The purpose of the present work is to describe the process of teaching students, considering such parameters as the level of competence, the level of motivation, the level of acceptance of the material. The method of random numbers was used for the evolution of parameters in time, as well as the hypothesis of  the dependence of the growth of competencies on other parameters. Several of such parameters have been tested. An algorithm and the software for it were developed, numerical experiments about the influence of parameters of studying on changes in students' competence over time were obtained. The plausibility of the different models of the teacher's influence on these parameters was estimated.