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Simple and contingent biconditional problem solving in three concept learning paradigms Hartman, Bryan Douglas 1971

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SIMPLE AND CONTINGENT BICONDITIONAL PROBLEM SOLVING IN THREE CONCEPT LEARNING PARADIGMS  by BRYAN DOUGLAS HARTMAN B.A., U n i v e r s i t y of B r i t i s h Columbia,  1968  A t h e s i s submitted i n p a r t i a l f u l f i l m e n t of the requirements f o r the degree of  Master of Arts  i n the Department of Educational Psychology  We accept t h i s t h e s i s as conforming t o the required standard  THE UNIVERSITY OP BRITISH COLUMBIA April,  1971  In p r e s e n t i n g an  this  thesis  in partial  advanced degree at the U n i v e r s i t y  the  Library  I further for  shall  make i t f r e e l y  agree t h a t permission  scholarly  h i s representatives.  of  this  written  thesis  of British  available  gain  I agree  copying o f t h i s  shall  that  n o t be a l l o w e d w i t h o u t  Bryan D. Hartman  Educational Psychology  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a  Date  March 20,  1971  Columbia  thesis  copying o r p u b l i c a t i o n  permission.  D e p a r t m e n t of  that  by t h e Head o f my D e p a r t m e n t o r  I t i s understood  f o r financial  Columbia,  f o r r e f e r e n c e and s t u d y .  f o r extensive  p u r p o s e s may be g r a n t e d  by  f u l f i l m e n t o f the requirements f o r  my  The  structure of a c l a s s i f i c a t i o n appears to consist of two  (a) relevant a t t r i b u t e s and  componentst  (b) the c l a s s i f i c a t i o n r u l e which combines the  relevant a t t r i b u t e s to describe  the c l a s s i f i c a t i o n .  An experiment was  conduc-  ted to separate a t t r i b u t e i d e n t i f i c a t i o n (Al) from r u l e learning (RL) and compare these with the complete learning (CL) of a c l a s s i f i c a t i o n which requires learning both components.  The comparison was  conducted f o r two  biconditional  c l a s s i f i c a t i o n r u l e s , a two a t t r i b u t e , simple b i c o n d i t i o n a l r u l e (SB), and three a t t r i b u t e , contingent b i c o n d i t i o n a l r u l e (CB), and f o r two t i o n strategy i n s t r u c t i o n s , an i n t r a - s t i m u l i (RA)  a  sets of s o l u -  strategy i n v o l v i n g  classifi-  cation according to the combination of relevant a t t r i b u t e s on each card, and  an  i n t e r - s t i m u l i (ER) strategy i n v o l v i n g c l a s s i f i c a t i o n according to the number of relevant a t t r i b u t e discrepancies focus card.  These three experimental f a c t o r s were combined with two  sized control f a c t o r s , sex and design.  problem order, I n a 3 x 2 x 2 x 2 x 2  hypothefactorial  Each of 48 grade ten Ss (24 male and 24 female) completed both bicon-  d i t i o n a l problems i n one of two was  between each stimulus card and an exemplar  counterbalanced problem orders.  recorded on s i x dependent v a r i a b l e s :  Performance  ( l ) T r i a l s ; (2) E r r o r s ; and  (3) Sec-  onds - a l l to a c r i t e r i o n of 27 consecutive correct responses; as w e l l as  the  p o s t - c r i t e r i o n v a r i a b l e s , (4) C l a s s i f i c a t i o n s , the number of c o r r e c t l y c l a s s i f i e d cards f o r a withheld subset of the stimulus population used f o r o r i g i n a l learning; (5) V e r b a l i z a t i o n , a verbal response which describes a c l a s s i f i c a t i o n r u l e that separates the cards i n t o two mutually exclusive and exhaustive categories; and  (6) Strategy, the c l a s s i f i c a t i o n of the verbal response as implying  the RA or ER strategy according to whether reference was bute combinations or relevant a t t r i b u t e  discrepancies.  made to relevant  attri-  In general, the r e s u l t s were as follows.  F i r s t , the obtained order of par-  adigm d i f f i c u l t y f o r the T r i a l s , E r r o r s , Seconds, C l a s s i f i c a t i o n s , and Verba l i z a t i o n v a r i a b l e s was  CL > Al > RL,  This r e s u l t was  interpreted as support  f o r the A l and RL component approach of Haygood and Bourne (1965), and as extension of t h i s approach to SB and CB r u l e s .  Second, the obtained order of  r u l e d i f f i c u l t y f o r the T r i a l s , E r r o r s , and Seconds variables was This r e s u l t was  an  CB >  SB,  interpreted as support f o r the r u l e r e s u l t s of Shepard, Hovland,  and Jenkins (1961), and as an extension of t h e i r r e s u l t s to include four dimension, bivariate stimuli. tegy i n s t r u c t i o n s was  Third, the obtained order of d i f f i c u l t y f o r the s t r a -  RA > ER,  s u l t s i g n i f i c a n t . Consideration ported the conclusion  But, only f o r the Seconds v a r i a b l e was  this re-  of the r e s u l t s f o r the Strategy v a r i a b l e sup-  that the i n s t r u c t i o n treatment was  overcome the tendency of Ss to choose t h e i r own  strategy.  not s u f f i c i e n t to Consequently, sev-  e r a l suggestions f o r a more e f f e c t i v e i n s t r u c t i o n treatment were offered. Fourth, the obtained c o r r e l a t i o n s between the C l a s s i f i c a t i o n s and t i o n variables were ,89 and r e s u l t was  Verbaliza-  ,79 f o r the SB and CB problems r e s p e c t i v e l y .  This  interpreted as an i n d i c a t i o n that f u r t h e r i n v e s t i g a t i o n of the  C l a s s i f i c a t i o n v a r i a b l e as a method of determining concept attainment would be worthwhile.  F i n a l l y , the educational  emplications of t h i s study were discussed.  Thesis Committee Chairman  Serial  !  Subject  1  Page(s)  1  L i s t of Tables  i  2  L i s t of Figures  i i  3  L i s t of Plates  i i i  4  Acknowledgement of Assistance  iv  5  Chapter 1 Problems and Related L i t e r a t u r e  1-14  6  Chapter 2 Purposes and Hypotheses  15-18  7  Chapter 3 Method  19-29  8  Chapter 4 Results  30-48  9  Chapter 5  49-54  Discussion  10  References  55-57  11  Appendix I Apparatus Description Appendix I I Instructions  58 - 60  12  6 l - 75  Table  Subject  Page(s)  1  Means for the Six Dependent Variables: Trials, Errors, Seconds, Classifications, Verbalization, and Strategy for Problems 1 - 4  31 - 32  2  Summary of Means and Standard Deviations for each of Six Dependent Variables Across Problems 1 - 4  33  3  Analysis of Variance for Trials, Errors, and Time (seconds) to Criterion for Problem 1  34  4  Analysis of Variance for Trials, Errors, and Time (seconds) to Criterion for Problem 2  34  5  Analysis of Variance for Trials, Errors, and Time (seconds) to Criterion for Problems 3 and 4  36  6  Analysis of Variance for the Classifications and Verbalization  37  Variables for Problems 3 and 4 7  Post Hoc. Mean Comparisons for the Paradigm Factor  40  8  A Comparison of the Strategy Instructions Given with the Strategy Verbalized for 48 Ss on SB and CB Problems Intercorrelations of Seven Dependent Variables for Problems 3 and 4  45  10  Response Frequencies on the Post-Criterion Variables: Classifications, Verbalization, and Strategy, for 96 Subject - Problem Combinations  48  11  A Comparison of the Classification and Verbalization Variables for Problem 4  50  9  47  Figure 1  Subject Six classification rules used by Shepard, Hovland,  Page(s) 5  and Jenkins (1961) 2  Dimensionally ordered stimulus array  22  3 4  Discrepancy ordered stimulus array Histogram of mean values of the Trials, Errors, and Seconds variables for three learning paradigms  27 38  5  Histogram of mean values of the Classifications and Verbalization variables for three learning paradigms  39  6  Histogram of mean values of the Trials, Errors, and Seconds variables for simple and contingent biconditional rules  42  7  Frequency polygon of mean values of the Trials and Errors variables for the simple and contingent biconditional rules across three learning paradigms  43  8  Histogram of the mean value of the Seconds variable for the intra- and inter-stimuli instruction treatments  44  ill  Plate  1  Subject  Learning Apparatus  Page  24  Acknowledgement o f A s s i s t a n c e  I w o u l d l i k e acknowledge  the u n s t i n t i n g a s s i s t a n c e  g i v e n t o me by t h e members o f ray t h e s i s c o m m i t t e e , R. F .  C o n r y , C h a i r m a n , S. S,  L e e , and R. L , R,  Drs, Overing.  I n a d d i t i o n , I w o u l d l i k e t o t h a n k my p a r e n t s f o r t h e i r i n v a l u a b l e s u p p o r t and encouragement t h r o u g h o u t my e d ucation.  F i n a l l y , I would l i k e t o t h a n k my w i f e , Dona,  f o r s o many  kinds o f a s s i s t a n c e , encouragement, and i n -  s p i r a t i o n that they defy  classification.  Chapter 1  Problems and Related L i t e r a t u r e  Following an i n v e s t i g a t i o n of c l a s s i f i c a t o r y behavior, Shepard, Hovland, and Jenkins learning involved: formation  ( l 9 6 l ) speculated that the process of c l a s s i f i c a t i o n ( l ) the abstraction of relevant dimensions, and (2) the  of r u l e s that are b u i l t by combining a number of the most elemen-  tary kinds of c l a s s i f i c a t i o n s ; such as, a f f i r m a t i o n , conjunction, and disjunction.  In the f i r s t part of t h e i r experiment, these i n v e s t i g a t o r s attempted t o  determine the d i f f i c u l t y of c l a s s i f i c a t i o n learning by comparing i t with ident i f i c a t i o n learning.  The l a t t e r i s defined as l e a r n i n g to associate a d i f f -  erent response with each stimulus, while the former i s defined as learning t o assign the same response t o several d i f f e r e n t s t i m u l i , such that the t o t a l set of s t i m u l i ultimately comprise two or more mutually exclusive and exhausti v e classes.  Shepard et a l . , note that since one need not discriminate among  s t i m u l i of the same c l a s s , l e s s information about a stimulus i s required t o c l a s s i f y i t than t o i d e n t i f y i t ; therefore, a c l a s s i f i c a t i o n should be easier to l e a r n than an i d e n t i f i c a t i o n .  Presumably, members of a c l a s s share common  elements which serve as c r i t e r i a f o r c l a s s membership.  A stimulus  general-  ization explanation of this contention comes from French (1953), who found that increasing the number of elements common to a response class decreased discrimination d i f f i c u l t y under high reinforcement ination diffuculty under low reinforcement  consistency, and increased discrimconsistency.  He argues that an i n -  crease in the number of common elements increases the amount of stimulus generalization among the stimuli, such that when these common-element stimuli are assigned to the same response class, stimulus generalization w i l l have a f a c i l i t a t i v e effect; but, when they are assigned to different response categories, the effect w i l l be inhibitive.  It i s the knowledge of these common  elements and the a b i l i t y to abstract them to classify other stimuli, which obviates the necessity of learning the characteristics of each stimulus. saving i s not effected in identification learning.  This  On the contrary, after learn-  ing to associate different labels with each stimulus, subsequent stimuli require the learning of their unique characteristics and the association of these characteristics with the correct one of a number of different responses. Attempts to c l a r i f y the relationship between classification and identification learning by combining both in a single task encounter several d i f f iculties.  First, converting an identification task into a classification  task reduces the total number of responses which must be kept in mind. this reduction alters the chance level of successful performance.  Second,  For example,  with eight stimuli and eight responses in an identification task, the proba b i l i t y of guessing the correct response i s one in eight.  In a classification  task, where four of the eight stimuli are associated with each of two responses, the probability i s one in two.  With both these factors affecting performance  in comparisons of identification and classification learning, i t i s d i f f i c u l t to assess the conceptual factor; i.e., the reduced need to learn the characteri s t i c s of each stimulus which i s occasioned by learning the characteristics  common to a class of s t i m u l i . In an attempt to c l a r i f y t h i s confusion, Shepard et a l , ,  (l96l)  noted  that the d i f f i c u l t y of a c l a s s i f i c a t i o n can be manipulated without changing either the s t i m u l i or responses, by a l t e r n a t i n g the assignments between them. For example, because of the several a t t r i b u t e s common to the class "dog" and several others common t o the class "horse", i t would be more d i f f i c u l t t o learn which two of four horses and which two of four dogs belonged i n category "A", than i t would be to learn that a l l four horses belong i n category "A" and a l l four dogs belong i n category "B",  Shepard et a l . , extend t h e i r  argument by s t a t i n g : The cross-species c l a s s i f i c a t i o n evidently e n t a i l s a l a r g e r component of rote learning and, might, indeed, be comparable i n d i f f i c u l t y t o learning a separate i d e n t i f y i n g response f o r each animal. Moreover, the d i f f e r e n c e i n d i f f i c u l t y of two such c l a s s i f i c a t i o n s could not be a t t r i b u t e d either t o changes i n the length of l i s t or i n chance expectation. C l e a r l y , then, the extent t o which the p o t e n t i a l r e duction i n d i f f i c u l t y from i d e n t i f i c a t i o n to c l a s s i f i c a t i o n learning i s r e a l i z e d depends upon how the s t i m u l i are grouped together i n t h e i r assignment t o responses ( 1 9 6 1 , p, 2 ) , By means of a l t e r n a t i n g the response assignments of a c l a s s i f i c a t i o n task, Shepard e t a l . , manipulated the rote component of a task i n an attempt t o c l a r i f y the r e l a t i o n s h i p between i d e n t i f i c a t i o n and c l a s s i f i c a t i o n learning. This manipulation was conducted within a stimulus population of three dimens i o n a l , b i v a r i a t e , geometric shapes which were c l a s s i f i e d i n t o  dichotomous  response categories, with four s t i m u l i being assigned t o each category. dimensions and t h e i r values were: and shape, square or t r i a n g l e .  These  s i z e , large or small; color, black or white;  This population produced a t o t a l of ?0 possible  C l a s s i f i c a t i o n s of the eight s t i m u l i (the number of combinations of four things taken from eight; i . e . , 8 1 / ( 4 ! ) = 70). 2  However, by applying the reductive  p r i n c i p l e that c l a s s i f i c a t i o n s are of the same basic type i f one can be obtained from the other by e i t h e r interchanging the r o l e s of the three dimensions or reversing the response assignment system, these 70 are reduced t o s i x s t r u c t u r -  a l l y d i s t i n c t c l a s s i f i c a t i o n s , each of which corresponds to a d i f f e r e n t c l a s s i f i c a t i o n r u l e f o r assigning stimulus - response contingencies. Figure 1 i l l u s t r a t e s the s i x c l a s s i f i c a t i o n r u l e s .  Type I, an affirmation  r u l e , i s based upon one relevant dimension; i . e . , color, where an exemplar must be black.  Type I I , a b i c o n d i t i o n a l r u l e , i s based upon two relevant dimensions,  color and shape, and an exemplar may be e i t h e r black and t r i a n g u l a r or neither black nor t r i a n g u l a r .  Types I I I , IV, and V are c a l l e d "single dimension with  exception" r u l e s , f o r they specify the values on one relevant dimension, plus the two exceptional  s t i m u l i f o r which the responses must be reversed; f o r ex-  ample, f o r Type IV, s i z e , color, and shape are relevant and an exemplar i s large except f o r the large, white square, which must be exchanged f o r a small, black t r i a n g l e .  