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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., University of Bri t i s h Columbia, 1968 A thesis submitted i n parti a l fulfilment of the requirements for the degree of Master of Arts in the Department of Educational Psychology We accept this thesis as conforming to the required standard THE UNIVERSITY OP BRITISH COLUMBIA Ap r i l , 1971 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Bryan D. Hartman Department of Educational Psychology The U n i v e r s i t y o f B r i t i s h C o l umbia Vancouver 8, Canada Date March 20, 1971 The structure of a cl a s s i f i c a t i o n appears to consist of two componentst (a) relevant attributes and (b) the cl a s s i f i c a t i o n rule which combines the relevant attributes to describe the c l a s s i f i c a t i o n . An experiment was conduc-ted to separate attribute identification (Al) from rule learning (RL) and com-pare 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 for two biconditional c l a s s i f i c a t i o n rules, a two attribute, simple biconditional rule (SB), and a three attribute, contingent biconditional rule (CB), and for two sets of solu-tion strategy instructions, an intra-stimuli (RA) strategy involving c l a s s i f i -cation according to the combination of relevant attributes on each card, and an inter-stimuli (ER) strategy involving c l a s s i f i c a t i o n according to the number of relevant attribute discrepancies between each stimulus card and an exemplar focus card. These three experimental factors were combined with two hypothe-sized control factors, sex and problem order, I n a 3 x 2 x 2 x 2 x 2 f a c t o r i a l design. Each of 48 grade ten Ss (24 male and 24 female) completed both bicon-ditional problems in one of two counterbalanced problem orders. Performance was recorded on six dependent variables: (l) T r i a l s ; (2) Errors; and (3) Sec-onds - a l l to a criterion of 27 consecutive correct responses; as well as the post-criterion variables, (4) Classifications, the number of correctly c l a s s i -f i e d cards for a withheld subset of the stimulus population used for original learning; (5) Verbalization, a verbal response which describes a c l a s s i f i c a t i o n rule that separates the cards into two mutually exclusive and exhaustive cate-gories; 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 made to relevant a t t r i -bute combinations or relevant attribute discrepancies. In general, the results were as follows. F i r s t , the obtained order of par-adigm d i f f i c u l t y for the T r i a l s , Errors, Seconds, Classifications, and Verb-alization variables was CL > Al > RL, This result was interpreted as support for the Al and RL component approach of Haygood and Bourne (1965), and as an extension of this approach to SB and CB rules. Second, the obtained order of rule d i f f i c u l t y for the T r i a l s , Errors, and Seconds variables was CB > SB, This result was interpreted as support for the rule results of Shepard, Hovland, and Jenkins (1961), and as an extension of their results to include four dimen-sion, bivariate stimuli. Third, the obtained order of d i f f i c u l t y for the stra-tegy instructions was RA > ER, But, only for the Seconds variable was this re-sult significant. Consideration of the results for the Strategy variable sup-ported the conclusion that the instruction treatment was not sufficient to overcome the tendency of Ss to choose their own strategy. Consequently, sev-eral suggestions for a more effective instruction treatment were offered. Fourth, the obtained correlations between the Classifications and Verbaliza-tion variables were ,89 and ,79 for the SB and CB problems respectively. This result was interpreted as an indication that further investigation of the Classification variable as a method of determining concept attainment would be worthwhile. Finally, the educational emplications of this study were discussed. Thesis Committee Chairman Serial ! 1 Subject Page(s) 1 L i s t of Tables i 2 List of Figures i i 3 List of Plates i i i 4 Acknowledgement of Assistance iv 5 Chapter 1 1 - 1 4 Problems and Related Literature 6 Chapter 2 15-18 Purposes and Hypotheses 7 Chapter 3 19-29 Method 8 Chapter 4 30-48 Results 9 Chapter 5 4 9 - 5 4 Discussion 10 References 55-57 11 Appendix I 58 - 60 Apparatus Description 12 Appendix II 6 l - 75 Instructions Table Subject Page(s) 1 Means for the Six Dependent Variables: Trials, Errors, 31 - 32 Seconds, Classifications, Verbalization, and Strategy for Problems 1 - 4 2 Summary of Means and Standard Deviations for each of Six 33 Dependent Variables Across Problems 1 - 4 3 Analysis of Variance for Trials, Errors, and Time (seconds) 34 to Criterion for Problem 1 4 Analysis of Variance for Trials, Errors, and Time (seconds) 34 to Criterion for Problem 2 5 Analysis of Variance for Trials, Errors, and Time (seconds) 36 to Criterion for Problems 3 and 4 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 45 Strategy Verbalized for 48 Ss on SB and CB Problems 9 Intercorrelations of Seven Dependent Variables for Problems 47 3 and 4 10 Response Frequencies on the Post-Criterion Variables: 48 Classifications, Verbalization, and Strategy, for 96 Subject - Problem Combinations 11 A Comparison of the Classification and Verbalization Variables for Problem 4 50 Figure Subject Page(s) 1 Six classification rules used by Shepard, Hovland, 5 and Jenkins (1961) 2 Dimensionally ordered stimulus array 22 3 Discrepancy ordered stimulus array 27 4 Histogram of mean values of the Trials, Errors, 38 and Seconds variables for three learning paradigms 5 Histogram of mean values of the Classifications 39 and Verbalization variables for three learning paradigms 6 Histogram of mean values of the Trials, Errors, 42 and Seconds variables for simple and con-tingent biconditional rules 7 Frequency polygon of mean values of the Trials 43 and Errors variables for the simple and contingent biconditional rules across three learning paradigms 8 Histogram of the mean value of the Seconds variable 44 for the intra- and inter-stimuli instruction treatments i l l Plate Subject Page 1 Learning Apparatus 24 Acknowledgement o f A s s i s t a n c e I would 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 the members o f ray t h e s i s committee , D r s , R. F . Conry , Chairman, S. S, L e e , and R. L , R, O v e r i n g . I n a d d i t i o n , I would l i k e t o thank my parent s f o r t h e i r i n v a l u a b l e support and encouragement throughout my ed-u c a t i o n . F i n a l l y , I would l i k e t o thank my w i f e , Dona, f o r so 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 t h a t they d e f y c l a s s i f i c a t i o n . Chapter 1 Problems and Related Literature Following an investigation of classificatory behavior, Shepard, Hovland, and Jenkins ( l 9 6 l ) speculated that the process of clas s i f i c a t i o n learning involved: (l) the abstraction of relevant dimensions, and (2) the formation of rules that are bu i l t by combining a number of the most elemen-tary kinds of classifications; such as, affirmation, conjunction, and disjunc-tion. In the f i r s t part of their experiment, these investigators attempted to determine the d i f f i c u l t y of cl a s s i f i c a t i o n learning by comparing i t with iden-t i f i c a t i o n learning. The latte r i s defined as learning to associate a d i f f -erent response with each stimulus, while the former i s defined as learning to assign the same response to several different stimuli, such that the total set of stimuli ultimately comprise two or more mutually exclusive and exhaust-ive classes. Shepard et a l . , note that since one need not discriminate among stimuli of the same class, less information about a stimulus i s required to class i f y i t than to identify i t ; therefore, a classification should be easier to learn than an identification. Presumably, members of a class share common elements which serve as c r i t e r i a for class 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 discrim-ination difficulty under high reinforcement consistency, and increased discrim-ination diffuculty under low reinforcement consistency. He argues that an in-crease in the number of common elements increases the amount of stimulus gen-eralization among the stimuli, such that when these common-element stimuli are assigned to the same response class, stimulus generalization will have a facilitative effect; but, when they are assigned to different response cat-egories, the effect will be inhibitive. It is the knowledge of these common elements and the ability to abstract them to classify other stimuli, which obviates the necessity of learning the characteristics of each stimulus. This saving is not effected in identification learning. On the contrary, after learn-ing to associate different labels with each stimulus, subsequent stimuli re-quire the learning of their unique characteristics and the association of these characteristics with the correct one of a number of different responses. Attempts to clarify the relationship between classification and identi-fication