This article examines the problem of creating the conditions for the existence of the independence of students, the combination of rigour and respect for the individual student. Teacher modeling modern lesson, should create conditions so that students in a collective search came to the opening, have postulated and proved their claims. In connection with the transition to next generation standards necessary connection of system and activity approach in teaching methodology as the GEF.

Keywords: modern mathematics lesson, the efficiency of educational process, research activity of students.

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