These exception r u l e s are based upon a s i n g l e dimension, but  with the exceptional  s t i m u l i t h i s number i s increased  to e i t h e r two  relevant  dimensions f o r Types I I I and V, or three relevant dimensions f o r Type IV. Type VI i s termed the "odd-even" r u l e by Shepard et a l . upon three relevant dimensions:  This r u l e i s based  f o r example, i n Figure 1 s i z e , shape, and  color are relevant and an exemplar may be t r i a n g u l a r ~  i n which case i t must  be e i t h e r large and black or neither large nor black —  or i t may be square  —  i n which case i t must be e i t h e r large and white or neither large nor white. Concerning the r e l a t i v e d i f f i c u l t y of the s i x r u l e types, Shepard et a l . , note that whereas Type I involves a f a m i l i a r kind of c l a s s i f i c a t i o n commonly used i n c l a s s i f i c a t i o n studies, Type VI may approach i n d i f f i c u l t y a rote i d e n t i f i c a t i o n task which requires to each stimulus.  the association of a d i f f e r e n t response  The d i f f e r e n t responses f o r the Type VI r u l e become apparent  when t h i s r u l e i s stated i n terms of the l o g i c a l connectives of conjunction and d i s j u n c t i o n , which produces a complete enumeration of the four s t i m u l i assigned to the exemplar category.  Shepard et a l . , further  speculate that i f the d i f f i -  c u l t y of a c l a s s i f i c a t i o n i s p o s i t i v e l y r e l a t e d e i t h e r to the stated  verbal  length of the r u l e required to s p e c i f y exemplars of each category or to the numb of l o g i c a l symbols required to express the r u l e then (putting aside the exceptior r u l e s I I I , IV, and V) i t i s possible to postulate three d i f f e r e n t l e v e l s of d i f f i c u l t y corresponding to Types I, I I , and VI.  Support f o r t h i s postulation comes  from a consideration of the increasing number of relevant dimensions: two,  i . e . , one,  and three f o r Types I, I I , and VI r e s p e c t i v e l y . Shepard et a l , ,  (1961), attempted  to answer two questions:  Does learning  d i f f i c u l t y vary across the s i x types of c l a s s i f i c a t i o n ? , and Does the learning of a c l a s s i f i c a t i o n t r a n s f e r to f a c i l i t a t e the learning of a new of the same type?  Their experimental procedure was  paradigm with two verbal responses, " A " or "B".  a modified  classification paired-associate  Eight s t i m u l i were i n d i v i d u a l l y  presented i n random sequences u n t i l , by the method of a n t i c i p a t i o n , an association between each stimulus'and one of the two responses was Ss completed a t o t a l of twenty tasks, comprising  established.  Each of s i x  f i v e successive tasks f o r four  of the s i x types of r u l e s (Because of t h e i r s t r u c t u r a l s i m i l a r i t y Types I I I , IV, and V were combined to y i e l d a s i n g l e measure.).  D i f f i c u l t y was determined by  the number of errors to s o l u t i o n . The r e s u l t s revealed two orders of s o l u t i o n d i f f i c u l t y . problems, the d i f f i c u l t y order was  I < II < ( i l l , IV, V) < VI,  On encountering the This order supported  the i n v e s t i g a t o r s ' contention that d i f f i c u l t y would be p o s i t i v e l y c o r r e l a t e d with the l o g i c a l and verbal lengths of the stated r u l e s ,  1  However, with  continued  1 This order also supported the i n v e s t i g a t o r s ' q u a l i f i e d hypothesis that problem d i f f i c u l t y would vary as a monotonically increasing function of the number of relevant dimensions. The q u a l i f i c a t i o n a r i s e s from the f a c t that within t h i s system of c l a s s i f i c a t i o n there i s a confounding i p s a t i v e r e l a t i o n s h i p between the relevant and i r r e l e v a n t dimensions, such that increasing the number of relevant dimensions n e c e s s a r i l y decreases the number of i r r e l e v a n t dimensions by an equal number, and vice versa. I t i s f o r t h i s reason that, based upon the r e s u l t s obtained f o r t h i s condition by Smith (1954) and by Wallach (1961), Shepard,,et a l . , postulated that c l a s s i f i c a t i o n d i f f i c u l t y increases monotonically as a function of the number of relevant dimensions. More recently, Kepros and Bourne (1966) have suggested that an invariance p r i n c i p l e may underlie performance i n r e l a t i o n to the number of relevant and i r r e l e v a n t dimensions. S p e c i f i c a l l y , performance decreases monotonically with the increase i n the number of stimulus dimensions, regardless of the r e l e vance of those dimensions.  A  A  B  •  A  A  •  EH  A  •  •  n  A  B  111  11  O  A  A  A  A  A  V  A  •  A  •  m  A  A  •  A  •  a  • V  • VI  Fig. 1. Six different classifications of the same set of eight stimuli used in Shepard, Hovland, & Jenkins, ( I 9 6 I ) . (Within each box the four stimuli on the l e f t belong in one class and the four stimuli on the right in the other class.)  practice each type becomes increasingly less d i f f i c u l t due to within-type positive transfer.  In particular, Type VI exhibited a  disproportionate  decrease in d i f f i c u l t y relative to the other types, such that i t became less d i f f i c u l t than Types (III, IV, V).  This decrease produced the second  order of problem d i f f i c u l t y , I < II < VI < ( i l l , IV, V).  In accordance with  their explanation of classification learning as the active abstraction of dimensions and formulation of rules, Shepard et a l , , hypothesized that during the series of five problems of a single type, the constancy of the c l a s s i f i cation rule allowed Ss to learn that rule and apply i t to later problems in the series.  This information substantially facilitated performance on the  later problems, thereby effecting within-type positive transfer, Haygood and Bourne (1965) have proposed a component theory of concept learning which may be used to clarify the results obtained by Shepard et a l . , (1961).  Haygood and Bourne (1965), and more recently Bourne (1966, 1967)»  postulated that concept learning consists of two processes:  attribute  identification (Al): the identification of relevant attributes, and rule learning (RL):  the discovery of the principle for partitioning the stimuli  in a problem and acquiring the rule in a form such that i t can be used in any problem of this type to f a c i l i t a t e the assignment of correct responses to the stimuli,  Occuring together in a concept learning situation, these  two components constitute the complete learning (CL) of a concept. Haygood and Bourne (1965) tested the assumption that concept learning consists of Al and RL components by varying the nature of a conceptual task across four conceptual rules.  The method of variation was as follows:  In  the RL condition, Ss were given the names of the relevant attributes for each problem.  Their task then was to learn the conceptual rule which associated  each stimulus with either of two response categories.  In the Al condition,  the rule for each problem was explained and illustrated.  The Ss were then  l e f t with the task of identifying the relevant attributes for each problem.  In the CL condition, Ss were given neither the conceptual rule nor the relevant attributes.  They were given only a description of the stimulus popula-  tion and the number of relevant dimensions for each problem. The results obtained for the number of t r i a l s and errors to criterion indicate that for each of four conceptual rules the order of d i f f i c u l t y was CL > Al > RL.  The fact that both Al and RL were less d i f f i c u l t than CL was  interpreted by Haygood and Bourne as support for the hypothesis that Al and RL are components of CL.  This interpretation has since received additional  support from a series of follow-up studies which have consistently found the order of paradigm d i f f i c u l t y to be CL > Al > RL (Bourne, 1967). In that the component theory separated concept learning into Al and RL behaviors, i t seems worthwhile to attempt to apply this theory to the classification problems used by Shepard et a l , , (1961),  In addition to providing  information about differences i n d i f f i c u l t y among the classification rules, this application w i l l provide information about differences in d i f f i c u l t y between components  within a single rule, and between rules for either of the  two components, Shepard et a l . , (1961) have also noted that some of their Ss learned a powerful reductive rule as they encountered successive Type VI problems. This, the "odd-even" rule, i s applied by remembering a single exemplar as a focus card, then comparing a l l other cards with this focus card to determine how many attributes (0, 1, 2, or 3) are different between the two cards. If there i s an even number of differences (0 or 2) the card i s an exemplar; i f there i s an odd number ( l or 3) the card i s a nonexemplar.  Given the i n -  troduction of this rule by some of the Ss for Type VI problems, and given that the greatest degree of positive transfer occurred for Type VI problems, i t seems worthwhile to determine the extent to which the introduction of the rule was i t s e l f responsible for the large degree of transfer.  This determin-  ation i s particularly important i n view of the fact that the second order of  problem d i f f i c u l t y noted by Shepard et a l . , i s a consequence of Type VI becoming less d i f f i c u l t than Types (III, IV, V). It appears to be possible to use either of two different strategies to solve both Type II and Type VI problems.  These are:  (l) an intra-stimuli  (RA) strategy, whereby S must concentrate upon each stimulus instance and formulate a rule for assigning a correct response to that instance, or (2) an inter-stimuli (ER) strategy, whereby S must concentrate upon the attribute value discrepancies among the stimuli, code the number of same and/or different attribute values, and formulate a rule to assign correct responses to each possible number of attribute discrepancies between the focus and stimulus cards.  An ER strategy i s most advantageous for those rules wherein more than  one attribute on a single dimension i s assigned to the exemplar category, and each of these attributes i s assigned an equal number of times to each response category.  Under these conditions, S may select any single card as a focus  instance and classify the remaining cards in relation to the focus instance. The rules appropriate for an ER strategy are considerably less complex than are those  for the RA approach.  For example, the RA Type II rule:  exem-  plars are red and circular or neither red nor circular, becomes the ER rule: exemplars d i f f e r from the focus card on 0 or 2 relevant dimensions. the RA Type VI rule:  Similarly,  exemplars are either single figures which are large and  circular or neither large nor circular} or they are double figures which are large and triangular or neither large nor triangular, becomes the ER rule: exemplars differ from the focus card on 0 or 2 relevant dimensions, 2 2 The stimuli could also be correctly classified in terms of their similarities, or in terms of an odd rather than an even number of changes from the focus instance. The choice of the statement: exemplars differ on either 0 or 2 relevant dimensions, was based upon two c r i t e r i a for the above exemplars. First, this was the form of the odd-even rule reported by Shepard et a l . , (1961). Second, this statement placed the focus card in the exemplar category, which according to Hovland and Weiss ( 1 9 5 3 ) would convey a greater amount of information and increase the likelihood of information assimilation by the S than would a negative focus instance. This i s particularly true when the Ss are not trained to use negative information (Friebergs & Tulving, I961).  The postulated coexistence of both these strategies i n the Shepard et a l . , study raises two questions:  (l) How d i f f i c u l t i s a Type VI pro-  blem when solved with an RA strategy?, and (2) How d i f f i c u l t i s a Type II problem when solved with an ER strategy?  A study that compares both  strategies i s required to answer these questions. Before attempting to answer these questions concerning problem solving strategies, the possibility that s t i l l another strategy, memorization, may have occurred in.the Shepard et a l . , study should be considered.  In the  reported analysis of rules verbalized by their Ss, Shepard et a l . , (1961) rated these rules on a scale of unnecessary rule complexity which ranged from Category 0, the most economical statement of a rule, to Category 5, the unnecessary enumeration of the attributes of every stimulus i n both response classes.  While no information about the number of rules assigned  to Category 5 i s given, the inclusion of this category appears to indicate that the classification learning results may i n part be attributable to behavior that was not consistent with the description of classification learning given by these investigators.  Shepard et a l . , (1961, p. 2)  note two c r i t e r i a that distinguish classification from identification learning.  First, classification learning i s the assignment of the same  response to several different stimuli; while identification learning i s the assignment of a different response to each stimulus.  Second, i t i s  not necessary to discriminate among stimuli that are classified together, but such discrimination i s necessary for identification learning.  Con-  cerning this second point, they note that members of a class apparently have something i n common, such that once the same name has been learned for some members of a class, l i t t l e , i f any, further learning i s required to extend this name to additional class members. With identification learning i t i s not possible to effect such a saving.  After different  responses have been learned for several members of a class, the association of s t i l l another response to another class member requires additional rote learning. With these c r i t e r i a in mind, consider the kinds of learning behavior that may be included in Category 5 of the Shepard et a l , , study.  F i r s t , for  problems other than Type VI, this category could include Ss that memorize the attribute combinations and associated classification responses for the entire stimulus set.  While these Ss undoubtedly learn the classification,  this kind of learning i s not equivalent to that of Ss who learn a rule that describes a common characteristic shared by each class member. Memorization of the attributes of each stimulus and i t s associated response does not i n volve the learning of a class of stimuli that share a common characteristic. It i s the S*s recognition of a common characteristic that initiates c l a s s i f i cation behavior by converting a collection of unrelated stimuli into a class of stimuli that can rationally be associated with a single response.  Accord-  ing to the definition of classification learning given above by Shepard et a l . , the memorization of what the S regards as unrelated stimuli and associated responses more closely approximates rote identification than c l a s s i f i cation learning.  Second, since the stimulus population was based upon only  three dimensions, this category could also include Ss who mastered an RA Type VI classification rule.  Shepard et a l , , (1961, p. 3) have noted that  for a Type VI rule a l l three dimensions are relevant, and i f this rule i s expanded in terms of i t s logical connectives of conjunction and disjunction, i t i s logically equivalent to a complete enumeration of the stimuli.  Con-  sequently, rule learners who master this d i f f i c u l t rule by means of the RA strategy that i s used for the other five problem types cannot be distinguished from memorizers who learn the stimulus-response pairs by rote.  