learning by combining both in a single task encounter several diff-iculties. First, converting an identification task into a classification task reduces the total number of responses which must be kept in mind. Second, this reduction alters the chance level of successful performance. For example, with eight stimuli and eight responses in an identification task, the prob-ability of guessing the correct response is one in eight. In a classification task, where four of the eight stimuli are associated with each of two responses, the probability is one in two. With both these factors affecting performance in comparisons of identification and classification learning, i t is difficult to assess the conceptual factor; i.e., the reduced need to learn the character-istics of each stimulus which is occasioned by learning the characteristics common to a class of stimuli. In an attempt to c l a r i f y this confusion, Shepard et a l , , (l96l) noted that the d i f f i c u l t y of a class i f i c a t i o n can be manipulated without changing either the stimuli or responses, by alternating the assignments between them. For example, because of the several attributes common to the class "dog" and several others common to the class "horse", i t would be more d i f f i c u l t to learn which two of four horses and which two of four dogs belonged i n cat-egory "A", than i t would be to learn that a l l four horses belong in category "A" and a l l four dogs belong i n category "B", Shepard et a l . , extend their argument by stating: The cross-species cla s s i f i c a t i o n evidently entails a larger component of rote learning and, might, indeed, be comparable i n d i f f i c u l t y to learning a separate identifying response for each animal. Moreover, the difference in d i f f i c u l t y of two such classifications could not be attributed either to changes in the length of l i s t or in chance expectation. Clearly, then, the extent to which the potential re-duction i n d i f f i c u l t y from identification to classification learning i s realized depends upon how the stimuli are grouped together i n their assignment to responses ( 1 9 6 1 , p, 2 ) , By means of alternating the response assignments of a cl a s s i f i c a t i o n task, Shepard et a l . , manipulated the rote component of a task i n an attempt to c l a r i f y the relationship between identification and class i f i c a t i o n learning. This manipulation was conducted within a stimulus population of three dimen-sional, bivariate, geometric shapes which were cl a s s i f i e d into dichotomous response categories, with four stimuli being assigned to each category. These dimensions and their values were: size, large or small; color, black or white; and shape, square or triangle. This population produced a tot a l of ?0 possible Classifications of the eight stimuli (the number of combinations of four things taken from eight; i.e., 81/(4!) 2 = 70). However, by applying the reductive principle that classifications are of the same basic type i f one can be obtained from the other by either interchanging the roles of the three dimensions or reversing the response assignment system, these 70 are reduced to six structur-a l l y distinct classifications, each of which corresponds to a different class-i f i c a t i o n rule for assigning stimulus - response contingencies. Figure 1 il l u s t r a t e s the six clas s i f i c a t i o n rules. Type I, an affirmation rule, i s based upon one relevant dimension; i.e., color, where an exemplar must be black. Type II, a biconditional rule, i s based upon two relevant dimensions, color and shape, and an exemplar may be either black and triangular or neither black nor triangular. Types III, IV, and V are called "single dimension with exception" rules, for they specify the values on one relevant dimension, plus the two exceptional stimuli for which the responses must be reversed; for ex-ample, for Type IV, size, color, and shape are relevant and an exemplar i s large except for the large, white square, which must be exchanged for a small, black triangle. These exception rules are based upon a single dimension, but with the exceptional stimuli this number i s increased to either two relevant dimensions for Types III and V, or three relevant dimensions for Type IV. Type VI i s termed the "odd-even" rule by Shepard et a l . This rule i s based upon three relevant dimensions: for example, i n Figure 1 size, shape, and color are relevant and an exemplar may be triangular ~ in which case i t must be either large and black or neither large nor black — or i t may be square — in which case i t must be either large and white or neither large nor white. Concerning the relative d i f f i c u l t y of the six rule types, Shepard et a l . , note that whereas Type I involves a familiar kind of cla s s i f i c a t i o n commonly used in clas 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 identification task which requires the association of a different response to each stimulus. The different responses for the Type VI rule become apparent when this rule i s stated in terms of the logical connectives of conjunction and disjunction, which produces a complete enumeration of the four stimuli assigned to the exemplar category. Shepard et a l . , further speculate that i f the d i f f i -culty of a classification i s positively related either to the stated verbal length of the rule required to specify exemplars of each category or to the numb of logical symbols required to express the rule then (putting aside the exceptior rules III, IV, and V) i t i s possible to postulate three different levels of d i f -f i c u l t y corresponding to Types I, II, and VI. Support for this postulation comes from a consideration of the increasing number of relevant dimensions: i.e., one, two, and three for Types I, II, and VI respectively. 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 six types of classification?, and Does the learning of a classification transfer to f a c i l i t a t e the learning of a new c l a s s i f i c a t i o n of the same type? Their experimental procedure was a modified paired-associate paradigm with two verbal responses, " A " or "B". Eight stimuli were individually presented in random sequences u n t i l , by the method of anticipation, an association between each stimulus'and one of the two responses was established. Each of six Ss completed a total of twenty tasks, comprising five successive tasks for four of the six types of rules (Because of their structural similarity Types III, IV, and V were combined to yield a single measure.). D i f f i c u l t y was determined by the number of errors to solution. The results revealed two orders of solution d i f f i c u l t y . On encountering the problems, the d i f f i c u l t y order was I < II < ( i l l , IV, V) < VI, This order supported the investigators' contention that d i f f i c u l t y would be positively correlated with the lo g i c a l and verbal lengths of the stated rules, 1 However, with continued 1 This order also supported the investigators' qualified 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 qualification arises from the fact that within this system of class-i f i c a t i o n there i s a confounding ipsative relationship between the relevant and irrelevant dimensions, such that increasing the number of relevant dimensions necessarily decreases the number of irrelevant dimensions by an equal number, and vice versa. It i s for this reason that, based upon the results obtained for this condition by Smith (1954) and by Wallach (1961), Shepard,,et a l . , postulated that classification 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 principle may underlie per-formance in relation to the number of relevant and irrelevant dimen-sions. Specifically, performance decreases monotonically with the increase in the number of stimulus dimensions, regardless of the rele-vance of those dimensions. A A A • EH • n B A • A • A B 11 111 O A V m A A • A A A • A • a A A A • • • V V I 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 left belong in one class and the four stimuli on the right in the other class.) practice each type becomes increasingly less difficult due to within-type positive transfer. In particular, Type VI exhibited a disproportionate decrease in difficulty relative to the other types, such that i t became less difficult than Types (III, IV, V). This decrease produced the second order of problem difficulty, 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 cl 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 facilitate 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 left with the task of identifying the relevant attributes for each problem. In the CL condition, Ss were given neither the conceptual rule nor the rele-vant 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 trials and errors to criterion indicate that for each of four conceptual rules the order of difficulty was CL > Al > RL. The fact that both Al and RL were less difficult 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 difficulty 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 