The Foundations for the Current Development of National Mathematical Education, Laid by its Leaders in the 20th Century

Abstract

The work analyzes the views on the development of mathematical education by G.V. Dorofeev and other leading Russian researchers of school mathematical education of the 20th century, including V.V. Firsov and A.Ya. Khinchin. Important for them were the idea of “humanitarianization of mathematical education” and the related concept of “education in mathematics”, in modern terminology – about meta-subject and personal results achieved in a mathematics course. The central areas of humanitarization of mathematical education are logic and language, rational thinking, and effective communication. Within the framework of these ideas, the importance of including in a mathematics course problems that “don’t know how to solve” (for a student who is offered such a problem), unexpected, shallenging, creative ones is considered. In the context of the ongoing digital transformation of education, the role of such tasks is increasing, and the role of routine, standard tasks is decreasing – they can be quickly and accurately solved using a computer. Respectively student and teacher resources can be reallocated. Another important concept discussed in this article is differentiation. There are different interpretations of this concept, common to which is the leading role of the student. The most important thing is “level differentiation”. This concept was introduced by V.V. Firsov in the 1980s. The central element of this concept is that each student achieves all intended goals. It obviously follows from this requirement that goals must be personal for each student. The simplest and most useful option seems to be one in which the goal is adapted to the student’s initial level, abilities and motives. In the context of the digital transformation of schools, the ideas of G.V. Dorofeev and his associates can be fully implemented in the education systems of the Russian Federation and the Republic of Kazakhstan.