In fact,  these rule learners are considered only to have achieved the highest degree  of unnecessary rule complexity, because for a Type VI rule i t i s possible to invoke an ER strategy to solve the problem. A method of discriminating between RA rule learning and memorization on a Type VI problem would be to add an irrelevant dimension to the stimulus population and ask Ss to verbalize their method of solving the problem. In that the extra dimension does not reliably discriminate between the two classes of stimuli, i t would be expected that rule learners would respond to this d i mension as an irrelevant one, while memorizers would not distinguish between the irrelevant and relevant dimensions. to discourage memorization behavior.  The extra dimension might also serve  In reference to the eight stimuli that  constituted the stimulus population used by Shepard et a l . , (1961), the addition of an extra dimension would increase the population to sixteen stimuli. In contrast to the eight stimuli, which are within the seven plus or minus two range of short term memory described by Miller (1956), the sixteen stimuli are beyond this range.  This additional memory load may dissuade Ss from  attempting to memorize the stimuli.  The additional dimension could also be  expected to generally increase problem d i f f i c u l t y .  Haygood and Stevenson  (1967) found a linear decrement i n performance as the number of irrelevant dimensions was increased from zero through two. In addition, they found the rate of decrement increased with problem d i f f i c u l t y (conjunction < inclusive disjunction < conditional) and with the concept learning paradigm (RL < Al < CL). The possibility that both rule learning and memorization behaviors could be included in the same category of rule verbalization i s not presented for the purpose of outlining the limitations of the rule verbalization measure.  Indeed, Shepard et a l . , (1961, p. 7) caution that this measure i s  not a rigorous one.  Rather, this analysis i s presented as a case for devising  a measure that w i l l discriminate between rule learning and memorization solutions of classification problems.  A measure that may serve this function has  been derived by the writer from the second criterion of classification learning noted by Shepard et a l , , (1961); that i s , once a classification i s learned, l i t t l e , i f any, further learning i s necessary to correctly classify subsequently encountered class members. This criterion suggests that a test of rule attainment would be to give Ss a single opportunity to classify additional members of the stimulus population used during original learning of the classification.  As i s the case for identification, memorization i n this situation  would require the additional learning of a new combination of attributes and an association of this combination with the correct classification response. Consequently, i t would be expected that rule learners would apply the rule and correctly classify a l l subsequently presented members of the class, while memorizers would engage i n additional learning and would correctly classify at no better than a chance level.  Furthermore, this post-task classification  measure requires the same kind of response behavior required during original learning.  This consistency avoids the ambiguity that can arise from using a  different measure of concept attainment,  Kvale (1968), i n an investigation  of "unconscious processes' i n concept formation, has noted that at present different measures of concept attainment are necessary to reliably determine i f Ss have attained a concept. I96I,  In a series of studies (Rommetveit, i960,  1965; Rommetveit & Kvale, 1965a, 1965b), several measures of concept  attainment were used, such as: free verbalization, drawing, sorting, and guessing (anticipation).  These investigators found that many Ss who were  not able to verbalize the concept indicated, by means of some or a l l of the other measures, that they had undoubtedly attained the concept. In that a search of the concept learning literature failed to yeild any studies which had employed a post-criterion classification measure as a method of measuring concept attainment, there i s a need to determine the r e l i a b i l i t y and validity of this measure.  Unfortunalely, such a determination was not  possible in the context of the present study.  A post-criterion classification  measure has t h e l i m i t a t i o n t h a t i t s r e l i a b i l i t y  i s i n f l u e n c e d by the  o f Ss who  T h i s l i m i t a t i o n can be  have memorized t h e o r i g i n a l s t i m u l i .  come by u s i n g a s t i m u l u s  population that i s s u f f i c i e n t l y large to  w i t h h o l d i n g a number of s t i m u l i t h a t w i l l  a l l o w the a d o p t i o n  population  of t h e p r e s e n t  population.  over-  permit  of a performance  c r i t e r i o n w e l l above t h a t which might be a t t a i n e d by g u e s s i n g . disadvantage of r e q u i r i n g a l a r g e r stimulus  guessing  T h i s has  In t h a t t h e  stimulus  experiment n e c e s s a r i l y approximated t h a t used  Shepard e t a l . , ( l 9 6 l ) , o n l y a s m a l l number o f s t i m u l i from t h e p o p u l a t i o n c o u l d be w i t h h e l d  the  by  original  for a post-criterion classification  measure.  C o n s e q u e n t l y , the r i s k of i n c o r r e c t i d e n t i f i c a t i o n o f l e a r n i n g s t r a t e g i e s was  accepted  i n order to estimate  c l a s s i f i c a t i o n and  the c o r r e l a t i o n between p o s t - c r i t e r i o n  v e r b a l i z a t i o n measures.  i n a c o n c e p t l e a r n i n g s i t u a t i o n may  An  estimate  y i e l d some i n d e x  of t h i s r e l a t i o n s h i p  of the d e s i r a b i l i t y  f u r t h e r development o f a c l a s s i f i c a t i o n measure t o d i s t i n g u i s h between Ss who  have l e a r n e d and  r e p r o d u c e i t , and o r i z e d s t i m u l i and  those  those  can a p p l y a c l a s s i f i c a t i o n r u l e , but cannot v e r b a l l y Ss who  cannot v e r b a l i z e a r u l e because t h e y have mem-  l e a r n e d no r u l e .  S t i l l a n o t h e r advantage o f a  classifi-  c a t i o n measure becomes a p p a r e n t upon c o n s i d e r a t i o n o f t h e s e v e r a l cases p o r t e d by but  Shepard e t a l . , (1961, p. 10)  where Ss had  s o l v e d the  c o u l d not v e r b a l i z e a r u l e t o r e p r o d u c e the c l a s s i f i c a t i o n .  i t was  of  not p o s s i b l e t o d e t e r m i n e how  these  re-  problem, Consequently,  Ss l e a r n e d t o s o l v e the  problem.  Chapter 2  Purposes and Hypotheses  The purposes of the present investigation are several.  The f i r s t i s to  apply the component approach of Haygood and Bourne (19^5) to the Type II and Type VI classification problems used by Shepard et a l . , (1961).  This appli-  cation w i l l provide information about the relative importance of the Al and RL components for the successful completion of a CL task.  Hypothesis 1 i s ,  therefore, that the order of paradigm d i f f i c u l t y expected for both the Type II and Type VI problems i s CL > Al > RL,  Support for this hypothesis comes  from Haygood and Bourne (1965), Bourne (1967), and Haygood and Stevenson (1967) —  a l l of which have found the order of d i f f i c u l t y to be as predicted  here. The second purpose of this study i s to assess the d i f f i c u l t y of Type II and Type VI classification problems for the three-learning paradigms.  Hypo-  thesis 2 i s , therefore, that for a l l three paradigms the expected order of d i f f i c u l t y of the problem types i s VI > II.  Support for this prediction comes  from the results of Shepard et a l . , (1961), which showed that for both the f i r s t and second orders of problem d i f f i c u l t y , Type VI problems were more d i f f i c u l t than Type II problems.  Further support for this prediction comes  from consideration of the number of relevant dimensions for Type II and Type VI problems:  two and three respectively.  This difference supports the rule  d i f f i c u l t y prediction for both the CL and Al paradigms because both involve learning the relevant attributes.  Similarly, the fact that the length of the  rule for Type VI i s greater than that for Type II for both the logical and verbal statements of this rule would also support the problem d i f f i c u l t y prediction for both paradigms, for both require the S to learn the classification rule.  Finally, in terms of Well's (1963) hypothesis that d i f f i c u l t y i s de-  termined by familiarity with the conceptual rules, the uniquity of the Type VI rule would further support the postulation that this rule would be more d i f f i c u l t than the relatively ubiquitous Type II rule,  Kepros and Bourne  (1966) indicate support for this last argument by noting that i n contrast to the results of Neisser and Weene (1962) and Hunt and Kreuter (1962), their results revealed no significant differences i n performance between conjunctive and biconditional rules for problems involving two relevant and one, two, or three irrelevant attributes.  These investigators contend that the discrep-  ancy i s explained by the amount of training upon biconditional rules that the S i s given prior to the experiment.  When, as i n their study, sufficient prac-  tice with biconditional rules i s allowed so that S becomes as familiar with biconditional rules as he generally i s with conjunctive rules, then application of either rule w i l l be equally d i f f i c u l t . In addition, Hypothesis 3 i s the expectation that no significant paradigm x problem type interaction w i l l occur.  This expectation  i s based upon  the fact that for a l l three learning paradigms the components of a Type VI problem are more d i f f i c u l t than are those of a Type II problem; i.e., i n comparison with a Type II rule a Type VI rule involves an additional relevant , dimension and a more complex rule as determined by the stated verbal or logical lengths of those rules. Another purpose of this study i s to investigate the two solution strategies, RA and ER, which occured i n Shepard et a l . , (1961) and which are postu-  lated to be applicable to Type II and VI rules.  Specifically, Hypothesis 4  is the prediction that problem solving by means of an ER strategy w i l l be more efficient than by means of an RA strategy.  This prediction i s based upon the  fact that an ER rule i s disjunctive for both problems, while the RA rules are both of a biconditional nature.  Furthermore, for Type VI problems, the results  of Shepard et a l . , give additional support to the strategy prediction.  They  noted that Ss who mastered this "powerful reductive rule" (ER rule) for a Type VI classification reached criterion with considerably fewer errors than did Ss who did not learn this rule. In addition, Hypothesis 5 i s that no interaction w i l l occur between the types of problems and the solution strategies.  As noted above, the difference  in rule complexity between Types II and VI for an RA strategy supports the hypothetical d i f f i c u l t y order VI > II,  And, even though the rules for Types  II and VI are identical disjunctive rules for an ER strategy, the addition of one relevant dimension and deletion of one irrelevant dimension for a Type VI rule has s t i l l been found to result in Type VI being more d i f f i c u l t than Type II (Smith, 195^;  Wallach, 196l).  Since both strategies involve separate RL  and Al components, i t i s also expected that the predicted order of paradigm d i f f i c u l t y , CL > Al > RL, w i l l be maintained for both strategies.  Hypothesis  6, therefore, i s that no significant paradigm x strategy interaction i s expected. Two factors, problem order and sex, have been included in the design as control factors.  While neither factor was considered to be germane to the  theoretical argument given above, both were included to detect any significant differences attributable to either factor.  Problem order; i.e., Type II f o l -  lowed by Type VI and vice versa, was counterbalanced for each factor in the study, while sex was controlled by including an equal number of male and female Ss for each c e l l in the design.  No directional hypotheses were stated  for either factor. The f i n a l purpose of this investigation i s to test a post-criterion classification task as a method of discriminating between memorization and rule learning solutions to classification problems.  Owing to several  that resulted from the simultaneous consideration  constraints  of several problems in this  study, i t was not possible to state and rigorously test a memorization hypothesis.  Consequently, the risk of incorrect classification of performance on  this variable that i s caused by the small number of post-criterion c l a s s i f i cation cards i s tolerated here in order to gain an estimate of the validity of such a measure by correlating the results of the post-criterion c l a s s i f i cation and rule verbalization variables.  Chapter 3 Method  Subjects In view of the complexity of the conceptual tasks in this experiment, and of the high correlation between intelligence test performance and concept learning performance reported by Osier and Fivel ( l 9 6 l ) , only those seventytwo grade ten students who had attained the highest total scores on a I968 administration  of the Henman - Nelson Tests of Mental Ability (Revised Edi-  tion i960, Grades 9 - 1 2 , Form B) were selected from a junior high school population of 263 grade ten students and asked to participate i n this experiment.  Of the seventy-two who were invited to participate, sixty-six  volunteered.  From this pool of Ss, the highest scoring twenty-four male  and twenty-four female students were i n i t i a l l y selected for the study. The elimination and replacement of thirteen of the i n i t i a l l y selected Ss was necessary for the following reasons:  F i r s t , within a limit of 1,350 t r i a l s ,  one S failed to reach criterion on the f i r s t warm-up problem while three and five Ss failed to reach criterion on the simple biconditional and contingent biconditional problems respectively. ^ i  n  addition, two Ss were dismissed  3 Types II and VI are both biconditional rules having two and three relevant attributes, respectively. The additional relevant attribute for Type VI causes the selection of either of two, two-attribute biconditional rules to be contingent upon the selection of the i n i t i a l attribute value of the third relevant attribute. In that the terms Type II and Type VI are particular to the Shepard et a l , , (I96l) experiment and f a i l to express the biconditional  because of emotional upset, and two Ss were dismissed due to apparatus malfunction.  The age range of the f o r t y - e i g h t Ss who completed the  experiment  was 15 years, 6 months to 16 years, 9 months, with a mean age of 15 years, 9.50  months and a standard deviation of 8.48 months.  scores of these Ss was  111  - 145 with a mean of  The range of I.Q.  122.50  and a standard devia-  t i o n of 8.48.  Stimulus Materials The stimulus instances consisted of sixteen geometric designs varying along four b i - l e v e l e d dimensions, which were printed on 2.5 cards.  x 3.5  inch paper board  The stimulus population was defined by the following four dimensions:  color of the f i g u r e s , red or blue; shape of the f i g u r e s , c i r c l e or t r i a n g l e j s i z e of the f i g u r e s , large or small; and the number of f i g u r e s , one or two. Each conceptual problem consisted of t h i r t e e n stimulus cards selected from the sixteen possible combinations of four b i - l e v e l e d dimensions.  Of  the remaining three cards, two were not included i n the problem set f o r any of the four problems used i n the study. c r i t e r i o n c l a s s i f i c a t i o n measure.  