class-ification problems used by Shepard et al , , (1961), In addition to providing information about differences in difficulty among the classification rules, this application will provide information about differences in difficulty between components within a single rule, and between rules for either of the two components, Shepard et al . , (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, is 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 is an even number of differences (0 or 2) the card is an exemplar; i f there is an odd number ( l or 3) the card is a nonexemplar. Given the in-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 itself responsible for the large degree of transfer. This determin-ation is particularly important in view of the fact that the second order of problem difficulty noted by Shepard et a l . , is a consequence of Type VI be-coming less difficult 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 is most advantageous for those rules wherein more than one attribute on a single dimension is assigned to the exemplar category, and each of these attributes is 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 differ from the focus card on 0 or 2 relevant dimensions. Similarly, the RA Type VI rule: 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 criteria for the above exemplars. First, this was the form of the odd-even rule reported by Shepard et al . , (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 is particularly true when the Ss are not trained to use negative infor-mation (Friebergs & Tulving, I961). The postulated coexistence of both these strategies in the Shepard et a l . , study raises two questions: (l) How difficult is a Type VI pro-blem when solved with an RA strategy?, and (2) How difficult is a Type II problem when solved with an ER strategy? A study that compares both strategies is 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 al . , (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 in both response classes. While no information about the number of rules assigned to Category 5 is given, the inclusion of this category appears to indicate that the classification learning results may in part be attributable to behavior that was not consistent with the description of classification learning given by these investigators. Shepard et al . , (1961, p. 2) note two criteria that distinguish classification from identification learning. First, classification learning is the assignment of the same response to several different stimuli; while identification learning is the assignment of a different response to each stimulus. Second, i t is not necessary to discriminate among stimuli that are classified together, but such discrimination is necessary for identification learning. Con-cerning this second point, they note that members of a class apparently have something in 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 is required to extend this name to additional class members. With identification learning i t is not possible to effect such a saving. After different responses have been learned for several members of a class, the asso-ciation of s t i l l another response to another class member requires additional rote learning. With these criteria in mind, consider the kinds of learning behavior that may be included in Category 5 of the Shepard et al,, study. First, 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 is 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 its associated response does not in-volve the learning of a class of stimuli that share a common characteristic. It is the S*s recognition of a common characteristic that initiates clas 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 al . , the memorization of what the S regards as unrelated stimuli and associ-ated responses more closely approximates rote identification than classifi-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 al, , (1961, p. 3) have noted that for a Type VI rule a l l three dimensions are relevant, and i f this rule is expanded in terms of its logical connectives of conjunction and disjunction, i t is logically equivalent to a complete enumeration of the stimuli. Con-sequently, rule learners who master this difficult rule by means of the RA strategy that is 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 is 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 di-mension as an irrelevant one, while memorizers would not distinguish between the irrelevant and relevant dimensions. The extra dimension might also serve to discourage memorization behavior. In reference to the eight stimuli that constituted the stimulus population used by Shepard et al. , (1961), the addi-tion 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 difficulty. Haygood and Stevenson (1967) found a linear decrement in performance as the number of irrelevant dimensions was increased from zero through two. In addition, they found the rate of decrement increased with problem difficulty (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 is not presented for the purpose of outlining the limitations of the rule verbalization measure. Indeed, Shepard et al. , (1961, p. 7) caution that this measure is not a rigorous one. Rather, this analysis is presented as a case for devising a measure that will discriminate between rule learning and memorization solu-tions of classification problems. A measure that may serve this function has been derived by the writer from the second criterion of classification learn-ing noted by Shepard et al, , (1961); that i s , once a classification is learned, l i t t l e , i f any, further learning is necessary to correctly classify subse-quently 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 class-ification. As is the case for identification, memorization in 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 in 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), in an investigation of "unconscious processes' in concept formation, has noted that at present different measures of concept attainment are necessary to reliably determine i f Ss have attained a concept. In a series of studies (Rommetveit, i960, I 9 6 I , 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 is a need to determine the reliability 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 the l i m i t a t i o n that i t s r e l i a b i l i t y i s influenced by the guessing of Ss who have memorized the o r i g i n a l s t i m u l i . This l i m i t a t i o n can be over-come by using a stimulus population that i s s u f f i c i e n t l y large to permit withholding a number of s t i m u l i that w i l l allow the adoption of a performance c r i t e r i o n well above that which might be a t t a i n e d by guessing. This has the disadvantage of r e q u i r i n g a l a r g e r stimulus population. In that the stimulus population of the present experiment n e c e s s a r i l y approximated that used by Shepard et a l . , (l96l), only a small number of s t i m u l i from the o r i g i n a l population could be withheld f o r a p o s t - c r i t e r i o n c l a s s i f i c a t i o n measure. Consequently, 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 of 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 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 c l a s s i f i c a t i o n and v e r b a l i z a t i o n measures. An estimate of t h i s r e l a t i o n s h i p i n a concept l e a r n i n g s i t u a t i o n may y i e l d some index of the d e s i r a b i l i t y of f u r t h e r development of a c l a s s i f i c a t i o n measure to d i s t i n g u i s h between those Ss who have learned and can apply 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 reproduce i t , and those Ss who cannot v e r b a l i z e a r u l e because they have mem-oriz e d s t i m u l i and learned no r u l e . S t i l l another advantage of a c l a s s i f i -c a t i o n measure becomes apparent upon consideration of the several cases r e -ported by Shepard et a l . , (1961, p. 10) where Ss had solved the problem, but could not v e r b a l i z e a r u l e t o reproduce the c l a s s i f i c a t i o n . Consequently, i t was not p o s s i b l e to determine how these Ss learned to solve the problem. Chapter 2 Purposes and Hypotheses The purposes of the present investigation are several. The fi r s t is to apply the component approach of Haygood and Bourne (19^5) to the Type II and Type VI classification problems used by Shepard et al. , (1961). This appli-cation will 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 difficulty expected for both the Type II and Type VI problems is 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 difficulty to be as predicted here. The second purpose of this study is to assess the difficulty 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 difficulty of the problem types is VI > II. Support for this prediction comes from the results of Shepard et al., (1961), which showed that for both the f i r s t and second orders of problem difficulty, Type VI problems were more difficult 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 