The dissertation is devoted to the solution of problems of continuous professional training of future teachers of mathematics. Based on the analysis of the scientific literature, the categorical and conceptual apparatus of the pedagogical component of the formation of professional competence of future mathematics teachers in the field of using ICT tools in professional activities has been clarified. The professional competence of future teachers of mathematics, which is formed in higher education, is considered as a qualification characteristic of the individual, which is formed in higher education and covers mathematical, methodological and technological training, pedagogical practice, which provides the necessary foundation for further development of mathematics in the studied aspect.
The analysis of foreign experience of the United States, Norway, Germany, Canada in the formation of professional competence of future teachers of mathematics showed the presence of common and different compared to domestic practice of training. Taking into account modern requirements of informatization of education in the dissertation the essence and structure of the concept "continuous professional training of the teacher of mathematics" are defined, the electronic educational resources used for studying of mathematics, electronic educational and methodical complexes, test programs are analyzed. The concept of continuous professional training of future teachers of mathematics, which contains theoretical, methodological and methodological concepts, is substantiated.
In the dissertation the integral system of continuous professional training of future teachers of mathematics by means of information-technological maintenance in a combination of motivational-value, cognitive-activity, personality-reflexive components is developed. The model is designed and the pedagogical conditions are substantiated system of professional competence formation of future mathematics teachers, the effectiveness of which is tested in training future mathematics teachers. It is proved that pedagogical conditions presuppose successful introduction of the model of continuous professional training of future mathematics teachers by creating an environment as close as possible to future professional activity, motivating students to personal and professional changes during training, stimulating them to professional growth. To verify the formation of professional competence of the graduate were used diagnostic methods of control and evaluation, taking into account the individual trajectory of training. It is based on a block-modular system of education with a rating taking into account the student's activity, the purpose of which is a comprehensive assessment of the quality of educational, independent and scientific work of the student in mastering educational programs of higher professional education.
The rating system had the following levels: content (level of didactic unit, level of discipline, level of cycle of disciplines, level of professional training) and organizational (level of individual student, level of academic group, level of flow)
It is determined that the formation of professional competence of future mathematics teachers is characterized by motivation to succeed; search for new sensations, as it stimulates emotions and imagination, develops creativity, and ultimately leads to personal growth; knowledge; ability to conduct self-control, self-assessment and self-analysis of the results of professional activity; skills such as organizational, communication, leadership, self-efficacy and learning self-efficacy.
It is proved that the modern model of the system of continuous professional training of future mathematics teachers determines the formation of professional competence of future mathematics teachers, which includes a system of five structural blocks (target, conceptual, content-procedural, structural-functional and criterion-diagnostic). to effectively communicate information about the purpose, objectives and results of the formation of professional competence of mathematics teachers and which can be obtained through the implementation of certain and reasonable pedagogical conditions.
The results of the experimental study indicate that the implementation of a system of continuous professional training of students by means of ICT in the context of blended learning has allowed students of the experimental group to increase their level of professional training.
