrated oil Table I I I ,  the combined effects of the three Torrance sub-test scores did account for a s i g n i f i c a n t amount of the variance i n a l l but three of the ten dependent variables. Given the consistency of the influence of fluency, f l e x i b i l i t y , and o r i g i n a l i t y when combined as covariates, i t became of some interest to the present researcher to determine  the degree to which each of the  three i n d i v i d u a l Torrance scores related to the problem solving measures examined i n this study.  To allow for this type of examination, ten  separate regression analyses were performed,  one for each dependent  variable, which entered each Torrance Sub-test score as a separate variable, with the C.T.B.S. scores of school achievement treated as a covariate. Table XI.  A summary of the results of these analyses are presented i n From these data i t becomes apparent that Fluency did not  s i g n i f i c a n t l y predict any of the ten problem solving measures, and that F l e x i b i l i t y accounted for a s i g n i f i c a n t amount of the variance i n four of the ten measures.  O r i g i n a l i t y proved to be the most powerful predictor  of performance i n that i t accounted for a s i g n i f i c a n t amount of the variance i n s i x of the ten problem-solving measures, and approached s i g n i f i c a n c e i n predicting two further measures.  From the correlations  presented on Table V i t can further be seen that the d i r e c t i o n of these relationships are consistently i n the positive d i r e c t i o n . Thus, while the results of the p r i n c i p a l regression analyses, which treated Torrance scores as covariates, indicated that a relationship did exist between this combined multi-dimensional measure of c r e a t i v i t y ,  103  TABLE XI RESULTS OF REGRESSION SCORES  AND  ANALYSES  SUB-TEST  PROBLEM SOLVING MEASURES  TORRANCY DEPENDENT VARIABLE  FOR TORRANCE  FLUENCY ob s  SUB-TEST  FLEXIBILITY ob s  ORIGINALITY ob s  X TOTAL TIME  .5892  .45  1.7410  .18  5.5357  .02  X PRIOR TIME  .6581  .42  5.1111  .02  1.7521  .18  X TOTAL QUES.  .2972  .59  3.5045  .06  7.6306  .007  X PRIOR QUES.  .7657  .38  7.5135  .007  3.6846  .05  X I.S. QUES.  .3793  .54  1.3706  .24  5.7155  .01  XC.S.QUES.  .4473  .51  5.7280  .01  3.0000  .08  3.0194  .08  4.7961  .02  12.7087  TOTAL SOLUTIONS  .9338  .33  2.3305  .12  .5289  .47  X RES. TIME.  .0894  .75  .0000  .95  2.6829  .10  X RES. QUES.  .0168  .86  .3529  .56  5.7226  .01  X H.S.  QUES.  .0008  104  the additional information presented i n Table XI makes i t apparent that i t i s not simply being able to generate many responses (fluency) that w i l l relate to performance on the types' of problem used i n this  research.  While the a b i l i t y to provide responses which f a l l into several d i f f e r e n t categories ( f l e x i b i l i t y ) i s of some influence, i t i s p r i n c i p a l l y the child's a b i l i t y to generate and willingness to report unique responses ( o r i g i n a l i t y ) that i s of the greatest predictive value.  105  CHAPTER V DISCUSSION  The present study was  designed to explore three major issues:  1. The nature of the relationship between cognitive s t y l e and processes employed during problem solving. 2. The nature of the relationship between conceptual tempo and processes employed during problem solving. 3. The effectiveness of training v i a programmed i n s t r u c t i o n to f a c i l i t a t e the use of analytic and r e f l e c t i v e modes of problem solving. The  following discussion w i l l deal with the results of this study as they  relate to each of these issues.  Cognitive The  Style and Problem Solving results of the present study indicate no  statistically  s i g n i f i c a n t relationship between measured cognitive s t y l e and measures of problem-solving, contrary  to prediction.  the  ten  The rationale for  the prediction that analytic children would spend morettimeoon the problems presented, ask more questions, and make fewer i r r e l e v a n t guesses was  based on the previous research of Gardner, Holtzman, Witkin, and Kagan  who  repeatedly found analytic children more capable than non-analytic i n  the use of such s k i l l s as information-gathering, hypothesis generation and t e s t i n g , and s e l e c t i v e attention to relevant as opposed to irrelevant information.  The  f a i l u r e of the present study to f i n d any marked  differences among these children can be explained on several bases.  106 F i r s t l y , the nature of the testing s i t u a t i o n may  have been such that i t  decreased the p r o b a b i l i t y of a non-analytic s t y l e of responding being measured. that was  S p e c i f i c attempts were made to develop a testing atmosphere as free from pressure as possible.  at least one solution was  By v i r t u e of the fact that  offered i n 355 of the t o t a l of 364 problems  presented (four each to eighty-one subjects), i t appears that the children interpreted the s i t u a t i o n as one that required at least one solution to be generated and reported..  Because the non-analytic  child  tends to lack the a b i l i t y to discriminate important components of a problem and extract meaningful information, he would have to spend a longer time on the problem and ask more questions of "at least one solution".  to meet this requirement  The a n a l y t i c c h i l d , on the other hand, i s  capable of performing the necessary information-gathering testing s k i l l s on his own  and  and would need to ask fewer questions  hypothesisand  spend less time on the problem than he i s optimally capable of, to meet this c r i t e r i a of "at least one solution".  As a consequence, the measured  performance of children at the two extremes of the cognitive s t y l e continuum do not d i f f e r , but this may have come about f o r very d i f f e r e n t reasons.  While i t ' i s not possible to substantiate this speculation on  the basis of the present study, i t could prove a f r u i t f u l area of investigation for future research. with a "No  By more c l e a r l y providing the c h i l d  Solution" response a l t e r n a t i v e , analogous to the use of the  "Ready" card i n this study, the r e l a t i v e tendencies of the two  cognitive  style groups to use this form of response could be assessed. A second possible explanation due to cognitive s t y l e may  for the f a i l u r e to f i n d an e f f e c t  be seen i n the r e s u l t s of the i n t e r a c t i o n  between cognitive s t y l e and conceptual  tempo.  It w i l l be r e c a l l e d that  107 on f i v e of the ten dependent measures, the i n t e r a c t i o n between s t y l e and tempo was  significant.  This i n t e r a c t i o n was  such that measured  impulsivity tended to moderate the effects of cognitive s t y l e , which resulted i n the non-analytic c h i l d spending as much time and asking as many questions as the more analytic c h i l d i f he was moderately impulsive.  either low  or  The moderating e f f e c t of conceptual tempo resulted  i n decreasing the predicted e f f e c t of cognitive s t y l e . A t h i r d explanation for the f a i l u r e of cognitive s t y l e of r e l i a b l y predict processes used i n problem solving may r e l a t i n g to creative thinking factors.  I t was  be found i n the data found that measured  creative thinking a b i l i t y p o s i t i v e l y related to problem solving.  It  was  further found that non-analytic children tended to score higher than moderately or highly analytic children on tests of creative ability.  thinking  Given these relationships, i t seems plausible to conclude that  the higher measured creative thinking a b i l i t y of the non-analytic c h i l d functioned  to decrease the performance differences between the non-analytic  and analytic children.  Conceptual Tempo and Problem Solving The results of the present study indicate that a s i g n i f i c a n t relationship exists between the two measures of conceptual tempo (MFF  errors and  time) and four of the measures of problem solving.  of p a r t i c u l a r interest to note that conceptual tempo predicted three of the time measures, but predicted of question-asking (Mean constraint-seeking  It i s  to a l l  to only one of the measures questions).  The more  r e f l e c t i v e c h i l d appears w i l l i n g to spend a longer t o t a l time on a  108 problem, and a longer period both p r i o r to and following the o f f e r i n g of the f i r s t solution, but he does not ask more questions or generate more solutions than does the impulsive c h i l d i n h i s shorter period of time with a problem.  The pattern of response for the impulsive group  i s a quick succession of questions and solutions with very b r i e f s i l e n t periods i n between.  The r e f l e c t i v e c h i l d asks the same number of  questions and offers an equal number of solutions, but intersperses these verbalizations with s i l e n t periods, during which he i s presumably "reflecting".  