difficulty 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 is greater than that for Type II for both the logical and verbal statements of this rule would also support the problem difficulty pre-diction for both paradigms, for both require the S to learn the classification rule. Finally, in terms of Well's (1963) hypothesis that difficulty is 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 difficult than the relatively ubiquitous Type II rule, Kepros and Bourne (1966) indicate support for this last argument by noting that in contrast to the results of Neisser and Weene (1962) and Hunt and Kreuter (1962), their results revealed no significant differences in 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 is explained by the amount of training upon biconditional rules that the S is given prior to the experiment. When, as in their study, sufficient prac-tice with biconditional rules is allowed so that S becomes as familiar with biconditional rules as he generally is with conjunctive rules, then appli-cation of either rule will be equally difficult. In addition, Hypothesis 3 is the expectation that no significant para-digm x problem type interaction will occur. This expectation is based upon the fact that for a l l three learning paradigms the components of a Type VI problem are more difficult than are those of a Type II problem; i.e., in 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 strat-egies, RA and ER, which occured in Shepard et al . , (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 will be more efficient than by means of an RA strategy. This prediction is based upon the fact that an ER rule is disjunctive for both problems, while the RA rules are both of a biconditional nature. Furthermore, for Type VI problems, the results of Shepard et al., 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 is that no interaction will 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 difficulty 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 difficult than Type II (Smith, 195^; Wallach, 196l). Since both strategies involve separate RL and Al components, i t is also expected that the predicted order of paradigm difficulty, CL > Al > RL, will be maintained for both strategies. Hypothesis 6, therefore, is that no significant paradigm x strategy interaction is ex-pected. 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 fe-male Ss for each cell in the design. No directional hypotheses were stated for either factor. The final purpose of this investigation is to test a post-criterion class-ification task as a method of discriminating between memorization and rule learning solutions to classification problems. Owing to several constraints that resulted from the simultaneous consideration of several problems in this study, i t was not possible to state and rigorously test a memorization hypo-thesis. Consequently, the risk of incorrect classification of performance on this variable that is caused by the small number of post-criterion class i f i -cation cards is tolerated here in order to gain an estimate of the validity of such a measure by correlating the results of the post-criterion class 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 seventy-two 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 in this ex-periment. 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 in i t i a l l y selected Ss was necessary for the following reasons: First, within a limit of 1,350 trials, one S failed to reach criterion on the fi 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 rele-vant attribute for Type VI causes the selection of either of two, two-attribute biconditional rules to be contingent upon the selec-tion 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 al,, (I96l) experiment and f a i l to express the biconditional because of emotional upset, and two Ss were dismissed due to apparatus mal-function. The age range of the forty-eight 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. The range of I.Q. scores of these Ss was 111 - 145 with a mean of 122.50 and a standard devia-tion of 8.48. Stimulus Materials The stimulus instances consisted of sixteen geometric designs varying along four bi-leveled dimensions, which were printed on 2.5 x 3.5 inch paper board cards. The stimulus population was defined by the following four dimensions: color of the figures, red or blue; shape of the figures, c i r c l e or trianglej size of the figures, large or small; and the number of figures, one or two. Each conceptual problem consisted of thirteen stimulus cards selected from the sixteen possible combinations of four bi-leveled dimensions. Of the remaining three cards, two were not included in the problem set for any of the four problems used in the study. These cards were used for the post-criterion c l a s s i f i c a t i o n measure. The remaining card was labelled an exem-plar of one of the categories and displayed as a focus instance for each of the treatment conditions. The use of the same focus card for a l l treatment conditions constituted an attempt to control across treatments for the memory load reduction which resulted from the continuous presence of an exemplar that was necessary in the ER treatment condition?. A pre-test of ten additional 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 level attainable by these grade ten students. nature of the rules that i s noted in the present study, they w i l l be replaced, by the names simple biconditional (SB) and contingent  biconditional (CB) respectively, except when direct 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, its 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 its values (see Figure 2 ) , In addition, each S was encouraged to ask about anything in 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 clar i -fying terms in the instructions by showing their referents on the stimulus array board. To facilitate the analysis of results, a two part design was employed. The f i r s t part included two warm-up problems. Problem 1 was an affirmation problem based upon the size dimension. 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 sol-ving ability 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 in 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 fe-male; 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 t o w n o e black white • o A • o A • o A O A A O A A @ O 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 in 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 acti-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 unob-trusively 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 is given in Appendix II. 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 prob-lems 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 prob-4 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 imme-diate 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 consis t of learning to co r r ec t ly c l a s s i f y each card with e i ther an " A " or "B" verbal response, then checking the accuracy of t h i s response by pressing the correspondingly l abe l l ed response button. For t h i s problem s i ze was the relevant dimension, with " A " designating large f igures and "B", small f igures . Problem 2 informed a l l Ss that t h i s problem a l so 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 add i t i on , separate ins t ruc t ions were given fo r each of the three learn ing paradigms. Ss i n the A l condi t ion were given the conceptual ru le fo 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 learn which charac-t 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 condi t ion were given the i d e n t i t y of the relevant a t t r ibu te used to d i s t i ngu i sh between the two categories..