Fuzzy Application on Rule Space Approach and Graphic Knowledge Structure Representation for Equality Axiom Concepts

The purpose of this study is to provide an integrated methodology of fuzzy approach on rule space and graphic knowledge structure analysis. The authors adopt fuzzy c-means based on the information of latent trait and standardized caution index of students, which are from item response theory (IRT) and S-P chart respectively. This method is similar to the utility of rule space, which is provided Tatsuoka, but it is fuzzy clustering in this study. Another characteristic of this study is the graphic representation on knowledge structure by fuzzy structural modeling (FSM) and it is an individualized knowledge structure analysis. The clustering results and individualized knowledge structure analysis could provide important information for remedial instruction.