Transitivity judgments, memory for premises, and models of children's reasoning*1

Abstract

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. Ever since the Greeks defined humankind as "the rational animal," the capacity for reasoning has been esteemed as a distinctive feature of human intelligence. In its broadest sense, "reasoning" refers to the explicit consideration of the reasons that can be adduced for believing, doing, or valuing one thing over another (Rescher, 1988). As such, it serves the related functions of decision making and ofjustifying the decisions which

The case for a dual-process theory of transitive reasoning

“…Indeed, it would also seem at odds with the vast literature on transitivity in non-human participants (e.g., Bond et al, 2003;MacLean et al, 2008;Vasconcelos, 2008;Wynne, 1998). On memory dependence versus independence in children, Chapman and Lindenberger (1992) found that older child groups exhibit better premise retention alongside better reasoning; and that within any age group, those participants better at retaining premises tend to exhibit better reasoning. This is in line with Trabasso's (1977) early conception of reasoning being highly dependent on memory.…”

Life Span Theory in Developmental Psychology

“…Generally, working memory denotes the ability to preserve information in one or more short-term stores while simultaneously transforming the same or some other information (Baddeley, 2000;Just et al, 1996). Age differences in working memory have been invoked as a possible cause for intellectual growth during childhood (Case, 1985;Chapman & Lindenberger, 1992;Halford, 1993;Pascual-Leone, 1970), and for age-based decrements during adulthood and old age (Craik, 1983;Oberauer & Kliegl, 2001). With respect to childhood, Neo-Piagetian theorists have argued that changes in working memory are among the primary pacemakers of intellectual child development (e.g., Pascual-Leone, 1970).…”

Constructing an understanding of mind: The development of children's social understanding within social interaction

“…Chapman employed the notion of the epistemic triangle to describe the role of social interaction in the development of knowledge in the area of children's reasoning on concrete operational tasks (Carpendale 1999a;Chapman & Lindenberger 1992). We take it to be the lowest common denominator for understanding development in general and it is equally applicable to children's reasoning regarding social matters.…”

“…This epistemic, or "knowing," triangle preserves the insights of Piaget and Vygotsky and facilitates thinking about how social interaction and subject-object experience can be reconciled in development. The epistemic triangle has much in common with Hobson's (1994; notion of a "relatedness triangle," except that the latter focuses almost exclusively on affective engagement, particularly in infancy.Chapman employed the notion of the epistemic triangle to describe the role of social interaction in the development of knowledge in the area of children's reasoning on concrete operational tasks (Carpendale 1999a;Chapman & Lindenberger 1992). We take it to be the lowest common denominator for understanding development in general and it is equally applicable to children's reasoning regarding social matters.…”