— the number of f igures — and were t o l d that t h e i r task was to learn how t h i s cha rac 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 condit ion were given nei ther the concept ru le nor the relevant a t t r i bu t e s ; ra ther , they were t o l d only the number of a t t r ibu tes relevant fo r each problem. In that the d i f f i c u l t y of an experimental task may vary as a function of knowledge of the number of a t t r ibu tes re levant fo r each problem, the num-ber of relevant a t t r ibu tes was s p e c i f i c a l l y given i n the ins t ruc t ions fo 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 cont ro l was necessitated by the fact that Ss i n the RL condi t ion are unavoidably given the number of relevant a t t r ibu tes i n -volved i n each problem when they are given the i d e n t i t y of those a t t r i b u t e s . Consequently, these Ss can immediately begin to form hypothet ical rules based upon only that number of a t t r i bu t e s . S i m i l a r l y , when Ss i n tha A l condi t ion were given a complete statement of the conceptual r u l e , they a l so 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. These instructions constituted the two levels of the Instruction factor. The ER Instruction involved placing before the S a mounted set of the entire array of stimulus cards, ordered and labelled in 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 in 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 prob-lem 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-deter-mined 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 in 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 in the RL condition were told the identities of the D I F F E 2 R E N G E S D I F F E 1 R E N C E 3 1, number C 1. shape D 1. size E 1. color O O A o TP 1. size 1. number 1. shape 1. shape 1. number 1, shape *~ * \J \S -L. WJ- m v - i . VJ. O A A ® o A F F E 3 R E N C E S u 1. size 1. size 1, color 1. number I L 2. color M 2 . color pj 2 . number Q 2 . size 3« shape 3« shane e A A A e A A D I P. F F 2, size 4, color E 4 R E N C E S Fig. 3 , Stimulus array ordered in terms of the number of attribute discrepancies between each card i n the array and the exemplar focus card. This array was presented to inter-stimuli Ss prior 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 in 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: All 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: All cards that contain ( ) AND either ( ) and ( ) or neither ( ) nor ( ) OR ( ) AND either ( ) and ( ) or neither ( ) nor ( ) forms of the three important charac-teristics 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, in 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 was recorded in terms of six dependent variables: (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 is 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. The Strategy variable, how-ever, revealed no such continuity and was, 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 is summarized in 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 in each case. In fact, in the analysis for Problem 1, Paradigm, Instruction, and Order were "dummy" var-iables. These "dummy" analyses were conducted to determine significant diff-erences in performance on the two warm-up problems. It 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 rel -atively simple Problems 1 and 2 would indicate possible sources of experimen-tal error. These analyses, which are summarized in Tables 3 and 4, indicate that, with the exception of the Paradigm factor for the Seconds variable of Problem 2, no significant differences in concept learning ability as indexed by Problems 1 and 2 existed prior to introducing the Instruction and Order factors. The exception, vrhich was statistically significant for the Seconds variable, F (2, 24) = 3.78 p < .05, indicates the effectiveness of the Para-digm 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 Classifi- Verbal- Strategy cations ization Sex Male 1 77.75 18.00 576.88 2.00 1.00 .00 2 34.54 4.29 135.92 2.00 1.00 .00 3 269.92 80.54 1225.46 1.62 .83 .21 4 436.42 124.21 2275.75 1.62 .67 .33 Female 1 58.42 12.50 286.83 2.00 1.00 .00 2 39.13 6.71 151.83 2.00 1.00 .00 3 303.29 100.92 1337.75 1.75 .82 .17 4 531.54 177.13 2447.58 1.83 .82 .29 Paradigm CL 1 91.63 25.30 589.50 2.00 1.00 .00 2 44.00 9.81 164.88 2.00 1.00 .00 3 515.00 177.63 2077.94 1.25 .63 .06 4 771.56 251.50 3079.38 1.62 .63 .25 RL 1 50.13 9.81 300.13 2.00 1.00 .00 2 27.69 0.93 90.31 2.00 1.00 .00 3 197.38 58.25 1016.00 1.94 1.00 .37 4 209.25 55.56 1261.06 2.00 1.00 .37 Al 1 62.50 12.44 405.94 2.00 1.00 .00 2 38.81 5.75 176.44 2.00 1.00 .00 3 174.44 36.31 750.88 1.87 .94 .12 4 471.13 144.94 2744.56 1.56 .88 .31 Continued,.. Table 1 (continued) Tr i a l s Errors Seconds C l a s s i f i - Verbal- Strategy-cations ization Instruction RA 1 77.38 16.88 409.13 2.00 1.00 .00 2 37.46 5.46 142.33 2.00 1.00 .00 3 274.83 84.25 1399.83 1.58 .79 .00 4 495.12 141.08 3047.13 1.71 .71 .04 ER 1 58.79 13.63 454.58 2.00 1.00 .00 2 36.21 5.5^ - 145.42 2.00 1.00 .00 3 298.38 97.21 1163.38 1.79 .92 .37 4 472.83 160.25 1676.21 1.75 .83 .58 Order SB CB 1 73.71 15.71 523.33 2.00 1.00 .00 2 34.54 4.54 128.63 2.00 1.00 .00 3 361.67 118.13 1685.46 1.62 .88 .21 4 495.50 151.92 3518.29 1.79 .89 .29 CB SB 1 62.46 14.79 340.38 2.00 1.00 .00 2 39.12 6.45 159.13 2.00 1.00 .00 3 211.54 63.33 877.75 1.75 .83 .17 4 472.46 149.42 2205.04 1.67 .75 .33 Problem Grand Mean 1 68.08 15.25 431.85 2.00 1.00 .00 2 36.83 5.50 143.88 2.00 1.00 .00 3 286.60 90.73 1281.60 I.69 .85 .19 4 483.98 150.67 2361.67 1.73 .77 .31 Summary of Means and Standard Deviations f o r each of Six Dependent Variables Across Problems 1 - 4 DEPENDENT VARIABLES PROBLEM 1 PROBLEM 2 PROBLEM 3 PROBLEM 4 MEAN SD MEAN SD MEAN 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 1 0 2 . 8 0 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 STRATEGY .00 .00 .00 .00 .19 .40 .31 .47 Analysis of Variance for T r i a l s , Errors, and Time (seconds) to Criterion for Problem 1 Source df Tri a l s Errors Time (seconds) MS F MS F MS F Sex (S) 1 4485.33 1.98 363.00 1.28 1009490.00 3.63 Paradigm (P) 2 7263.07 3.22 344.31 2.99 343011.60 1.23 Instruction (i) 1 4144.08 1.83 126.75 .45 24797.52 .08 Order (0) 1 1518.75 .67 10.08 .03 481685„00 1.44 SP 2 5067.57 2.24 537.93 1.91 246840.40 .88 SI i 3952.08 4.14 1180.08 4.19 35806.48 .12 PI 2 6741.57 2.98 599.31 2.12 57136.25 .20 SO 1 30.08 .01 200.08 .71 90046.00 .32 PO 2 484.74 .21 110.39 .39 466794.00 1.68 10 1 147.00 .06 33.33 .11 73711.50 .26 SPI 2 2932.56 1,30 200.01 .71 53946.22 .19 SPO 2 770.55 .34 72.76 .25 230172.50 .82 SIO 1 616.33 .27 12.00 .04 93368.44 .33 PIO 2 1452.21 .64 135.39 .48 255965.30 .92 SPIO 2 220.53 .09 146.67 .52 349907.70 1.26 Replications (SPIO) 24 2256.06 281.49 277599.20 * v< .05 TABLE 4 Analysis of Variance for T r i a l s , Errors, and Time (seconds) to Criterion for Problem 2 Source df Tri a l s Errors Time (seconds) MS F MS F MS F Sex (S) 1 252.08 .67 70.08 .56 3040.08 .32 Paradigm (P) 2 1111.39 2.97 315.21 2.53 34962,03 3.73* Instruction (I) 1 18.75 .05 .83 .00 114.08 .01 Order (0) 1 252.08 .67 44.08 .35 11163.00 1.19 SP 2 85.27 .22 30.39 .24 2519.50 .26 SI 1 320.33 ,85 85.33 .68 1704.08 .18 PI 2 114.06 .30 65.14 .50 7125.52 .76 SO 1 26.99 .07 5.33 .04 767.99 .08 PO 2 189.02 .50 81,52 .65 5917.68 .63 TO 1 280.33 .75 26.99 .21 107.99 .01 SPI 2 647.01 1.73 156.64 1.25' 11276.89 1.20 SPO 2 971.05 2.59 275.27 2.21 27959.78 2.98 SIO 1 70.08 .18 80.08 .64 12160.33 1.29 PIO 2 275.01 .73 57.93 .46 12051.78 1.28 SPTO (SPIO) 2 190.13 .50 19.77 .15 19568.39 2.09 Replications 24 373.74 - - — 124037 — — — — 9355.71 * p < .05 seconds to criterion for the CL, Al, and RL paradigms respectively, — are in accord with the paradigm difficulty results obtained by Haygood and Bourne ( 1 9 6 5 ) , and also with the predicted difficulty order of this factor for Pro-blems 3 and 4, A third analysis of variance, which is summarized in Tables 5 a n d 6, was conducted for the 2 x 3 x 2 x 2 x 2 factorial design on the combined results for Problems 3 and 4. 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 difficulty 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 difficulty (CL > Al > RL) predicted in 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 ; Sec-onds, F ( 2 , 24) = 8 . 6 3 p< . 0 0 5 ; Classifications, F ( 2 , 24) = 6 . 0 2 p< . 0 1 ; and Verbalization, F ( 2 , 24) = 6 . 0 0 p < . 0 1 (Tables 5 and 6 ) . 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 dif-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 difficulty, CL > Al > RL, significant differences in difficulty were found between the CL 5 This test is defined in Winer ( 1 9 6 2 ) , as T a - T b q = »,.,.. t , where VMS error/rT = Mean of a l l Ss in paradigm A T D = Mean of a l l Ss in paradigm B MS error = Mean Square from the analysis of variance n = Number of Ss in each paradigm: n = 1 6 Analysis of Variance for Trials, Errors, and Time (seconds) to Criterion for Problems 3 and 4 Source df Trials Errors Time (seconds) MS F MS F MS F Sex (S) 1 99073.50 .98 3 2 2 3 0 . 0 0 2.42 484362.00 . 2 5 Paradigm (P) 2 1687241.00 16.71* 220459.00 16.60* 16722800.00 8.63* Instruction (i) 1 9.37 . 0 0 6 1 9 2 . 0 9 .46 1 5 5 0 1 9 2 0 . 0 0 8 . 0 0 * Order ( 0 ) 1 179920.10 1 . 7 8 19694.01 1.48 7 5 3 9 2 8 5 . 0 0 3.89 Type (T) 1 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* SP 2 2 6 9 5 5 . 0 0 . 2 6 1 0 7 5 . 3 7 .08 883880.00 . 4 5 SI 1 5 1 9 8 7 . 0 0 . 5 1 11682.07 .87 9184.00 . 0 0 PI 2 6 0 7 6 2 . 8 1 . 6 0 14049,08 1 . 0 5 4227928.00 2.18 so 1 16748.19 .16 2 1 9 4 . 5 7 .16 5 5 4 0 3 9 . 0 0 .28 PO 2 4 5 3 6 5 . 4 4 . 4 4 9 9 7 4 . 8 4 .75 I O 6 9 . 5 0 . 0 0 1 0 1 20709.38 . 2 0 5875.01 . 4 4 1 7 8 9 5 5 . 0 0 . 0 9 ST 1 22877.19 . 4 4 6353.75 .93 2 1 2 6 4 , 0 0 . 0 1 PT 2 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 IT 1 1 2 6 0 3 . 3 1 .24 231.18 . 0 3 7 7 2 1 9 6 8 . 0 0 4.07 OT 1 9 6 9 0 0 . 5 6 I . 8 9 16406.37 2.40 1466912.00 . 7 7 SPI 2 24459.50 .24 5 3 2 6 . 1 2 .40 1121688.00 .57 SPO 2 1 9 9 5 2 5 . 9 0 1.97 3 4 3 0 8 . 0 3 2.58 1232732.00 .63 SIO 1 20827.00 . 2 0 6 3 8 6 . 3 6 .48 184537.00 . 0 9 PIO 2 4 9 8 0 4 . 8 1 .49 12138.32 .91 1087914.00 . 5 6 SPT 2 42109.41 .82 939L59 1.37 2680808.00 1 . 5 0 SIT 1 2482.31 .04 2410.05 .35 388944.00 . 2 0 PIT 2 1 1 9 2 1 . 5 3 . 2 3 4984.42 .73 3386976.00 1.78 SOT 1 64998.75 1.27 10731.55 1.57 1 7 6 9 3 5 3 . 0 0 .93 POT 2 288.78 . 0 0 5 4 3 . 8 4 . 0 7 822898.50 . 