The modern approach to teaching mathematics, generated by changes in the information environment, the widespread introduction of new technologies, which children become familiar with from an early age, and other similar factors, involves setting new goals in order to meet the demands of the modern times, and, consequently, the search for new forms of teaching. In this paper, we present a study on the potential use of an active form of learning called mathematical debates as an integral part of the educational process.

The idea of mathematical debates is based on a well-known form of mathematical group competitions for gifted children called mathematical battles, which was conceived in the mid 60-ies by Verebeychik [1]. In this article, we discuss the possibility and describe our experience of utilizing mathematical debates not as a competition, but for educational purposes for students of different ages and mathematical skill levels.

The main part of the article is devoted to strategies of selecting the appropriate educational material for the debates, based on the intended objectives and common methodological problems. Examples of actual mathematical debates we held are presented, with a detailed explanation of the manner in which the game process leads to the realization of the intended goals.

mathematical debates, teams, presenter, opponent, representation and defense of solutions, opposition.