The collective monograph considers various approaches to solving modern problems of teaching theory, upbringing and mathematics methods, including selected problems of special methods of teaching mathematics and promising developments of young scientists in the field of pedagogy and mathematics methods. The works of scientists of the scientific school of mathematical development and the laboratory of didactics of the rural school, headed by a doctor of pedagogical sciences, an academician of the Russian Academy of Social Sciences, an Honored Worker of the Higher School of the Russian Federation, Professor M. and . Zaikin . The monograph is intended for specialists in the field of teaching theory and methods of teaching mathematics, teachers, students and postgraduates of pedagogical universities interested in modern problems of teaching theory, education and methods of mathematics .