Children's judgments of certainty and uncertainty on a problem where the possible solutions differ in likelihood

In the present study, the authors adapted a task introduced by Piaget (1987) to assess children's appreciation of indeterminacy under conditions in which the possible solutions to a problem are not equally likely. The task involved identifying or predicting the number of chips that must be drawn from a box in order to determine its contents with certainty. Children 7 through 12 years old were presented with this task and with Pieraut-Le Bonniec's (1980) box task (a standard measure of the ability to distinguish determinate from indeterminate conditions). The tasks produced parallel developmental functions, although there was some indication that appreciating indeterminacy was easier on Piaget's problem than on the standard task. Information about likelihoods did not influence children's judgments of certainty and uncertainty. In general, recognizing that a problem is determinate precedes recognition of indeterminacy, which, in turn, precedes success at predicting the moves needed to establish certainty on a problem.