Abstract
Much of the material provided in science courses consists of sample solutions to problems. This study is concerned with how such structured material is understood, what is earmarked for storage, what remains stored and how useful this is for later ability to recreate the problem solution.
Understanding was assumed to be the result of a cognitive process in which information about the material understood is stored in memory. Twelve S's were required to “think aloud” as they understood three problem solutions: the solution of the Missionaries and Cannibals problem, a geometry proof, and a plan for another geometry proof. Each solution was presented step by step as requested by S. Immediately after he had understood the solution S was asked to recall the “outstanding points.” A week later he was asked to repeat the recall and to reproduce the solution.
A hand coding of the “thinking aloud” protocol was analysed by a computer programme. Patterns detected by the programme suggest that the understanding process of an S has some consistency for different tasks. An analysis of the recalls of outstanding points showed that the kinds of points best retained were the context of the problems and subproblems within the solution. In the Missionaries and Cannibals task subproblems were positions reached. S's who recalled positions rather than moves reproduced the solution faster. In the geometry tasks the subproblems were steps with two or more premises. S's who recalled more of these reproduced the solution faster. In the geometry proof these S's had more adequately processed these steps when they were attempting to understand the solution. The importance of the S's method for deciding when he understands is suggested.
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For many of the ideas presented in this paper I am indebted to Dr. H. Clark, Dr. B. F. Green, Dr. L. W. Gregg, Dr. R. J. Hays and in particular Professor H. A. Simon. The research was carried out at Carnegie-Mellon University, under grants from the Science Research Council of Great Britain and the National Institute of Mental Health of the U.S.A. (MH-07722).
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Brée, D.S. Understanding of structured problem solutions. Instr Sci 3, 327–350 (1975). https://doi.org/10.1007/BF00051900
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DOI: https://doi.org/10.1007/BF00051900