A Novel Hybrid Student Model for Personalized Education - Advances in Personalized Web-Based Education - page 89

Example 7 Anna's current student model has the following values: KL = 2,
ErrTyp = “prone to logical errors”, PrK = “Pascal”. The value KL = 2 comes off
her current overlay model (Table 3.7 , column 'before'). ErrTyp is “prone to logical
errors” due to the fact that she had made usually errors that concern the semantics
and operation of the commands. PrK = “none” indicates that Anna knows the pro-
gramming language 'Pascal'.
She is examining in C 3.2 : “if…else if” and is succeeding 72 %. So, the quin-
tet, which describes Anna's knowledge level on C 3.2 , is (0, 0, 1, 0, 0). However,
according to the “strength of impact” of the knowledge dependencies that exist
between the domain concepts of the learning material (Table 2.2 ) , C 3.2 affects
100 % the concept C 3.1 (C 3.1 affects 50 % C 3.2 ) and 64 % the concept C 3.3 .
According to the fuzzy rules (Figs. 3.6 and 3.7 ) the following occur (Table 3.7 ,
column 'after'):
• According to R8 is X 3.1 = ( 1 − 0.5 ) × 86.9 + MIN[0.5 × 86.9, 0.5 × 72] =
79.45. Therefore, μ Kn (C 3.1 ) = 0.11 and μ L (C 3.1 ) = 0.89. So, the quintet for C 4.3
is (0, 0, 0.11, 0.89, 0).
• According to R4 (a) μ Kn (C 5.4 ) = 0.64 and it remains 36 % 'Learned'
( μ L (C 5.4 ) = 0.36). So, the quintet for C 5.4 is (0, 0, 0.64, 0.36, 0).
Consequently, Anna's knowledge level has been deteriorated. Therefore, the sys-
tem does not transit Anna to another knowledge level stereotype category (KL
remains 2). It consults her to revise the above domain concepts. Furthermore,
Anna made errors concerning the equality operator. In particular, she used the
symbol “ = ” rather that “ == ”. However, the system does not consult her to revise
the corresponding domain concept. It informs her only about the particular error.
This is happened, due to the fact the value of PrK of Anna's student model is
'Pascal'. Therefore, the system infers that Anna used the symbol “ = ” for equality
operator due to confusion with her previous knowledge on Pascal.
3.7 Conclusions
In this section, a novel hybrid student model was presented. The presented student
model combines an overlay model and stereotypes with fuzzy logic techniques. In
particular, the student model is based on an overlay model, which represents the
knowledge level of a learner. The determination of the student's knowledge level
of each domain concept, as well as the updating of the student model are based
on the fuzzy logic technique that have been incorporated into the student model.
Fuzzy sets are used in order to describe how well each individual domain con-
cept is known, learned and assimilated. In addition, the student model includes a
mechanism of rules over the fuzzy sets, which is triggered after any change of the
value of the knowledge level of a domain concept and updates the values of the
knowledge level of all the related domain concepts with this.