ПІДГОТОВКА МАЙБУТНІХ УЧИТЕЛІВ МАТЕМАТИКИ В СИСТЕМІ НЕПЕРЕРВНОЇ ОСВІТИ (ГІМНАЗІЯ – ЛІЦЕЙ – УНІВЕРСИТЕТ)

The article deals with the actual problems of preparing future mathematics teachers for professional activity in higher education and analyses the degree of their solution in the system of continuing education (lyceum - gymnasium - university). A modern mathematics teacher should be prepared for professional activities aimed at identifying and developing students' mathematical abilities. A special role in this direction is played by the organisation of learning activities for students with pronounced mathematical abilities, individual support for mathematically gifted students, including within the framework of additional mathematical education programmes. Pedagogical activities aimed at determining the level of their special methodological competence were conducted for current teachers and students, future mathematics teachers, which revealed a number of systemic problems. The formation of special methodological competence of future mathematics teachers and additional mathematics education programmes should be ensured at the stage of obtaining higher pedagogical education. The entire training of future mathematics teachers needs to update the existing system of methodological training of students, ensuring the formation of graduate readiness to design and implement mathematics education programmes in the context of individualisation of education, to develop individual educational routes of study and support for mathematically gifted students. In this context, the system of methodological training of a future mathematics teacher should include a cross-cutting subjectmethodological line within the content of disciplines and practices in the organisation of project-research and practical training of students. It is important to use special teaching technologies, such as individualisation of learning, for future mathematics teachers, involving them in practical work with gifted students.