Interpreted i n terms of Kagan's (1966) approach-avoidance  theory, the impulsive c h i l d seeks quick success, so he spends l i t t l e time between responses to evaluate their merits, while the r e f l e c t i v e c h i l d i s more anxious over making a mistake and considers each response he makes, whether i t be a question or a solution, before he offers i t . This interpretation could also be applied to the finding that impulsive children asked more constraint-seeking questions, but did not ask more hypothesis-seeking questions ( i . e . make more i r r e l e v a n t guesses) than r e f l e c t i v e children.  Perhaps during the s i l e n t periods the r e f l e c t i v e  c h i l d asks himself the constraint-seeking questions which allow him to avoid the tendency to take the r i s k of making irrelevant guesses, while the impulsive c h i l d asks these constraint-seeking questions overtly. Again i t should be noted that cognitive s t y l e and conceptual tempo tended to modify each other.  The highly impulsive c h i l d w i l l  behave i n a r e f l e c t i v e manner i f he i s also highly a n a l y t i c .  This  finding could account f o r the lack of e f f e c t due to conceptual tempo on the majority of problem solving measures.  In addition, the finding that  greater measured creative thinking a b i l i t y i s demonstrated by impulsive thinkers could also have functioned to diminish the main e f f e c t of  109  conceptual tempo. In summary, the consistency of the relationships between cognitive s t y l e , conceptual tempo, and performance on a variety of tasks found i n previous research did not manifest i t s e l f i n the majority of problem solving measures collected i n the present study.  While r e f l e c t i v e  children were found to spend a greater amount of time during problem solving, they were not found to d i f f e r from more impulsive peers i n general question-asking behavior or i n the number of solutions generated. In addition, measured analytic a b i l i t y was not found to be s i g n i f i c a n t l y related to any of the measures of problem solving.  Perhaps what i s more  important than this lack of e f f e c t , however, i s the interactions which were found to exist between style and tempo.  With the exceptionsof the  e a r i l y work of Kagan, research i n this area has tended to deal with either s t y l e or tempo, and has not directed i t s e l f to the examination of the interaction between the two variables.  The present study indicates  that each of these dimensions i s s u f f i c i e n t l y powerful to moderate the other, and suggests an area that warrants further research.  By employing  a t o t a l sample size that would insure a larger number of children to be c l a s s i f i e d into each of the nine c e l l s of a s t y l e by tempo matrix than was possible i n theppcesent study, this interaction could be more thoroughly examined.  In addition, a larger sample would allow for the  examination of the three-way interaction of t r a i n i n g , s t y l e , and tempo, which was not possible i n the present study due to the existance of several "empty" c e l l s .  110  Training and Problem Solving The  t h i r d major issue to which this study addressed i t s e l f  was  the f e a s i b i l i t y of teaching children analytic and r e f l e c t i v e methods of problem solving v i a programmed i n s t r u c t i o n . that this form of training was and  The results indicate  e f f e c t i v e i n increasing both the t o t a l time  the time p r i o r to o f f e r i n g the f i r s t solution, the t o t a l number of  questions asked, and the number of constraint-seeking The  training was  questions asked.  also marginally r e l i a b l e i n bringing about superior  performance on three additional measures: p r i o r questions and  information-  seeking questions asked, and time spent following theooffering of  the  f i r s t solution.  two  The  lack of difference between the scores of the  control groups on a l l but one of the problem solving measures would atest to the fact that i t was  the content of the training program and  not  simply exposure to programmed i n s t r u c t i o n a l materials which brought about this increase  i n performance.  The superiority of the trained group i s  additionally meaningful i n l i g h t of the fact that one of the  control  groups consistently scored higher on measured fluency and o r i g i n a l i t y as determined by the Torrance Verbal C r e a t i v i t y Test.  I t w i l l be r e c a l l e d  from studies reviewed i n Chapter II that measured creative  thinking  a b i l i t y has been found to bear a p o s i t i v e relationship to problem solving (Maier and Janzen, 1970;  Davis, 1973;  This p o s i t i v e relationship was  Curtchfield and Covington, 1963).  also found to e x i s t with the measures of  problem solving employed i n the present study.  On this basis, one  could  assume that the control groups, by v i r t u e of their being more fluent and o r i g i n a l , were predisposed to be superior problem solvers.  In spite  of t h i s bias i n favor of the control groups, the t r a i n i n g program was  Ill s u f f i c i e n t l y e f f e c t i v e to bring about superior performance of the trained group on at least four of the measures of problem solving. Of p a r t i c u l a r i n t e r e s t i s the finding that this form of t r a i n i n g was  e f f e c t i v e i n i i n c r e a s i n g not only the t o t a l number, but also the  quality of the questions  asked, as evidenced by the increased i n  constraint-seeking questions. 1965;  Several authors (Ault, 1973; Anderson,  Denney, 1973) have characterized the use of these questions as  evidence of a more advanced, mature and r e f l e c t i v e approach to problemsolving.  To have brought about a q u a l i t a t i v e change of this nature  through what might be characterized as a rather minor intervention technique, suggests a promising area for further investigation into the remediational p o s s i b i l i t i e s of this type of material i n coordination with other i n s t r u c t i o n a l procedures such as classroom discussion. The need for this type of further investigation i s made more apparent by the attribute-treatment  i n t e r a c t i o n which was found to  exist between both s t y l e and tempo with t r a i n i n g on f i v e of the problemsolving measures.  These interactions indicated that while both  moderately and highly analytic and moderately and highly r e f l e c t i v e children benefitted from the t r a i n i n g materials, the non-analytic and highly impulsive  children did not.  I t was further found that  impulsive  and non-analytic and highly impulsive  children did not.  I t was further  found that impulsive and non-analytic  children tended to spend a  shorter period of time completing these self-paced materials than did the more analytic and r e f l e c t i v e children.  A number of authors have  written extensively with regard to this type of i n t e r a c t i o n (Cronbach, 1965;  Cronbach, 1967; C a r r o l l , 1967; Cronbach and Snow, 1969; Hunt and  S u l l i v a n , 1974; Bracht, 1970).  Of the 108 aptitude-treatment  interaction  112 studies reviewed by Bracht (1970) however, only five provided s t a t i s t i c a l evidence of the existence  of a d i s o r d i n a l i n t e r a c t i o n .  On the basis of  this low incidence, i t was anticipated i n the present study that the training program would be equally e f f e c t i v e f o r children at a l l points along the s t y l e and tempo continuums.  The interaction results on  several of the measures ( t o t a l time, t o t a l questions, information-seeking questions, residual time, and residual questions) indicate that this method of t r a i n i n g was not as e f f e c t i v e f o r children who f e l l at the low end of the s t y l e and tempo continuums.  I t should be noted, however, that  the strength of these interactions was p a r t l y due to the unusually high performance of the low analytic and low r e f l e c t i v e children i n the combined control groups.  A p a r t i a l explanation  f o r this finding can be  found i n the fact that this group of control children consistently outscored a l l other groups on some measures of creative thinking a b i l i t y . It s t i l l remains apparent, however, that the benefit derived by children of d i f f e r i n g analytic and r e f l e c t i v e a b i l i t y was not the same, given one s t y l e of i n s t r u c t i o n .  While the more highly analytic and r e f l e c t i v e  c h i l d was capable of working through the programmed i n s t r u c t i o n a l materials  on h i s own, at a pace that would r e s u l t i n the desired  behavioral objectives being acquired,  this form of instructionawas  inadequately structured for the more impulsive and non-analytic.  It is  possible that the imposition of more structure i n the form of constant checks on thoroughness of completion of each of the exercises, or a teacher-set  pace rate would bring about s i m i l a r b e n e f i c i a l results f o r  these impulsive,  non-analytic  children.  A r e p l i c a t i o n of the present  study along with an additional t r a i n i n g group exposed to a more externally controlled presentation  of the program would allow f o r t h i s a t t r i b u t e -  113  treatment interaction to be more c a r e f u l l y examined. In summary, the programmed i n s t r u c t i o n a l materials were successful in bringing about superior performance for the trained group i n the majority of the problem solving measures, while simple exposure to programmed i n s t r u c t i o n a l material of unrelated content was not.  