In modern conditions, the quality of higher education does not depend on the volume of an individual's actual knowledge, but on his / her mastery of key competencies, one of which is self-educational competence as indicated in the modernization strategies of Kazakhstani and Russian education. The formation of students' self-educational competence is influenced by the design of learning outcomes as a complex ability for continuous professional self-development of subjects of higher education. The development of self-educational competence is determined not so much by fixed learning outcomes as by the ability to determine and plan the necessary time to achieve the best learning outcomes. The purpose of the article is to present a methodology for determining the time to achieve learning outcomes based on a mathematical model in the process of self-educational activity of subjects of an educational organization of higher education.

The study was conducted on the basis of the Kazakh National Women's Teacher Training University (Almaty, Republic of Kazakhstan) and the State University of Humanities and Technology (Orekhovo-Zuyevo, Russian Federation). The results of the study were obtained on the basis of a comparative analysis of the development of self-educational competence of the subjects of the Kazakh and Russian educational organizations of higher education, the method of designing the applied orientation of teaching pedagogy, the mathematical method using the "didactics equation". The following methods were used: theoretical analysis, comparison, survey, expert observation.

The criteria for the manifestation of self-educational competence by future specialists have been defined: subjective (the student's awareness of the content and functions of self-educational competence, the innovative orientation of the individual); instrumental (predictive skills, information and analytical skills, organizational skills). According to the results of scientific research of the subjective activity of students of the Kazakhstani university, an underestimation of the importance of the formation of algorithmic skills for monitoring the achievements of learning outcomes was revealed: 58% of future teachers have a low level of self-educational competence; 44% of students have difficulties in self-planning self-educational activities. 38% of Russian university students were found to be unable to independently choose an algorithm of actions when planning and controlling the time of self-educational activities and productively implement it in the course of the module "Innovative technologies of educational activity". A mathematical method has been developed using the "didactics equation" (M.I. Poteyev), which allows determining the necessary time for effective learning in the process of self-educational activity of university students.

The self-educational competence of subjects of higher education, as shown by a study at a Kazakhstani university, is not significantly manifested. A study at a Russian university revealed that the nature of the traditionally implemented types of pedagogical control does not ensure the identification of the required quality of development of self-educational competence that contributes to the achievement of learning success. Thus, the pedagogical task of developing the self-educational competence of future specialists can be solved by means of a mathematical method using the "didactics equation".