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(for example, in Fig.
2.10
the domain concept C
3
is delivered to the learner
before the domain concept C
5
); “part-of” that declares that a concept belongs to
another concept (for example, in Fig.
2.10
the domain concept C
2
in includes the
domain concepts C
10
, C
11
and C
12
); the dependence relation that declares that the
knowledge level of a domain concept is affected by the learner's knowledge level
on another related concept (For example, in Fig.
2.10
the knowledge level of the
domain concepts C
14
, C
8
and C
9
is affected by the learner's knowledge level on
the concept C
15
).
The dependence relations allow the tutoring system to identify how the knowl-
edge level of a concept is affected by the learner's knowledge level on other
related concepts. A dependence relation is characterized by the symbol '
+
' or the
symbol '
−
' and a number (strength of impact). The symbol depicts the order in
which the two related concepts are delivered to the learner. If the symbol '
+
' is
labeled on the arc that connects Ci
i
with C
j
with direction from Ci
i
to C
j
(C
i
ₒ
C
j
),
then it denotes that Ci
i
is taught before Ci
j
. Otherwise, if the symbol that is labeled
on the particular directed arc is the symbol '
−
', then it denoted that that C
j
is
taught before Ci.
i
. The numbers that are labeled on the directed arcs depict the
degree at which the knowledge level of a domain concept is affected regarding
the knowledge level of its related domain concepts. In other words, they depict
the “strength of impact” of a domain concept on a related concept. The particu-
lar numbers are only positive. This is happened due to the fact that the increase
of the knowledge level of a domain concept leads to the increase of the knowl-
edge level of a depended domain concept, and the decrease of the knowledge level
of a domain concept leads to the decrease of the knowledge level of a depended
domain concept. Therefore, the numbers of the directed arcs that depict the
knowledge dependencies belong to the interval (0, 1]. For example, in Fig.
2.10
,
the value '
+
0.8' that is labeled on the directed arc, which connects C
10
with
C
13
(C
10
ₒ
C
13
), denotes that the concept C
10
is delivered to the learner before
the concept C
13
and the “strength of impact” of C
10
on C
13
is 0.8. Similarly, the
value '
−
0.72' that is labeled on the directed arc, which connects C
15
with C
14
(C
15
ₒ
C
14
), denotes that the concept C
15
is delivered to the learner after the
concept C
14
and the “strength of impact” of C
15
to C
14
is 0.72.
The arcs in the FR-CN, which represent the domain concepts' dependencies
of the knowledge domain, are bidirectional. Furthermore, the value of the arc
C
i
ₒ
C
j
is not essentially equal to the value of the arc Ci
j
ₒ
C
i
. This is hap-
pened due to the fact that changes on the knowledge level of Ci
i
may affect the
knowledge level of Ci.
j
in a different degree than changes on the knowledge level
of C
j
affect the knowledge level of Ci.
i
. It has to be clear that the value 1 on the
directed arc that connects two dependent domain concepts does not mean that
the two dependent concepts are the same. It implies that if a learner knows a
domain concept of a section, s/he may know a related concept of another sec-
tion at the same degree. The percentage of increase or decrease of the knowledge
level of a domain concept that occurs due to changes on the knowledge level of
another concept related with this domain concept is defined by experts of the
knowledge domain.
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