A Novel Hybrid Student Model for Personalized Education - Advances in Personalized Web-Based Education - page 67

The results of the application of the particular fuzzy rules update the overlay
model of the hybrid student model.
3.3.2 Overlay Model
One of the most popular and common used student models is the overlay model.
It was invented by Stansfield et al. (1976) and has been used in many systems ever
since. The main assumption underlying the overlay model is that a student may
have incomplete but correct knowledge of the domain. Therefore, according to the
overlay modeling, the student model is a subset of the domain model (Martins et al.
2008; Vélez et al. 2008), which reflects the expert-level knowledge of the subject
(Brusilovsky and Millán 2007; Liu and Wang 2007). The differences between the
student's and the expert's set of knowledge are believed to be the student's lack
of skills and knowledge, and the instructional objective is to eliminate these dif-
ferences as much as possible (Bontcheva and Wilks 2005; Michaud and McCoy
2004; Staff 2001). Consequently, the domain is decomposed into a set of ele-
ments and the overlay model is simply a set of masteries over those elements
(Nguyen and Do 2008). The pure overlay model assigns a Boolean value, yes
or no, to each element, indicated whether the student knows or does not know
this element, while in its modern form, an overlay model represents the degree
to which the user knows such a domain element by using a qualitative measure
(good-average-poor) or a quantitative measure such as the probability that the
student knows the concept (Brusilovsky and Millán 2007).
A fuzzy-weighted qualitative overlay model is used in the presented hybrid
student model. A qualitative weighted overlay model is an extension of the pure
overlay model that can distinguish several levels of student's knowledge about
each concept representing user knowledge of a concept as a qualitative value
(Brusilovsky and Anderson 1998; Papanikolaou et al. 2003). In the presented
novel hybrid student model, the overlay model uses qualitative values, like
('unknown', 'insufficiently known', 'known', 'learned'), which corresponds to the
fuzzy sets. Furthermore, it uses a set of fuzzy values ( µ FS 1 , µ FS 2 , µ FS 3 , ... , µ FS N ) ,
which expresses the degree in which each of the above fuzzy sets (qualitative
values) are active. For example, if ('unknown', 'insufficiently known', 'known',
'learned') are the qualitative values and (0, 0.3, 0.6, 0.1) is the fuzzy values that
characterize the concept C 1 in the overlay model, then it means that the particular
concept is 30 % 'insufficiently known', 60 % 'known' and 10 % 'learned'. That
is the reason for the name 'fuzzy-weighted qualitative overlay model'.
Figure 3.3 depicts an example of the presented fuzzy-weighted qualitative
overlay model. The concepts, which are colored green, belong to the subset of
the domain model that the learner knows or has assimilated. The presented fuzzy-
weighted qualitative overlay model is used to model the variations of the learner's
knowledge level. Particularly, it is used to inform the system which domain