An Extension of Ordering Theory on Scoring and Its Application in Cognition Diagnosis of Capacity Concepts

Ordering theory method was used to determine existing hierarchies within a set of items. But the method is restricted to dichotomously scored items. This limitations narrow its application in many empirical data. The purpose of this study is to introduce polytomous ordering theory (POT), developed by Y. H. Lin , W. M. Bart and K. J. Huang, and apply it in the knowledge structure analysis of capacity concepts. It can be used to analyze data set not only of dichotomous items but also of polytomous items. In addition to item hierarchies, the methodology of concepts hierarchies is also an important issue. Therefore, the authors apply POT in the investigation capacity concepts for pupils. The results of data analysis will provide references for the remedial teaching and the design of teaching materials. Key-Words: capacity concepts, knowledge structure, ordering theory, polytomous items 1 Background and Motivation The ordering relationship among elements in a complex system is an important issue in many research fields. With the benefit of ordering analysis, the hierarchies and relationship could be clearly understood. Quite a few methodologies, like interpretive structural modeling, fuzzy ordering and fuzzy structural modeling, are useful method in management and engineering [13] [15] [16]. As to psychological and educational measurement, the investigation of ordering and hierarchies between items or concepts are useful in education environment [1] [17]. It is because this information could supply the remedial instruction and cognition diagnosis. Therefore, [2] provided ordering theory (OT) for dichotomous scoring items. This dichotomous method analysis could be used to identify a hierarchical organization among items. And ordering theory has its primary intent either the testing of hypothesized hierarchies among items or the determination of hierarchies among items. With the analysis of OT, the test data can be analyzed so that prescriptive and diagnostic information can be provided for teachers and researchers [2] [3]. Besides, OT is usually used as cognitive diagnosis in education and cognitive development stage validation. Proceedings of the 7th WSEAS International Conference on Simulation, Modelling and Optimization, Beijing, China, September 15-17, 2007 146