![](bg2.png)
performance based policy and predictor, in Section 6
the experimental results and least the conclusions.
2 RELATED WORK
Many Machine Learning techniques have been used
to ameliorate ITS, especially in order to extend learn-
ing potential for students and reduce engineering ef-
forts for designing the ITS. The most used technol-
ogy for sequencing is Reinforcement Learning (RL),
which computes the best sequence trying to maximize
a previously defined reward function. Both model–
free and model–based (Malpani et al., 2011; Beck
et al., 2000) RL were tested for content sequenc-
ing. Unfortunately, the model–based RL necessitates
of a special kind of data sets called exploratory cor-
pus. Available data sets are log files of ITS which
have a fixed sequencing policy that teachers designed
to grant learning. They explore a small part of the
state–action space and yield to biased or limited in-
formation. For instance, since a novice student will
never see an exercise of expert level, it is impossible
to retrieve the probability of a novice student solv-
ing some contents. Without these probabilities the
RL model cannot be built (Chi et al., 2011). Model–
free RL, instead, assumes a high availability of stu-
dents on which one can perform an on-line training.
The model does not require an exploratory corpus but
needs to be built while the users are playing with the
designed system. Given the high cost of an exper-
iment with humans, most authors exploit simulated
single skill students based on different technologies
like Artificial Neural Networks or self developed stu-
dent models (Sarma and Ravindran, 2007; Malpani
et al., 2011). Particularly similar to our approach is
(Malpani et al., 2011), where contents are sequenced
with a particular model–free RL based on the actor
critic algorithm (Konda and Tsitsiklis, 2000), which
was selected because of its faster convergence in com-
parison with the classic Q–Learning algorithm (Sut-
ton and Barto, 1998). Unfortunately, RL algorithms
still need many episodes to converge and will always
need preliminary trainings on simulated students.
Our developed content sequencer is based on stu-
dent performance predictions. An example of state of
the art method is Bayesian Knowledge Tracing (BKT)
and its extensions. The algorithm is built on a given
prior knowledge of the students and a data set of bi-
nary student performances. It is assumed that there
is a hidden state representing the knowledge of a stu-
dent and an observed state given by the recorded per-
formances. The model learned is composed by slip,
guess, learning and not learning probability, which
are then used to compute the predicted performances
(Corbett and Anderson, 1994). In the BKT exten-
sions also difficulty, multiple skill levels and person-
alization are taken into account separately (Wang and
Heffernan, 2012; Pardos and Heffernan, 2010; Par-
dos and Heffernan, 2011; D Baker et al., 2008). BKT
researchers have discussed the problem of sequenc-
ing both in single and in multiple skill environment in
(Koedinger et al., 2011). In a single skill environment
the most not mastered skill is selected, whereas in the
multiple skill this behavior would present a too dif-
ficult content sequence. Consequently, the contents
with a small number of not mastered skills are se-
lected. Moreover, (Koedinger et al., 2011) point out
how in ITS multiple skill exercises are modeled as
single skill ones in order to overcome BKT limita-
tions. We would like to stress that the sequencing
requires an internal skills representation and conse-
quently, together with the performance prediction al-
gorithm, is domain dependent.
Another domain dependent algorithm used for
performance prediction is the Performance Factors
Analysis (PFM). In the latter the probability of learn-
ing is computed using the previous number of failures
and successes, i.e. the representation of score is bi-
nary like in BKT (Pavlik et al., 2009). Moreover, sim-
ilarly to BKT, a table connecting contents and skills is
required.
Matrix Factorization (MF) is the algorithm used
in this paper for performance prediction. It has many
applications like, for instance, dimensionality reduc-
tion, clustering and also classification (Cichocki et al.,
2009). The most common use is for Recommender
Systems (Koren et al., 2009) and recently this con-
cept was extended to ITS (Thai-Nghe et al., 2011).
We selected this algorithm for several reasons:
1. Domain independence. Ability to model each
skill, i.e. no engineering/authoring effort in in-
dividuating the skills involved in the contents.
2. Having comparable results with BKT latest im-
plementations (Thai-Nghe et al., 2012).
3. Possibility to build the system with a common
data set, i.e. without an exploratory corpus.
4. Small computational time on a 3rd Gen Ci5/4GB
laptop and Java implementation: 0.43 s for build-
ing the model with already 122000 lines, negligi-
ble time for performance prediction.
3 CONTENT SEQUENCING IN
ITS
The designed system consists of two main blocks.
The first one is the environment and is represented by
CSEDU2014-6thInternationalConferenceonComputerSupportedEducation
26