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backgrounds. Examples of such backgrounds are physics, mathematics, computer
science, education, human and social science.
At the beginning, all learners were considered to be novices. At the next inter-
actions, the system delivered to them the appropriate learning material for each
individual student's needs by adapting instantly to the learner's individual learning
pace. The system's adaptation decisions were based on the values of the student
model. The student model is updated each time the learner interacts with the system
and takes a test. There were two kinds of tests: (1) the tests that corresponded to
each individual domain concept of the learning material (practice tests), (2) the
final tests that corresponded to the sections of the learning material (they included
exercises of a variety of domain concepts). In particular, each time the learner read
a domain concept (Ci),
i
), s/he had to complete a corresponding practice test. When,
the learner had completed successfully (
μ
A
(C
i
)
=
1 or
μ
A
(C
i
)
+
μ
L
(C
i
)
=
1)
all the practice tests of the domain concepts of a section (e.g. iterations with
concrete number of loops, arrays, sub-programming), then s/he had to com-
plete the final test of the section. If s/he succeeded to the final test (
μ
A
(C
i
)
=
1
or
μ
A
(C
i
)
+
μ
L
(C
i
)
=
1 for all the concept Ci
i
of the particular section), then
s/he transited to a next section. Otherwise, s/he had advised to revise some domain
concepts. Representative examples of the system's implementation follow.
Example 1
Elena's current student model has the following values: KL
=
3,
ErrTyp
=
“prone to syntax errors”, PrK
=
“none”. The value KL
=
3 comes off
her current overlay model (Table
3.3
, column 'before'). ErrTyp is “prone to syn-
tax errors” due to the fact that she had made usually errors that concern anagram-
matism of commands' names or invalid symbolisms of operands or commands'
names. Also, PrK
=
“none” indicates that Elena does not have previous knowledge
on computer programming.
She is examining in C
4.2
: “calculating sum in a 'for' loop” and is succeeding 92 %.
So, the quintet, which describes Elena's knowledge level on C
4.2
, is (0, 0, 0, 0, 1).
However, according to the “strength of impact” of the knowledge dependencies that
45 % the concept C
4.3
, 81 % the concept C
4.4
, 100 % the concept C
5.2
, 45 % the con-
cept C
5.3
, and 39 % the concept C
5.4
.
According to the rule R2 (d) over the fuzzy sets (Fig.
3.6
) the following occur
(Table
3.3
, column 'after—interaction I'):
•
μ
A
(C
4.3
)
=
0.45 and it remains 55 % 'Unknown' (
μ
Un
(C
4.3
)
=
0.55) So, the
quintet for C
4.3
is (0.55, 0, 0, 0, 0.45).
•
μ
A
(C
4.4
)
=
0.81 and it remains 19 % 'Unknown' (
μ
Un
(C
4.4
)
=
0.19) So, the
quintet for C
4.4
is (0.19, 0, 0, 0, 0.81).
•
μ
A
(C
5.2
)
=
1. So, the quintet for C
5.4
is (0, 0, 0, 0, 1).
•
μ
A
(C
5.3
)
=
0.45 and it remains 55 % 'Unknown' (
μ
Un
(C
5.3
)
=
0.55) So, the quintet
for C
5.3
is (0.55, 0, 0, 0, 0.45).
•
μ
A
(C
5.4
)
=
0.52 and it remains 55 % 'Unknown' (
μ
Un
(C
5.4
)
=
0.48). So, the
quintet for C
5.4
is (0.48, 0, 0, 0, 0.52).
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