VALIDATING A PRIORI INSTRUCTIONAL HIERARCHIES

The works of Gagne and his collaborators (Gagne, 1962, 1968; Gagne & Bassler, 1963; Gagne & Paradise, 1961; Gagne, Mayor, Garstens, & Paradise, 1962) represent the classic examples of research focused upon the specification and validation of hierarchical task networks. As an outgrowth of the interest in task analysis and programmed instruction which characterized the early 1960's, Gagne sought to define hierarchies of tasks which were prerequisite to the performance of various terminal objectives. These hierarchies were posited on the basis of rational analysis and sought to identify the order in which the tasks were learned. The early studies by Gagne and his associates have spawned numerous similar studies (e.g., Cox & Graham, 1966; Ford & Meyer, 1966; Kropp, Stoker, & Bashaw, 1966; Merrill, Barton, & Wood, 1970; Resnick, 1967; Walbesser, 1968; White, 1973). Crucial to the investigation of instructional hierarchies is the need to demonstrate that the hypothesized prerequisite relations among tasks in a hierarchy are confirmed by student learning data. To date, the methodological strategies used to validate hierarchical task networks have been limited by two factors. First, the hierarchies investigated generally have been non-linear in their patterns of prerequisite relationships. That is, the systems of prerequisite relations are such that a single task is often a prerequisite to two or more tasks, or, alternatively, two or more tasks are often immediately prerequisite to a single higher level task. Guttman Scalogram Analysis (Guttman, 1944, 1950) and its extensions (Lingoes, 1963), the most prevalently used methods for ordering tasks into a hierarchy, are constrained to defining only linear orders among tasks (Torgerson, 1958). Thus, Guttman-type methods cannot handle the complexities involved in validating non-linearly ordered task hierarchies (Wang, 1969). A second limitation of prior validation studies is more conceptual than methodological in nature. To date, validation studies have focused attention solely upon those prerequisite relationships posited a priori. Other, non-posited, potential prerequisite relationships among tasks in the hierarchy rarely have been subjected to analysis. To realize the richness inherent in the study of instructional hierarchies and to add rigor to hierarchy validation procedures, it is important to have methodologies which can generate the best fitting hierarchy from a data set independent of any a priori hypothesized hierarchy. Such methodologies would be both theory-generating and theory-confirming. They would be theory-generating in that they would permit data to be analyzed post hoc to determine whether and in what form prerequisite relations exist in the data. Such procedures would be especially helpful in those areas where a paucity of theory prevents a priori definition of hierarchies (Bart & Airasian, 1974). The methodologies would be theory-confirming since they could be used to define the best fitting hierarchical network among a set of tasks. This empirically derived network then could be compared to the hypothesized, a priori network to determine the correspondence between the two. Such a comparison of correspondence would afford a