Stochastic Models for the Learning Process

SINCE 1949 psychologists have increasingly used mathematics in the study of the learning process. Probability theory has been the keynote in these applications, and thus there is considerable unity in the published work. The applications described here are typical of those made by W. K. Estes, C. J. Burke, and their students (2, 3, 11,12,13,14,15,16,17,18,19), by G. A. Miller, F. C. Frick, and W. J. McGill (25, 26), by F. Restle (27, 28), and by R. R. Bush and F. Mosteller (1, 4, 5, 6, 7, 8, 9, 10, 23). The purpose of this paper is to give the flavor of these new developments through a few examples, rather than to survey the literature. Three experiments illustrate the use of the new mathematics to provide: (1) a summary description of the course of learning in an experiment; (2) a qualitative distinction between two theoretical positions; (3) a test of the correspondence between elements in one theory and those in the physical world. We also mention a new mathematical problem, interesting in its own right, that has arisen from these applications.

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