Abstract. The article contains the concept of developing a motivation model aimed at supporting activity of both students and teachers in the process of implementing and using an open and distance learning system. Proposed motivation model is focused on the task of filling the knowledge repository with high quality didactic material. Open and distance learning system assures a computer space for the teaching/learning process in open environment. The structure of the motivation model and formal assumptions regarding the task of solving the model were described. The proposed approach to solving the task bases on the games theory.

Abstract. The competence-based learning-teaching process is a significant approach to the didactical process organization. In this paper the mathematical model of the competence-based learning-teaching process is proposed. The model integrates three models: a knowledge representation model (based on the ontological approach), a motivation model (as a behavioral-incentive model) and a servicing model (in a form of the queuing model). The proposed integrated model allows to control the learning-teaching process on different levels of management. The learning-teaching process can be interpreted as competence-based due to Open and Distance Learning (ODL) philosophy. We assume that the competence is a result of fundamental, procedural and project knowledge acquisition in accordance to the incoming European Qualification Framework.

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Abstract. Motivation and social aspects as interaction among teachers and students are essential for a successful learning process in an Open Distance Learning environment, and the goal of this paper is to develop an interactive model to manage motivation between the participants of that process. The article contains the concept of developing a motivation model aimed at supporting activity and cooperation of both the students and the teacher. The structure of the motivation model and formal assumptions are presented. The proposed model constitutes a theoretical formalization of a new situation in which a teacher and the students are obligated to elaborate on a didactic material repository content in accordance with the competence requirements. A mathematical method based on game theory and simulation is suggested. The conditions for applying simulation to the model are analyzed in two simulated cases. The educational experience is constituted through sustained interaction and communication between and among learners, teachers, and learning objects. In ODL this process can be facilitated through asynchronous and synchronous communication and participation through students' teamwork [6,7].Motivation is a key factor in learning in case of the face-toface educational contexts [5] as well as in online learning environments [8]. Traditionally online learners have been understood as independent, self-directed and intrinsically motivated [6], but this is not the case. Motivation of the learner is complex, multifaceted and sensitive to situational conditions [8].The implementation of ODL assumes modification of the traditional organization of learning processes. The special attention is subject to a change in designing the structure and content of the specific educational elements. However, the opportunities of relations between students and the teacher seem to be crucial. The ODL, combined with the new possibilities and strategies of distance learning, provides a basis for active collaboration between teachers and students, between students and students, as well as between students and the university [9].These new possibilities urge universities to consider the new status of the potential students. This means that, on the one hand, students must be able to achieve knowledge, skills and competences connected to the goals in their curriculum. On the other hand, the universities have to provide the students with an active role in the learning process, to motivate them to work on an independent study program under the supervision of a teacher [10].

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