The  existence of the attribute-treatment interactions make i t clear,.however, that these materials were not b e n e f i c i a l i n their present form for highly impulsive, low a n a l y t i c children.  Additional research using modified  forms of presentation of the training program w i l l be required to determine the extent to which these materials can benefit the very impulsive, non-analytic c h i l d .  Relationship Between Process and Product It i s clear from the results of the data analysis that none of the independent variables selected for examination i n this study accounted for a s i g n i f i c a n t amount of the variance i n t o t a l numberoof of solutions offered, i n spite of the fact that children were found to be using different processes.  I t i s possible that this may be due to  the procedure used i n scoring solutions, for no attempt was made to d i f f e r e n t i a t e solutions by their q u a l i t y or comprehensiveness. research on problem-solving  The  reviewed i n Chapter II tended to employ  s o l e l y product-related dependent variables with very l i t t l e attention given to those which assess process, beyond measures of time or t r i a l s to solution.  The results of this study suggest, however, that a great  deal of meaningful information may be gained concerning problem solving i f the major emphasis i s placed on the examination of thepprocesses the  114  c h i l d uses as opposed to his a b i l i t y to generate acceptable solutions only.  Limitations of This Study Over a succession of v i s i t s to each of the three classrooms during the course of this research, i t became very apparent 1  to this  writer that the children had been exposed to very different teaching styles during the preceding eight months of the school year.  The teacher  of the class exposed to the training program, who had many more years of teaching experience than the teachers of the two control groups, consistently employed a very teacher-centered, authoritarian teaching s t y l e . Children were required to remain non-participative during lesson presentation, and work s i l e n t l y through assigned seat-word with no discussion permitted among peets.  The contrast between the atmosphere  i n this classroom and that i n the remaining two was very marked.  Both  of the teachers of the control classes were observed to r e l y heavily on a student—centered fcrm of i n s t r u c t i o n which emphasized p a r t i c i p a t i o n on the part of the children.  Students were frequently observed working i n  small groups on several d i f f e r e n t aspects of some topic the teachers had presented, or i n presenting o r a l reports of projects to their classmates while the teacher sat at the back of the classroom and observed.  In  both classes, these teachers created an. atmosphere which encouraged students to p a r t i c i p a t e , ask questions, and searchoout information both independently and i n small groups. These differences between classrooms could be interpreted to imply that the control groups were being trained by their teachers i n the use  115 of the types of problem-solving s k i l l s this study was designed to examine.  The trained group, on the other hand, had been exposed to a  teaching s t y l e that tended to minimize independent  inquiry behavior.  While this additional information tends to increase the significance of the a f f e c t of the training program, i t also makes i t apparent that care should have been taken, p r i o r to beginning the research, to determine that a l l classrooms involved were similar not only i n student characteri s t i c s , but also on this teaching s t y l e variable. I t was noted previously that the number of solutions provided by the students bore no s t a t i s t i c a l relationship to any of the  independent  variables, or to the processes employed by students i n problem-solving. The scoring procedure used f o r enumeration of solutions may have been inadequate.  Any response the c h i l d indicate to be a solution by turning  over the "READY" card was stated as a question.  accepted by the researcher, unless i t was  These solutions d i f f e r e d considerably i n quality  and complexity, but a l l were given an equal score of one.  In retrospect,  i t appears that a more stringent c r i t e r i a should have been used.  One  way  this could be accomplished would be to have an independent panel of judges rate solutions on a four or five-point scale i n terms of quality and complexity.  The use of such a procedure would result i n more  meaningful data being derived with regard to the relationship between process and product i n problem-solving. This study found that conceptual style did not account for a s i g n i f i c a n t amount of the variance i n any of the problem-solving measures. The f i f t e e n items of Denney's (1971) Form A version of the CST were used to measure analytic a b i l i t y , r e s u l t i n g i n scores which ranged from 0 to 15.  116  Kagan's (1963) e a r l i e r work with, cognitive s t y l e employed a CST,  thus allowing for a greater range of scores.  possible CST  Had  thirty-item  the range of  scores i n the present study been increased to t h i r t y by  using both Form A and Form B of Denney's CST,  the predictive power of  this style variable may  to an increase i n  a b i l i t y of the CST  have been greater due  the  to discriminate more f i n e l y between levels of  analytic  ability. The post-test problems and many of the problems used i n the training materials a l l came from the same source, The Productive Thinking Programme (Covington, Crutchfield, Davis and Olton, 1972).  A l l of these  problems involved a "mystery or crime to be solved" format. s i m i l a r i t y between the post-test problems and materials may  a portion of the  have accounted for the superiority  solving only this one  s p e c i f i c class of problems.  to moderate the effects of other variables,  Crutchfield  training  of the training group i n Since content may  the g e n e r a l i z a b i l i t y of  results i s limited to problems having s i m i l a r structure. and  The  act the  While Covington  (1965) contend that the problem solving s k i l l s acquired  through working with their programmed i n s t r u c t i o n a l materials have a great degree of g e n e r a l i z a b i l i t y , the p o s s i b i l i t y that this would also occur with the present training materials cannot be assessed without further  research. One  The  further l i m i t a t i o n i s the short term nature of this study.  differences  that were found to exist for the training group  immediately following the training period may a longer period of time.  not have been observed over  The novelty of the use of the programmed  i n s t r u c t i o n a l materials by the training class that was  accustomed to a  117 teacher-centered s t y l e of i n s t r u c t i o n may also have affected the r e s u l t s . A further l i m i t a t i o n of the results of this study derived from problems associated with the use of regression analysis.  One such  problem i s the absence of well defined procedures for c o n t r o l l i n g the o v e r a l l error rate when (a) one i s working with correlated dependent variables, and (b) there i s overlap  i n variance  attributed to independent  variables which, are not t r u l y independent of each other, even though attempts are made to p a r t i a l out the variance by c o n t r o l l i n g the order of entry of terms into the regression model.  Thus, the r i s t of a Type I  error cannot be p r e c i s e l y estimated, imposing some l i m i t a t i o n s on the confidence with which " s i g n i f i c a n t " results can be interpreted. Secondly, to examine interactions which are found to be s i g n i f i c a n t i n regression analysis i s not possible without the a r t i f i c i a l l e v e l l i n g of continuous variables.  The present "state of the a r t " of regression  analysis suggests no alternatives, however.  In studies such as the  present one, i n which interactions among continuous variables are of importance, this s t a t i s t i c a l r e s t r i c t i o n could impose l i m i t a t i o n s on the information  that can be obtained from the data.  Recommendations for Further Research Several areas which require further research have been mentioned throughout this discussion.  A systematic analysis of the i n t e r a c t i o n  between cognitive s t y l e and conceptual tempo that was found to e x i s t i n this study i s warranted.  Examination of the effectiveness of modified  versions of the t r a i n i n g program with impulsive, non-analytic needed.  children i n  The t r a n s f e r a b i l i t y of the e f f e c t s of t r a i n i n g over both time and  118 problem types could prove to be a f r u i t f u l area of research.  Finally,  i n the present study, a reasonably large number of predictor variables were examined as they r e l a t e to problem-solving.  