These cards were used f o r the post-  The remaining card was l a b e l l e d an exem-  p l a r of one of the categories and displayed as a focus instance f o r each of the treatment conditions. The use of the same focus card f o r a l l  treatment  conditions constituted an attempt to control across treatments f o r the memory load reduction which resulted from the continuous presence of an exemplar that was necessary i n the ER treatment condition?. A pre-test of ten a d d i t i o n a l students whose IQ scores ranged from 115 - 120 revealed a need to reduce the d i f f i c u l t y of the task to a l e v e l attainable by these grade ten students. nature of the rules that i s noted i n the present study, they w i l l be replaced, by the names simple b i c o n d i t i o n a l (SB) and contingent b i c o n d i t i o n a l (CB) r e s p e c t i v e l y , except when d i r e c t reference i s made to Shepard et a l . , (1961).  This reduction took the form of a concentrated attempt to familiarize Ss with the stimuli prior to their attempting the classification tasks.  To increase  the likelihood that a l l Ss would be familiar with each stimulus dimension, i t s attributes, and the ways these could be combined to produce a set of unique stimuli, an ordered array of the entire set of sixteen cards, with each dimension labelled, was presented to each S at the beginning of the experiment, along with a written description of each dimension and i t s values (see Figure 2),  In addition, each S was encouraged to ask about anything i n the instructions  he didn't understand, and a l l questions were answered until S indicated that he understood the instructions.  Generally, these answers took the form of c l a r i -  fying terms i n the instructions by showing their referents on the stimulus array board. To f a c i l i t a t e the analysis of results, a two part design was employed. The f i r s t part included two warm-up problems. problem based upon the size dimension.  Problem 1 was an affirmation  This problem was common for a l l Ss, and  was included to identify Ss who differed i n i t i a l l y in conceptual problem solving a b i l i t y as indexed by a relatively simple problem.  This problem also  served the purpose of allowing Ss to become familiar with the stimulus materials, the apparatus, and the procedure. Problem 2 was also an affirmation problem, but one based upon the.number dimension.  In this problem the three learning  paradigm treatments were effected for the purpose of familiarizing Ss i n each condition with the nature and format of their particular paradigm. The second part of the design included the experimental problems 3 and 4, as specified by a 3 x 2 x 2 x 2 x 2 factorial design, which included three learning paradigms (Paradigm), CL, Al and RL; two sexes (Sex), male and female; two experimental provlem types (Type), SB and CB; two orders of problem presentation (Order), SB followed by CB and vice versa; and instructions for two solution strategies (instructions), RA and ER. The Sex and Order factors  COLOR  black white  •  t w o  o n e  o o  • •  @  A A  o  A  O  A  A  O O  A A  A A  circle  triangle SHAPE  Fig. 2 , Dimensionally ordered stimulus array presented to a l l Ss at the beginning of the experiment, and presented again to Ss i n the intra-stimuli condition prior to the beginning of Problem 3.  were included as control factors, while the Paradigm, Type, and Instruction factors were crossed experimental factors. Apparatus For the purpose of minimizing the interaction between S and E, E constructed a stimulus presentation device capable of presenting cards continually at a S-paced rate (see Plate l ) .  For a complete description of the apparatus see  Appendix 1. In addition, the machine supplied correct response feedback by means of green (right) and red (wrong) signal lights.  The lights were a c t i -  vated by the S for a S-determined interval, beginning immediately upon the S's pressing one of two labelled response buttons.  By means of a second set  of feedback lights located on the back of the machine, E was able to unobtrusively record S performance on protocol sheets. Procedure At the outset, each S was given a written set of general instructions and the dimension—ordered stimulus array, both of which served to explain and illustrate the four dimensions and their values,  A complete set of instruc-  tions for each experimental condition i s given in Appendix I I . In addition, these instructions explained the general nature of the learning tasks, the functioning of the apparatus, the fact that S determined the pace of the task, the equal importance of speed and accuracy of responses, the number of problems to be completed, the number of consecutive correct responses required to reach criterion; i.e., 27, and the request to "say out loud" the letter of each response choice prior to pushing the button bearing that label. ^ The specific instructions for Problem 1 informed a l l Ss that this prob4 Pre-tests revealed these verbalizations served a valuable check function. Not only did they allow E to immediately correct any response programming errors made, but also they allowed immediate correction when, as several Ss did, S pushed a button not in agreement with his verbalized choice. This check was introduced to minimize the possibility of Ss assimilating incorrect information from either source of experimental error.  EXPERIMENTER'S VIEW PLATE I. LEARNING APPARATUS  lem Involved one "important c h a r a c t e r i s t i c " , and would c o n s i s t of l e a r n i n g to c o r r e c t l y c l a s s i f y each card with e i t h e r an " A " or "B" v e r b a l response, then checking the accuracy of t h i s response by pressing the correspondingly l a b e l l e d response button.  For t h i s problem s i z e was the r e l e v a n t dimension,  with " A " d e s i g n a t i n g large f i g u r e s and "B", s m a l l f i g u r e s . Problem 2 informed a l l Ss that t h i s problem a l s o involved one important c h a r a c t e r i s t i c , and the responses were " G " and " H " .  In a d d i t i o n , separate  i n s t r u c t i o n s were given f o r each of the three l e a r n i n g paradigms.  Ss i n the  A l c o n d i t i o n were given the conceptual r u l e f o r t h i s problem; i . e . , that the d i s t i n c t i o n between the two classes was determined by the presence of one form of the important c h a r a c t e r i s t i c , and t h e i r task was to l e a r n which charact e r i s t i c was important so they would be able to c l a s s i f y the cards c o r r e c t l y . Ss i n the RL c o n d i t i o n were given the i d e n t i t y of the r e l e v a n t a t t r i b u t e used t o d i s t i n g u i s h between the two categories..— the number of f i g u r e s — and were t o l d that t h e i r task was t o l e a r n how t h i s c h a r a c t e r i s t i c was used so they would be able to c l a s s i f y the cards c o r r e c t l y .  Ss i n the CL c o n d i t i o n were  given n e i t h e r the concept r u l e nor the r e l e v a n t a t t r i b u t e s ; r a t h e r , they were t o l d only the number of a t t r i b u t e s r e l e v a n t f o r each problem. In that the d i f f i c u l t y of an experimental task may vary as a f u n c t i o n of knowledge of the number of a t t r i b u t e s r e l e v a n t f o r each problem, the number of r e l e v a n t a t t r i b u t e s was s p e c i f i c a l l y given i n the i n s t r u c t i o n s f o r each paradigm i n an attempt to keep constant the d i f f i c u l t y l e v e l due to t h i s v a r i able across paradigms.  This c o n t r o l was n e c e s s i t a t e d by the f a c t that Ss i n  the RL c o n d i t i o n are unavoidably given the number of relevant a t t r i b u t e s i n volved i n each problem when they are given the i d e n t i t y of those  attributes.  Consequently, these Ss can immediately begin to form h y p o t h e t i c a l r u l e s based upon only that number of a t t r i b u t e s .  S i m i l a r l y , when Ss i n tha A l c o n d i t i o n  were given a complete statement of the conceptual r u l e , they a l s o were i n d i -  rectly informed of the number of relevant attributes in the problem, and could use that information to organize their search for the identity of the relevant attributes.  For these reasons i t was necessary to t e l l Ss in the CL condition  the number of attributes relevant to each problem, so they too could guide their component Al and RL behaviors accordingly. Following Problem 2, a l l Ss were given one of two sets of instructions for solving Problems 3 and k. of the Instruction factor.  These instructions constituted the two levels  The ER Instruction involved placing before the S  a mounted set of the entire array of stimulus cards, ordered and labelled i n terms of the number of differences (0, 1, 2, or 3) between each card and an exemplar focus card (see Figure 3).  In addition, Ss were asked to read a  complete written description of the identity of and total number of differences for each of the sixteen cards i n the array.  These instructions also stressed  that determination of only the total number of important differences; i.e., the total number of differences for relevant attributes, would assist problem solution.  The corresponding RA Instruction given was a summary of the  i n i t i a l general instructions which described each stimulus in RA terms. In addition, the dimension-ordered stimulus array presented at the beginning of the experiment again was presented.  This repetition of the RA instructions  constituted an attempt to equate inter-problem time lapse and activity for both Instruction conditions. Following this set of instructions, each S received a paradigm-determined set of instructions for either Problem 3 or 4, depending upon the Order he was assigned to.  In brief, these instructions were as follows:  (l) For  both the RA and ER conditions, Ss i n the CL condition were told only that Problems 3 and 4 involved two and three important characteristics, respectively, and that the response names were "P" and "Q" for Problem 3 and "X" and "Y" for Problem 4; (2) Ss i n the RL condition were told the identities of the  D I F F E 1R E N C E  2  D I F F E  TP  1. s i z e  *~ *  \J \S -L.  WJ-  3 1, number C 1. shape  O A O  1. number  m  v -i.  u  I F F E 3R E N C E S  1. shape  1. s i z e L 2 . color  e e D I F F E 4 R E N C E S  1, color 1. number pj 2 . number Q 2 . s i z e 3« shape 3« shane  A A  A  P.  2, s i z e  1, shape  O  A 1. s i z e M 2 . color  1. number  A o A  VJ.  ®  E 1. color  o  1. shape  R  E N G E S  D 1. s i z e  4,  A A  color  F i g . 3 , Stimulus array ordered i n terms of the number of a t t r i b u t e discrepancies between each card i n the array and the exemplar focus card. This array was presented to i n t e r - s t i m u l i Ss p r i o r to Problem 3,  important characteristics; i.e., color and shape for Problem 3 and number, shape and size for Problem 4; (3) Ss in the Al paradigm condition were told the number of important characteristics, and the response names to be used in each problem.  In addition, for each of the combined. Problem - Instruction  conditions, Ss were given a written statement of the rule wherein blanks were used to indicate the number of attribute values and method for combining them, followed by an example of the rule i n which the blanks were replaced by a t t r i bute values corresponding to a correct example.  For the Problem 3 RA condition  this rule was: A l l cards that contain ( ) and ( ) or neither ( ) nor ( forms of the two important characterisitcs are members of the "P" category, while a l l cards that do not have these forms of the two important characteristics are members of the "Q" category.  )  The example used the attribute values one figure and large or neither one figure nor large.  In contrast the ER rule for this problem was:  For the two important characteristics only, a l l cards that are either the same (0 differences) as the example card, or different from the example card on both (2 differences) of the important characteristics are members of the "P" category; while a l l cards that do not contain 0 or 2 important differences from the example card are members of the "Q" category. For Problem 4 the RA rule was: A l l cards that contain ( ) AND either ( ) and ( ) or neither ( ) nor ( ) OR ( ) AND either ( ) and ( ) or neither ( ) nor ( ) forms of the three important characteristics are members of the "X" category; while a l l cards that do not have these forms of the three important characteristics are members of the "Y" category. The example used the attribute values large and either red and circular or neither red nor circular or small and either red and triangular or neither red nor triangular.  Again, i n contrast, the ER rule was:  For the three important characteristics only, a l l cards that are either the same (0 differences) as the example card, or different from the example card on any two (2 differences) of the three important characteristics are members of the "X" category; while a l l cards that do not contain 0 or 2 important differences from the example card are members of the "Y" category.  Following the completion of each problem, S was asked to classify the  two  post-criterion classification cards by using the appropriate response labels for that problem.  The number of correct classifications was recorded, then  S was asked, "What was your basis for separating the cards into two  classes?"  The verbal responses were summarized and recorded on the protocol sheet for each S, Performance of Problems 1 - 4 variables:  was recorded in terms of six dependent  (l) Trials, (2) Errors, and (3) Seconds to a criterion of 27  consecutive responses, and the post-criterion variables (4) Classifications, the number of correct classifications of the two cards withheld from the ;  stimulus population used during pre-criterion learning (0, 1, or 2 correct classifications): (5) Verbalization, in response to the question, "What was your basis for separating the cards into two classes?" —  this i s the  verbalization of a conceptual rule that would correctly classify the stimuli by expressing the correct relationship among the relevant attributes only (0 = incomplete verbalization, 1 = complete verbalization); and (6) Strategy, the type of strategy i.e., RA or ER, as indicated by the response to the Verbalization question; for example, responses expressing the attribute values of stimuli were rated RA responses, while those expressing the number of differences between the focus card and the stimuli were rated ER (0 = RA strategy, 1 = ER strategy).  This last variable was included to determine  the effectiveness of the Instruction treatments.  In that the number of  Classifications was limited only by the number of available post-criterion classification cards and the Verbalizations given varied continuously  be-  tween the limits incomplete and complete verbalization, i t was assumed that both these measures were, continuous variables. ever, revealed no such continuity and was,  The Strategy variable, how-  therefore, assumed to be a dicho-  tomous variable. Finally, each S was thanked for participating and asked not to discuss the experiment with other students.  Chapter 4  Results  Performance on Problems 1 - 4 for each of the six dependent variables i s summarized i n Table 1 (main effect means) and Table 2 (means and standard deviations).  Separate analyses of variance were performed on the data  for Problems 1 and 2| a 2 x 3 x 2 x 2 factorial design with the factors being Sex, Paradigm, Instruction, and Order, was applied i n each case.  In fact, i n  the analysis for Problem 1, Paradigm, Instruction, and Order were "dummy" variables.  These "dummy" analyses were conducted to determine significant d i f f -  erences i n performance on the two warm-up problems.  I t was assumed that since  the subject-cell combinations of this design were the same as those of the design for Problems 3 and 4, significant differences between cells on the r e l atively simple Problems 1 and 2 would indicate possible sources of experiment a l error.  These analyses, which are summarized i n Tables 3 and 4, indicate  that, with the exception of the Paradigm factor for the Seconds variable of Problem 2, no significant differences i n concept learning a b i l i t y as indexed by Problems 1 and 2 existed prior to introducing the Instruction and Order factors.  