PERSONAL-PSYCHOLOGICAL DIMENSION OF THE STUDENT’S MATHEMATICAL COMPETENCE: STRUCTURAL-MATHEMATICAL THINKING

Abstract

The paper delves into the students’ structural-mathematical thinking as a pivotal structural element of the personal-psychological dimension of mathematical competence. Given the Cartesian implementation of the internal manifestation of mathematical competence, structural-mathematical thinking is combined with retention for mathematical material, experience of mathematical activity, self-awareness (self-concept of the individual) and mathematical abilities. A content analysis of the phenomenon under study was carried out using systemic analysis, thus its components were established and typological characteristics were outlined. It was found that in the conceptual-categorical segment, structural-mathematical thinking is a type of theoretical thinking, which embodies the specifics of mathematical reflection of reality, axiomatic and constructive methods of theory construction. Further, it was substantiated that the essential structural-functional characteristics of structural-mathematical thinking represent the components of the mathematical structure. Thus, the work ensures compliance with the deductive essence of Mathematics, and also emphasizes the phenomenological characteristics of structural-mathematical thinking – the mental process of reflecting reality in accordance with the content components of the mathematical structure. The introduction of such a logical scheme into the process of teaching Mathematics involves the use of structural-mathematical analysis of educational material as a content-theoretical action and at the same time a type of systemic analysis. Drawing on the activity approach, the study established an operational structure, while also creating a model that highlights the course of students’ structural-mathematical thinking. Its classification basis was the content-theoretical actions outlined in the paper. This allowed us to distinguish the following types of structural-mathematical thinking: analytical, abstract, generalizing, planning and reflective.