2 2 IOT 1 120.43 . 0 0 9 6 9 . 0 5 .14 4 6 0 4 5 8 . 0 0 .24 SPIO 2 1 5 1 5 9 . 1 9 . 1 5 5 9 2 3 . 3 6 . 4 4 2304734.00 1.18 SPIT 2 1882.84 . 0 3 281.86 ...04 849440.00 . 4 4 SPOT 2 2 3 6 2 2 . 4 1 .46 3192.60 .46 5 1 7 3 2 4 . 0 0 .27 SI or 1 5 8 8 0 6 . 5 6 1.14 8 9 I 2 . 3 8 1.30 1486247.00 .78 PIOT 2 22750.28 . 4 4 5327.13 .78 136792.50 . 0 7 Replications ^ PIO) 24 100941.30 ____ 13281.09 1937011.00 SPIOT 2 7438.47 .14 1168.46 .17 7 0 2 0 0 8 . 0 0 .37 RT(SPIO) 24 51165.46 6825.98 ____ 1895985.00 * p < .05 Analysis of Variance f o r the C l a s s i f i c a t i o n s and Verbalization Variables f o r Problems 3 and 4 Classifications Verbalization Source df MS MS F F Sex (S) 1 .66 1.78 .37 2.00 Paradigm (P) 2 2.26 6.02* 1.12 6.oo* Instruction (I) 1 .37 1.00 .37 2.00 Order (0) 1 .00 .00 .04 .22 Type (T) 1 .04 .11 .16 2.66 SP 2 .07 .19 .12 .66 SI 1 1.04 2.77 .37 2.00 PI 1 .40 1.08 .12 .66 SO 1 .16 .44 .37 2.00 PO 2 .09 .25 .04 .22 IO 1 .04 .11 ,04 .22 ST 1 .04 .11 .16 2.66 PT 2 .94 2.25 .16 2.66 IT 1 .16 .44 .00 .00 or 1 .37 1.00 .00 .00 SPI 2 .51 1.36 .12 .66 SPO 2 1.07 2.86 .87 4.66* SIO 1 .37 1.00 .04 .22 PIO 2 .44 1.19 .29 1.55 SPT 2 .26 .69 .04 .66 SIT 1 .66 1.77 .16 2.66 PIT 2 .13 .36 ,00 .00 SOT 1 .04 .11 .00 .00 POT 2 .03 .08 .12 1.99 i or 1 .00 .00 .16 2.66 SPIO 2 .21 .58 .04 .22 SPIT 2 .07 .19 .04 .22 SPOT 2 .01 .02 — SIOT 1 .16 .44 ____ PIOT 2 .09 .24 .04 .66 Replications (SPIO) 24 .37 .18 --<-_ SPI OT 2 .19 .52 .00 ,00 RT(SPIO) 24 .37 .06 * P < .05 TRIALS 800 600 400 ERRORS 200 -300 -200 -100 -3000 -CL CL Al PARADIGM Al PARADIGM RL RL SECONDS 2000 -1000 -CL Al PARADIGM RL F i g . 4 . Mean values of the T r i a l s , Errors, and Seconds variables across three learning paradigmsI complete learning, attribute identif-ication, and rule learning, for Problems 3 and 4. 1.50 -NUMBER OF | I CORRECT 1.00 -CLASSIFICATIONS .50 -,00 I 1 1 1 1 CL Al RL PARADIGM Complete 1,00 RULE VERBALIZATION .75 .50 .25 A Incomplete .00 CL A l PARADIGM RL Fig, 5 . Mean values of the number of correct Classifications and the completeness of the rule Verbalization across three learning paradigms; complete learning, attribute identification, and rule learn-ing, for 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 * RL Trials — — 1.33 Errors — — 1.17 Seconds — — — 1.74 1 * q 3 ( 24 = 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. Support for this predic-tion was obtained for the following variables: 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 ) . In contrast, hypothesis 3 (Paradigm x Type interaction) was not supported. The Paradigm x Type interaction, illustrated in Figure 7( was significant for the Trials and Errors variables, F (2, 24) = 4.21 p < .05 , 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, com-pared with the RA instructions, the ER instructions as indexed by time are res-ponsible 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 cor-rectly 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 learn-ing 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 Classifi-cation 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 ERRORS SECONDS 400 -300 -200 -100 -Simple Biconditional Contingent Biconditional PROBLEM TYPE 300 J 200 J 100 J Simple Biconditional PROBLEM TYPE Contingent Biconditional 2500 , 2000 1500 J 1000 500 Simple Biconditional Contingent Biconditional PROBLEM TYPE Fig. 6. Mean numbers of T r i a l s , Errors, and Seconds to criterion across two types of biconditional rule for Problems 3 and 4. Fig. 7 . Mean numbers of T r i a l s , and Errors for two kinds of biconditional rules, Simple and Contingent, across three learning paradigms, Complete Learning, Attribute Identification, and Rule Learning. 2500 -i 2000 -SECONDS 1500 • 1000 • 500 Intra-stimull Inter-stimuli INSTRUCTIONAL TREATMENT Fig. 8. Mean number of Seconds to criterion for two instructional treatments, Intra- and Inter-3timuli, 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 in-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 SB CB Instruction RA ER RA ER RA 24 15 23 10 Strategy ER 0 9 1 14 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 is 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 is 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 relation-ship, 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 v = .89 for the SB rule and r c v = .79 for the CB rule, where r = .29 P < .05. These correlations suggest that the ability to verbalize a classification rule is 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 con-cept attainment reported by Rommetveit and Kvale (1965a, I965), the discrep-ancy may be attributable to the use of the Classifications measure of concept attainment in the present study. Finally, Table 10 summarizes the responses for 96 subject-problem com-binations 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 in 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 post-criterion 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 Variables for Problems 3 and 4 Problem 3 Problem 4 1 2 3 4 5 6 7 8 9 10 11 12 PROBLEM 3 1 Trials 1.00 2 Errors .97* 1.00 3 Seconds .85* .83* 1.00 4 Classifications - .40* - .38* - .32* 1.00 5 Verbalization - .37* - .35* - .28 .89* 1.00 PROBLEM 4 6 Trials .57* .56* .40* - .39* - .42* 1.00 7 Errors .56* .56* .34* - .41* - .43* .96* 1.00 8 Seconds .18 .19 .20 - .33* - .35* .74* .63* 1.00 9 Classifications - .15 - .14 - .14 .22 .32* - .38* - .39* - .28 1.00 10 Verbalization - .21 - .19 - .14 .57* - .61* - .33* - .32* - .28 .79* 1.00 11 IQ .09 .14 .14 - .05 - .04 .02 .05 .02 •03 .07 1.00 12 Age .03 .01 .03 .09 .13 .08 .06 - .00 - .01 .11 - .03 1.00 * r = .29 p < .05 df = 46 Response Frequencies on the Post Criterion Variables, Classifications, Verbalization, and Strategy, for 96 Subject-Problem Combinations PARADIGM C L R L A I TOTALS INSTRUCTION R A E R R A E R R A E R PROBLEM 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 +4 PERFORMANCE CONDITION 0 COM RA 0 COM ER 0 INC RA 2 1 2 1 1 1 5 3 8 0 INC ER 1 COM RA 2 1 2 1 3 1 COM ER l 1 1 1 INC RA 2 2 2 1 1 1 3 6 9 1 INC ER 2 COM RA 2 4 5 2 8 8 2 2 6 4 6 1 29 21 5 0 2 COM ER l 4 5 6 1 2 4 8 15 23 2 INC RA 1 1 2 2 2 INC ER 48 48 96 0 COM 0 INC 2 1 2 l 1 1 5 3 8 1 COM 2 1 1 3 1 4 1 INC 2 2 2 l 1 1 3 6 0 2 COM 2 4 6 6 8 8 7 8 6 5 8 5 37 36 73 2 INC 1 1 2 2 48 48 06 0 RA 2 1 2 1 1 l 5 3 8 0 ER 1 RA 4 2 2 1 1 2 5 7 12 1 ER 1 1 1 2 RA 2 5 5 2 8 8 2 2 6 5 6 1 21 23 52 2 ER 1 4 5 6 3 2 4 8 15 23 48 48 96 COM RA 4 4 5 2 8 8 2 2 6 4 6 2 31 22 53 COM ER l 4 6 6 1 2 4 9 15 24 INC RA 4 4 2 2 2 3 2 8 11 19 INC ER 48 48 96 0 2 1 2 1 1 1 5 3 8 1 4 2 2 l 1 l 2 6 7 13 2 2 5 6 6 8 8 7 8 6 6 8 5 ?? 38 75 48 48 96 COM 4 4 6 6 8 8 8 8 6 5 8 6 4o 37 77 INC 4 4 2 2 2 3 2 fl 11 19 48 48 96 RA 8 8 7 4 8 8 2 2 8 7 6 4 39 33 72 ER 1 4 6 6 1 2 4 9 15 24 48 48 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 incom-plete rule verbalizations respectively, and RA and ER refer to intra-and inter-stimuli rule type verbalizations respectively. Chapter 5 Discussion Support for Hypothesis 1 is revealed by the obtained order of Paradigm difficulty CL > Al > RL, though the post hoc comparison of means re-vealed that the ordering of the Al and RL paradigms is 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 difficulty between paradigms approximated those obtained in the present study; i.e., CL considerably more difficult than Al, and Al approximately equal in difficulty 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 difficulty is 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 difficulty 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 fully understood their less complex rule and immediately employed i t to identify attributes. Support for this explanation is 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 1 2 complete - 1 10 Post-Criterion Verbalization " incomplete 2 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 difficulty in which special attention is paid to the rule instructions for Al Ss. The need for further research of paradigm difficulty is emphasized s t i l l more by the possibility that the within-type positive transfer obtained by Shepard et al., (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 re-mained constant and only the relevant attributes for each problem were var-ied, 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 prob-lem, 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 success-ive problem contributes to the S*s knowledge of the rule and to his ability to apply i t to the remaining problems. Whether knowledge of the classification rule is 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 prob-lems of that type less difficult than when these problems are i n i t i a l l y en-countered and correspond to a CL paradigm. The difference between the CL and Al paradigms is a knowledge of the classification rule; perhaps i t is this same knowledge that represents the differences among the i n i t i a l and subsequent prob-lems in the Shepard et al,, (1961) problem sequence, and which might have been responsible for the within-type positive transfer obtained by these investi-gators. However, at present this alternative explanation of the Shepard et al., results