The exception, vrhich was s t a t i s t i c a l l y significant for the Seconds  variable, F (2, 24) = 3.78 p < .05, indicates the effectiveness of the Paradigm treatment introduced in Problem 2, for the results — 589, 405, and 300  Means for the Six Dependent Variables: Trials, Errors, Seconds, Classifications, Verbalization, and Strategy for Problems 1 - 4  Trials  Errors  Seconds  77.75 34.54 269.92 436.42  18.00 4.29 80.54 124.21  576.88 135.92 1225.46 2275.75  58.42 39.13 303.29 531.54  12.50 6.71 100.92 177.13  91.63 44.00 515.00 771.56  1 2 3 4  1 2 3 4  Classifications  Verbalization  Strategy  2.00 2.00 1.62 1.62  1.00 1.00 .83 .67  .00 .00 .21 .33  286.83 151.83 1337.75 2447.58  2.00 2.00 1.75 1.83  1.00 1.00 .82 .82  .00 .00 .17 .29  25.30 9.81 177.63 251.50  589.50 164.88 2077.94 3079.38  2.00 2.00 1.25 1.62  1.00 1.00 .63 .63  .00 .00 .06 .25  50.13 27.69 197.38 209.25  9.81 0.93 58.25 55.56  300.13 90.31 1016.00 1261.06  2.00 2.00 1.94 2.00  1.00 1.00 1.00 1.00  .00 .00 .37 .37  62.50 38.81 174.44 471.13  12.44 5.75 36.31 144.94  405.94 176.44 750.88 2744.56  2.00 2.00 1.87 1.56  1.00 1.00 .94 .88  .00 .00 .12 .31  Sex Male 1 2 3 4 Female 1 2 3 4 Paradigm CL 1 2 3 4 RL  Al  Continued,..  Table 1 (continued)  Trials  Errors  Seconds  Classifications  Verbalization  Strategy-  1 2 3 4  77.38 37.46 274.83 495.12  16.88 5.46 84.25 141.08  409.13 142.33 1399.83 3047.13  2.00 2.00 1.58 1.71  1.00 1.00 .79 .71  .00 .00 .00 .04  1 2 3 4  58.79 36.21 298.38 472.83  13.63 5.5^97.21 160.25  454.58 145.42 1163.38 1676.21  2.00 2.00 1.79 1.75  1.00 1.00 .92 .83  .00 .00 .37 .58  73.71 34.54 361.67 495.50  15.71 4.54 118.13 151.92  523.33 128.63 1685.46 3518.29  2.00 2.00 1.62 1.79  1.00 1.00 .88 .89  .00 .00 .21 .29  62.46 39.12 211.54 472.46  14.79 6.45 63.33 149.42  340.38 159.13 877.75 2205.04  2.00 2.00 1.75 1.67  1.00 1.00 .83 .75  .00 .00 .17 .33  68.08 36.83 286.60 483.98  15.25 5.50 90.73 150.67  431.85 143.88 1281.60 2361.67  2.00 2.00 I.69 1.73  1.00 1.00 .85 .77  .00 .00 .19 .31  Instruction RA  ER  Order SB CB 1 2 3 4 CB  SB 1 2 3 4  Problem Grand Mean 1 2 3 4  Summary of Means and Standard Deviations f o r each of S i x Dependent Variables Across Problems 1-4  DEPENDENT VARIABLES  PROBLEM 1 MEAN  PROBLEM 2 SD  MEAN  PROBLEM 3 SD  MEAN  PROBLEM 4 SD  MEAN  SD  TRIALS  68.08  51.42  36.83  19.22  286.60  251.30  484.00  363.20  ERRORS  15.25  17.24  5.50  10.62  90.73  98.40  150.70  153.80  SECONDS  431.90  513.60  143.90  102.80  1282.00  1062.00  2362.00  I857.OO  CLASSIFICATIONS  2.00  .00  2.00  .00  1.69  .66  1.73  .57  VERBALIZATION  1.00  .00  1.00  .00  .85  .36  .77  .42  .00  .00  .00  .00  .19  .40  .31  .47  STRATEGY  Analysis of Variance f o r T r i a l s , E r r o r s , and Time (seconds) to C r i t e r i o n f o r Problem 1 Trials  Source  df  Sex (S) Paradigm (P) Instruction ( i ) Order (0) SP SI PI SO PO  10  SPI SPO SIO PIO SPIO Replications  (SPIO)  1 2 1 1 2 i 2 1 2 1 2 2 1 2 2 24  MS  Errors MS  F  4485.33 1.98 7263.07 3.22 4144.08 1.83 .67 1518.75 5067.57 2.24 3952.08 4.14 6741.57 2.98 .01 30.08 484.74 .21 147.00 .06 2932.56 1,30 .34 770.55 .27 616.33 .64 1452.21 .09 220.53 2256.06  Time (seconds) F  363.00 1.28 344.31 2.99 .45 126.75 10.08 .03 537.93 1.91 1180.08 4.19 599.31 2.12 200.08 .71 110.39 .39 .11 33.33 200.01 .71 72.76 .25 12.00 .04 .48 135.39 146.67 .52 281.49  MS  F  1009490.00 343011.60 24797.52 481685„00 246840.40 35806.48 57136.25 90046.00 466794.00 73711.50 53946.22 230172.50 93368.44 255965.30 349907.70 277599.20  3.63 1.23 .08 1.44 .88 .12 .20 .32 1.68 .26 .19 .82 .33 .92 1.26  * v< .05 TABLE  4  Analysis of Variance f o r T r i a l s , Errors, and Time (seconds) to C r i t e r i o n f o r Problem 2 Source Sex (S) Paradigm (P) Instruction (I) Order (0) SP SI PI SO PO TO SPI SPO SIO PIO SPTO Replications (SPIO)  * p < .05  df  1 2 1 1 2 1 2 1 2 1 2 2 1 2 2 24  Trials MS  252.08 1111.39 18.75 252.08 85.27 320.33 114.06 26.99 189.02 280.33 647.01 971.05 70.08 275.01 190.13 373.74  F  .67 2.97 .05 .67 .22 ,85 .30 .07 .50 .75 1.73 2.59 .18 .73 .50 - - —  Errors MS  F  70.08 .56 315.21 2.53 .83 .00 44.08 .35 .24 30.39 85.33 .68 65.14 .50 .04 5.33 81,52 .65 26.99 .21 156.64 1.25' 275.27 2.21 .64 80.08 .46 57.93 19.77 .15 124 37 — — — — 0  Time (seconds) MS F  3040.08 .32 34962,03 3.73* 114.08 .01 11163.00 1.19 2519.50 .26 .18 1704.08 7125.52 .76 .08 767.99 5917.68 .63 107.99 .01 11276.89 1.20 27959.78 2.98 12160.33 1.29 12051.78 1.28 19568.39 2.09 9355.71  seconds to criterion for the CL, Al, and RL paradigms respectively, — are in accord with the paradigm d i f f i c u l t y results obtained by Haygood and Bourne (1965),  and also with the predicted d i f f i c u l t y order of this factor for Pro-  blems 3 and 4, A third analysis of variance, which i s summarized i n Tables 5 d 6 , was a n  conducted for the 2  x  for Problems 3 and 4.  3  x  2  x  2  x  factorial design on the combined results  2  In addition to revealing that the postulated control  factors, Order and Sex, did not attain significance on any dependent variable, this analysis reveals strong support for the predicted order of d i f f i c u l t y for Hypothesis 1 (Paradigm), Hypothesis 2 (Type), and a lesser degree of support for Hypothesis 4 (Instruction).  The results for the Paradigm factor, which  are illustrated in Figures 4 and 5 i support the order of paradigm d i f f i c u l t y (CL > Al > RL) predicted i n Hypothesis 1 , for each of five dependent variables: Trials, F ( 2 , 24) = 1 6 . 7 1 p < . 0 0 1 ; Errors, F ( 2 , 24) = 1 6 . 6 0 p < . 0 0 1 ; Seconds, F ( 2 , 24) = 8 . 6 3 p < . 0 0 5 ; Classifications, F ( 2 , 24) = 6 . 0 2 p < and Verbalization, F ( 2 , 24) = 6 . 0 0 p < . 0 1 (Tables 5 and 6 ) .  .01;  It should be  noted that the Classifications and Verbalization variables were not included as indices for the Paradigm hypothesis.  Rather, these variables were included  as indices of concept attainment and further analysis of these measures d i f fered from that of the pre-criterion variables.  Using Tukey's (A) test, a  post hoc comparison of mean values for the Paradigm factor was conducted upon the pre-criterion variables.-'  Results of these post hoc analyses are given in  Table 7 , which reveals that for the obtained order of Paradigm d i f f i c u l t y , CL > Al > RL, significant differences in d i f f i c u l t y were found between the CL 5  This test i s defined i n Winer q  =  (1962),  as  T - T »,.,.. , where VMS error/rT a  b  t  = Mean of a l l Ss in paradigm A T = Mean of a l l Ss in paradigm B MS error = Mean Square from the analysis of variance n = Number of Ss i n each paradigm: n = 1 6 D  Analysis of Variance for Trials, Errors, and Time (seconds) to Criterion for Problems 3 and 4 Errors  Trials Source  df  Sex (S) Paradigm (P) Instruction ( i ) Order ( 0 ) Type (T) SP SI PI so PO  1ST0  PT IT OT SPI SPO SIO PIO SPT SIT PIT SOT POT IOT SPIO SPIT SPOT SI or PIOT Replications ^PIO) SPIOT RT(SPIO)  * p <  .05  1 2 1 1 1 2 1 2 1 2 1 1 2 1 1 2 2 1 2 2 1 2 1 2 1 2 2 2 1 2 24 2 24  MS  F  MS  Time (seconds) F  MS  F  2.42 484362.00 .25 1687241.00 16.71* 220459.00 16.60* 16722800.00 8.63* 9.37 .00 6 1 9 2 . 0 9 .46 1 5 5 0 1 9 2 0 . 0 0 8 . 0 0 * 179920.10 1 . 7 8 19694.01 1.48 7 5 3 9 2 8 5 . 0 0 3.89 9 3 4 9 6 5 . 0 0 18.27* 8 6 2 2 0 . 0 6 1 2 . 6 3 * 27996830.00 14.76* .08 2 6 9 5 5 . 0 0 .26 1075.37 883880.00 .45 .87 11682.07 . 5 1 51987.00 9184.00 . 00 60762.81 . 6 0 14049,08 1 . 0 5 4227928.00 2.18 .16 .16 16748.19 2194.57 5 5 4 0 3 9 . 0 0 .28 .75 45365.44 .44 9974.84 IO69.50 .00 20709.38 .20 5875.01 .44 1 7 8 9 5 5 . 0 0 .09 .93 6353.75 22877.19 .44 2 1 2 6 4 , 0 0 .01 2 I 5 4 7 I . 8 0 4 . 2 1 * 2 5 9 4 6 . 4 7 3 . 8 0 * 6 1 5 2 4 6 4 . 0 0 3.24 .24 231.18 .03 12603.31 7 7 2 1 9 6 8 . 0 0 4.07 16406.37 9 6 9 0 0 . 5 6 I.89 2.40 1466912.00 .77 .24 24459.50 5 3 2 6 . 1 2 .40 1121688.00 .57 34308.03 .63 199525.90 1.97 2.58 1232732.00 20827.00 . 2 0 12138.32 6 3 8 6 . 3 6 .48 184537.00 .09 .49 .91 49804.81 1087914.00 .56 42109.41 .82 939L59 1.37 2680808.00 1 . 5 0 .04 2410.05 .35 2482.31 388944.00 .20 4984.42 .73 . 2 3 11921.53 3386976.00 1.78 10731.55 1.57 64998.75 1.27 1 7 6 9 3 5 3 . 0 0 .93 288.78 .00 543.84 ..14 07 822898.50 .22 120.43 .00 969.05 4 6 0 4 5 8 . 0 0 .24 15159.19 .15 5923.36 . 4 4 2304734.00 1.18 281.86 ...04 1882.84 .03 849440.00 .44 .46 .46 23622.41 3192.60 5 1 7 3 2 4 . 0 0 .27 5 8 8 0 6 . 5 6 1.14 8 9 I 2 . 3 8 1.30 1486247.00 .78 .78 22750.28 136792.50 .44 5327.13 .07 100941.30 ____ 13281.09 1937011.00 99073.50  .98  32230.00  7438.47 51165.46  .14  1168.46 6825.98  .17  ____  702008.00  1895985.00  .37  Analysis of Variance f o r the C l a s s i f i c a t i o n s and V e r b a l i z a t i o n Variables f o r Problems 3 and 4  Classifications Verbalization Source Sex (S) Paradigm (P) Instruction (I) Order (0) Type (T) SP SI PI SO PO IO ST PT IT  or  SPI SPO SIO PIO SPT SIT PIT SOT POT i or SPIO SPIT SPOT SIOT PIOT Replications (SPIO) SPI OT RT(SPIO) * P < .05  df  MS  1 2 1 1 1 2 1 1 1 2 1 1 2 1 1 2 2 1 2 2 1 2 1 2 1 2 2 2 1 2  .66 2.26 .37 .00  24  2  24  .04  .07  1.04 .40  .16 .09  F  1.78 6.02* 1.00 .00 .11 .19 2.77 1.08 .25 .11 .11 2.25  .44  1.00 1.36 2.86 1.00 1.19 .69 1.77 .36 .11  .26 .66 .13  .04  .03 .00 .21 .07 .01 .16 .09 .37 .19 .37  .37 1.12 .37  .04  .16 .12 .37 .12 .37  .44  .04 .04 .94  .16 .37 .51 1.07 .37  MS  .04 ,04  .16 .16 .00 .00 .12 .87  .44  .04  .29  .04  .16 ,00 .00 .12 .16  .08  .00 .58 .19 .02  .44 .24  .52  .04 .04  F  2.00 6.oo* 2.00 .22  2.66 .66 2.00  .66  2.00 .22 .22  2.66 2.66 .00 .00  .66 4.66* .22  1.55 .66 2.66  .00 .00  1.99 2.66 .22 .22  —  ____  .04 .18  .00 .06  .66  --<-_  ,00  800  600  TRIALS  400  200 -  CL  Al  RL  PARADIGM 300 -  200 ERRORS 100 -  CL  Al  RL  PARADIGM 3000 -  2000 SECONDS 1000 -  CL  Al  RL  PARADIGM  F i g . 4 . Mean values of the T r i a l s , E r r o r s , and Seconds v a r i a b l e s across three learning paradigmsI complete learning, a t t r i b u t e i d e n t i f i c a t i o n , and r u l e learning, f o r Problems 3 and 4.  1.50 NUMBER OF CORRECT  1.00  |  I  1  1  -  CLASSIFICATIONS  .50 ,00  I  CL  1  1 Al  RL  PARADIGM  Complete  1,00  .75 RULE VERBALIZATION  .50 .25  Incomplete  .00  A CL  Al  RL  PARADIGM  F i g , 5 . Mean values of the number of correct C l a s s i f i c a t i o n s and the completeness of the r u l e V e r b a l i z a t i o n across three learning paradigms; complete learning, a t t r i b u t e i d e n t i f i c a t i o n , and r u l e l e a r n i n g , f o r Problems 3 and 4,  TABLE 7  Post Hoc Mean Comparisons (q - values) for the Paradigm (p) Factor for Three Pre-Criterion Variables  CL  •  Al  RL  CL Trials  —  4.20 *  5.54 *  Errors  —  4.30 *  5.47 *  Seconds  —  2.38  4.13 *  Trials  —  —  1.33  Errors  —  —  1.17  Seconds  —  — —  1.74  RL  1  * q  3 ( 2  4 = 3.53 P < .05  and Al or Rl paradigms for a l l except the CL - Al comparison on the seconds variable.  The difference between the Al and RL paradigms, however, was not  significant for any of the post-criterion variables.  The results for the Type  factor, illustrated in Figure 6, support Hypothesis 2, that a C3 problem would be more difficult to solve than would a SB problem. tion was obtained for the following variables:  Support for this predic-  Trials, F (1, 24) = 18.27 P  < .001; Errors, F ( l , 24) = 12.63 p< .005; and Seconds, F ( l , 24) = 14.76 p < .001 (Table 5 ) . was not supported.  In contrast, hypothesis 3 (Paradigm x Type interaction) The Paradigm x Type interaction, illustrated in Figure 7  (  was significant for the Trials and Errors variables, F (2, 24) = 4.21 p < . 0 5 , and F (2, 24) = 3.80 p < .05 respectively (Table.5). Finally, Figure 8 reveals limited support for Hypothesis 4:  that problem  solving would be more difficult for the RA than for the ER condition. While the nonsignificant results for this factor on the Trials and Errors variables raises a question about the effect of the Instruction treatments, the results on the Seconds variable, F ( l , 24) = 8.00 p < .01, would suggest that, compared with the RA instructions, the ER instructions as indexed by time are responsible for more efficient concept learning. The means and standard deviations for the Classifications and Verbalization variables, which are presented in Table 2, reveal that for Problems 1 and 2 no variance was obtained for any of these measures, for a l l Ss classified correctly both withheld cards, verbalized a complete affirmation rule, and stated that rule in RA terms.  These results further indicate that, for these rela-  tively simple concepts, there were no significant differences in concept learning performance in the sample selected.  Table 6, a summary of the analysis of  variance conducted upon these variables for Problems 3 and 4, reveals that in addition to the significant results on the Paradigm factor for the Classification and Verbalization variables; the Strategy variable produced significant results for both the Instruction and Type factors, F ( l , 24) = 1 8 . 6 l p < ,001 and F ( l , 24) = 5.99 p < .025 respectively.  Table 8 , a comparison of the  400 -  300 200 100 -  Simple Biconditional  Contingent Biconditional PROBLEM TYPE  300 J  ERRORS  200 J 100 J  Simple Biconditional PROBLEM TYPE  Contingent Biconditional  2500 , 2000 SECONDS  1500 J 1000 500  Simple Biconditional  Contingent Biconditional PROBLEM TYPE  F i g . 6. Mean numbers of T r i a l s , E r r o r s , and Seconds t o c r i t e r i o n across two types of b i c o n d i t i o n a l r u l e f o r Problems 3 and 4.  Fig. 7 . Mean numbers of T r i a l s , and Errors f o r two kinds of b i c o n d i t i o n a l r u l e s , Simple and Contingent, across three learning paradigms, Complete Learning, Attribute I d e n t i f i c a t i o n , and Rule Learning.  2500 -i 2000 SECONDS  1500  •  1000 • 500  Intrastimull  Interstimuli  INSTRUCTIONAL TREATMENT Fig. 8. Mean number of Seconds t o c r i t e r i o n f o r two i n s t r u c t i o n a l treatments, I n t r a - and I n t e r - 3 t i m u l i , across Problems 3 and 4,  Instructions given with the Strategy verbalized for the 48 Ss who completed both the SB and CB problems, reveals that the Instruction treatment was i n sufficient as a controlled experimental factor.  Table 8 indicates that the  TABLE 8 A Comparison of the Strategy Instructions Given with the Strategy Verbalized for 48 Ss on SB and CB Problems  Problem Instruction  SB  CB  RA  ER  RA  ER  RA  24  15  23  10  ER  0  9  1  14  Strategy  ER instruction was ineffective for both problems, but i t was particularly so for the SB problem.  This differential effectiveness might explain the sig-  nificance of the Type factor for this measure.  The dichotomous Strategy var-  iable was included in the experimental design as a method of determining the effectiveness of the Instruction treatments.  Based upon the frequency of  discrepant Instruction - Strategy cases apparent in Table 8, i t i s apparent that the Instruction treatment, particularly for the ER condition, was  not  adequate to cause a l l Ss to employ the strategies they were instructed to employ. A three factor interaction, Sex x Paradigm x Order i s significant for the Verbalization variable, F ( 2 , 24) = 4.66 p < .025 (Table 6 ) . In view of the fact that neither the Sex nor Order factors were significant, and that a  graphical anaylsis of this result failed to reveal any interpretable relationship, this result appears to have no logical explanation. A summary table of intercorrelations of the following seven dependent variables are presented in Table 9 for Problems 3 and 4: Trials (t), Errors (e), Seconds (s), Classifications (c), Verbalization (v), IQ ( i ) , and Age (a). Of particular interest are the correlations between the Classifications and Verbalization  variables, r  c  rule, where r = .29 P < .05.  v  = .89 for the SB rule and r  c  v  = .79 for the CB  These correlations suggest that the a b i l i t y to  verbalize a classification rule i s generally associated with being able to correctly classify additional class members.  While this result appears to  conflict with the generally low correlations between various measures of concept attainment reported by Rommetveit and Kvale (1965a, I965), the discrepancy may be attributable to the use of the Classifications measure of concept attainment i n the present study. Finally, Table 10 summarizes the responses for 96 subject-problem combinations on the three post-criterion variables for Problems 3 and 4. Of particular interest are the results for the Classifications and Verbalization variables.  