Abstract:

The article actualizes the problem of modernizing the methodical training of a mathematics teacher on the basis of modern achievements in science in the system of additional vocational education, which, on the one hand, ensures the improvement of knowledge of specialists for performing a new type of professional activity, and, on the other, ensures obtaining additional qualifications. The conceptual idea of the synergy of mathematics, informatics and innovative didactics in order to strengthen the technological and vocational-mathematical component of the innovative retraining of a mathematics teacher, personal and professional self-development, self-organization and mastering a broad-profile qualification is crucial in the system of additional education.

The authors developed and presented a draft of an additional professional program of professional retraining "Improvement of the methodical training of the teacher of mathematics for school and vocational education on the basis of modern achievements in science", which was implemented on the basis of Bunin Yelets State University. The basis of innovation is the mastery of the theory of visual modeling of mathematical knowledge, the concept of the foundation of the experience of an individual, the ideas and principles of the integrative approach (mathematical and gaming activity (using the example of chess) the real and virtual components of the developing environment), the technologies for developing synergies in mathematical education, meaningful for the future professional activity of the teacher. The content of the program implies active learning process of the psychological and pedagogical patterns of operating with complex mathematical abstractions (fractal geometry, fuzzy-logic, coding and encryption theory, generalized functions of S.L. Sobolev and L. Schwartz theory of distributions, theory of chaos and catastrophes), and methodology of an effective mathematical activity on the basis of system-environment, thought-activity and synergetic approaches. Informatization of mathematical education is represented by systems of computer algebra (MathCad, MathLab, Maple, Mathematica), dynamic geometry (GeoGebra, Aphtograph) and small informatization tools (ClassPad400).

The obtained results provide an opportunity for further improvement of the methodical training of a mathematics teacher, as well as for the actualization of self-organization and self-development processes on the basis of modern achievements in science and an effective implementation of the models and technologies proposed in this study with a view to further raising the level of professionalism.

Keywords:

Additional education, synergy of mathematical education, modern achievements of science.