serves only to indicate the need for a careful study of positive transfer, both within and between paradigms. With regard to problem difficulty, the obtained result that CB problens are significantly more difficult than SB problems supports the finding of Shepard et al., (1961) that type VI problems are more difficult than Type II problems. This result also extends the Shepard et al. , finding to include problems involving four dimensional, bivariate stimulus instances. The result CB > SB also supports the method of determining problem difficulty 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 difficult than SB problems. This result is consistent with the Shepard et al., result that a Type VI problem was more difficult than a Type II prob-lem 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 condi-tions employed a solution strategy different from that which they vrere in-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 is worthwhile, for i t may facilitate the apparently necessary task of designing RA and ER instructions that will 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 difficulty 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 bi-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 bi-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 is 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 clarified 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 ex-perience 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 difficulty seems advisable because the addition of a fourth dimension in the stimulus population so in-creased the difficulty 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 is 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 classifi-cation instances would reduce the probability of reaching criterion by gues-sing. With such control, this measure may serve as a valid method of discri-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 is 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 learn-ing, then clarification of the two-component nature of concept learning im-plies 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 difficulties. 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, instruc-tion that provides either the rule or the relevant attributes might be found optimally to facilitate the learning of particular kinds of concepts; for ex-ample, 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. Jr. Human conceptual behavior, Boston, Allyn & Bacon, 1966, Bourne, L. E, Jr. Learning and u t i l i z a t i o n of conceptual rules. In B, Kleinmuntz (Ed,), Concepts and the structure of memory. New York, John Wiley & Sons, I 9 6 7 . Bourne, L, E, Jr. & Guy, D. E. Learning conceptual rules: Some interrule transfer effects. Journal of Experimental Psychology, 1 9 6 8 , 7_6 (3), 4 2 3 - 4 2 9 . Freibergs, V., & Tulving, E. The effect of practice on u t i l i z a t i o n of i n -formation from positive and negative instances in concept i d e n t i f i c a -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 in a discrimination learning task. Journal of Experimental Psychology, 1 9 5 3 , 41, 2 5 - 3 4 . Haygood, R. C , & Bourne, L, E. Jr, Attribute - and rule - learning aspects of conceptual behavior. Psychological Review, I 9 6 5 , £ 2 , (3), 1 7 5 - 1 9 5 . Haygood, R, C. & Stevenson, M. Effects of number of irrelevant dimensions in nonconjunctive concept learning. Journal of Experimental Psychology, 1 9 6 7 , 7_4, ( 2 , Pt. 1 ) 3 0 2 - 3 0 4 . Hovland, C. I,, & Weiss, W. Transmission of information concerning concepts through positive and negative instances. Journal of Experimental Psychology. 1 9 5 3 , 4_5_, 1 6 5 - 182. Hunt, E. B., & Kreuter, J. M, The development of decision trees i n concept learning. I I I . Learning the connectives. Los Angeles, Western Management Sciences Institute, 1 9 6 2 , 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 . Canadian J o u r n a l o f P s y c h o l o g y . I966, 20, (2), 198 - 207. K v a l e , S. "Unconsc ious p roce s se s " i n concept f o r m a t i o n : An e m p i r i c a l f a c t o r a t h e o r e t i c a l c o n s t r u c t i o n ? 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 . J o u r n a l o f V e r b a l  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 two . P s y c h o l o g i c a l  Review. 1956, 63_, 81 - 97. N e i s s e r , 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 , J o u r n a l o f  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 . The r o l e o f age and i n t e l l i g e n c e i n concept a t t a i n m e n t by i n d u c t i o n . J o u r n a l o f E x p e r i -mental P s y c h o l o g y . 196l, 62, 1 - 8 , Rommetveit , R, Stages 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 -t i o n i n g . Scand inav ian J o u r n a l o f P s y c h o l o g y , i960, I , 115 - 124. Rommetveit , R. 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, Stages i n concept f o r m a t i o n . I I . 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 the concept and o f s t i m u l u s p r e d i f f e r e n t i a t i o n . Scand inav ian 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 . I I I . F u r t h e r i n q u i r i e s i n t o the 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 , Scan-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, 65 - 74. (a) Rommetveit, R,, & Kvale, S, Stages i n concept formation, IV, A temporal analysis of effects of an extra intention to verbalize, Scandinavian  Journal of Psychology. I965, 6, 75 - 79. (b) Shepard, R. N,, Hovland, C, I., & Jenkins, H. M. Learning and memory of classi f i c a t i o n s . Psychological Monographs, I96I, 7J3, (13, Whole No. 517). Smith, S. L. Concept formationt Stimulus dimensions in human learning. Unpublished doctoral dissertation, Massachusetts Institute of Tech-nology, 1954, 02139. Wallach, Lise. The complexity of concept attainment. American Journal of  Psychology. 1962, 7_5_, (2) 277 - 283. Wells, H, Effects of transfer and problem/structure i n disjunction concept formation. Journal of Experimental Psychology, 1963, 65_, 63 - 69. Winer, B. S t a t i s t i c a l Principles in Experimental Design. Toronto: McGraw -H i l l , 1962. 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 con-trol 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 trip 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 trip mechanism of the following card when i t reached the centre of the window. The response feedback was provided by a movable trip lever located in the centre of each card holder. This lever could be placed in 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 trip mechanism on each card. Positioning of the trip 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 non-exemplar 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, its trip 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 is a learning program designed to teach you to classify a set of cards into two categories. Look at the sixteen cards in front of you and notice that no two cards are exactly the same. Each of the cards has four characteristics; (l) the SHAPE of its figures, (2) the NUMBER of its figures, (3) the SIZE of its figures, and (4) the COLOR of its figures. Notice that each characteristic can occur in one of two different forms; that i s , the SHAPE of figures can occur either in the form of Circles or in the form of Triangles; the NUMBER of figures can occur either in the form of One figure on a card or Two figures on a card; the SIZE of figures can occur either in the form of Large figures or Small figures; and the COLOR of figures can occur either in 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 will appear in 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 is to learn what the diff-erences are between the two categories, so that you will be able to class-ify each of the cards correctly by telling the experimenter which category you think each card appearing in the window belongs in, 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 will be told in the instructions for each problem how many of the four characteristics i t is necessary to consider to solve the problem. While each card has four characteristics, some of the characteristics, though they may differ across cards, will 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 will 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 in 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 charac-teristics you will have to include in 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 in the window and t e l l the experimenter which category you think the card belongs in. You will have to guess for the fi 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 will appear. Your goal is to learn to classify a single set of cards correctly. Do not waste time trying to memorize the order in which the cards appear, for there is more than one set in 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 separ-ates 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 character-istics to help you learn to classify the cards correctly. Problem Two (Complete learning condition) PROBLEM TWO This problem will involve one important characteristic which sep-arates 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 of the number of important c h a r a c t e r i s t i c s and the example card to help you learn to c l a s s i f y the cards c o r r e c t l y . REMEMBER - Only the one important c h a r a c t e r i s t i c i s used to separate the cards i n t o two categories. Problem Two (Rule l e a r n i n g condition) PROBLEM TWO This problem w i l l involve one important c h a r a c t e r i s t i c , the NUMBER of f i g u r e s , which separates the cards i n t o two categories. This time the two categories are "G" and " H " , and the example card i s a member of the "G" category. Use your knowledge of the important c h a r a c t e r i s t i c and the example card to help you lea r n which form of the important c h a r a c t e r i s t i c i s associated with each category, so that you w i l l be able to c l a s s i f y the cards c o r r e c t l y . REMEMBER - Only the one important c h a r a c t e r i s t i c , NUMBER i s used to separate the cards i n t o two categories. 