We consider some problems and perspectives of school mathematics education, and present a vision of ways to enhance the quality of mathematical preparation of students. Areas of work with mathematically gifted children, and forms of specialized training are systemized. Profile and specialized education tasks, the role of information technology in mathematical education are determined in particular.

Keywords: school mathematics education, multilevel textbooks, mathematically gifted children, information technology in mathematical education.

The main purpose of the article is the theoretical basis and technological description of non-traditional approach to the organization of students’ self-directed activity in the preparation for the exam in mathematics.

Keywords: final examination, unified state exam, self-directed work, personal approach, role approach.