It has been advocated that pedagogical content knowledge as well as subject matter knowledge are important for improving classroom instructions. To develop pedagogical content knowledge, it is argued that understanding of students' mental representations of concepts is deemed necessary. Yet assessing and comparing mental model of each individual…

Although conventional student assessments are extremely convenient for calculating student scores, they do not conceptualize how students organize their knowledge. Therefore, teachers and students rarely understand how to improve their future learning progress. The limitations of conventional testing methods indicate the importance of accurately…