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 This problem w i l l involve one important c h a r a c t e r i s t i c which separates the cards i n t o two categories. This time the two categories are "G" and "H", and the example card i s a member of the "G" category. The r u l e a p p l i e d to t h i s c h a r a c t e r i s t i c i s : I f the oard shows the presence of or.e form of the important c h a r a c t e r i s t i c i t i s a "G", but i f the card shows the presence of the other form i t i s an " H " . For exarple, i f c o l o r were the important 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 is used to separate the cards into two categories, and the defining rule is 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 difficult problems, look again at the sixteen cards in front of you. Notice that each of the cards has four characteristics; (l) the SHAPE of its figures, (2) the NUMBER of its figures, (3) the SIZE of its figures, and (4) the COLOR of its figures. Notice also that each characteristic can occur in one of two different forms; that i s , the SHAPE characteristic can occur either in the form of Circles or in the form of Triangles; the NUMBER characteristic can occur either in the form of One figure on a card or Two figures on a card; the SIZE characteristic can occur either in the form of Large figures or Small figures; and the COLOR characteristic can occur either in 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 will be fi r s t , to note from the information about the number of important characteristics given in 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 partic- ular 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 in 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 difficult 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 will 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 will notice that the cards are exactly the same (0 differences). If you compare the example card with cards B, C, D, and E you will 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 is a Circle, while card C is a Triangle; the SIZE of figures for card D, the example figure is Large, while the card D figure is Small; and the COLOR of figures for card E, the example is Red, and card E is Blue. In like manner, i f you compare the example card with each of the cards in the "2 DIFFERENCES" category, you will 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 will notice that each card is 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 will 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 is a Circle and card P is a Triangle; and COLOR, the example is Red and card P is 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 will appear in the window, your task will be to f i r s t , note from the information about the number of important char-acteristics given in the instructions for each problem, how many character-istics 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 in the window for the important  characteristics only, and learn which total numbers of important differ-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 in 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 will involve two important characteristics which separate the cards into two categories. The two categories are "P" and "Q", and the example card is 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 will 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 will involve two important characteristics which separate the cards into two categories. The two categories are "P" and "Q", and the example card is 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 cat-egory "P" and the total number of important differences associated with category "Q", so that you will 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 will 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 is 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 will 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 will 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 is 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 will 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 will involve two important characteristics which separate the cards into two categories. The two categories are "P" and "Q", and the example card is a member of the "P" category. The rule which is applied to the two important characteristics to separate the cards into two cat-egories is: 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 character-istics and which forms of these characteristics are associated with each of the two categories, so that you will be able to classify the cards cor-rectly, REMEMBER - Only the two important characteristics are used to separate the cards into two categories, and the defining rule is applied only to these two characteristics. Problem Three (Attribute identification - Inter-stimuli condition) PROBLEM THREE This problem will involve two important characteristics which separate the cards into two categories. The two categories are "P" and "Q", and the example card is a member of the "P" category. The defining rule which is 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 exam-ple 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 will be able to classify the cards correctly, REMEMBER - Only the two important characteristics separate the cards into two categories, and the defining rule is applied only to these two characteristics. Problem Four (Complete learning - Intra-stimuli condition) PROBLEM FOUR This problem will involve three important characteristics which sep-arate the cards into two categories. The two categories are "X" and "Y", and the example card is 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 character-istics are associated with the "X" category, and which forms are associated with the "Y" category, so that you will 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 will involve three important characteristics which sep-arate the cards into two categories. The two categories are "X" and "Y", and the example card is 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 will 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 will 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 is 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 will 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 will 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 will be "X" and "Y", and the example card is 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 will 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 will involve three important characteristics which separate the cards into two categories. The two categories are "X" and "Y", and the example card is a member of the "X" category. The rule which is applied to the three important characteristics to separate the cards into their two categories i s : All 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 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 (red) nor (circular) OR (SMALL) AND either (red) and (triangular) or neither (red) nor (triangular) would be members of the "X" category. 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 ass-ociated with each of the two categories, so that you will be able to class-ify the cards correctly, REMEMBER - Only three characteristics separate the cards into two categories, and the defining rule is applied only to these three character-istics. Problem Four (Attribute identification - Inter-stimuli condition) PROBLEM FOUR This problem will involve three important characteristics which separate the cards into two categories. The two categories are "X" and "Y", and the example card is a member of the "X" category. The rule which is 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 impor-tant 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 will be able to classify the cards correctly, REMEMBER - Only three characteristics separate the cards into two categories, and the defining rule is applied only to these three character-istics. 

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