Determination of the ordering among seven Piagetian tasks by an ordering-theoretic method.

Abstract

This study applied a method of generating task hierarchies (ordering theory) to seven Piagetian tasks. Thirty subjects were individually administered three concrete operational and four formal operational tasks. Analysis of the response patterns on the dichotomously scored tasks revealed the following findings. First, the Piagetian theory that success on concrete operational tasks is a necessary prerequisite to success on formal operational tasks was confirmed. Second, the seven tasks were closely interrelated with an array of prerequisite relations more complex than a simple linear hierarchy. The methodology utilized appears to have value for defining nonlinear lines of implication among behavioral science phenomena.The purpose of this study was to explicate ordering theory, a measurement model which identifies necessary and sufficient performance conditions between test items or tasks, by analyzing seven Piagetian tasks. Ordering theory is an extension of Guttman (1944Guttman ( , 1950 scaling procedures in that it identifies nonlinear as well as linear hierarchies among items or tasks. Scalogram analysis is used to order a group of items or tasks into a linear hierarchy and to evaluate whether or not the hierarchy is unidimensional and cumulatively hierarchical. The degree to which a group of items or tasks is judged to be unidimensional and cumulative is determined by the extent to

Knowledge Management on Concept Structure Analysis with Weighted Polytomous Ordering Theory and Cluster Analysis

“…It is important to explore the ordering relationship and hierarchical structure among concepts of students so that the adaptive instruction design will be more effective and feasible [2] [3][4] [5]. Ordering theory (OT) was developed by Bart and Krus and it aims to find the precondition between dichotomous items [6] [7].…”

The Hierarchical Structure of Formal Operational Tasks

“…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.…”

A Structural Approach to the Validation of Hierarchical Training Sequences. Task 1. Technical Report

“…However, the validation procedures used to examine the prerequisite-skills assumption are extremely time consuming and may not be suitable for broad scale application. (Guttman, 1944), multiple scalogram analysis (Lingoes, 1963), and the ordering tneoretic method (Bart & Airasian, 1974;Bart & Krus, 1973) has been faulted on similar grounds. None of these procedures provides a suitable statistical test for prerequisite relations (Airasian, Madaus, & Woods, 1975;Dayton & Macready, 1976;White, 1974 Proctor, 1970;White & Clark, 1973).…”