A Bayesian Network Based on the Differentiated Pedagogy to Generate Learning Object According to FSLSM

—In this paper we propose a model that generates learning objects in an adaptive learning system according to the Felder Silverman learning styles, based on the Bayesian networks and taking into consideration the recommendations of the differentiated pedagogy which requires creating multiple versions of the same learning object. The proposed model includes also correcting the non-learning paths which is the main reason behind the choice of versioning the learning objects.


INTRODUCTION
The adaptive learning systems are an important class of the e-learning systems, the significance position they gained in the field, is due primarily to the endless possibilities they offer in terms of personalizing learning path, according to the needs, prerequisites and more importantly the learning styles, which translate obviously to a more satisfactory results on the learner side. Most of the adaptive learning systems build a learner model based on the learner's characteristics. An adaptive learning system is able to provide specific learning object according to the model built previously which create at the end a specific learning path. Somehow the generated learning paths may not be the leading ones. This translates, assessment wise, with a negative result in the evaluation.
Through this paper, we propose a model that generates learning objects based on the Bayesian network, using the FSLSM [1] and based on the recommendations of the differentiated pedagogy [2] which advocate offering multiple versions of the same learning object [3], on which we will rely on to correct the non-leading paths.
This paper is organized as follows: The first section is dedicated to the related work, then we will be discussing the Felder and Silverman learning style model in section 2. Later in section 3 we will explore the Index of Learning Style as seen by Felder and Silverman. The relationship between the Learning Objects and Learning Style will be seen in section 4, then in section 5 we will discuss the differentiated pedagogy and how it will serve for the approach used in this paper. Next we present the adaptation model and the Bayesian network in section 6 and 7 in a row. Finally some conclusions are drawn in section 8

II. RELATED WORK
There are several approaches that fall into the direction of personalizing learning path and offering an adapted content to the learner's profiles, those works can be summarized into two categories: The first category contains systems who tend to use implicit methods for identifying learning styles based mainly on the analysis [4], [5] and observation [6], [7] of the learners behaviors in the system, The reason behind this choice is to not overwork the learner by offering him multiple forms to fill. However those methods are not completely reliable given the fact that a learner can engage in other activities during the learning process which can be misleading for the designer.
The second category contains the content adaptation systems that use explicit methods for identifying learning styles by using e-questionnaires [8], [9], [10] or letting the learners express their preferences [11] personal characteristics [12] or using the FSLSM [1], [13]. In both cases the systems propose the same learning objects, and it's only a matter of suitable sequence for everyone.
None of those works presented above questioned at any stage the cognitive level of the learning object, it is assumed that the proposed learning objects are valid for all learners, and it's only a matter of appropriate order. That's why the authors in [3] presented a model of versioning the LO which we will be adopting and exploring through this paper. The reason behind this choice is to remedy the problem of non-leading paths, by offering the most relevant versions, as most computing systems are based upon the initial calculating of profiles, [14], [15] and do not offer any correction of learning paths in case of a failure in an assessment.

III. FSLSM
There are many models about learning styles in literature such as Kolb [16], Dunn & Dunn [17], Honey & Mumford [18], and Myers-Briggs [19]. This model is based on Felder and Silverman's Learning Styles Model, because of its applicability to e-learning and compatibility to the principles of interactive learning systems design [20].
Students learn in many way by seeing and hearing; reflecting and acting; reasoning logically and intuitively; memorizing and visualizing and drawing analogies and building mathematical models; steadily and in fits and PAPER A BAYESIAN NETWORK BASED ON THE DIFFERENTIATED PEDAGOGY TO GENERATE LEARNING OBJECT ACCORDING… starts [21]. The ways in which an individual characteristically acquires, retains, and retrieves information are collectively termed the individual's learning style [22]. In 1988 R. Felder and L.Silverman proposed a learning style model that classifies five dimensions of learning styles. Lately, inductive/deductive was excluded from the model, so now we deal only with four dimensions (Figure 1).
In Table I is how those dimensions are translated learning Wise.