The results of the  regression analyses demonstrate that the t o t a l amount of variance accounted for by the sum of these variables never exceeded f i f t y - o n e percent, with the average being approximately t h i r t y - f i v e percent.  It i s  clear that some additional.factors, or combination of factors must relate s i g n i f i c a n t l y to problem-solving.  Other learner variables should  be examined, such as achievement motivation, verbal aptitude, and. deductive reasoning a b i l i t y to attempt  to account for thella^ge amount of  error variance.  F i n a l Comment This study was not intended, nor has i t succeeded i n providing decisive answers to the question of the effects of cognitive s t y l e and conceptual tempo on problem solving processes, or to the optimal procedure f o r t r a i n i n g a l l children to be e f f e c t i v e problem-solvers. However, i t has served to highlight several issues of important to educators whose goal i t i s to f a c i l i t a t e the optimization of performance of every c h i l d .  F i r s t , children of similar levels of a b i l i t y w i l l d i f f e r  i n their effectiveness as problem-solvers, and these differences w i l l in part be due to the degree to whibht'they are analytic and r e f l e c t i v e . Second, the processes used by a c h i l d i n problem-solving are subject to modification, and this modification can come about by short-term t r a i n i n g i n the form of programmed i n s t r u c t i o n .  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Annual Review of Psychology, 1968, 19, 135-168. Kagan, J . Impulsive and r e f l e c t i v e children: significance of conceptual tempo. In J.D. Krumbolz (Ed.) Learning and The Educational Process. Chicago: Rand McNally, 1965(a), 133-161. Kagan, J. children.  Reflection-impulsivity and reading a b i l i t y i n primary grade Child Development, 1965(b), 36, 609-628.  Kagan, J.A.A developmental approach to conceptual growth. In H.J. Klausmeier and C.W. Harris (Eds.) Analysis of Concept Learning. New Academic Press, 1966(a), 97-115.  York:  Kagan, J. Developmental studies i n r e f l e c t i o n and analysis. In A.H. Kidd and J..H. Rivoire (Eds.) Perceptual and Conceptual Development i n Children, New York: Internation University Press, 1966(b). Kagan, J . and Kogan, N. I n d i v i d u a l i t y i n cognitive performance. In P.H. Mussen (Ed.) Carmichael's Manual of Child Psychology, Vol. 1, Third Edition. New York: Wiley, 1970. Kagan, J. and Moss, H.A. Psychological significance of styles of conceptualization. Monographs for the Society for Research i n Child Development, 1963, 28(2). Kagan, J . , Pearson, L. and Welch, L. M o d i f l a b i l i t y of an impulsive tempo. Journal of Educational Psychology. 1966, 57, 359-365. Kagan, J . , Pearson, L. and Welch, L. Conceptual impulsivity and inductive reasoning. Child Development, 1966, 37(3), 583-594. Kagan, J . and Rosman, B.L. Cardiac and respiratory correlates of attention and an analytic attitude. Journal of Experimental Child Psychology. 1964, 1, 50-63.  125  Kagan, J . , Rosman, B.L., Daty-, D. , Albert, J. , and P h i l l i p s , W. Information processing i n the c h i l d . Psychological Monographs, 1964, 78(1). Kendler, H.H. and Kendler, T.S. E f f e c t of verbalization on reversal s h i f t s i n children. Science, 1961, 134, 1619-20. Kinglsey, H.L. and Garry, R. The Nature and Contitions of Learning, Second Edition. Englewood C l i f f s : Prentice-Hall, 1957. Klausmeier, H.J. and Laughlin, L.J. Behaviors during problem solving among children of low, average, and high i n t e l l i g e n c e . Journal of Educational Psychology, 1961, 52(3), 148-152. Kohler, W.  The Mentality  Kopfstein, D. Risk-taking 44(1), 190-192.  of Apes.  New York: Harcourt Brace, 1925.  behavior and cognition.  Child Development, 1973,  Lee, L.C., Kagan, J . , and Rabson, A. The influence of a preference f o r analytic categorization upon concept a c q u i s i t i o n . Child Development, 1963, 34, 433-442. Luchins, A.S. Mechanization of problem solving: The effects of Einstellung. Psychological Monographs, 1942, 54 (6), 248. Maier, N.R.F. Reasoning i n humans: The mechanisms of equivalent s t i m u l i and of reasoning. Journal of Experimental Psychology, 1945, 35, 349-360. Maier, N.R.F. and Burke, R.J. Test of the concept of " A v a i l a b i l i t y of Functions" i n problem solving. Psychological Reports, 1966, 19, 119-125. Maier, N.R.F. and Janzen, J.C. Are good problem solvers also creative? In N.R.F. Maier (Ed.) Problem Solving and C r e a t i v i t y , Belmont: Brooks/Cole, 1970. Maltzman, I. Thinking: From a b e h a v i o r i s t i c point of view. Review, 1955, 66, 367-386.  Psychological  Mann, L. Differences between r e f l e c t i v e and impulsive children i n tempo and quality of decision making. Child Development, 1973, 44, 274-279. Meadow, A. and Parnes, S. Evaluation of training i n creative problem solving. Journal of Applied Psychology, 1959, 43, 189-194. Meichenbaum, D. and Goodman, J . Reflection-impulsivity and verbal of motor behavior. Child Development, 1969, 40, 785-799.  control  Meichenbaum, D.H. and Goodman, J . Training impulsive children to talk to themselves. Journal of Abnormal Psychology, 1971, 77(2), 115-126. Mendelsohn, G.A., Griswold, B.B. and Anderson, M.L. Individual differences i n anagram solving a b i l i t y . Psychological Reports, 1966, 2, 429-439.  126 Messer, S. The effect of anxiety over i n t e l l e c t u a l performance on r e f l e c t i o n - i m p u l s i v i t y i n children. Child Development, 1970, 41, 723-735. Newell, A., Simon, H.A. and Shaw, J.C. Elements of a theory of human problem solving. Psychological Review, 1958, 65, 151-166. Newell, A. and Simon, H.A. Computer simulation of human thinking. Science, 1961, 134, 2011-2017. Olver, R.R. and Hornsby, J.R. On equivalence. In J . Bruner, R.R. Olver, P.M. Greenfield (Eds.) Studies i n Cognitive Growth. New York: Wiley, 1966, 68-85. Odom, R.D., Mclntyre, C.W., and Neale, G.S. The influence of cognitive s t y l e on perceptual learning. Child Development, 1971, 42, 883-891. Ostfeld, B.M. and Neimark, E.D. Effect of response time r e s t r i c t i o n upon cognitive s t y l e scores. Proceedings of the 75th Annual American Psychological Association, 1967, 2, 169-170. Overall, J. and Spiegal, D. Concerning least squares analysis of experimental data. Psychological B u l l e t i n , LXXII. 1969, 311-22. Reitman, W.R. Cognition and Thought: An Information-Processing Approach. New York: Wiley, 1965. Ridberh, E.H., Parke, R.D. and Hetherington, E.M. Modification of impulsive and r e f l e c t i v e cognitive styles through observation of f i l m mediated models. Developmental Psychology, 1971, 5(3), 369-377. Ripple, R.E. and Dacey, J . The f a c i l i t a t i o n of problem solving and verbal c r e a t i v i t y by exposure to programmed i n s t r u c t i o n . Psychology i n the Schools, 1967, 4(3), 240-245. Robinson, F.G. Can you draw me a picture? November, 1973.  The Educational Courier,  Robinson, F.G., T i c k l e , J . and Brison, D.W. Inquiry Training: Fusing theory and practice. P r o f i l e s i n P r a c t i c a l Education, No. 4, Ontario Institute for Studies i n Education, 1972. Roettger, D.M. The effects of directed and non-directed training upon the v i s u a l discrimination performance of r e f l e c t i v e and impulsive children. Dissertation Abstract International, 1972 (March), 32(9-A), 5047. Russell, D.G. and Sarason, I.G. Test anxiety, sew, and experimental conditions i n r e l a t i o n to anagram solution. Journal of Personality and Social Psychology, 1965, 1, 493-496. Safren, M.A. Associations, sets, and the solution of word problems. Journal of Experimental Psychology, 1962, 64, 40-45.  127  Sheerer, M.  Problem solving.  S c i e n t i f i c American, 1963, 208(4), 118-128.  Shulman, M. Seeking styles and i n d i v i d u a l differences i n patterns of inquiry. School Reviewy 1965, 73, 258-266. Siegelman, E. R e f l e c t i v e and impulsive observing behavior. Development, 1969, 40, 1213-1222.  Child  Simon, H.A. and Barenfeld, M. Information processing analysis of perceptual processes i n problem solving. Psychological Review, 1969, 76, 473-483. Skinner, B.F. An operant analysis of problem solving. In B. Kleinmuntz (Ed.) Problem Solving, Chicago: Rand McNally, 1966, 225-257. Staats, A.W. An integrated-functional learning approach to complex human behavior. In B. Kleinmuntz (Ed.) Problem Solving, Chicago: Rand McNally, 1966, 259-339. Stokes, L.W. Training for problem solving s k i l l s u t i l i z i n g a C.A.I, method. Unpublished thesis. 1968, Psychology Department, "University of C a l i f o r n i a , Berkeley, C a l i f o r n i a . Thorndike, E.L. Animal Intelligence.  Psychological Monographs, 1898, No. 8.  Torrance, E.P. Torrance Tests of Creative Thinking, Norms-Technical Manual. Personnel Press, Princeton, 1966. Treffinger, D.J. and Ripple, R.E. The effects of P.I. i n productive thinking on verbal c r e a t i v i t y and problem solving among elementary school p u p i l s : F i n a l report. E.R.I.C., 1968, ED030156. VanHorn, K.R. and Bartz, W.H. Information seeking strategies i n cognitive development. Psychonomic Science, 1968, 11, 341-342. Walberg, H. Generalized regression models i n educational research. American Educational Research Journal, VIII, 1971, 71-91. Wallas, G.  