Pavel Gorev

The article describes the main trends in the use of modern training and educating students. Particular attention is drawn to the results of the use of innovative learning tools to create an effective learning environment in which students can achieve not only high performance in teaching, but also to develop their potential in research work, based on the solution of problems of scientific creativity through participation replicated in Lyceum number 21 of Kirov innovative projects.

The author describes the organizational aspects of additional mathematical education of high school students. The main organizational forms include supplying with specialized courses and study groups, organization of the complete system of mathematical competitions and organization of the summer school mathematical camps. The author gives the examples from his teaching experience in Lyceum #21 in Kirov.

The paper proposes a variant of the organization of extra classes in mathematics for students in the 5-6-grade in order to expand and deepen their knowledge on the subject. Be organized cyclic model that includes five stages: problem solving session for notebooks based on the circuit, solving problems in the form of competition; experimental mathematics lesson, a seminar on home reading, lesson mainstream sci-entific creativity

This paper describes the possibility of constructing a system of geometric problems (namely, the equality signs triangles) based on the consideration of educational problems of open type, the supply of creative and meaningful perception of the material to promote the development of critical thinking of students

The article reveals the history of the summer school camps, training, "Math. Creativity. Intelligence", working at the Lyceum № 21 Kirov in 2001. The description of the basic content of the lines, the changes in them, as well as methodological aspects of the work in the camp of stu-dents who receive educational profile specialty "Mathematics"