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The article reviews the actual problems of mathematics education. The difficulties encountered by a modern schoolchild when solving tasks of monitoring research in mathematics are indicated. Methodological recommendations are given that should increase the productivity of interaction between a modern teacher and a modern schoolchild, and, accordingly, the quality result of training, through the improvement of pedagogical techniques, an increase in the level of professionalism of teachers, their motivation, initiatives, the creative and emotional component of the educational process, professional competence of the teacher.