The Art of Thought, New York: Harcourt Brace, 1926.  Ward, W.C. Reflection-impulsivity i n kindergarten children. Development, 1968, 39, 867-874. Weir, M.W. Developmental changes i n problem-solving Psychological Review, 1964, 71, 473-490.  Child  strategies.  Witkin, H.A. Origins of cognitive s t y l e . In D. Scheere (Ed.) Cognition: Theory, research and promise. New York: Harper & Row, 1964.  128  Witkin, H.A., Dyk, R.M. , Faterson, E.F., Goodenough, D.R., Psychological D i f f e r e n t i a t i o n . New York: Wiley, 1962.  and Karp, S.A.  Yando, R.M. and Kagan, J . The e f f e c t of teacher tempo on the c h i l d . Child Development, 1968, 39, 27-34.  129  APPENDICES  r  130  APPENDIX A  THE T E S T PROBLEMS  AND  CLASSIFICATION  OF Q U E S T I O N T Y P E S  Problem  1  ........... .131  Problem  2  . .133  Problem  3  Problem  4  •  135 I 3 7  131  Escape in an Elevator One night a small boy captured the secret plans of a gang of spies. When he got the plans, he was to go to the roof of a nearby building, where a helicopter would be waiting to help him escape from the gang. He ran to the building as fast as he could and jumped into the elevator. The gang ran into the building just as the elevator door closed. Hoping they could head the boy off, they started to run up .the stairs. Even though the elevator was the fastest way to the roof, the boy got out at the third floor and ran the rest of the way up the stairs to the roof! Shown at the right is a picture of the eight-story building. It shows the elevator stopped at the third floor, the boy running up the stairs with the gang after him, and the helicopter waiting on the roof.  Your problem is to figure out why the boy got out at the third floor and ran up the stairs to the roof instead of taking the elevator all the way.  132 Sample Questions Problem 1 "Escape i n an Elevator"  In f o rma t ion—S eekin ^Questions: How many spies were there? How old was the boy?  (Three.)  (About your age.)  Is this a door on the roof?  (Yes.)  I • ,-  How t a l l was the building?  (Eight stories high.)  Constraint-Seeking Questions: Was there a power f a i l u r e at the time of the escape? Was anything wrong with the elevator? Was the boy a very fast runner?  (No.)  (No.)  (No, about average.)  Is this the kind of elevator that stops at every floor?  (Only i f you  press the button for that floor.) Hypothesis-Seeking Questions: Why did he get out at the t h i r d floor? How did he escape from the gang? Did the elevator break down?  (That's what I want you to guess.)  (That's what I want you to guess.)  (Are you ready to make that a guess?)  Did he think i t was faster to run up the s t a i r s ? that a guess?)  (Are you ready to make  133  The Mystery of the S t o l e n Jewel Mrs. Mnney, a r i c h widow, had a b i r t h d a y party l a s t n i g h t . Three peopl<=» were at. the partv. The f i r s t two ppople w^re Mr. and Mrs. Smith. Mr. Smith owned the pet store i n town. In the l a s t few years, he was not able to s e l l many pets, so he needed a large sum of money to keep the pet store running. The other person at the p a r t v was Mr. L i o n , the famous A f r i c a n hunter. Mr. Lion d i d not l i k e Mrs. Money because t^o years ago she had not loaned him enough money to go on a hunting t r i p . Mr. L i o n decided to come to the party because he l i k e d Mr. and Mrs. Smith. A l l three guests brought presents f o r Mrs. Money. As Mrs. Money was opening the presents, the l i g h t s i n the l i v i n g room went out. There was a scream. Twenty seconds l a t e r , Mrs. Money found one of the l i g h t switches. The only t h i n g missing from the room was the jewel which had been around Mrs. Money's neck. The p o l i c e , who were i n v e s t i g a t i n g the mystery, could not f i n d the jewel i n the room. They looked everywhere. They even looked outside around the only open window i n the l i v i n g room. The ground was muddy and there were no f o o t p r i n t s o u t s i d e . No one had hidden the jewel i n t h e i r c l o t h e s . Your f i r s t problem removed„from the l i v i n g on t h i s problem f i r s t . which might be clues to  i s to f i n d out how the jewel had been room when the l i g h t s were out. Work There were 4 t h i n g s found i n the room s o l v i n e t h i s . They were:  1. A rose from Mrs. Smith's present 2. A small box 3. A feather 4. Mr. Smith's umbrella which had been opened  134 Sample Questions Problem 2 "The Mystery of the Stolen Jewel"  Information-Seeking Questions: Who screamed?  (Mrs. Money)  Whose umbrella was i t ?  (Mr. Smith's)  How b i g was theijewel?  (About the s i z e of a peanut)  What color was the feather?  (Grey)  Constraint-Seeking Questions: Was the box a present?  (No.)  Was something i n the box?  (Yes.)  Why are there holes i n the box?  (To l e t a i r in.)  Could the umbrella handle come off?  (No, i t was nailed i n place.)  Hypothesis-Seeking Questions: Was the jewel i n the rose (box, umbrella)?  (Are you ready to make that  a guess?) How could the thief get out?  (That's what I want you to t r y to guess.)  What i s the feather for?  (That's what I want you to t r y to guess.)  Was Mr. Smith the thief?  (Are you ready to make that a guess?)  135  The t r a c k s i n the Snow  A f t e r a snowstorm, a man entered a s m a l l c l e a r i n g surrounded by t r e e s . In the c l e a r i n g he n o t i c e d these t h r e e d i f f e r e n t kinds o f animal t r a c k s :  B  C  Most o f these t r a c k s l e d t o a s m a l l pond i n the c e n t e r o f the c l e a r i n g where the i c e had melted. Here i s a p i c t u r e o f what the man saw:  The problem i s t o e x p l a i n what happened i n the c l e a r i n g t o cause such a p u z z l i n g p a t t e r n o f t r a c k s .  136  Sample Questions Problem 3 "The Tracks i n the Snow"  Information-Seeking Questions: How b i g i s the pond?  (About as b i g as t h i s room.)  What kind of tracks are these? What time of day was i t ?  (A-racoon, B-deer, C-bear.)  (About lunch time.)  What, d i r e c t i o n do the tracks go?  (Which one do you want to know about?  Specifies direction by pointing.)  Constraint-Seeking Questions: Can racoons (bears, deer) swim? Are the tracks man-made ?  (Yes, i f they have to._)_  (No.)  Were there any shovel marks around? Did any of the animals die?  (No.)  (Yes.)  Hypothesis-Seeking Questions: How come there are no deer tracks going away?  (That's what I want you to  guess)) What happened i n the clearing? How did the bear get over here?  (That's what I want you to guess.) (That's what I want you to guess.)  How come the racoon went straight across? guess).  (That's what I want you to  137  The Man in the Pit A man, wearing only his hiking shorts, gets lost during a summer hike and falls into a pit. The pit is circular. It is about thirty feet across and twenty feet deep. The walls of the pit are of smooth, hard stone and rise straight up. There are no handholds or footholds for climbing. The bottom of the pit is also hard stone. A narrow stream of water flows over the edge of the pit and runs straight down the wall; the water then disappears into a small hole in the floor of the pit. The pit is completely empty except for three things: • Exactly in the middle of the pit is the stump of a dead tree sticking straight up. • Near the tree stump is a loose flat rock. • T w o boards are also lying near the tree stump.  Your problem is to figure out how the man escapes from the pit.  1  Sample Questions Problem 4 "The Man i n the P i t "  Information-Seeking Questions: How deep i s the p i t ?  (Twenty feet.)  How wide i s the pit?  (Thirty feet.)  How b i g i s the rock?  (About the size of this tape recorder.)  How b i g i s the hole?  (About half the s i z e of this tape recorder.)  Constraint-Seeking Questions: Can the man l i f e the rock?  (Yes.)  How long would i t take the p i t to f i l l with water i f the hole was plugged?  (About an hour.)  W i l l the log float?  (Yes.)  Is there a ranged station near by?  (No.)  Hypothesis-Seeking Questions: How did he get out?  (That's what I want you to guess.)  How can he fasten the two boards together?  (That's what I want you to  guess.) Why doesn't he just c a l l for help?  (Are you ready to make that a guess  Does he use the rock to make foot holes? guess?)  (Are you ready to make that a  139  APPENDIX B COGNITIVE  STYLE  TEST  Instructions Sample  Item  MATCHING FAMILIAR Instructions Sample  .140  Item.  141 FIGURES  TEST 142 .143  140  COGNITIVE  STYLE  TEST  INSTRUCTIONS "On  each page i n t h i s  pictures. B, or C.  your two  alike  I want  you t o l o o k v e r y  Then c h o o s e two or go t o g e t h e r  choice  first  circle  Then  either  A,  a t the t h r e e  the l e t t e r s  think  under the  t u r n t h e page and do t h e  s e t of p i c t u r e s .  Keep  to make s u r e  going  until  Take as much  T h e r e i s no need to h u r r y .  