These results show eight subject-problem combinations i n which the  S failed to classify any of the post-criterion classification cards correctly. Of these eight, not one combination produced a complete rule verbalization. In addition, of the 75 combinations which correctly classified both postcriterion stimuli, 73 were able to verbalize a complete classification rule. Of the thirteen combinations which correctly identified one of the two stimuli, four combinations included a complete rule verbalization, while the remaining nine included incomplete verbalizations.  These results suggest that further  investigation of the post-criterion classification measure would be worthwhile to determine the validity of this measure as an index of concept attainment.  Intercorrelations of Seven Dependent f o r Problems 3 and 4  1  2  Problem 3  PROBLEM 3  3  4  5  6  Variables  7  8  Problem 4  9  10  11  12  1.00  1  Trials  2  Errors  .97*  3  Seconds  .85*  1.00 .83* 1.00  - .38* - .32* 1.00  4  Classifications  - .40*  5  Verbalization  - .37* - .35* - .28  .89*  1.00  PROBLEM 4  - .39* - .42* 1.00  6  Trials  .57*  .56*  .40*  7  Errors  .56*  .56*  .34* - .41* - .43*  .96*  8  Seconds  .18  .19  .20  .74*  9  Classifications  10 Verbalization  .63*  1.00  .32* - .38* - .39* - .28  - .15 - .14 - .14  .22  - .21 - .19 - .14  .57* - .61* - .33* - .32* - .28  11 IQ  .09  .14  .14  12 Age  .03  .01  .03  * r = .29 p < .05 df = 46  - .33* - .35*  1.00  - .05 - .04 .09  .13  .02  .05  .08  .06  .02  1.00 .79* 1.00 •03  - .00 - .01  .07  1.00  .11 - .03 1.00  Response Frequencies on the Post Criterion Variables, Classifications, Verbalization, and Strategy, for 96 Subject-Problem Combinations  PARADIGM INSTRUCTION PROBLEM PERFORMANCE CONDITION 0 COM RA 0 COM ER 0 INC RA 0 INC ER 1 COM RA 1 COM ER 1 INC RA 1 INC ER 2 COM RA 2 COM ER 2 INC RA 2 INC ER 0 COM 0 INC 1 COM 1 INC 2 COM 2 INC 0 0 1 1 2 2  COM COM INC INC  R A  C L  3  4  E R 3 4  2  1  2  2  2  2  4  1  E R 3  4  l 2  5l  2 4  8  8  2 4 1  1  4  2  RA ER RA ER  4  2  2 5  2  6  2  R A  A I  3  4  1  1  5  4  6  2  6  8  8  8  2  5  2 4  8  5  2 4 2  8  l  8  8  1 2  E R 3  4 1 1  5  2 6  1 1 5 1  8  1  2 1  1  1  3  6  3 1 9  1 4  29 8  21 15 2  23 2  48  48  96  3  8 4 0  1 1 1 5  l  1  1  2 6 2  1 4  2 6  6  4 1  6  2 4 2  2 4 2  1 2  2  5  6  6  8  8  7  8  4 4  4 4  6 2  6  8  8  8  8  8  8  7 1  4 4  8  l  2 2 6  3  1 1 6  1  l 6  8  1 2 5  6 2  5  8  6  8  7 1  6  3  2  2  3 +4  8  1  2  4  3  1  2  3  5  5 3  2  2 6  6  62  TOTALS  1  6  4  8  6  4  2 6  4  2  1  l  7  2  1  1  l  1  2  RA ER  4  1  RA ER RA ER RA ER  COM INC  3  R L  2  2 2 2 2  0 1 2  R A  4 4  5  3 3 37  1 6  36  48 5  2 48 3  5  7  1 21 23 8 15 48 48 31 22 9 15 8 11  48  48  6  7 38 48  5  ?? 48  3  4o 37 fl 11 48 48 39 33 9 15 48 48  50  73  2  06  8  12 1 52 23 96  53  24 19  96  8 13 75 96 77 19  96  72 24  96 NOTE - The symbols 0, 1, and 2 refer to the number of post-criterion correct card classifications, COM and INC refer to complete and incomplete rule verbalizations respectively, and RA and ER refer to intraand inter-stimuli rule type verbalizations respectively.  Chapter 5  Discussion  Support for Hypothesis 1 i s revealed by the obtained order of Paradigm d i f f i c u l t y CL > Al > RL, though the post hoc comparison of means revealed that the ordering of the Al and RL paradigms i s questionable. While the Paradigm result extends the component theory of Haygood and Bourne (1965) to include SB and CB classification problems, the nonsignificant difference between the Al and RL paradigms and a significant Paradigm x Type interaction (see Figure ?) indicate a need for further investigation of this finding , A comparison of the obtained Paradigm results with those of Haygood and Bourne (1965 p. 183) revealed that for two of four concept rules used in their study the relative differences in d i f f i c u l t y between paradigms approximated those obtained in the present study; i.e., CL considerably more d i f f i c u l t than Al, and Al approximately equal in d i f f i c u l t y to RL.  While Haygood and Bourne (1965)  have not provided information about the significance of differences between paradigm pairs, the similarity of results between the two studies raises the possibility that the order of paradigm d i f f i c u l t y i s particular to each type of concept rule, rather than generally applicalbe to a l l types of concept rules. Analysis of the Paradigm x Type interaction reveals that the d i f f i c u l t y order CL > Al > RL applied only to the CB problem.  For the S3 problem, this order  was CL > RL > Al for the Trials, Errors, and Seconds variables (though the  last of these just failed to reach significance at  a = .05).  This result may  be a consequence of Al Ss not understanding or following the instructions for the complex CB rule that this constituted a given rule.  SB Ss, on the other  hand, may have f u l l y understood their less complex rule and immediately employed i t to identify attributes.  Support for this explanation i s indicated in Table  11, which reveals that of the 16 Ss given the CB rule, 5 were not able to corr-  Table 11 A Comparison of the Classification and Verbalization Variables for Problem 4 Number of Correct Post-Criterion Classifications  0 complete  -  incomplete  2  1 1  2 10  Post-Criterion Verbalization  " 3  -  ectly classify both post-criterion classification cards, nor were 5 of the 6 able to verbalize the rule they were i n i t i a l l y given.  These results indicate  a need for further research on the order of paradigm d i f f i c u l t y in which special attention i s paid to the rule instructions for Al Ss. The need for further research of paradigm d i f f i c u l t y i s emphasized s t i l l more by the possibility that the within-type positive transfer obtained by Shepard et a l . , (l96l) might be explained as a transition from one learning paradigm to another.  Specifically, because the Shepard et a l . , Ss were re-  quired to complete five successive problems for which the conceptual rule remained constant and only the relevant attributes for each problem were varied, rule learning may have occurred, such that later problems in the series were not equivalent to earlier problems.  Upon encountering the stimuli for  the f i r s t problem of any type, the task corresponds to a CL paradigm, wherein both the appropriate conceptual rule must be learned and the relevant a t t r i butes identified.  Upon solving the f i r s t problem, however, the following prob-  lems of the same type may have corresponded to some varying and unknown degree for each S to an Al paradigm, for upon successful completion of the f i r s t problem, the entire rule or some part thereof may have been learned and applied to the remaining four problems.  This would imply that subsequent problems in such  a series would correspond increasingly to an Al paradigm, because each successive problem contributes to the S*s knowledge of the rule and to his a b i l i t y to apply i t to the remaining problems.  Whether knowledge of the classification  rule i s given to the S, as in the Al paradigm, or he learns i t while solving classification problems, i t should have the effect of making subsequent problems of that type less d i f f i c u l t than when these problems are i n i t i a l l y encountered and correspond to a CL paradigm.  The difference between the CL and  Al paradigms i s a knowledge of the classification rule; perhaps i t i s this same knowledge that represents the differences among the i n i t i a l and subsequent problems in the Shepard et a l , , (1961) problem sequence, and which might have been responsible for the within-type positive transfer obtained by these investigators.  However, at present this alternative explanation of the Shepard et  a l . , results serves only to indicate the need for a careful study of positive transfer, both within and between paradigms. With regard to problem d i f f i c u l t y , the obtained result that CB problens are significantly more d i f f i c u l t than SB problems supports the finding of Shepard et a l . , (1961) that type VI problems are more d i f f i c u l t than Type II problems.  This result also extends the Shepard et a l . , finding to include  problems involving four dimensional, bivariate stimulus instances.  The result  CB > SB also supports the method of determining problem d i f f i c u l t y by means of calculating either the number of logical connectives or the number of words required to state the classification rule.  Furthermore, the Paradigm x Type  interaction reveals that for both the CL and Al paradigms, CB problems are more d i f f i c u l t than SB problems.  This result i s consistent with the Shepard  et a l . , result that a Type VI problem was more d i f f i c u l t than a Type II problem for both the i n i t i a l and later problems of the problem series. In that a large number of Ss for both the RA and ER Instruction conditions employed a solution strategy different from that which they vrere i n structed to use, i t must be concluded that the results for this factor are not sufficiently clear to permit an adequate test of the Strategy hypotheses. Nevertheless, some of the information obtained about this factor in the present study i s worthwhile, for i t may f a c i l i t a t e the apparently necessary task of designing RA and ER instructions that w i l l overcome the propensity of Ss either to memorize the stimuli or to employ an altermate solution strategy. First, i t would be advisable to include problems that approach the d i f f i c u l t y level of the experimental problems in a strategy familiarization task, and either require that these problems be solved by means of assigned solution strategies or stratify Ss according to the strategy used for these problems. In the present study, i t appears that for several Ss the complexity of the b i conditional problems caused them to adopt a less efficient memorization strategy to solve these problems. To increase the number of rule learning solutions i t may be necessary to supply Ss with the prerequisite behaviors required to solve the complex b i conditional problems.  Bourne and Guy ( 1 9 6 8 ) have noted that the magnitude of  transfer between training and test problems appears to be a function of their similarity in assigning stimulus classes to categories.  These investigators  contend that performance on biconditional rules improves with the number of different types of rules encountered during training. Particularly effective in terms of inter-rule transfer i s training on a conditional rule.  This rule  forces Ss to note that both the conjoint presence and the conjoint absence of relevant attributes can be combined to define exemplars.  Lee ( 1 9 6 8 )  has  c l a r i f i e d the Bourne and Guy results by noting that a biconditional concept constitutes a learned hierarchy of lower level concepts; i.e., joint denial, conditional, and conjunctive, and that the learning of a l l three lower level concepts facilitates acquisition of a biconditional concept at an optimal rate. This result indicates that by using different lower level rules as training tasks, i t should be possible to control the prerequisite behaviors required for a biconditional problem, and increase the number of rule learning solutions of biconditional problems.  In addition, the incidental comments of several Ss  during the present experiment support the conclusion that the warm-up experience using only the RA strategy predisposed several Ss in the ER condition to abandon that strategy in favor of the RA strategy that had earlier been successful. Second, careful consideration of general problem d i f f i c u l t y seems advisable because the addition of a fourth dimension in the stimulus population so i n creased the d i f f i c u l t y of both experimental problems that several Ss adopted less efficient strategies; i.e., memorization and an RA strategy, rather than persist in trying to learn a conceptual rule - particularly a rule couched in the unfamiliar terms of an ER strategy. With regard to the relationship between Classifications and Verbalization, the correlations for Problems 3 and 4 ( r  c v  = .89 and r  C v  = .79 respectively)  lend support to the argument that the inability to verbalize a conceptual rule i s generally indicative of a lack of knowledge of that rule.  It should again  be noted, however, that the post-criterion classification measure was highly subject to the effect of guessing.  Consequently, this correlation must be  considered to be only a rough estimate of the relationship between these variables.  It serves to indicate that further study of this measure appears  to be worth-while.  A sufficiently large number of post-criterion c l a s s i f i -  cation instances would reduce the probability of reaching criterion by guessing.  With such control, this measure may serve as a valid method of d i s c r i -  minating between rule learning and memorization solutions of a classification task, and do so by requiring the same kind of behavior required in the original learning situation. The most important educational implication of this study i s the additional support for the Haygood and. Bourne (1965) theory that concept learning involves two  components, attribute identification and rule learning.  If one  considers  the important role of concept learning in education, as this learning serves to reduce the complexity of the environment and the necessity for constant learning, then clarification of the two-component nature of concept learning implies that concept instruction can be considerably facilitated by the careful consideration of the effects of both components in planning learning exercises. Consideration  of both components offers the possibility of more precise con-  cept instruction and improved diagnosis of concept learning d i f f i c u l t i e s . Another important implication comes from consideration of the components as variables that would permit several different kinds of instruction. If these components were ordered on a continuum, then at one extreme a CL task might approximate discovery learning, while at the other extreme, instruction that provided both the conceptual rule and the relevant attributes would approximate a didactic method of instruction. Between these extremes, instruction that provides either the rule or the relevant attributes might be found optimally to f a c i l i t a t e the learning of particular kinds of concepts; for example, i t may be the case that the concept learning paradigm that produces optimal learning of any particular concept may be a function of the number of relevant and irrelevant attributes and the complexity of the concept rule, rather than simply the relative amounts of information provided in the paradigms Whatever the case, the component approach appears to offer the promise of clarifying considerably our understanding of the process of concept learning.  References  Bourne, L. E. J r .  Human conceptual behavior,  Bourne, L. E, J r .  Learning and u t i l i z a t i o n of conceptual r u l e s .  Kleinmuntz  (Ed,),  John Wiley & Sons,  Boston, A l l y n & Bacon, 1966,  Concepts and the structure of memory. New York, I 9 6 7 .  Bourne, L, E, J r . & Guy, D. E. Learning conceptual r u l e s : transfer effects. 423  -  In B,  Some i n t e r r u l e  Journal of Experimental Psychology, 1 9 6 8 , 7_6 (3),  4 2 9 .  Freibergs, V., & Tulving, E. The e f f e c t of practice on u t i l i z a t i o n of i n formation from p o s i t i v e and negative instances i n concept tion.  Canadian Journal of Psychology, 1 9 6 1 , 15_, 1 0 1 - 1 0 6 ,  French, R, S.  Number of common elements and consistency of reinforcement  i n a d i s c r i m i n a t i o n learning task. 1953,  41,  2 5  -  of conceptual behavior.  A t t r i b u t e - and r u l e - learning aspects  Psychological Review,  Haygood, R, C. & Stevenson, M.  ( 2 ,  Pt.  1)  302  Hovland, C. I , , & Weiss, W.  