IV. THE INDEX OF LEARNING STYLE
The Index of Learning Styles (ILS) developed by Felder and Soloman, is a questionnaire of 44 items to identify learning styles according FSLSM. As mentioned earlier, each student has a personal preference for each dimension. These preferences are expressed with values ranging from +11 to -11 per dimension, with steps + / -2 . This range has eleven questions that are asked for each dimension. In response to a question, for example, with an active preference, one is added to the value of the active / Reflective dimension while a response to a preference Reflective decreases the value of 1. Therefore, each question is answered either with a value of 1 (answer a) or -1 (answer b). Answer a is a preference for the first pole of each dimension (active, sensing, visual, or sequential), answer b is to the second pole of each dimension (Reflective, Intuitive, verbal or Global). The ILS is an index often used and well-studied to identify learning styles. Each learning style dimension seems to include different characteristics. In an empirical study [10], the groups of preferences within each dimension of FSLSM were analyzed and their relevance for each dimension was investigated. Table II shows the proposed groups as well as the related answers of ILS questions [23] for each group. A question may appear twice in the table, if the two possible answers to the question point to two different groups.

I. THE RELATIONSHIP BETWEEN THE LEARNING OBJECTS AND THE LEARNING STYLES
Based on the theoretical descriptions about leaning styles' characteristics of Felder-Soloman [23], and on the practical research of [24]- [25]- [26], the learning objects are labeled as described in Table III.
However more than one pedagogical activity might be shared between one or more learning styles as shown in Figure 2.  Require reading or lecture Sequential Step by step Global Big picture

II. VERSIONING ACCORDING TO THE DIFFERENTIATED PEDAGOGY
To differentiate is to break with a pedagogy that is frontal, the same lessons, the same exercises etc…for all learners. The goal is to put everyone in an optimal learning situation. This organization is to use all the educational resources available so that each learner is constantly or at least very often confronted with the most fruitful teaching situation. The following part is based on the works of [3], in fact the authors chose to emphasize the following versions of every learning object presented in the system based on the recommendations of [2].
As the chart below ( Figure 3   Instruction Model: The instruction model is the pedagogical model responsible for designing the learning object included in the domain object. Adaptability model: The adaptation model is the one generating learning objects according to the characteristics of learners (prerequisis, learning styles) and the learning objects that match them. (See fig 2) Evaluation: The evaluation is the critical part in this adaptive learning system as it remains the only way to correct learning paths if it appears that the generated learning path is not the leading one ( see section 10)

IV. THE BAYESIAN NETWORK MODEL
A Bayesian Network (BN) is a graphical model for efficiently representing a joint probability distribution over a set of random variables V. A BN is denoted by (G, P); where G is a Directed Acyclic Graph (DAG) defined over V (such graph encodes independence relationships among the variables in V); and P denotes a set of local probability distributions, one for each variable conditioned on its parents. Variables are represented for nodes denoting "concepts" and edges indicating cause/effect dependencies among concepts. Final nodes can be seen as "effects" (values collected from the learning environments), while highest-level nodes can be thought as "causes". Every node can have two or more possible results; each result is named a state of the variable. Thus, once the learner's profile is defined (Learning style according to Felder-Silverman and prerequisis) the learner model can be built. The BN shown above enables creating the most suitable learning object for every learner while taking into consideration mostly his learning style and perquisites, the mathematic formula is given in the upcoming section right after discussing the learning styles combinations. V. THE LEARNING PATH CORRECTION One of the major disadvantages of the Adaptive learning system discussed in the Related work section, is that they consider work done once they generate the suitable learning objects and as a result a learning path. However those learning path may not be the leading ones, which translates to a negative result on the learner's side. Of course the evaluation remains the only way to detect whether a specific path is the leading one or not.
Every evaluation has two outcomes, a positive or a negative result; we are interested with the negative one's case, since we intend to correct the learning path of the learner experiencing difficulties. In fact this correction is done by calculating the similarity between the struggling learner and the learners who have passed successfully the evaluation provided that they have the same initial profile. Those calculations are based on the behavioral indicators (NBREXR, NBREXM, NBRAST, DSB, TMPTH, FC, TEC, DP) developed by the authors of [27].

VI. CONCLUSION
Through this paper we presented a probabilistic approach for an adaptation model of learning objects based on the differentiated pedagogy and Felder-Silverman learning style model, using the Bayesian Network. The model operate mainly using the prerequisis and the learning style at the early stage, then by calculating the probability of suitability of every learning object to a learning style, this model also corrects the learning path in case of a negative result in an assessment, by offering the learner experiencing difficulties, the best learning path according to the similarity with the learner who has adopted the same behavior within the system. Later we intend to develop a method to eliminate from the system the most irrelevant learning objects or versions to avoid overloading the system with poorly used learning objects.