Different developmental patterns of simple deductive and probabilistic inferential reasoning.

In three studies, we examined simple counterexample-based and probabilistic reasoning in children 6, 7, and 9 years of age. In the first study, participants were asked to make conditional (if-then) inferences under both categorical (certain or uncertain) and probabilistic instructions. Results showed that 6-year-olds respond to both forms of inference in similar ways, but whereas probabilistic conditional inferences showed little development over this period, categorical inferences clearly improved between 6 and 7 years of age. An analysis of the children's justifications indicated that performance under categorical instructions was strongly related to counterexample generation at all ages, whereas this was true only for the younger children for inferences under probabilistic instructions. These findings were replicated in a second study, using problems that referred to concrete stimuli with varying probabilities of inference. A third study tested the hypothesis that children confused probability judgments with judgments of confidence and demonstrated a clear dissociation between these two constructs. Overall, these results show that children are capable of accurate conditional inferences under probabilistic instructions at a very early age and that the differentiation between categorical and probabilistic conditional reasoning is clear by at least 9 years ofage. These results are globally consistent with dual-process theories but suggest some difficulties for the way that the analytic-heuristic distinction underlying these theories has been conceptualized.