The article considers categories of abilities and giftedness. The characteristic of gifted students is presented. The question of creating conditions for the development of abilities and talents is revealed, and the role of the teacher as the creator of the space of support and development of students’ abilities and talents is pointed out. The basic elements of didactic system are described, i.e. goals and tasks of education, content, methods, means, organizational forms of educational space training, which promotes the development of abilities and talents. Moreover, the role of a teacher and a student in the process of teaching and learning is depicted.