**7. Conclusion and perspective**

We also find how each node contributes with respect to the set of nodes in front of it. In this evaluation, the marginal improvement of the node "Learning Activity" mean that the influence of this node is larger compared to the target node. We also notice that even if the marginal cost of the two different sensors is the same, the sensor that is the most evolved reflects the marginal

All this reflects that the success of a learner in the learning situation pertains his success in the

We validated each node of our learner model Bayesian network, and present in this section

Figure 13 presents the entire Bayesian network validation results. In this evaluation of our network, we consider that the learner has successfully passed the pretest and the learning situation. The marginal variable of the node evaluation is 79.71 % in this case. A change in one of these two nodes will affect the marginal variables of our network in a probabilistic manner.

Based on the results and validation of each node of the Bayesian network, we were able to

When a learner begins to take a course in an adaptive hypermedia system, he must first successfully pass the functional requirement "Pretest", which is composed of two functional requirements that measure the learner's knowledge and skills in the chosen field. After validation of the pretest, the learner is automatically assigned to the functional requirement "Learning Activity", which is composed of two types, static and dynamic. At the end of the

cost of the variables of the node "Learning Activity".

184 E-Learning - Instructional Design, Organizational Strategy and Management

**Figure 12.** The evaluation results of the node Learner

**6.2. Bayesian network evaluation**

learning activity more than in the assessment or pretest.

the validation results of the entire Bayesian network.

manage the operation of the network in a comprehensive manner.

We have shown how from a theoretical point of view and considering the analysis of the literature, it seems justified to select Bayesian networks as an effective tool to manage the learner model. The use of Bayesian networks to formally manage the problem of uncertainty in the learner model in an adaptive educational system gives us satisfactory results to address the problem of probabilistic and real-time management of all of a learner's actions in a learning situation.

The experiments presented in this article are arguments in favor of our hypothesis on the modeling of the learner model in a probabilistic way, using all the nodes as sensors to measure and evaluate the entire model.

The proposed rules for processing use case diagrams that schematize the actions of a learner in an adaptive system can be applied to many use cases in different systems.

We see two main directions in which to continue this work; on the one hand, by combining Bayesian networks with other modeling methods of the learner, such as overlay models; and on the other hand, by transforming the Bayesian networks developed for the management of the learner model into a machine-readable language, such as ontologies. Or, as we already proposed [11], by using probabilistic ontologies as a formalism that gives us the possibility to combine Bayesian networks with ontologies.
