Optimal management of the acquiring and evaluating the competencies process of university students

Purpose of study. In the Russian Federal State Educational Standards of higher education, the fundamental role is assigned to the need for students to acquire a set of competences in the process of training. The list of competences is given in the standards. At the same time, universities in accordance with the law “On Education in the Russian Federation” must also take into account the requirements of professional standards for the development of the students’ labor functions, required for work in the chosen profession. The task of the university in planning of the educational process is to form the necessary set of educational disciplines and practices, rational distribution among them the number of credit units (СU) and specifying the order to study these disciplines in time (by semester). This task is traditionally solved by universities expertly on basis of normative documents and the available experience of developing curricula in the university. At the same time, neither the effectiveness of the draft curriculum as a whole nor the impact of individual decisions and interference on this effectiveness are quantitatively evaluated. The next task is to evaluate the effectiveness of the implementation of the working curriculum, i.e. management of the educational process, taking into account unforeseen and accidental factors. This task is being solved by monitoring the current progress of students, but the degree of achievement of the required level of competences is not usually evaluated. Therefore, the task of assessment of the of the actual level of required competencies and the necessary corrective actions is also relevant.

Materials and methods. In the paper, an attempt is made to formalize the above tasks and describe the process of acquiring competences in the form of a dynamic system, subject to interference. The management of this process is formulated as the problem of analytical design of the optimal controller A.Letov [1], and the state estimation is in the form of a R. Kalman’s filter [2].

Results. A method is proposed for calculating the optimal trajectories of the growth of competencies in the learning process and the control actions for the implementation of these trajectories. The methodology makes it possible, based on the cognitive model of the educational process and in setting priorities, to calculate the optimal plan for increasing competencies and allocating credit units for this purpose. When implementing the curriculum, the correction of control actions is calculated, depending on the actual state of the educational process. An example is given of the synthesis of the optimal dynamics of growth over the terms of three groups of competences (general cultural, general professional and professional) and the resources necessary for this in the form of the number of credit units in the planning of the curriculum for training of bachelors. The qualitative coincidence of calculation results with traditional planning is shown, as well as the stability of the competence management process to the resulting interference.

Conclusion. It is clear that the university staff, experts in this field of knowledge and pedagogical activity, carry out the final decisionmaking in the design of the educational process. However, the proposed theory makes it possible to determine the structure of solutions, to assess priorities and the impact of various process parameters on the quality of the decisions. The advantage of the methodology, in the opinion of the authors, is that it is possible to easily vary the degree of detail of the accounting of competences – from the total accounting of all competencies, accounting by their types – GC, GP and P, to arbitrary grouping them, up to the allocation of individual or even all competencies. The methodology is based on matrix mathematics, so increasing the dimension of the problem does not cause a change of the calculation algorithms.

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