one f o r p r a c t i c e  three  When you have made  have c h o s e n two p i c t u r e s on each page.  time as you want. the  i n some way.  t h a t you have c h o s e n . the next  carefully  see  of t h e p i c t u r e s t h a t you  of two p i c t u r e s ,  same t h i n g w i t h you  you w i l l  Below each p i c t u r e i s a l e t t e r ,  pictures. are  booklet  Let's t r y  you know what  to  141  142  MATCHING  FAMILIAR FIGURES TEST INSTRUCTIONS  " I am g o i n g ones.  Look v e r y  itself.  to show you some p i c t u r e s , l i k e carefully  at t h i s  One o f t h e s i x p i c t u r e s  same as t h e one a t t h e t o p . down'here t h a t Take as much very  i s exactly  picture  down h e r e  i s by  i s e x a c t l y the  Your j o b i s t o f i n d  the p i c t u r e  t h e same as t h e one a t t h e t o p .  time as you want, and l o o k  carefully.  that  these  When you have f o u n d  at a l l the p i c t u r e s  t h e one t h a t  i s exactly  the  same as t h e one a t t h e t o p , p o i n t  t o i t so t h a t  see  which  try this  practice  one you have c h o s e n . t o make  sure  that  Let's  I can  one f o r  you know what to do."  143  145  A P P E N D I X TASK THE  A N A L Y S I S T R A I N I N G  OF  P R O B L E M  C S O L V I N G  146  P R O G R A M  B o o k l e t  1,  S a m p l e  E x e r c i s e s . . .  ...147  B o o k l e t  2,  S a m p l e  E x e r c i s e s  149  B o o k l e t  3,  S a m p l e  E x e r c i s e s  151  B o o k l e t  4,  S a m p l e  E x e r c i s e s  153  B o o k l e t  5,  S a m p l e  E x e r c i s e s .  155  B o o k l e t  6,  S a m p l e  E x e r c i s e s . . . . .  .157  146  Task Analysis of Problem Solving  Overall Objective: On completion of the program, the student w i l l use analytic and r e f l e c t i v e strategies i n problem solving: i . e . w i l l look at and think about a l l stimulus elements i n the problem material presented, w i l l ask constraint-seeking questions to a i d i n i d e n t i f i c a t i o n of relevant cues-, w i l l ask. information-seeking questions when information i s Inadequate, w i l l offer several solutions, and w i l l take the time to think about and give reasons for selecting h i s f i n a l solution among the several other possible solutions he has hypothesized. Task 1: The student w i l l be able to v i s u a l l y analyze the elements i n the stimulus population to such a degree that the parts as w e l l as the whole are i d e n t i f i e d and discriminated. Task 2: The student w i l l be able to i d e n t i f y and select those elements i n the stimulus display presented to him that w i l l a s s i s t him i n solving a given problem through the use of constraint-seeking questions. Task 3: The student w i l l be able to i d e n t i f y where information i s Inadequate i n a presented problem and w i l l ask information-seeking questions to obtain that needed for problem solution. Task 4: The student, when presented a problem, w i l l be able to provide more than one possible hypothesis f o r solution. Task 5: When more than one solution i s provided, the student w i l l think about and be able to provide reasons f o r the r e l a t i v e merits of each solution. Task 6: When given a problem, the student w i l l be able to provide more than one solution, w i l l think about each solution, and w i l l select one solution which he thinks best f i t s the facts, and w i l l be able to provide reasons for h i s selection of that one solution over his other possible solutions.  147  Page 10. Our eyes help us t o f i n d out what i s happening i n the world around us. But we have to remember to look c a r e f u l l y or we may not notice some t h i n g s .  People l i k e s c i e n t i s t s and  detectives who solve problems a l l the time are always on the lookout f o r clues that w i l l help them.  They have  learned t o look c a r e f u l l y at what i s i n the world around them.  They know t h a t i f you look at something too q u i c k l y  you may miss some information. Here are some exercises that w i l l show you how important i t i s to take a good look at what i s i n the world around you. Look very c a r e f u l l y at t h i s p i c t u r e .  There are >  things to be seen i n i t . Can you f i n d 3 things? down what you see i n t h i s p i c t u r e .  Write  Then t u r n the page.  148 Page I  am  H e r e  t h i n k i n g  a r e  f l o w e r .  o f  one  o f  I t  has  f i v e  I t  has  a  I t  has  t h r e e  t h e 1.  C r o s s l o n g  3.  C r o s s 3  Now  y o u  s h o u l d  t h e  c o r r e c t  H e r e  a r e  t h e  c l u e s :  p e t a l s .  s t e m .  f o l l o w  o f f  any  l e a v e s . t h a t  w i l l  h e l p  y o u  t o  f i n d  f l o w e r  t h a t  d o e s  n o t  have  5  a n y  f l o w e r  t h a t  d o e s  n o t  h a v e  a  a n y  f l o w e r  t h a t  d o e s  n o t  t h e  p e t a l s . o f f s t e m . o f f  s m o o t h be  f l o w e r s .  s m o o t h  t o  l a r g e 2.  l a r g e  l o n g  s t e p s C r o s s  t h e s e  2 3 .  l e f t  f l o w e r ?  have  l e a v e s . w i t h A  B  o n l y C  one D  f l o w e r . E  F  W h i c h  one  i s  149  Page 30. H e r e  i s  i s  t h e  u p  o f  I f  s t a r t  y o u  t o  Now  see  y o u  p a r t s :  2  T r y  W h e n  p i c t u r e  f i g u r e  y o u  h w l p  a  b y  f i n d  t h e  i f  t h e r e  have  a  j u s t  a  s m a l l  A  l a r g e  b o a t .  H i d d e n  d r e w .  Remember,  l o o k i n g  t h e  f i n d  y o u  o f  t r i a n g l e  /  somewhere t h e  i n  t h i s  f i g u r e  i s  b o a t made  \  r e c t a n g l e f o r  one  o f  t h e s e  s h a p e s ,  i t  w i l l  f i g u r e .  t r i a n g l e i s  f o u n d  a  somewhere  l a r g e  t h e  i n  r e c t a n g l e  f i g u r e ,  go  Now  t h e  u n d e r n e a t h  o v e r  t u r n  b o a t .  i t  t o  w i t h  t h e  i t . y o u r  n e x t  p e n c i l .  p a g e .  150  Page 43. Here i s another 20 questions game. the objects below. answer YES or NO.  I am thinking of one of  You can ask me questions, but I can only Find the object I am thinking o f . You  should only have to ask 3 questions. Look at the 8 p i c t u r e s . Can you divide them into 2 b i g groups?  Try to ask a question that w i l l l e t you cross o f f  one h a l f (4) o f the p i c t u r e s . What i s your f i r s t  question?  Write i t here and turn the page.  C A T  p»Wfc  TULIP  €L.6PV4ANT  151  Page 6 6 , L o o k t o  a t  go  t h e t o  map.  t h e  town  a n s w e r g e t  t h e  t o  a l l  T h e r e o n  t h i s  t o  town t h e  t h i s  t h e  are  Y o u o f  i n  t h e  town  by  t h e  q u i c k e s t  p r o b l e m  n e c e s s a r y  s e v e r a l o f  a r e  E l d o n  R i c e  y o u  t h e  need  i n f o r m a t i o n .  d i f f e r e n t t o  w i l l  o f  r o u t e s  town  o f  R i c e t o  a s k  S t u d y  y o u  c a n  E l d o n .  a n d  y o u  r o u t e .  u s e  One  f i n d  some  t h e  q u e s t i o n s  map  t o  w a n t  To  c a r e f u l l y .  g e t  r o u t e  f r o m  i s  m a r k e d  map.  RICE  T o  f i n d  a s k  o u t  t h e s e  i f  t h i s  f o u r  1.  How  2.  What  3 .  How  f a r i s f a r  i s  W i t h how  t h e l o n g  What  i s  I s  t h e  q u i c k e s t  f r o m  s p e e d i t  t o  r o u t e  y o u  w o u l d  n e e d  l i m i t  a l o n e  s p e e d  t o  t h e s e  w o u l d  R i c e  Bow  t o  Bow  a l o n g Road  Road  a l o n g  h i g h w a y t o  t h e  H i g h w a y  10?  10?  H i g h w a y  10  t a k e  t o  l i m i t 4  a l o n g  Bow  q u e s t i o n s  y o u  g e t  R o a d ? c o u l d  f i g u r e  f r o m  R i c e  t o  E l d o n  Now  t u r n  t o  t h e  a l o n g  o u t t h i s  r o u t e .  !  t o  E l d o n ?  t h e  a n s w e r s i t  i t  t h e  t u r n - o f f 4 .  i s  q u e s t i o n s :  n e x t  p a g e .  152 Page A s k i n g n e e d  t h e  t o  s o l v e  n e c e s s a r y Two go  t o  r i g h t  g o o d  see  a  t o  e a r n  e n o u g h  t h e  some  g r o c e r y  s t o r e .  p u t  a l l  t h e m . y o u  f o r t h e W i n  w i l l  f i n i s h e d ,  l 2.  .  t h e  _  f o r  t h i s  e a t  a n d  c o u l d  h o u s e s  a n d  c a n  k e e p  m o v i e  a n d  p o p c o r n .  t o  have a s k  t o  t h e  _  a l l  s o l v e  n e x t  t h e y  t h i s  T h e y  a s k  y o u  t h e  a r e  money  i t  t h e y  f r i e n d s e v e n l y  W r i t e p r o b l e m .  a l l  T o  t h e  p a r e n t s  t h e  i n  t o  e a c h  t h e r e .  a l l  t h e m  l i k e  w o u l d  p o p c o r n ,  c a s h  T h e  s p l i t  p a g e .  f a c t s  w o u l d  c o l l e c t  t h e  enough: money? t o  t h e c a n  t h e y  t h e  t h e y  a n d  y o u  t h a t  w h i l e  T h e y  t o g e t h e r  i f  g e t  a f t e r n o o n .  m o v i e  t h a t  t o  p r o b l e m .  d e c i d e d  t o  t h e  see  t h e i r  t.frey  t u r n  h a v e  y o u  i n  money  n e e d  s o l v e  S a t u r d a y  s a i d  a r e  h e l p s L e t ' s  p o p c o r n  f r i e n d s t h a t  i t  o n  money  b o t t l e s  u s e  t o  f r i e n d s  m o v i e  b u y  2  p r o b l e m .  q u e s t i o n s  l i k e  o f  a  q u e s t i o n s  71.  p o p  a t  t h e  g e t  a n d  w i l l  t h e m  b e t w e e n t h e  When  q u e s t i o n s y o u  h a v e  153  Page 8 5 .  