Concept structure analysis is an important issue for the knowledge management of teachers because realization concept analysis of students will help remedial instruction more feasible. This study provides the weighted polytomous ordering theory (WPOT) in the analysis concept structure. WPOT considers the weight on precondition relations between elements and it improves the limitation of dichotomous scoring of traditional ordering theory. Owing to the variation of concept structures among students, cluster analysis is needed to classify students so that homogeneity within the same group exist and the instruction design could be based on the characteristics of each group. Therefore, cluster analysis based on the information of student problem chart and item response theory is applied to process clustering. The empirical testing data of fraction addition for pupils is analyzed in this study. The results show the relationship and hierarchies among concepts in different groups vary. Finally, further suggestions and recommendations are also discussed.