**6. Results**

**• Theglobalconfusionmatrix(GCM),**computedfortheselectedtargetnodeandallthechosen

**• Probability of Correct Classification (PCC):** The probability of correct classification calculated from the global confusion matrix considering all evidence nodes in the Bayesian

**• Marginal PCC (MPCC):** The probability of correct classification calculated from the global confusion matrix considering all evidence nodes in the Bayesian network other than the one

**• Marginal Improvement (MI):** The probability of correct classification calculated from the global confusion matrix considering all evidence nodes in the Bayesian network and gained

**• Individual PCC (IPCC):** The probability of correct classification computed from the LCM

Before presenting the evaluation results of each node of our Bayesian network modeling the learner model in an adaptive system, we begin by presenting the combined Bayesian network

Figure 8 provides a map of the combined network, in which marginal variables of each node of our network are developed. We can observe the change in the marginal variables of each node in our network, simply by changing one or more marginal variable of one or more parent nodes

**• Cost Rate:** The individual probability of correct classification over the cost ratio.

by adding the node presented in the row to the rest of other nodes.

considering only the evidence presented in the row.

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

**5.3. The combined Bayesian network**

**Figure 8.** The combined Bayesian network of the learner model

through the UnBBayes software.

of the selected node.

evidence nodes.

presented in the row.

network.

In this section, we present all the results of our experiments on our Bayesian network.

#### **6.1. Node evaluation**

To evaluate the performance of each node of our network and its contribution value within a single node or within the entire network, we first began by choosing the node we wanted to evaluate as an evidence node, and chose the parents of these nodes as target nodes. We then defined a sample size that represented how often the software would repeat the simulations.

Using the metrics presented in the previous section, we evaluated the influence of each node within its parent node and within our entire Bayesian network built.

### *6.1.1. Evaluation of the node "Pretest"*

For the pretest node, there are two parent nodes: Knowledge and Skills. We chose the node Pretest as a target node and its parents as evidences nodes, and obtained the results shown in Fig. 10.

**Figure 10.** The evaluation results of the node Pretest

According to the results presented in the table, we find the following. By adding evidence nodes into our evaluation of the target node, the percentage of the probability of correct classifications increases. Furthermore, by measuring the probability of correct classification of each node, we see how each node contributes independently to classification. In this evalua‐ tion, we find that the node "Skills" is the node that contributes the most.

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 "Skills" mean that the influence of this node is larger compared to that of 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 cost of the variables of the node "Skills".

All of this reflects that to pass the pretest, the learner in this learning situation must rely more on skills than on knowledge.

#### *6.1.2. Evaluation of the node "Learning activity"*

For the "Learning Activity" node, there are two parent nodes: Static and Interactive. We chose Learning Activity as a target node and its parents as evidence nodes, and obtained the results shown in Fig. 11.

**Figure 11.** The evaluation results of the node learning activity

*6.1.1. Evaluation of the node "Pretest"*

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

**Figure 10.** The evaluation results of the node Pretest

cost of the variables of the node "Skills".

*6.1.2. Evaluation of the node "Learning activity"*

on skills than on knowledge.

shown in Fig. 11.

Fig. 10.

For the pretest node, there are two parent nodes: Knowledge and Skills. We chose the node Pretest as a target node and its parents as evidences nodes, and obtained the results shown in

According to the results presented in the table, we find the following. By adding evidence nodes into our evaluation of the target node, the percentage of the probability of correct classifications increases. Furthermore, by measuring the probability of correct classification of each node, we see how each node contributes independently to classification. In this evalua‐

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 "Skills" mean that the influence of this node is larger compared to that of 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 of this reflects that to pass the pretest, the learner in this learning situation must rely more

For the "Learning Activity" node, there are two parent nodes: Static and Interactive. We chose Learning Activity as a target node and its parents as evidence nodes, and obtained the results

tion, we find that the node "Skills" is the node that contributes the most.

According to the results in the table, we find the following. By adding evidence nodes into our evaluation of the target node, the percentage of the probability of correct classifications increases. Furthermore, by measuring the probability of correct classification of each node, we see how each node contributes independently to classification. In this evaluation, we find that the node "Static" is the node that contributes the most.

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 "Static" means that the influence of this node is larger compared to that of 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 cost of the variables of the node "Static".

All this reflects that the learner in the learning situation has followed a learning activity; the learner must focus on static activity grains more than the grains of interactive activities to increase the chances of succeeding in this learning activity.

#### *6.1.3. Evaluation of the node "Learner"*

For the Learner node, there are three parent nodes: Pretest, Learning Activity and Evaluation. By choosing Learner node as a target node and its parents as evidence nodes, we obtain the results shown in Fig. 12.

According to the results in the table, we find the following. By adding evidence nodes into our evaluation of the target node, the percentage of the probability of correct classifications increases. Furthermore, by measuring the probability of correct classification of each node, we see how each node contributes independently to classification. In this evaluation, we find that the node "Learning Activity" is the node that contributes the most.

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

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

All this reflects that the success of a learner in the learning situation pertains his success in the learning activity more than in the assessment or pretest.

#### **6.2. Bayesian network evaluation**

We validated each node of our learner model Bayesian network, and present in this section the validation results of the entire Bayesian network.

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 manage the operation of the network in a comprehensive manner.

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

**Figure 13.** The evaluation of the entire learner model's Bayesian network

course, the learner takes an evaluation expressed in the functional requirement "Evaluation", and the result of this test takes the learner in the case of failure to the functional requirement "Remediation", to retake the learning activities in which the student could not succeed.

Failure in a learning situation requires calling a tutor by activating the functional requirement "Call Tutor", which then activate two functional requirements, "System Awareness" and "Reading History Learner". These two requirements are related to features of the hypermedia system.