I 9 6 5 ,  £ 2 ,  (3),  E f f e c t s of number of i r r e l e v a n t  i n nonconjunctive concept learning. 7_4,  Journal of Experimental Psychology,  3 4 .  Haygood, R. C , & Bourne, L, E. J r ,  1967,  identifica-  -  175  -  1 9 5 .  dimensions  Journal of Experimental Psychology,  3 0 4 .  Transmission of information concerning concepts  through p o s i t i v e and negative instances. Journal of Experimental Psychology. 1 9 5 3 , 4_5_, 1 6 5 - 182. Hunt, E. B., & Kreuter, J . M, learning.  The development of d e c i s i o n trees i n concept  I I I . Learning the connectives.  Management Sciences I n s t i t u t e , 1 9 6 2 ,  Los Angeles, Western  e f f e c t s o f number o f r e l e v a n t and i r r e l e v a n t d i m e n s i o n s . Journal of Psychology. K v a l e , S.  Canadian  I966, 20, (2), 198 - 207.  "Unconscious p r o c e s s e s " i n concept f o r m a t i o n :  or a t h e o r e t i c a l construction?  An e m p i r i c a l f a c t  A c t a P s y c h o l o g l c a , 1968, 28, (4),  344 - 362. Lee, S. S.  T r a n s f e r from l o w e r t o h i g h e r l e v e l c o n c e p t .  Journal of Verbal  L e a r n i n g and V e r b a l B e h a v i o r . 1968, 7_» 930 - 937. M i l l e r , G. A .  The m a g i c a l number s e v e n , p l u s o r minus t w o .  Psychological  R e v i e w . 1956, 63_, 81 - 97. Neisser,  U . , & Weene, P .  H e i r a r c h i e s i n concept a t t a i n m e n t ,  Journal of  E x p e r i m e n t a l P s y c h o l o g y . 1962, 64, 640 - 645. O s i e r , S . F . , & F i v e l , M . W. Concept a t t a i n m e n t :  I.  i n t e l l i g e n c e i n c o n c e p t a t t a i n m e n t by i n d u c t i o n .  The r o l e o f age and Journal of E x p e r i -  m e n t a l P s y c h o l o g y . 196l, 62, 1 - 8 , Rommetveit, R , tioning. Rommetveit, R.  S t a g e s i n concept f o r m a t i o n and l e v e l s o f c o g n i t i v e f u n c S c a n d i n a v i a n J o u r n a l o f P s y c h o l o g y , i960, I , 115 - 124. P e r c e p t u a l , b e h a v i o r a l , and I d e a t i o n a l components o f  d i s c r i m i n a t o r y and c o n c e p t u a l a c t i v i t i e s .  A c t a P s y c h o l o g l c a . I96I, 18,  201 - 217. Rommetveit, R ,  S t a g e s i n concept f o r m a t i o n .  II.  E f f e c t s o f an e x t r a  i n t e n t i o n t o v e r b a l i z e t h e c o n c e p t and o f s t i m u l u s  predifferentiation.  S c a n d i n a v i a n J o u r n a l o f P s y c h o l o g y . I965, 6, 59 - 64. Rommetveit, R . , & K v a l e , S .  Stages i n concept f o r m a t i o n .  III.  Further  i n q u i r i e s i n t o t h e e f f e c t s o f an e x t r a i n t e n t i o n t o v e r b a l i z e , dinavian Journal of Psychology.  I965, 6, 65 - 74.  (a)  Scan-  Rommetveit, R,, & Kvale, S,  Stages i n concept formation, IV, A temporal  a n a l y s i s of e f f e c t s of an extra intention t o v e r b a l i z e , Journal of Psychology.  I965, 6, 75 - 79. (b)  Shepard, R. N,, Hovland, C, I . , & Jenkins, H. M. classifications. Smith, S. L.  Scandinavian  Psychological Monographs,  Concept formationt  Learning and memory of  I96I, 7J3, (13, Whole No. 517).  Stimulus dimensions i n human learning.  Unpublished d o c t o r a l d i s s e r t a t i o n , Massachusetts I n s t i t u t e of Tech-  nology, 1954, 02139. Wallach, L i s e .  The complexity of concept attainment.  Psychology. 1962, Wells, H,  7_5_, (2) 277 - 283.  E f f e c t s of t r a n s f e r and problem/structure i n d i s j u n c t i o n concept  formation. Winer, B.  American Journal of  Journal of Experimental Psychology, 1963, 65_, 63 - 69.  S t a t i s t i c a l P r i n c i p l e s i n Experimental Design.  H i l l , 1962.  Toronto: M Graw c  Appendix I  The presentation device was a 12 x 12 x 36 inch black wooden box, which was placed on an 8 inch platform so that a 2.5 x 3.5 inch window on the front of the apparatus was approximately at eye level,  A hinged panel, 3 x 4  inches  served as a window cover which permitted E_ to rotate the cards past the window for the purposes of response programming and preventing S from seeing the f i r s t card of each problem before a start signal occurred.  To the right of the window  a control panel appeared which contained the red and green response feedback lights, two one half inch red response buttons, each with a corresponding label that could be changed, and a three quarter inch red "advance" button, which caused the mechanism to advance the next card into the window, A similar cont r o l panel, lacking only the response buttons, was placed on the rear of the machine to allow E to unobtrusively record S performance and record the feedback for each problem.  The stimulus cards were placed in 27 card holders fixed to  a 54 inch continuous V belt, which rotated horizontally about the axes of two 8 inch pulleys which were mounted on two 1/2 x 9 inch vertical shafts, which, in turn, rotated within four l/2 inch horizontal thrust bearings, with centres placed 27 inches apart.  The driving mechanism was a 30 RPM, l/lO horsepower,  Dayton gearmotor with a solenoid brake.  A seven to one reduction ratio was  obtained by means of a one inch pulley on the motor and a seven inch pulley on the belt drive shaft.  This ratio allowed each card to stop centred in the  window, with an inter-card interval of one second duration.  Continual centering  of each of the cards in the window was effected by means of a single pole, double throw microswitch activated by a t r i p mechanism located in the centre of each card holder.  This mechanism would open the motor circuit and  simultaneously  activate the solenoid brake, which instantly stopped the motor armature and held each card in the centre of the window. To advance to the next card, a  single pole, single throw, push button microswitch was installed across the alternate circuit of the lever-activated, microswitch.  Closing this circuit  by pushing the button had the effect of advancing the tripping lever beyond the contact range of the lever-activated microswitch, thereby, transferring, without interruption, the motor's electrical circuit from the open to the closed poles of the lever-activated switch, where again the circuit could be broken by means of the t r i p mechanism of the following card when i t reached the centre of the window. The response feedback was provided by a movable t r i p lever located in the centre of each card holder.  This lever could be placed i n one of two  positions, which corresponded to each of the two response buttons.  Each res-  ponse button closed one of two circuits for each of two lever-activated, single pole, double threw microswitches which were fastened in tandem in a position where they could be activated by the movable t r i p mechanism on each card. Positioning of the t r i p lever and this circuitry permitted E to program the res ponse feedback system for each problem prior to beginning that problem. Upon beginning a problem, each lever placed in the position corresponding to an exemplar of the concept would activate the two oppositely wired microswitchesj such that, for one switch, the circuit between the exemplar button and the green light was closed while the circuit between the non-exemplar button and the green light was open.  With the tandem arrangement of the lever-activated  switches, the circuit on the second microswitch was closed between the nonexemplar button and the red light, and open between that button and the green light.  Consequently, i f an exemplar appeared in the window, the S would see  a green light i f he pushed the exemplar button, or a red light i f he pushed the non-exemplar button.  However, i f a non-exemplar appeared in the window,  i t s t r i p lever was so placed that i t would not contact the switches; therefore, the entire circuitry was reversed.  This reversal caused S to light a green  light i f he pushed the non-exemplar button, and a red light i f he pushed the exemplar button.  The light circuitry was stepped down by a transformer rated  at one ampere, 110 volt primary - 6.3 volt secondary.  A Complete, Problem-ordered Set of Instructions Given for Each of the Experimental Conditions  General Instructions LEARNING PROGRAM INSTRUCTIONS General Information  This i s a learning program designed to teach you to classify a set of cards into two categories.  Look at the sixteen cards i n front of you  and notice that no two cards are exactly the same. Each of the cards has four characteristics; (l) the SHAPE of i t s figures, (2) the NUMBER of i t s figures, (3) the SIZE of i t s figures, and (4) the COLOR of i t s figures. Notice that each characteristic can occur i n one of two different forms; that i s , the SHAPE of figures can occur either i n the form of Circles or in the form of Triangles; the NUMBER of figures can occur either i n the form of One figure on a card or Two figures on a card; the SIZE of figures can occur either i n the form of Large figures or Small figures; and the COLOR of figures can occur either i n the form of Red figures or Blue figures.  The sixteen different cards on the board show you a l l the possible  ways of combining the two different forms of the four characteristics. The cards that w i l l appear i n the window of the apparatus have already been sorted into two categories, which are represented by the two lettered buttons on the front of the machine.  Your task i s to learn what the d i f f -  erences are between the two categories, so that you w i l l be able to classi f y each of the cards correctly by telling the experimenter which category you think each card appearing i n the window belongs i n , then pressing the button for that category to see i f your answer was right (green light) or wrong (red light). To learn the difference between the two categories, you w i l l be told  in the instructions for each problem how many of the four characteristics i t i s necessary to consider to solve the problem.  While each card has  four characteristics, some of the characteristics, though they may differ across cards, w i l l not help you learn the basis for distinguishing between the two categories.  Concentrate upon using your knowledge of the number  of important characteristics given in the instructions for each problem to try to determine which characteristics are important for that problem, and which characteristics can be ignored.  When you learn which characteristics  are important for each problem, then you w i l l have to learn which forms are associated with each of the two categories; for example, the problem may involve only one important characteristic, such as, the color of the figures, with the red figures put into one category and the blue figures i n the other.  On the other hand, the problem may involve two or three important  characteristics, so check each set of instructions to see how many characteristics you w i l l have to include i n your attempt to learn the basis for differentiating between the two categories. When you finish reading the instructions, ask the experimenter to l i f t the window cover, then study the card which appears i n the window and t e l l the experimenter which category you think the card belongs in.  You w i l l  have to guess for the f i r s t few cards, until you have seen enough cards to gain some information about the differences between categories. Say out loud the letter of the category you choose, then press the button labelled with that letter to determine i f your answer was right (green light) or wrong (red light).  When you decide you are finished looking  at a card, press the advance button and a new card w i l l appear. is to learn to classify a single set of cards correctly.  Your goal  Do not waste time  trying to memorize the order i n which the cards appear, for there i s more than one set i n the machine, and each set has a different order. Understand that some of the problems are quite complex, so do not  become discouraged i f you have difficulty solving them.  Also, for each  of the problems to follow, the speed at which you progress and the accuracy of your performance are of equal importance.  Try your best I  Problem One (All experimental conditions)  PROBLEM ONE  This problem will involve one important characteristic which separates the cards into two categories.  The two categories are "A" and "B",  and the example card is a member of the "A" category.  Your task is to  learn which one of the four characteristics is used to separate the cards into their two categories, and identify which of the two forms of that characteristic is associated with the "A" category and which form is associated with the "B" category.  The other three characteristics are  not used in any way to separate the two categories; they are not important, and will not help you solve the problem; therefore, you should seek a solution for the problem which involves only one important characteristic. Study the forms of the four characteristics represented on the example card, then use i t and your knowledge of the number of important characteristics to help you learn to classify the cards correctly.  Problem Two (Complete learning condition)  PROBLEM TWO  This problem will involve one important characteristic which separates the cards into two categories.  This time the two categories are  "G" and "H", and the example card is a member of the "G" category.  Use  your knowledge o f t h e number o f i m p o r t a n t c h a r a c t e r i s t i c s and t h e example c a r d t o h e l p you l e a r n t o c l a s s i f y t h e cards c o r r e c t l y . REMEMBER - Only t h e one i m p o r t a n t c h a r a c t e r i s t i c i s used t o s e p a r a t e the cards  i n t o two c a t e g o r i e s .  Problem Two (Rule l e a r n i n g  condition)  PROBLEM TWO  T h i s problem w i l l i n v o l v e one i m p o r t a n t c h a r a c t e r i s t i c , t h e NUMBER of f i g u r e s , which s e p a r a t e s  the cards  i n t o two c a t e g o r i e s .  T h i s time t h e  two  c a t e g o r i e s a r e "G" and " H " , and t h e example c a r d i s a member o f t h e  "G"  category.  Use your knowledge o f t h e i m p o r t a n t c h a r a c t e r i s t i c and t h e  example c a r d t o h e l p you l e a r n which form o f t h e i m p o r t a n t i s a s s o c i a t e d with  each c a t e g o r y ,  characteristic  so t h a t you w i l l be a b l e t o c l a s s i f y  the c a r d s c o r r e c t l y . REMEMBER - Only t h e one i m p o r t a n t c h a r a c t e r i s t i c , NUMBER i s used t o separate  t h e c a r d s i n t o two c a t e g o r i e s .  Problem Two ( A t t r i b u t e i d e n t i f i c a t i o n  condition)  PROBLEM TWO  T h i s problem w i l l i n v o l v e one i m p o r t a n t c h a r a c t e r i s t i c which the c a r d s i n t o two c a t e g o r i e s . "H",  T h i s time t h e two c a t e g o r i e s a r e "G" and  and t h e example c a r d i s a member o f t h e "G" c a t e g o r y .  to t h i s c h a r a c t e r i s t i c i s :  separates  I f t h e oard  The r u l e a p p l i e d  shows t h e presence o f or.e form o f  the i m p o r t a n t c h a r a c t e r i s t i c i t i s a "G", b u t i f t h e c a r d shows t h e p r e s e n c e of t h e o t h e r form i t i s an " H " .  F o r e x a r p l e , i f c o l o r were t h e i m p o r t a n t  characteristic, then the presence of the red form of this characteristic might define the "G" category, while the presence of the other form, blue, would define the "H" category.  Use your knowledge of the defining rule  and the example card to help you learn to classify the cards correctly, REMEMBER - Only the one important characteristic i s used to separate the cards into two categories, and the defining rule i s applied only to this characteristic.  Solution Strategy Instructions Problems Three and Four (intra-stimuli condition)  PROBLEMS THREE AND FOUR SOLUTION INSTRUCTIONS  Before attempting to solve some d i f f i c u l t problems, look again at the sixteen cards i n front of you.  