The purpose of this study is to analyze misconceptions based on Student-Problem Chart (S-P Chart), Grey Relational Analysis (GRA), and Receiver
Operating Characteristic (ROC). Firstly, S-P Chart is used to calculate the caution index for students and the caution index for problems, which help teachers diagnose student learning conditions. Secondly, GRA is
used to calculate Gamma value for students and Gamma value for problems. Finally, ROC method is used to test and decide misconceptions of students and problems. The synthesis of the results of the S-P chart, GRA and ROC allows analyzing misconceptions based on the given conditions. In this paper, the researchers used the results of two classes in the seventh grade of the same school on a math paper test in Taiwan. The research results show that this method will be useful for teachers as well as students to improve teaching and learning process; moreover, it is not only an objective research method, but also can evaluate the comprehensive academic achievement of students, and selecting problems in the teaching process.