Application of Fuzzy Clustering and FSM to Represent Graphic Concept Structures on Assessment Database

Abstract

The purpose of this study was to apply the fuzzy structural modeling (FSM) in analyzing the concept structures of algebra for 4-graders. The authors utilized the response data of 4-graders in 2007 from Taiwan Assessment of Student Achievement. After the calibrating of equating, the distributing of the abilities of task-takers was clustered into 4 groups with the method of fuzzy clustering analysis. The authors chose the vector center for sample from each group, drew the individual concept structure graphs, and analyzed the hierarchical structures of Algebra concepts. Under the frame of IRT, the study showed the structural characteristics of Algebra concepts from Taiwan pupils. Moreover, the FSM graphs of the task-takers in each group had been analyzed and compared their differences.