The purpose of this paper is to specify the essence and the specifics of implementation of the pedagogic technology of forming the basics of future mathematics teachers' professionalism using the potential of multimedia in higher education. The major research method is pedagogical experiment (comprising analytical search, ascertaining, forming, and control stages) aimed at verifying the efficiency of the pedagogical technology of forming the basics of future mathematics teachers' professionalism; statistic methods have also been employed for checking efficiency and reliability of the experimental research results. The participants of the pedagogical experiment have been 290 students (150 students of the experimental group and 140 students of the control group) of the training area 44.03.01 "Pedagogical education", skills profile "Mathematics". Theoretical issues on the nature, structure, criteria, indicators and levels of formation of the basics of future mathematics teachers' professionalism have been disclosed; the notion-category apparatus of the theory of the teacher professionalism has been specified; there has been scientifically grounded and developed the pedagogical technology of forming the basics of future mathematics teachers' professionalism that corresponds to the structure of the holistic pedagogical process and includes: target orientations, conceptual bases and regulations, procedural characteristics, program-methodological support, and an appropriate combination of traditional and multimedia tools. The results of the gradual introduction of the pedagogical technology of forming the basics of future mathematics teachers' professionalism by means of multimedia technologies indicate significant positive shifts in the formation of all the components of the basics of students' professionalism, which was reflected in the positive dynamics of the criteria for all indicators and generally indicates the effectiveness of the proposed pedagogical technology. Research materials can be used to further improve the theory and practice of the professional training, in particular, in the training of future mathematics teachers in the process of qualification improvement and personnel retraining, and in the selfeducational activity of teachers.

The purpose of the research is to build a methodological system for teaching stochastics to university students of the Biology specialization in the context of implementing a professional-applied orientation. The leading method of researching this aspect is the modeling of the conceptual basis of the methodological system for teaching stochastics, which allows to form a system of mathematical knowledge and skills necessary for understanding the fundamentals of the process of mathematical modeling and statistical processing of biological data in professional activity; to develop practical application skills of statistical methods in biological research. In this article, the authors' methodology of forming professional competence of future specialists of the Biology specialization through the implementation of professionally-applied teaching stochastics is presented. The specificity of our methodology for teaching stochastics to university students of the Biology specialization is that between the theoretical and practical aspects of stochastics, a deep content-methodological interrelationship has been established; the authors' system of professionally-applied tasks has been proposed, which includes, among other things, real tasks from the discipline of Biology that facilitates the integration of natural science knowledge based on the modeling method. The research carried out by the authors proved the effectiveness of the suggested methodology for teaching stochastics to university students of the Biology specialization. The article materials can be useful for lecturers of higher educational institutions and teachers of secondary schools with in-depth Biology studying when the suggested methodology for teaching the probability theory and mathematical statistics is applied.

One of the ways to improve the quality of math and natural science education is to develop the pedagogical community of STEM education. On the one hand, according to the forecasts, an increase in the number of students and teachers is expected by an average of 20 % in both Russia and worldwide. On the other hand, there is definitely some specificity in the pedagogical community as compared with any other labor collective, since the pedagogical community develops alongside with the student one. In this perspective, the age heterogeneity of the teaching staff is of particular relevance. Consequently, the key point in the management of math and natural science education is the analysis of the age structure of STEM educators. The following subjects are taken to conduct a further analysis of STEM education: mathematics, handicraft, physics, biology, and chemistry. Accordingly, the purpose of the article is to analyze and forecast the heterogeneous development of the age structure of STEM teachers. The authors of the article justify the necessity for changes in the personnel policy on the basis of the assessment of the capacity of the teaching staff of STEM education in schools of the European part of Russia. The leading research approach is the method of the normal and natural distribution of age groups in the structure of the STEM education pedagogical community. As a result of a study conducted in 569 schools of the European part of Russia in 2016-2018, the authors of the article have found out the following: the average age of STEM school teachers in the European part of Russia is 6.8 years higher than the average age of teachers in Russia; there is a significant shortage of STEM teachers aged under 35; the average rate of the teaching load of a STEM school teacher in an academic subject is 0.72, but the load is distributed very unevenly, math teachers having the highest teaching load. The theoretical significance of the research lies in its contribution to the development of scientific ideas concerning the age heterogeneity of STEM school teachers. The research results can be used in building development trajectories of STEM education teaching staff by implementing a series of managerial and organizational measures to achieve the normal state of the age structure of teachers.Keywords: STEM education, age heterogeneity of teachers, age structure of the pedagogical community, seniority of teachers, normal distribution of age groups

Actuality of the matter under investigation is stipulated by the necessity of exploring the issues of development of "Self-concept of creative self-development" of students, which can be defined not only as the "Theory of Self" or as the effect of realization of one's own "Self", but also as the regulation mechanism of all types of creative activity of a human being. The purpose of this article is to analyze and systemize pedagogical conditions of effective development of the "Self-concept of Creative Self-development" of students. The method leading to the research of this issue was a pedagogical experiment on testing pedagogical conditions of effective development of the "Self-concept of Creative Self-development" of students during the study of "Pedagogics" as an educational discipline. The main result of this article is the conclusion that application of the system of creative, research related tasks targeted to the development of the "Self-concept of Creative Self-development" of students, leads to significant growth of all the backbone elements of "selfness". The experiment confirmed the effectiveness of designing the "Self-concept of Creative Self-development" of students through the training process (on the basis of the pedagogical disciplines' training material) based on the integration of the pedagogical conditions: system of diagnostics and self-diagnostics of "self" processes, enrichment of training sessions on pedagogical disciplines with the specialized tasks on stimulating reflexive thinking, aimed at self-actualization of one's own creative development processes, assistance to students in realizing indicators and criteria of principle backbone elements of creative development, periodical self-correction of the "Self-concept of Creative Self-development"; implementation of the education and training integration links. Information in this article may be useful for educators of higher education institutions, involved in generating the "Self-concept of Creative Self-development" of students in the framework of professional education.

The modern neural network, as a prototype of artificial intelligence, becomes not just an assistant in student learning, but its co-author, co-creator, a partner and a mentor. The ever-increasing and less-controlled capabilities of artificial intelligence in the field of collecting and analyzing information, organizing experiments, modeling and forecasting, generating original content, call into question the very principle of freedom of human creativity. The concept of "digital freedom" is introduced in the article to describe the new conditions of students' creative activity. The information environment is considered as a resource and, at the same time, a barrier for traditional approaches, which are adopted in pedagogy, to project creative activities of students. In the situation of digital freedom, new effective models and strategies for organizing, conducting and evaluating student projects arise. The article provides a review and comparative analysis of group and individual design strategies, introduces and describes new strategies for project activities based on collective leadership and co-creation with artificial intelligence. The experiences of project creative work performed by bachelor's students and master's students of the Higher School of Journalism of the Institute of Social and Philosophical Sciences and Mass Communications, the Institute of International Relations and the Institute of Psychology and Education of KFU were analyzed.