When t o  f i r s t  t h e  y o u  and  n o t a r e  y o u  T r e e t o  t h e  i f  p r o b l e m  y o u  g u i d e and  o f  b r o a d  s i b i l i t i e s  f o r  a l l  t h e  T h i s  y o u  a  p o s s i b l e  t h i s  a n o t h e r  l i k e b i g  a  s m a l l  g u i d e  way,  t r e e  l i m b s  b o r a d ,  -  o n  a n  g e n e r a l  t h e  o u t  o f  one  o f  s t i l l  have  o t h e r s  up  a t  many  o f  i d e a s  i s  t o  o f  t h e s e  i d e a s  h e l p s  i n  t o  i f  i d e a s  w o r k  y o u  t h i n k  o n  t h a t  y o u r  a r e  up  g e n e r a l  i d e a s  p o s s i b i l i t i e s  one  s o l v e  y o u r  a l l .  p a r t i c u l a r  p a r t i c u l a r  I t  c a n i s  n e x t .  t o  s o l v e  g e n e r a l i t  m i g h t  s e a r c h  t h e  p o s -  f o r  s u g g e s t . a l l  t h e  be  i d e a  t r e e .  r e p r e s e n t  T h e  p o s s i b i l i t i e s . o n  e a c h  o f  l i m b  i d e a s  t h e  shown  s o m e t h i n g  t r e e  p a r t i c u l a r e a c h  w o r k s  t o o .  t h e  b r a n c h e s  f o r  t h a t  i m p r o t a n t t o  i d e a s .  How i n  f i n d  e a c h  w h i c h  i s c a n  g e n e r a l  e x p l o r e  i t  y o u  p l a n f u l  t h i n k  y o u  p l a n ,  p r o b l e m  s o l u t i o n s  t h i n k  T h e n  g i v e s  y o u  b e i n g t o  a  i d e a s  y o u  any  t o  t o  t h e n  t h i n k  s o l v e  d i f f e r e n t  l a t e r  w i t h o u t  h e l p  One  p r o b l e m .  a l l  t h e  l e f t  f i r s t ,  F i r s t ,  t r y i n g  o f T h e n  w i l l  p l a n f u l . i d e a s  a r e  s o l v e n o t  I t  I d e a  t h i n k  p r o b l e m .  d o e s  T h e  few t h e  T h e s t a n d  g r o w i n g  g e n e r a l  p o s s i b i l i t i e s .  Y o u s e a r c h w i l l  n e e d  G e n e r a l f r o m  w i l l  f o r  i t .  now  l e a r n  s o l u t i o n s t o  be  a b l e  P o s s i b i l i t y L e t ' s  use  t h i s  g u i d e  i n  d i f f e r e n t  p r o b l e m s .  t o  r e c o g n i z e  t h e  and  s t a r t  t o  t o  a  w i t h  P a r t i c u l a r some  T u r n  a  p l a n f u l  T o  b e g i n ,  d i f f e r e n c e I d e a  t h a t  b e t w e e n  b r a n c h e s  e x a m p l e s .  t o  t h e  n e x t  p a g e .  y o u a o f f  154 Page S a v i n g T o d a y  t h e  A m e r i c a  w h o o p i n g  i s  i n  o f  t h e  few  y e a r s  t h e  c r a n e .  c r a n e ,  d a n g e r  c a r e l e s s n e s s . many  A s  o f  man  c r a n e ' s  ago  t h e a  few  C r a n e  w h i t e  o u t ,  c o n q u e r e d  n a t u r a l  so  huge  d y i n g  s c i e n t i s t s  S i n c e  W h o o p i n g  b i r d  p a r t l y  t h e  f e e d i n g  b e g a n  t o  b i r d s  were  8 6 .  n a t i v e  t o  b e c a u s e  N o r t h  o f  m a n ' s  w i l d e r n e s s ,  he  and  g r o u n d s .  n e s t i n g  e x p l o r e  w a y s  l e f t ,  no  d e s t r o y e d  o f  A  s a v i n g  i d e a  c o u l d  be  o v e r l o o k e d . T h u s , a p p r o a c h , s a v i n g  t h e  t h e  G e n e r a l  s c i e n t i s t s '  w h i c h  l e d  them  s e a r c h  t o  two  P o s s i b i l i t y  A :  F i n d  ways  P o s s i b i l i t y  B:  F i n d  i t  t h e  s c i e n t i s t s  c a r e f u l l y B e l o w  t o  a r e  5  what  D e c i d e  g e n e r a l  p o s s i b i l i t y .  t o .  T h e  t u r n  t o  B  w h i c h  i d e a  f i r s t t h e  one  n e x t  p l a n f u l f o r  p l a n e s  f r o m  H a t c h  S e t  f o r A  y o u .  o f  t h e  number  o f  P o s s b i l i t y i t  B  i n  and  m i g h t  s a v i n g  o r  number  y e a r .  b e l o n g s  g e n e r a l  f o r  t h e  w h o o p i n g  u n d e r f r o n t  e a c h o f  p o s s i b i l i t y When  y o u  e x p l o r e d  s u g g e s t .  e a c h  i t  have  b e l o n g s f i n i s h e d ,  f l y i n g w i l l  w h o o p i n g  t o o  n e a r  n o t  be  c r a n e s  t h e  -  n e s t i n g  f r i g h t e n e d  a r e a s  away  e g g s .  t o  e x t r a  t r a p s  h u n t i n g  c r a n e s  f o o d  have  t h e  w h i c h  e a c h  I d e a s  i d e a s  e i t h e r  done  f r o m  t h e  need  w i l l  i d e a s  t h e s e  a g a i n s t  t h e i r  P r o v i d e n o t  d e c r e a s e  G e n e r a l  t h e  y e a r .  p a g e .  Keep  t h a t  t o  k i l l e d  e a c h  Put  i s  l a w s  so  o f  3how  t o  P a s s  as  a  i n c r e a s e e a c h  P a r t i c u l a r  p a r t i c u l a r  c r a n e .  p a r t i c u l a r  t o o k  see  t o  b o r n  w a y s  c r a n e s N e x t ,  f o r  p o s s i b i l i t i e s  c r a n e s .  c r a n e s G e n e r a l  c a l l e d  g e n e r a l  a t o  i n f l y e g g s  w i n t e r  i n  b e t t e r c a t c h  w e a s e l .  so  t h o u s a n d s a  o f  t h e  ^ c r a n e s  d a n g e r o u s  l a b o r a t o r y  c h a n c e t h e  t h a t  t o  c r a n e ' s  so  w i l l  m i l e s  t h a t  t h e  s o u t h . c h i c k s  l i v e . n a t u r a l  e n e m i e s  s u c h  155 106  Page The A i s  d r i v i n g  200 i s  l a r g e  f o o t _  s t o p s  50  b a c k  t o  m o u n t a i n s ,  f i g u r e c a r s  o u t  p u l l  how u p  s u g g e s t i o n s  He  b e h i n d a b o u t  he  h i m , he  He  t o  i s  o f  h e a v y  d r i v e r f i n d s  t h e  t h a t  t u n n e l . t u n n e l .  f i g u r e  o u t  how  r o a d  i n  a  t o w i l l  g r e a t  t h r o u g h  t h i s  and  t h e  c a n  s o l v e  a t r u c k i s  T h e c a n  d r i v e r  t o  He  c a n ' t S e v e r a l  g i v i n g  p r o b l e m .  d r i v e  t h r o u g h  t u n n e l .  s t a r t  a  g e t  h i m  h u r r y .  d r i v e r s  h i s  a r o u n d  t a k e  l o n g  h i s  he  t u r n  t o  T h e r e  t h e  w a n t  m a c h i n e r y  comes  o f  d o e s n ' t  g e t  how  end  f u l l  The  t h r o u g h  a n o t h e r  b e c a u s e c a n  b o x e s  r o a d .  o t h e r  where  he  t h e  t r i e s  t u n n e l .  w i t h  p a s s  t h e  and  P r o b l e m  m o u n t a i n s .  i n  t o  a t  t r u c k  t h e  m i l e s  t h e  t a l l  s t a t i o n  t h r o u g h  t h e  t u n n e l  t o o  t h e  l o a d e d  t h r o u g h  l o n g  i n c h  s e r v i c e  t r u c k  T u n n e l  h i m  One  d r i v e r  s a y s :  Y o u  c a n  o u t  o f  s o l v e v o u r  y o u r  t i r e s .  p r o b l e m T h i s  b y  w i l l  t a k i n g make  some  t h e  o f  t r u c k  t h e 1  a i r i n c h  l o w e r . T o  d e c i d e  i f  t h i s  i s  a  g o o d  s o l u t i o n ,  y o u  m u s t  l o o k  a t  a l l  Page T o  d e c i d e  must  i f  t h e  c o n s i d e r  t h e  t h e s e  q u e s t i o n s .  1.  much  How  s o l u t i o n  l o w e r  f a c t s .  must  t u n n e l ?  2.  How  he  F r o m  t h e  i s  good  a  page  Read  t h e  t h e  t r u c k  i s  106  a  s t o r y  be  t o  g o o d  a g a i n  f i t  one  y o u  and  t h r o u g h  answer  t h e  ;  w i l l  when  o n  107.  t h e g e t s  f a c t s  d r i v e r  be  t h r o u g h  t h a t  s o l u t i o n  y o u t o  a b l e  t h e  have  t h e  f i l l  u p  t h e  t i r e s  c o l l e c t e d , d r i v e r * s  do  y o u  t h i n k  p r o b l e m ?  NO  Now  a g a i n  t u n n e l ?  t r a c k  Y E S  t o  t u r n  t o  t h e  n e x t  p a g e .  t h i s  157  Page 125. H e r e  i s A  o f  a  y o u r b o y  f i r s t  i s  f r i e n d ' s  a c r o s s  the  h o l e  bends  H e r e  i s  p l a y i n g  a  h o u s e .  He  l a w n t o  y o u r  f i n d  t h e  q u e s t i o n s y o u  w i l l  and  one  game  o f  p i n g - p o n g  m i s s e s  r o l l s  i n t o  t h e a  b a l l  s m a l l  i n a n d  b u t  t h e i t  b a c k y a r d b o u n c e s  d e e p  h o l e .  T h e  s i d e .  p r o b l e m : How  T o  p r o b l e m .  d o e s  s o l u t i o n  f i r s t have  t o  t o  t h e t o  g e t  a s k ,  b o v t h i s  a l l t h e n  g e t  t h e  b a l l  p r o b l e m ,  t h e t u r n  f a c t s . t o  t h e  y o u  o u t  o f  w i l l  W r i t e n e x t  t h e  have  a l l p a g e .  t h e  h o l e ? t o  a s k Q u e s t i o n s  158  Page 126. Here i s a l i s t of questions that you w i l l need to ask to solve t h i s problem, and the answers to these questions. Question 1 . How deep i s the hole? 2. How b i g around i s the hole? 3.  How  long i s the boy's arm?  4. How big around i s the boy's arm?  Answer 26 inches 6 inches 20 inches 3 inches  5. Are these any t o o l s i n the yard that could be used by the boy?  Yes. There i s a shovel, a long s t i c k , and a water hose.  6. Is i t a l r i g h t i f the boy digs up the lawn?  No. The f r i e n d ' s mother says that the boy i s not to dig up the lawn.  7.  No, a s t i c k w i l l not pass by the bend i n the hole.  W i l l the s t i c k f i t down the hole and around the bend?  You have a l o t more information that w i l l help you to solve t h i s problem. Read the problem again, and pay c a r e f u l attention to the l i s t of t o o l s that the boy could use. How does he get the b a l l out of the hole? Write your s o l u t i o n below, then turn the page. The boy gets the b a l l out of the hole by_  APPENDIX D SUMMARY TABLES OF RESULTS OF REGRESSION ANALYSES Mean T o t a l  Time.....  Mean P r i o r  Time....  Mean T o t a l  Questions...  Mean P r i o r  Questions  Mean I n f o r m a t i o n - S e e k i n g  160 .