This dissertation proposes theoretical and methodological generalization and the new solution of the scientific problem of modernization of the system of methodical training of the future mathematics teachers. The terminology of the research question was thoroughly studied. The dissertation also determines structural components of the system of methodical training of the future mathematics teachers such as: purpose; content; subjects of the educational process; pedagogical tools: traditional and innovative pedagogical tools, methods and means of teaching; the results of training. It is established that the relevant relations that exist between the components of the system should be considered in two
aspects: major and secondary. Such relations as purpose – content, content – subjects of educational process, subjects of educational process – results of training, results of training – purpose, purpose – subjects of educational process – should be considered major relations, because in the absence of at least one of them the function of the system is not fulfilled. At the same time, such relations as: content – pedagogical tools, subjects of the educational process – pedagogical tools, pedagogical tools – the results of training are secondary because they are aimed at organizing of the methodological training, improving the functioning of the whole system.
The concept of systematic methodological training of the future teachers of mathematics is constructed and scientifically substantiated, includes:
‒ formation of a professionally competent mathematics teacher ready to work on a competitive basis in the digitalized society;
‒ creating favorable conditions for the formation of methodical competence of the future teachers of mathematics at all three stages of study;
‒ determining the content of methodological training of future mathematics teachers in accordance with the specific stages of its implementation: preparatory, factual and praxeological;
‒ creation of a reflective educational environment and directing traditional and innovative forms, methods and teaching aids for updating and intensifying methodological training of the future mathematics teachers, supporting their creative and professional development, changing the roles of subjects of educational process;
‒ control of knowledge and skills of the future mathematics teachers in the context of methodological preparation at each stage, taking into account its peculiarities on the basis of integrated approach.
On the basis of the defined conceptual background the model of system of methodical preparation of future teachers of mathematics is constructed and scientifically substantiated, which contains: four components: personality-mental, theoretical-methodological,
organizational-semantic, effective-evaluative. It is established that the process of methodical training of future mathematics teachers is through and goes through three stages: preparatory during the teaching of mathematical disciplines.The ways and means of carrying out methodical preparation in the process of teaching mathematical disciplines include: realization of cross-curricular links of mathematical disciplines with the school course of mathematics; mastering students' methodical skills in explaining ways and methods of solving mathematical problems; development of mathematical modeling skills; rational combination of traditional and innovative forms, methods and teaching aids; actual in the process of studying the course «Methods of teaching mathematics» and the disciplines of methodological direction, students' performance of research activities. It is established and substantiated that the modernization of the content of this
course should be based on the regulations of the Concept of the New Ukrainian School and educational trends, the implementation of innovative learning technologies, among which it is advisable to distinguish blended learning, elements of distance learning, project activity,
educational training interactive technologies, ICT etc.; praxeological during the students' pedagogical practice and other types of practical training. It is established that one of the most important types of practical training, aimed at forming the methodological competence of future mathematics teachers, is pedagogical practice. It has been found out that the involvement of students in educational volunteering activities as a form of social activity and organization of practical and methodological training of future mathematics teachers is of great importance in the current conditions of modernization of the educational process in IHE.
It is experimentally confirmed that the implementation of the developed system of methodological training of future mathematics teachers significantly influences the level of formation of methodological competence of future mathematics teachers.