Notice that each of the cards has  four characteristics; (l) the SHAPE of i t s figures, (2) the NUMBER of i t s figures, (3) the SIZE of i t s figures, and (4) the COLOR of i t s figures. Notice also that each characteristic can occur i n one of two different forms; that i s , the SHAPE characteristic can occur either i n the form of Circles or in the form of Triangles; the NUMBER characteristic can occur either i n the form of One figure on a card or Two figures on a card; the SIZE characteristic can occur either i n the form of Large figures or Small figures; and the COLOR characteristic can occur either i n the form of Red figures or Blue figures.  The sixteen different cards on the board show  you a l l the possible ways of combining the two different forms of each of the four characteristics. When you are satisfied that you understand the nature of the four characteristics, your task w i l l be f i r s t , to note from the information about the number of important characteristics given i n the instructions for each problem  how many characteristics are important for that problem.  second, to learn which of the four characteristics are used to separate the cards into two categories for that problem, and third, to learn which particular forms of the Important characteristics are associated with each of the two categories. REMEMBER - When reading the Instructions for each problem, take careful note of the number of Important characteristics involved i n each problem, then learn which of the four are the important characteristics, and how they separate the cards into two categories.  Solution Strategy Instructions Problems Three and Four (Inter-stimuli condition)  PROBLEMS THREE AND FOUR SOLUTION INSTRUCTIONS  Now that the practice problems have made you familiar with the four characteristics, let's try to solve some d i f f i c u l t problems by learning a different method of grouping the set of cards.  If you compare the example  card with any of the cards on the card board in front of you, you w i l l see that each card can be put into one of five difference categories.  If you  ignore the border of the cards, then compare the example card with card A on the card board, you w i l l notice that the cards are exactly the same (0 differences).  If you compare the example card with cards B, C, D, and E  you w i l l notice that each of these cards differs by one characteristic: NUMBER of figures for card B, the example has One figure, while card B has Two figures) the SHAPE of figures for card C, the example i s a Circle, while card C i s a Triangle; the SIZE of figures for card D, the example figure i s Large, while the card D figure i s Small; and the COLOR of figures for card E, the example i s Red, and card E i s Blue. In like manner, i f you compare the example card with each of the cards in the "2 DIFFERENCES" category, you w i l l see that each card differs by  two characteristics: card F by SIZE and COLOR, card G by NUMBER and COLOR, card H by SHAPE and SIZE, card I by SHAPE and COLOR, card J by NUMBER and SIZE, and card K by SHAPE and NUMBER. Again, i f you compare the example card with any of the cards labelled "3 DIFFERENCES", you w i l l notice that each card i s different from the example card by three characteristics: card L by SIZE, COLOR, and NUMBER; card M by SIZE, COLOR, and SHAPE; card N by COLOR, NUMBER, and SHAPE; and card 0 by NUMBER, SIZE, and SHAPE. Finally, i f you compare the example card with card P, you w i l l see that they are different by four characteristics:  SIZE, the example has a  Large figure and card P has Small figures; NUMBER, the example has One figure and card P has Two figures; SHAPE, the example i s a Circle and card P i s a Triangle; and COLOR, the example i s Red and card P i s Blue.  Study  these differences carefully until you are satisfied that you understand them. When you understand how to recognize the differences between the example card and the cards that w i l l appear i n the window, your task w i l l be to f i r s t , note from the information about the number of important characteristics given i n the instructions for each problem, how many characteri s t i c s are important for that problem.  Second, learn which of the four  characteristics are used to separate the cards into the two categories used for that problem, then, identify the total number of differences between the example card and each card i n the window for the important characteristics only, and learn which total numbers of important d i f f e r ences (0, 1, 2, 3» or 4) are associated with one category and which total numbers of important differences are associated with the other category, REMEMBER - Compare the example card with each card that appears i n the window and count the total number of important differences, then learn which numbers of important differences are associated with each of the two categor-  ies.  Problem Three (Complete learning - Intra-stimuli condition)  PROBLEM THREE  This problem w i l l involve two important characteristics which separate the cards into two categories.  The two categories are "P" and "Q", and  the example card i s a member of the "P" category.  Use your knowledge of  the number of important characteristics and the example card to learn which two of the four characteristics are important, then which forms of both important characteristics are associated with the "P" category, and which forms are associated with the "Q" category so that you w i l l be able to classify the cards correctly. REMEMBER - Only the two important characteristics are used to separate the cards into two categories.  Problem Three (Complete learning - Inter-stimuli condition)  PROBLEM THREE  This problem w i l l involve two important characteristics which separate the cards into two categories.  The two categories are "P" and "Q", and  the example card i s a member of the "P" category.  Use your knowledge of  the number of important characteristics and the example card to count the total number of important differences between the example and problem cards, then learn the total number of important differences associated with category "P" and the total number of important differences associated with category "Q", so that you w i l l be able to classify the cards correctly.  REMEMBER - Only the two important characteristics are used to separate the cards into two categories.  Problem Three (Rule learning - Intra-stimuli condition)  PROBLEM THREE  This problem w i l l involve two important characteristics, the COLOR of the figures and. the SHAPE of the figures, which separate the cards into two categories. The two categories are "P" and "Q", and the example card i s a member of the "P" category.  Use your knowledge of the two important  characteristics and the example card to learn how the forms of the two characteristics are associated with each category, so that you w i l l be able to classify the cards correctly, REMEMBER - Only the two important characteristics, COLOR and SHAPE, are used to separate the cards into two categories.  Problem Three (Rule learning - Inter-stimuli condition)  PROBLEM THREE  This problem w i l l involve two important characteristics, the COLOR of the figures and the SHAPE of the figures, which separate the cards into two categories. The two categories are "P" and "Q", and the example card i s a member of the "P" category.  Use your knowledge of the two important  characteristics and the example card to count the total number of important differences between the example and problem cards, then learn the total number of important differences associated with category "P" and the total number of important differences associated with category "Q", so that you  w i l l be able to classify the cards correctly, REMEMBER - Only the two important characteristics, COLOR and SHAPE, separate the cards into two categories.  Problem Three (Attribute identification - Intra-stimuli condition)  PROBLEM THREE  This problem w i l l involve two important characteristics which separate the cards into two categories.  The two categories are "P" and "Q", and  the example card i s a member of the "P" category.  The rule which i s applied  to the two important characteristics to separate the cards into two categories i s : (  A l l cards that contain (  ) and (  ) or neither (  ) nor  ) forms of the two important characteristics are members of the "P"  category; while a l l cards that do not have these forms of the important characteristics are members of the "Q" category.  For example, i f number  and size were the two important characteristics, then a l l cards that had (one figure) and were (large) or neither had (one figure) nor were (large) would be members of the "P" category.  Use your knowledge of the defining  rule and the example card to learn which are the two important characteri s t i c s and which forms of these characteristics are associated with each of the two categories, so that you w i l l be able to classify the cards correctly, REMEMBER - Only the two important characteristics are used to separate the cards into two categories, and the defining rule i s applied only to these two characteristics.  Problem Three (Attribute identification - Inter-stimuli condition)  PROBLEM THREE  This problem w i l l involve two important characteristics which separate the cards into two categories.  The two categories are "P" and "Q", and the  example card i s a member of the "P" category.  The defining rule which i s  applied to the two important characteristics to separate the cards into two categories i s : For the two important characteristics only, a l l cards that are either the same (0 differences) as the example card, or different from the example card on both (2 differences) of the important characteristics are members of the "P" category; while a l l cards that do not contain 0 or 2 important differences from the example card are members of the "Q" category. For example, i f number and size were the important characteristics, an example of this rule would be a l l cards which are the came as the example card for the two important characteristics (one figure and large), or a l l cards which are different for both important characteristics from the example card (two figures and small) are members of the "P" category. Use your knowledge of the defining rule and the example card to learn which are the two important characteristics that go together with the defining rule so that you w i l l be able to classify the cards correctly, REMEMBER - Only the two important characteristics separate the cards into two categories, and the defining rule i s applied only to these two characteristics.  Problem Four (Complete learning - Intra-stimuli condition)  PROBLEM FOUR  This problem w i l l involve three important characteristics which separate the cards into two categories.  The two categories are "X" and "Y",  and the example card i s a member of the "X" category.  Use your knowledge  of the number of important characteristics and the example card to learn which characteristics are important, then which forms of these characteri s t i c s are associated with the "X" category, and which forms are associated with the "Y" category, so that you w i l l be able to classify the cards correctly. REMEMBER - Only the three important characteristics separate the cards into two categories.  Problem Four (Complete learning - Inter-stimuli condition)  PROBLEM FOUR  This problem w i l l involve three important characteristics which separate the cards into two categories. The two categories are "X" and "Y", and the example card i s a member of the "X" category.  Use your knowledge  of the number of important characteristics and the example card to count the total number of important differences between the example and problem cards, then learn the total number of important differences associated with the "X" category, and the total number of differences associated with the "Y" category, so that you w i l l be able to classify the cards correctly, REMEMBER - Only the three important characteristics separate the cards into two categories.  Problem Four (Rule learning - Intra-stimuli condition)  PROBLEM FOUR  This problem w i l l involve three important characteristics, the NUMBER  of figures, the SIZE of figures, and the SHAPE of figures, which separate the cards into two categories.  The two categories are "X" and "Y", and  the example card i s a member of the "X" category.  Ose your knowledge of  the three important characteristics and the example card to learn which forms of the three characteristics are associated with each category, so that you w i l l be able to classify the cards correctly, REMEMBER - Only the three important characteristics, NUMBER, SIZE, and SHAPE, separate the cards into two categories.  Problem Four (Rule learning - Intra-stimuli condition)  PROBLEM FOUR  This problem w i l l involve three important characteristics, the NUMBER of figures, the SIZE of figures, and the SHAPE of figures, which separate the cards into two categories.  The two categories w i l l be "X" and "Y", and  the example card i s a member of the "X" category.  Use your knowledge of  the three important characteristics and the example card to count the total number of important differences between the example and problem cards, then learn the total number of important differences associated with category "X" and the total number of important differences associated with category "Y", so that you w i l l be able to classify the cards correctly. REMEMBER - Only the three important characteristics, NUMBER, SIZE, and SHAPE, separate the cards into two categories.  Problem Four (Attribute identification - Intra-stimuli condition)  PROBLEM FOUR  This problem w i l l involve three important characteristics which separate the cards into two categories.  The two categories are "X" and "Y", and the  example card i s a member of the "X" category.  The rule which i s applied  to the three important characteristics to separate the cards into their two categories i s : A l l cards that contain (  ) AND either (  ) and (  ) and (  )  or neither (  ) nor (  (  ) forms of the three important characteristics are members  ) nor (  ) OR (  ) AND either (  ) or neither  of the "X" category; while a l l cards that do not have these forms of the important characteristics are members of the "Y" category.  For example,  i f size, color, and shape were the three important characteristics, then a l l cards that are (LARGE) AND either-(red) and (circular) or neither nor (circular) OR (SMALL) AND either (red) and (triangular) or neither nor (triangular) would be members of the "X" category.  (red) (red)  Use your knowledge  of the defining rule and the example card to learn which are the three important characteristics, and which forms of these characteristics are associated with each of the two categories, so that you w i l l be able to classi f y the cards correctly, REMEMBER - Only three characteristics separate the cards into two categories, and the defining rule i s applied only to these three characteristics.  Problem Four (Attribute identification - Inter-stimuli condition)  PROBLEM FOUR  This problem w i l l involve three important characteristics which separate the cards into two categories.  The two categories are "X" and "Y", and  the example card i s a member of the "X" category.  The rule which i s applied  to these characteristics i s : For the three important characteristics only,  a l l cards that are either the same (0 differences) as the example card, or a l l cards that, are different from the example card on any two of the three important characteristics are members of the "X" category; while a l l cards that do not contain 0 or 2 important differences from the example card are members of the "Y" category.  For example, i f size, color, and shape were  the three important characteristics, then a l l cards which are the same as the example card (large red circles) or different on two of the three important characteristics (large blue triangles, small red triangles, and small blue circles) are members of the "X" category.  Use your knowledge of the  defining rule and the example card to learn which are the three important characteristics that go together with the defining rule, so that you w i l l be able to classify the cards correctly, REMEMBER - Only three characteristics separate the cards into two categories, and the defining rule i s applied only to these three characteristics.  

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