-161 ..162 163 Questions  164  Mean C o n s t r a i n t - S e e k i n g Q u e s t i o n s  165  Mean H y p o t h e s i s - S e e k i n g  166  Total  Solutions  Mean R e s i d u a l Time Mean R e s i d u a l Q u e s t i o n s  Questions  167 .....168 169  APPENDIX RESULTS OF REGRESSION  SOURCE OF VARIATION  AR  2  D •  ANALYSIS FOR MEAN TOTAL TIME ( Y l )  df  F , obs .  P<  . 0533  1  6.5000  . 01  . 0881  3  3.5813  . 01  . 0002  1  . 0244  . 84  . 0003  1  . 0365'  .82  . 0308  1  3 .7560  . 05  .0279  1  3.4024  . 06  .0594 .  1  7.2439  . 009  . 0012  1  . 1463  . 1296  1  15.8048  . 0009  •1  . 1097  .73  . 0228  1  2.7805  .09  . 0044  2  .2683  .76  . 0024  1  .2926  .59  . 0230  1  2 .8048  .09  . 0432  1  5 . 2682  . 02  . 0001  1  . 0121  .87  . 0162  1  . 0000  1  TOTAL  . 5038  21  ERROR  . 4962  59  l  X  (x ,x ,x )* 2  X  5  X  6  X  7  X  8  X  9  X  10  X  6 7  X  6 8  X  7 8  3  4  X  X  X  (x x ,x x )* 5  9  X  6 9  X  6 10  X  7 9  X  7 10  X  8 9  5  10  X  X  X  X  X  x x g  1 0  * Indicates  that  terms  1.9756 . 0000  . 70 .0003  .16 .95  i n p a r e n t h e s e s were e n t e r e d  as a s e t .  A P P E N D I X R E S U L T S  SOURCE  O F  O F R E G R E S S I O N  V A R I A T I O N  A R  A N A L Y S I S  2  161  D FOR  df  MEAN  F  P R I O R  , o b s .  TIME  (Y2)  P<  . 0165  1  1. 7 0 1 0  .19  . 0880  3  3.0206  .03  . 0004  1  . 0412  . 82  . 0071  1  .7319  . 40  . 0572  1  . 0068  1  .7010  . 1008  1  10 .39.18  . 017 9  1  1.8454  . 17  . 0166  1  1.7113  . 19  . 0021  1  .2164  . 0603  1  6.2164  . 0141  2  .7268  .49  . 0098  1  1.0103  .32  . 0003  1  . 0309  . 83  . 0041  1  . 4 2'2 6  .52  . 0043  1  .4432  . 51  . 0004  1  . 0412  .82  X  .0100  1  T O T A L  .4166  21  ERROR  . 5834  59  l  X  ( X 2  X  5  X  6  X  7  X  8  X  9  X  10  j  X  6 7  X  6 8  X  7 8  j  X ^ )  X  X  X  ( X ^ X g  X  6 9  X  6 10  X  7 9  X  7 10  X  8 9  X  8 10  X  X  X  X  X  , X^X^Q)  5 .8969  1.0309  . 01 . 41 . 002  .64 . 01  . 31  162 APPENDIX D RESULTS OF REGRESSION  ANALYSIS FOR MEAN TOTAL QUESTIONS (Y3)  SOURCE OF VARIATION  AR  2  df  F , obs .  P<  . 0262  1  2 . 5940  .10  . 1269  3  4 . 1881  . 009  . 0010  1  . 0990  . 0170  1  . 0013  1  . 0157  1  1. 5544  . 21  . 0486  1  4 .8119  . 03  . 0083  1  .8218  4:05 8 9  1  5 .8316  . 01  . 0121  1  1.1980  .27  . 0070  1  . 6930  .41  . 0176  2  .8713  .42  . 0378  1  3.7425  .05  . 0043  1  .4257  .52  . 0003  1  . 0297  .84  . 0010  1  . 0990  .74  . 0035  1  . 3465  . 56  .0012  1  . 1188  .72  TOTAL  . 3887  21  ERROR  .6113  59  l  X  (^2> X g » X ^ ) X  5  X  6  X  7  X  8  X  9  X  10  X  6 7  X  6 8  X  7 8  X  X  X  (X^Xg , X^X^ Q ) X  6 9  X  6 10  X  7 9  X  7 10  X  8 9  X  8 10  X  X  X  X  X  X  1.6831 . 1287  . 74 . 19 . 71  .37  APPENDIX D RESULTS  OF REGRESSION ANALYSIS FOR MEAN PRIOR QUESTIONS (Y4)  SOURCE OF VARIATION  AR  2  df  F , ob s .  P <  . 0190  1  1.8269  . 17  . 1428  3  4 .2532  . 008  . 0030  1  . 2884  .59  . 0022  1  .2115  .65  . 0364  1  3 .5000  . 06  . 0236  1  2.2692  . 13  . 0286  1  2.7500  . 09  .0568  1  5.4615  .02  . 0056  1  .5384  .47  . 0067  1  . 6442  . 43  . 0455  1  4.3750  . 03  . 0058  2  .2788  .76  . 0041  1  .3942  • 53  1  . 0384  .82  . 0021  1  . 2019  . 65  . 0006  1  . 0576  .79  . 0012  1  . 1153  .73  . 0001  1  . 0096  .88  TOTAL  .3744  21  ERROR  . 6256  59  l  X  ( X 2 »X^,X^) X  5  X  6  X  7  X  8  X  9  X  10  X  6 7  X  6 8  X  7 8  X  X  X  (x x ,x x 5  g  X  6 9  X  6 10  X  7 9  X  7 10  X  8 9  X  8 10 ,  X  X  X  X  X  X  5  1 0  )  -.0004  164 APPENDIX D RESULTS OF REGRESSION ANALYSIS FOR MEAN  INFORMATION-  SEEKING QUESTIONS (Y5)  SOURCE OF VARIATION  A R  2  df  F , obs .  P<  . 0310  1  2.9807  . 08  . 0866  3  2.7756  . 04  . 0058  1  . 0204  1  1.9613  . 16  . 0041  1  .3942  .53  . 0043  1  .4134  .53  . 0303  1  2 .9135  . 08  . 0109  1  1. 0480  .31  .0578  1  5 . 5576  . 02  . 0077  1  .7403  .39  . 0114  1  1.0961  .30  . 0214  2  1.0288  .36  . 0673  1  6.4711  . 01  . 0108  1  1.0384  . 31  . 0013  1  .1250  .72  . 0011  1  . 1057  .74  . 0015  1  . 1442  .70  . 0015  1  . 1442  .70  TOTAL  .3753  21  ERROR  .6247  59  X  l >X^)  s X  5  X  6  X  7  X  8  X  9  X  10  X  6 7  X  6 8  X  7 8  : X  X  X  X  5 9' 5 10 X  X  6 9  X  6 10  X  7 9  X  7 10  X  8 9  X  8 10  X  X  X  X  X  X  X  X  •  )  . 5576  . 46  165 APPENDIX D RESULTS OF REGRESSION  ANALYSIS  FOR MEAN  CONSTRAINT-  SEEKING QUESTIONS ( Y 6 ) .  SOURCE OF VARIATION  l  X  (^2 >X^ >X^) X  5  X  6  X  7  X  8  X  9  X  10  X  6 7  X  6 8  X  7 8  X  X  X  (x x ,x x 5  g  X  6 9  X  6 10  X  7 9  X  7 10  X  8 9  X  8 10  X  X  5  1 Q  )  AR  2  df  F , OD S .  P <  .0219  1  2.1262  . 14  . 1046  3  3.3851  . 02  . 0088  1  .8543  . 36  . 0279  1  2.7087  . 10  . 0001  1  . 0097  .88  . 0408  1  3 .9611  .04  .0858  1  8.3301  . 005  . 0090  1  .8738  . 0218  1  2.1165  . 14  . 0155  1  1.5048  . 22  . 0005  1  . 0485  .81  . 0158  2  .7670  . 47  . 0074  1  .7184  .40  . 0037  1  . 3592  . 55  . 0012  1  .1165  .73  . 0001  1  . 0097  . 88  . 0129  1  1.2524  . 26  .0009  1  . 0873  .3785  21  .6215  59  .35  X  X  X  X  TOTAL ERROR  .76  166. APPENDIX D RESULTS  OF REGRESSION  ANALYSIS FOR MEAN  HYPOTHESIS-  SEEKING QUESTIONS ( Y 7 ) .  SOURCE OF VARIATION  A R'  df  . 0001  1  .0097  (%2 ' X-j » X^ )  .2114  3  6 .7115  X^  . 0022  1  .2095  65  x,  . 0057  1  . 5428  47  X.  . 0001  1  . 0097  88  X,  . 0138  1  1. 3142  .25  X,  . 0178  1  1.6952  , 19  X  . 0017  1  .1612  . 0358  1  3 .4095  . 0056  1  .5333  ,47  . 0002  1  .0190  .86  . 0426  2  2 . 0285  . 0019  1  .1890  . 0191  1  1.8190  . 0034  1  . 3238  .57  . 0003  1  .0285  .84  . 0005  1  . 0476  .81  . 0068  1  . 6476  . 42  10  X  6 7  X  6 8  X  7 8  X  X  X  (x x ,x x ) 5  g  X  6 9  X  6 10  X  7 9  X  7 10  X  8 9  X  8 10  X  X  X  X  X  X  5  1Q  TOTAL  .3691  21  ERROR  . 6309  59  ob s  88 0006  .69 . 06  . 13 .67 . 17  167 APPENDIX D RESULTS  OF REGRESSION ANALYSIS  FOR  TOTAL  SOLUTIONS  (Y8)  A R  df  . 0321  1  2 .5275  11  ( X 2 > x^»x^)  . 0459  3.  1.2047  31  x^  .0255  1  2.0078  15  .0169  1  1.3307  25  . 0083  1  . 6535  42  . 0135  1  X,  . 0001  1  . 0078  89  X  . 0027  1  .2126  ,65  . 0005  1  .0393  ,82  . 0017  1  . 1338  ,71  . 0056  1  . 4409  , 51  . 0332  2  1.3070  .0025  1  . 1968  . 66  . 0022  1  . 1732  . 68  . 0210  1  1. 6535  .20  . 0020  1  . 1574  .69  . 0045  1  .3543  . 56  . 0143  1  1.1259  TOTAL  . 2325  21  ERROR  . 7675  59  SOURCE OF  VARIATION  X. x  i  10  X  6 7  X  6 8  X  7 8  X  X  X  ( 5 9» 5 io^ X  X  X  6 9  X  6 10  X  7 9  X  7 10  X  8 9  X  8 10  X  X  X  X  X  X  X  X  ob s  1.0629  P<  30  .27  .29  168 APPENDIX D RESULTS  OF R E G R E S S I O N TIME  SOURCE  OF V A R I A T I O N  ANALYSIS  FOR MEAN  RESIDUAL  (Y9).  A R  df  . 0294  1  2.9696  08  . 0342  3  1.  1481  33  X^  . 0000  1  . 0000  95  X,  . 0063  1  . 6363  43  X.  . 0008  1  . 0808  76  X,  . 0624  1  X,  . 0026  1  X  .0184  1  . 1017  1  10.2727  . 0000  1  .0000  . 95  . 0000  1  . 0000  . 95  . 0249  2  1.2576  .29  .0161  1  1.6262  .20  . 0344  1  3 .4747  . 06  . 0366  1  3.6969  .05  . 0012  1  .1212  .72  . 0256  1  2.5858  . 10  . 0059  1  .5959  . 44  . 4004  21  . 5996  59  X. (X^  ,X^)  10  X  6  X  7  X  6  X  8  X  7  X  8  ( 5 9 X  X  X  6  X  9  X  6  X  10  X  7  X  9  X  7  X  10  X  8  X  9  X  8  X  10  TOTAL ERROR  »  X  5  X  10^  ob s  6.3030 . 2626 1.  8586  P<  01 .61 • . 17 , 002  169 APPENDIX D RESULTS  OF REGRESSION ANALYSIS FOR MEAN QUESTIONS  SOURCE OF VARIATION  _K  2  RESIDUAL  (Y10) .  df  F , ob s .  . 0160  1  1.4953  . 22  , 0725  3  2 .2585  . 08  . 0000  1  . 0000  . 95  . 0222  1  2.0747  . 15  . 0081  1  .7570  • 39  .0040  1  .3738  .55  . 0345  1  3.2243  . 07  . 0022  1  .2056  .65  . 0821  1  7.6728  . 0089  1  . 8317  . 36  . 0015  1  . 1401  .70  . 0255  2  1.1916  . 31  . 0513  1  4.7943  . 03  . 0058  1  . 5420  .47  . 0036  1  .3364  .57  .0038  1  . 3551  .56  . 0119  1  1. 1121  .29  . 0017  1  . 1588  .69  TOTAL  . 3558  21  ERROR  .6442  59  l  X  9X^ > X  5  X  6  X  7  X  8  X  9  X  10  X  6 7  X  6 8  X  7 8  )  X  X  X  ( X  5 9' 5 10 X  X  6 9  X  6 10  X  7 9  X  7 10  X  8 9  X  8 10  X  X  X  X  X  X  X  X  )  . 007  170  APPENDIX E  MEAN RESIDUALS OF MEAN RESIDUAL FOR TRAINED  QUESTIONS  ( T l ) AND UNTRAINED (T23)  SUBJECTS AT THREE LEVELS OF COGNITIVE STYLE  (CST)  171  MEAN RESIDUALS OF MEAN RESIDUAL TIME FOR TRAINED  ( T l ) AND UNTRAINED  (T23) SUBJECTS  AT THREE LEVELS OF IMPULSIVITY (MFF ERRORS).....172  171  APPENDIX MEAN RESIDUALS TRAINED THREE  DEPENDENT MEAN TOTAL  OF MEAN RESIDUAL  ( T l ) AND UNTRAINED  VARIABLE QUESTIONS  R E S I D U A L  Q U E S T I O N S  QUESTIONS FOR  (T23) SUBJECTS AT  LEVELS OF COGNITIVE  MEAN I . S . QUESTIONS  M E A N  E  STYLE  (CST).  Tl  CST  T23  L  -1.5275  +  .4729  M  +  .8078  +  .0202  H  + .6911  -  .5506  L  -1.2470  +  .3453  M  +  .4676  +  .0886  H  +  .6235  r- . 5205  L  -1.0856  + .6281  M  - .0019  -  H  +  - .5189  .6686  .0920  172  APPENDIX E MEAN RESIDUALS  OF MEAN RESIDUAL TIME FOR  ( T l ) AND UNTRAINED  TRAINED  (T23) SUBJECTS AT THREE LEVELS  OF IMPULSIVITY (MFF ERRORS).  DEPENDENT VARIABLE  MEAN TOTAL  TIME  MEAN RESIDUAL  TIME  IMPULSIVITY  Tl  T23  H  -26.9955  + 16 . 3435  M  +18.2701  -  L  +12.7831  -10 . 6031  H  -16 .6180  +18 .9627  M  +22.6722  -  8.7247  L  -  -  8.2443  1.0177  6.3983  

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