Some Speed, Error and Difficulty Relationships within a Problem-solving Situation

Mathematics – Probability

Scientific paper

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Scientific paper

DURING the past three years, experiments have been conducted with subjects who have been given the task of solving mental-test items of a particular type1 (Thurstone `letter-series' items). Suppose PC be the probability that a particular subject will continue to work at a particular problem for some time t before giving it up, and let PE be the probability that if a solution is recorded within this time it will be the correct one. If the universe of discourse is now restricted to correctly solved items, the probability (PS) that a particular correct solution will be returned within a period of t sec. after the moment the problem is presented will be a function both of the dynamics of the problem-solving process as such and also of PC, for if PC ≠ 1 at time t then PS must be modified, and if PC = 0, PS must be zero also. Let PS be defined as the probability which would obtain if PC = 1 for t = ∞. No comprehensive statement can be made about a person's ability to solve a problem which does not involve at least these three probabilities, that is, any attempt to measure `intelligence' by mental-test methods should involve assessments of PC, PE and PS.

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