Psychological Monographs: General and Applied Learning and Memorization of Classifications1

ion and the Formulation of Rules As we have just seen, the hypothesis that responses can be conditioned only to ele14 Dattman and Israel (19.il) have proposed a principle to account for Heidbreder's results that is very similar to the notion that the cue corresponding to each possible classification has a certain weight (or "salience"). According to them: "the relative ease with which concepts arc attained is directly dependent upon the degree of perceptual effectiveness with which the instances serve to present the features to be conceptualized. " This principle evidently suffers from the same lack of predictive force as the weighted-cue idea, since no objective method is proposed whereby the "perceptual effectiveness" can be measured independently of the results of the concept task itself. mentary properties (i.e., to the properties that define Type I classifications) seems to be disconfirmed by the fact that Ss can learn Type V I classifications. On the other hand, the hypothesis that responses can be conditioned to arbitrary combinations of elementary properties (such as that defining a Type V I classification) removes the predictive force of the conditioning models. Moreover, the notion that such a combination of elementary properties can itself serve directly as a cue seems implausible in view of the kinds of verbalizations actually produced by 5s. In describing a single stimulus, our 5s used words like "large," "black," etc. (in Experiment I I ) or like "candle," "trumpet," etc. (in Experiment I ) . These clearly referred to the elementary properties. For the statement that a stimulus is "black," for example, is essentially equivalent to the statement that it belongs within the group of black stimuli that are set apart by the Type I classification based upon color. In no instance was an individual stimulus described by referring to a property that would correspond in this way to the particular group of stimuli set apart by, say, a Type V I classification. Indeed, even when the stimuli are sorted out according to a Type V I classification, 5 s are unable to see the four stimuli in either class as having" any one property in common. And when (as in Experiment I) some 5s eventually do discover a way of characterizing the stimuli that go together in such a classification, they invariably do this by formulating an elaborate rule in terms of the elementary properties. As an example of a relatively simple rule, they might finally say: "The figures on the left must be black and small and triangular or else have just one of these three [Type I ] properties. " But even after discovering a rule of this kind, . 9s do not then regard it as a unitary property of a stimulus and, surely, they would not subsequently invoke it in describing a single stimulus—however completely. Outline of an alternative to the conditioning models. In view of the preceding considerations, we are led to consider that only the properties defining Type I classifications act directly as cues, and that classifications other than Type I can be learned only by conLEARNING AND MEMORIZATION OF CLASSIFICATIONS 33 structing appropriate rules for them in terms of Type I classifications. Accordingly, 6"s are no longer regarded as passively confronting one population of cues after another while a certain crucial subset becomes gradually connected to the correct response. Rather, they are regarded as actively abstracting (or attending to) dimensions, and then formulating and testing rules about how the values on those dimensions combine and interact to determine which classificatory response will be correct. The development of an explicitly detailed model for this kind of process will not be undertaken here. The present study, together with others, might serve as a useful basis for such an undertaking. But the development itself would require a further investigation implemented, perhaps, by the new tool of computer simulation (Hovland & Hunt, 1960; Newell, Shaw, & Simon, 1957; Newell & Simon, 1959). Nevertheless the tentative description of the learning process, given here only in general outline, is sufficient to lead to certain expectations about the relative difficulties of our six types of classifications as well as about how these difficulties are influenced by certain of the conditions imposed in the present experiments. The initial difficulties of the six types. I f the foregoing description of the learning process is correct, the difficulty of any given classification should be directly related to the complexity of the rules required to build it up out of Type I classifications. That these rules may be largely formulated and used at the verbal level is suggested by the high correlations, found in both Experiments I and I I , between accuracy of performance (in sorting or responding to stimuli) for each type of classification and the simplicity of the rules that could be stated by Ss for the same type of classification. Of course the rules verbalized by the ^s varied in detail from one S or occasion to another. Still, since the number of possible combinations of values increases very rapidly with the number of dimensions considered, the difficulty of a classification should increase with the number of dimensions (or Type I classifications) that are required for the specification of that classification. Thus we should at least expect the ranking I < I I < V I . Furthermore, the other types ( I I I , IV, and V) are presumably intermediate between I I and V I . For, although all three dimensions are relevant for each of these classifications, some (but not all eight) of the stimuli can be properly classified by knowing the values on just two of the three dimensions. Actually there are many different measures that could be used to express the difficulty of building up a classification out of Type I classifications. We could, for example, use the minimum length of a logic expression that defines the classification by means of conjunctions and disjunctions of the elementary properties. (We already noted in the introduction that such an expression is much longer for a Type V I than for a Type I classification.) We could also base it upon the number of relay contacts required for the physical realization of the Boolean function corresponding to the given classification (Higonnet & Grea, 1958). Or we could base it upon the average number of single-dimensional binary decisions required to place a randomly selected stimulus in the appropriate class when the sequence of decisions is made in the optimum order. But these (and many other) measures all agree with the ranking derived above in a more informal manner. In particular, they arc all consistent with the ranking I < I I — I I I ^ IV — V < V I . The only disagreements concern the predictions of ties among the intermediate types ( I I through V) . The one quantitatively defined measure that has seemed most satisfactory to us reflects the extent to which the information about the classification is distributed over the three dimensions (rather than confined to a single dimension—as in a Type I classification). In the appendix this measure is shown to lead to the ranking that corresponds most precisely with that found empirically; namely, I < I I < ( I I I , IV, V) < V I . Transfer of classificationlearning. The tentative description of the learning process in terms of abstraction and the formulation of rules also has some implications for the transfer of classification learning. In particular, if S is faced with a new classification problem that, however, he has reason to 34 R. N. SHEPARD, C. I. HOVLAND, and H, M. JENKINS believe is of the same type as several preceding problems, there is the possibility of a certain amount of positive transfer. If, for example, the problems have all been of Type I I , S might learn to proceed directly to testing rules about the interaction of values on pairs of dimensions without wasting any time in testing useless one-dimensional rules. Actually the most pronounced positive transfer was observed in the case of Type V I , and the unique degree of transfer in this case probably comes from the intervention of a somewhat different process. In particular, when S has formulated the oddeven rule, he has apparently performed an abstraction on a higher level than in the case of the simple abstraction of relevant dimensions. Indeed this higher level abstraction is most effective precisely when the abstraction of individual dimensions would preclude solution of the problem—i.e., for Type V I . The effectiveness of the odd-even rule can be appreciated by considering that >Ss who apply it with maximum efficiency need only learn the response to the first stimulus; each following stimulus then calls for that same response if and only if it has an odd number of properties in common with the first stimulus. Indeed, the one 6" in Experiment I who most completely mastered this odd-even rule (viz., Si) made altogether only one error on the last four Type V I problems. This is to be compared with the 50 errors she made during the first Type V I problem (before discovering this powerful reductive rule). This kind of consideration can be used to predict the ranking of the asymptotic difficulties of the six types: i.e., the ranking that presumably would be achieved if a sufficient number of problems of the same type were consecutively supplied. For, if S has really abstracted a rule that uniquely defines a given type of classification, the difficulty of learning a new classification of that type should be directly determined by the fraction of the 70 possible classifications that corresponds to that type. Thus Type V I should become even easier than Type I (as it did for Si) because, whereas six of the 70 possible classifications are Type I, only two are Type V I . I f S knows that he is going to have a Type I problem, he knows that only one dimension will be relevant, but he does not know which of