Subject materials can be viewed as a tree diagram comprising chapters, sections, sub-sections
and key concepts to be learned (see Fig. 1). This approach offers an overall cognition of the
subject contents, but additional information is required to diagnose student learning status. For
example, if a student fails to learn the concept ‘‘common divisor’’, this may be because he/she did
not learn the concept ‘‘factors’’ well. In this case, we would suggest that the student study ‘‘factors’’ more thoroughly before attempting ‘‘common divisor’’. That is, when the relationships
among those concepts are identified, it is possible to determine the learning problems of individual
students and provide suggestions.