Transitivity Judgments, Memory for Premises, and Models of Children’s Reasoning

A distributional model of the relation between judgments on transitivity tasks and memory for premise comparisons is proposed, according to which a total population of children solving a transitivity task can be divided into two subpopulations: (a) The operational subpopulation consists of all children who infer their transitivity judgments (e.g., stick A is longer than stick C) from a composition of premise relations (A is longer than B and B is longer than C); (b) the nonoperational subpopulation consists of all children who infer their transitivity judgments in some other way. In the operational subpopulation, memory for premises should be accurate (because operational composition of premise comparisons depends on the retention of those premises), and transitivity judgments should be correct (because operational composition leads to a correct judgment “by necessity”). In the nonoperational subpopulation, memory for premises should be stochastically independent of transitivity judgments. The assumptions of this distributional model are tested against data on transitive reasoning in 120 first, second, and third graders and found to be reasonable. From the distributional model, an equation is derived allowing the researcher to compute the minimum proportion of operational reasoners required to reject the null hypothesis of independence between judgments and memory in a sample drawn from a mixed (nonoperational + operational) population. Reports of reasoning-remembering independence in previous studies are reinterpreted in light of the present findings.