**1. Introduction**

First of all, to clarify our purpose, it seems important to note that the work presented in this chapter lies within learner modeling in an adaptive educational system, construed as a computational modeling of the learner; that is to say, the representation and specification of the learner's knowledge. Different approaches have been taken to manage modeling of the

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learner with multiple objectives, from the evaluation of the learner's knowledge to the recognition of the plan followed in problem solving.

Despite these various attempts at modeling learning characterized by a dynamic aspect, we always find that there are difficulties in achieving this goal. The proposed approaches provide us with only a static view of the learner model, yet this model is always in development (the learner's knowledge is evolving within the same module). Therefore, a dynamic view is essential. In order to monitor the behavior of the learner in real time and during formation, we must adopt a dynamic modeling approach when managing learner modeling.

The actions of the learner in a learning situation are not limited to valid or invalid actions (true and false), yet it is the actions that characterize the formation of the learning path. From this observation, we cannot represent information from the system of each learner using relative data. Rather, we must place our work in a probabilistic context due to changes in the learner model during formation.

The problems presented in this chapter can be summarized as follows: How should we represent the different functions of a learner model? And what approaches can be used to perform updates on the different characteristics of such a model?

In this work, we propose the use of Bayesian networks as a probabilistic formalism to resolve the issue of management and dynamic update of the learner model. To resolve this issue, we must first ask: Why and how can we represent a learner model with Bayesian networks? How can we go from a dynamic representation of the Unified modeling language diagram of the model to a probabilistic representation with Bayesian networks? Is this consideration experi‐ mentally justified?
