Knowing about guessing and guessing about knowing: preschoolers' understanding of indeterminacy.

In this article we investigate preschool children's understanding of indeterminacy by examining their ability to distinguish between determinate situations--in which the available evidence eliminates all uncertainty about an outcome--and indeterminate situations--in which it does not. We argue that a full understanding of indeterminacy requires the coordination of 3 processes: search, evaluation, and mapping. We describe 3 experiments aimed at discovering the extent to which these processes, each of which has been implicated in previous accounts of indeterminate reasoning, are developed in preschoolers and the extent to which different children organize the processes into different strategies. Experiment 1 examines 5-year-olds' performance on 1- versus 2-solution problems having different configurations of irrelevant information. Experiments 2 and 3 extend the possible sources of indeterminacy from 2 to 4 and vary the amount of consistent, inconsistent, and to-be-discovered evidence. Our results show that 4- and 5-year-old children readily give "Can tell" responses to determinate problems, as well as "Can't tell" responses when they think that the evidence warrants such a response. In addition, we report 2 new findings: (a) different children use different strategies to process determinate evidence, and these strategies, in turn, predict their performance on indeterminate problems; (b) evidence patterns in which a single positive instance is contrasted with 1 or more negative or unknown instances are particularly difficult to resolve. Many children use a decision rule--the Positive Capture rule--that produces consistent errors on this type of problem.