Individual Differences in Speed, Accuracy and Persistence: a Mathematical Model for Problem Solving^1,2

Abstract

Traditional tests of cognitive abilities are of two main types. Some, exemplified by the Thurstone tests of primary mental abilities, include problems which span a broad range of specific types of ability. Tests of this type typically yield single scores for each of the ability types (such as verbal, numerical, spatial, or perceptual, for example), and a single, global score for what has usually been called “general ability”. Other tests, exemplified by the Raven Progressive Matrices tests, include problems which, though differing in difficulty, are essentially of a single type. Tests of this sort also tend to yield but a single global score for general ability. More often than not the cognitive test of conventional design is administered in such a manner that the individual’s score is the number of problems correctly solved within a time limit. Such scores depend in part on the choice of problems attempted, in part on the rate at which the subject works, in part on the accuracy of the subject’s responses to the problems and in part on the extent to which he abandons problems which, given greater persistence, he might well solve. Furthermore, the extent to which these different aspects of the subject’s performance influence his total score is quite unknown. Clearly, such a single score can be only an incomplete and quite inadequate summary of a very complicated problem-solving performance.