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An Experimental Investigation of a Mathematical Learning Model

Best, Phillip J.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
National Science Foundation (NSF), Office of Naval Research, Cats, Learning Theories, Mathematical Models, Reinforcement


The purpose of the present study is to determine the scientific usefulness of a special case of a model derived by Audley and Jonkheere (1956). This special case of the model is a direct mathematical formulation of Thorndike's Law of Effect and is isomorphic to a model proposed by Gulliksen (1934). The model has three parameters. One parameter represents the initial probability of a correct response. The other two parameters are learning parameters. They represent the effect of a reinforcement of a correct response on the strength of a correct response and the effect of nonreinforcement of an incorrect response on the strength of an incorrect response. If simple functional relationships are found between the parameters for a group of subjects on a set of problems, then these parameters could be used to predict the performance of these subjects on new problems or of new subjects on the original problems. The model was applied to data from two experiments in which cats were trained on visual discrimination problems. In both experiments, no significant differences were found between the model and the data. The model was therefore considered to fit the data well. The high reliability and presence of a two-factor solution for the learning parameters indicate that these parameters follow simple functional transformations from one problem to another and from one cat to another. The presence of simple functional relationships indicates that the parameters obtained from the performance of a new cat on any one problem can give a good approximation of his performance on the other problems. Even though the initial performance parameters could be accounted for by a one-factor solution, the low reliability indicates that this parameter may not be useful as a predictor across cats or across problems. However, the initial performance parameter is useful within any single cat and problem. (JGL)

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