Fuzzy Logic in Student Modeling - Advances in Personalized Web-Based Education - page 33

education, the knowledge domain is described in terms of hierarchies (Virvou
et al. 2006). Also, Siddappa et al. (2009) have developed a multilevel hierarchical
model for the representation of knowledge domain of an intelligent tutoring system
for numerical method (ITNM). This multilevel hierarchical model was based on
various aptitude levels of students. An example of hierarchical representation is
depicted in Fig. 2.7 .
Hierarchies give information about the order in which the learning material
should be taught, but they do not clearly depict the relations among the domain
concepts. The network of concepts gives this kind of information. In a network of
concepts, nodes represent concepts and arcs represent relations between concepts
(Fig. 2.8 ). Many adaptive tutoring systems, such as Web-PTV (Tsiriga and Virvou
2003a, 2003b), DEPTHS (Jeremi´ et al. 2009) and IDEAL (Khamis 2011) use
a network of concepts for representing the knowledge domain. However, in a
network of concepts the relations between concepts are restricted to “part-of”,
“is-a” and prerequisite relations. They do not depict how the knowledge of a
domain concept may be affected by the knowledge of another concept. They do
not give answers to the questions: “If a student learns the concept Ci, i , which will
be her/his knowledge level of the depended domain concept C j ?”; “If the student's
knowledge of concepts Ci i improves, how will be affected her/his knowledge of the
Fig. 2.7 A hierarhical tree