The effect of problem size on representation in deductive problem solving

Abstract

Adult Ss attempted to solve logical deductive reasoning problems that varied systematically in amount of information presented. Methods Ss employed in representing the problem were classified into five main types or modes. The proportion of Ss using a matrix mode of problem representation increased moderately with problems containing large amounts of information. The performance of Ss using a matrix mode of representation suggested that this advantage is related to ease of applying and/or storing the results of logical operations in such a problem space rather than to any facilitative effects of encoding processes. Specific limits to normal processing are hypothesized.A major component in a problem-solving task is the encoding of the problem elements and their interrelationships into a particular representation or space. This process serves to isolate the elements pertinent to solution and delimits a set of relevant operations that directs transformations of these elements (Newell, Shaw, & Simon, 1958;Greeno, 1973). Hence, a central task for investigators of human problem solving has been to define the constituent elements of a solver's problem space and the types or modes of representation employed in various situations.Schwartz (1971) reported a study that explored some modes of representation that Ss employed when a ttempting to solve several "who-done-it" type deductive reasoning problems. An example of this type of problem is presented in Table 1. The elements of these problems varied systematically on a number of dimensions or categories (e.g., spy's name, contact location, specialty, etc.), with each dimension having a number of attributes or values (e.g., Boris, Edmond, George, Irving; Peking, London, Tokyo, Paris; etc.).The Ss were presented a series of such problems and were encouraged to show all work as they attempted to solve them. The resulting protocols were then classified into five categories according to the manner in which the S represented or structured the problem information: (1) a matrix format, (2) a more general grouping mode, (3) a network or graphic representation, (4) a rewriting of the problem in sentence form, or (5) a miscellaneous category.Schwartz ( performance. Though only about 25% of the Ss employed a matrix format for representing the problem information, 75% of those doing so correctly solved the problems. This compared with solution rates varying from 25% to 50% for Ss using the other categories of problem representation. It was suggested that the effect of particular task variables on solution performance was largely a function of the degree to which they influenced the mode of representation that Ss used in structuring the problem information.The present study was designed to extend this hypothesis by investigating the influence of information q uan ti ty on representation type and solution performance. The amount of information in these tasks can be controlled systematically by varying the number of dimensions and values, as well as by varying the Table 1 Example of Dedu...

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