DIDACTIC CONDITIONS OF EFFECTIVE TEACHING OF SCHOOLCHILDREN TO GEOMETRIC PROOF: A SOCIOCULTURAL APPROACH
The article theoretically substantiates an experimentally confirmed pattern: schoolchildren's mastery of a generalized way of performing geometric evidence in a teaching-learning situation ensures the effectiveness of the process of mastering geometric concepts by them. The central basis is the differentiation of types of learning in mathematics - instrumental, premental, and value-oriented, proposed by the authors, each of which represents a specific area of mathematical knowledge (substantive, procedural, or contextual), as well as a certain type of scientific knowledge (declarative, procedural or value). In line with the developed concept of a sociocultural approach, value-oriented learning, representing the contextual area of mathematical knowledge, comes to the fore. We are talking about mathematical knowledge, skills, cultural abilities as forms of learning cultural values, as well as the formation of a valuable attitude of students to mathematical categories, objects and methods as carriers of cultural values. Geometry on the Lobachevsky plane in the Hilbert scheme was chosen as the substantive material of the practical course for grades 8-9. The experimental methodology was based on the author's concept, focused on a three-stage presentation of educational material: the stages of understanding, mastering and applying, corresponding to three levels of learning. The results of the comparative analysis of the deductive-axiomatic construction of geometry in textbooks recommended for use in educational institutions are given by the authors. Disclosed substantively identified by the authors didactic conditions for the effective organization of the assimilation of geometric proof by schoolchildren.