The Hierarchical Structure of Formal Operational Tasks

Abstract

The hierarchical structure of the formal operational period of Piaget's theory of cognitive development was explored through the application of ordering theoretic methods to a set of data that systematically tapped the various formal operational schemes. The results suggest that the tasks within some schemes are empirically equivalent. While the response patterns were quite varied, the results do suggest that some common structure may underlie performance on the tasks, thus supporting Piaget's notion of the integrative structure of the period. Inhelder and Piaget (1958) proposed that the most advanced period of cognitive development is termed the period of formal operations, in which formal operational schemes (or operational skills) emerge concurrently and become coordinated into a structure; those schemes are necessary for an individual to solve problems in a formal operational manner. Empirical research with regard to the integrative structure of formal operations is necessary to understand this level of Piaget's theory of cognitive development.Three problems emerge from previous research into the nature of this integrative structure. First, research which focuses on intraindividual differences is scarce (Martorano, 1977). Most formal-level research has investi-APPLIED PSYCHOLOGICAL MEASUREMENT Vol. 3. No.3 Summer 1979 pp. 343-350 @ Copvright 1979 West Publishing Co.gated group performance differences. Second, studies which have focused on intraindividual performance differences have not used a method of analysis that allowed exploration of the relationships among the tasks and, thus, of the integrative nature of the stage (Jackson, 1965;Lovell, 1961;Martorano, 1977). Third, studies which have used an analysis method designed to investigate hierarchical relationships have used only a limited subset of tasks and have exhibited no systematic effort to use tasks that tap the same operational schemes (Bart & Airasian, 1974).One purpose of the present study was to investigate the hierarchical structure of formal operations through the application of ordering theoretic methods to a set of data that systematically tapped the various formal operational schemes. This would provide a more comprehensive test of the nature of the schemes and the tasks designed to measure them and would give insight into the integrative structure of the cognitive period. MethodThe data that were analyzed in the present study were collected by Martorano (1977). She administered 10 of the formal operations tasks to 4 groups of 20 6th-, 8th-, 10th-, and 12th-grade adolescents. The tasks were representative at FLORIDA INTERNATIONAL UNIV on June 2, 2015 apm.sagepub.com Downloaded from

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