Traditional assessment theory is unable to provide effective information that teachers can diagnose the wrong concepts of students. Cognitive Diagnostic Assessment (CDA) focuses on the relationship between the latent knowledge structure and the response process of students and has significant outcomes. The study plans to follow the mathematics curriculum development and research provided by Asiala et al. and applies APOS theory to analyze the concept and competence indices of triangle area and trapezoidal area in elementary school. The study will use the above as base to design frame of genetic decomposition, instruction activity, and assessment framework of triangle area and trapezoidal area. After that, the study will design items, revise items, implement test, and use CDM to analyze data in order to understand the instruction effects and master proficiency of students’ concepts or skills. In addition, the study will evaluate the appropriate cognitive diagnostic model (CDM) for every item to provide interaction between concept and skill in each item. Teachers can improve the instruction by the item CDM information. In the long run, the study hopes to build effective instruction model and CDA in order to promotion and application in future.
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