PSYCHOLOGICAL AND PEDAGOGICAL CONDITIONS AND METHODOLOGY FOR DEVELOPING THE STRUCTURAL-MATHEMATICAL THINKING OF STUDENTS IN MATHEMATICS EDUCATION

Abstract

The paper highlights the psychological and pedagogical conditions while advancing a methodology for cultivating students’ structural-mathematical thinking within the domain of Mathematics education. By examining the content and components of such thinking, alongside its significance and role within the framework of mathematical competence, the rationale is substantiated, and the methodology for developing the studied phenomenon is elaborated. The conceptual foundation of the research was predicated on the assertion that the development of students’ structural-mathematical thinking is achieved through the actualization of the external manifestations of mathematical competence (content-theoretical, process-activity, referential-communicative dimensions) in educational-mathematical activities – the process of interiorization. The psychological and pedagogical conditions necessary for the development of students’ structural-mathematical thinking include organizing their educational and mathematical activities in alignment with the third type of learning, as well as adhering to the fundamental principles of the theory regarding the gradual formation of mental actions and methodologies of cognitive activity. This includes cultivating the primary indicators of each of the six dimensions of mathematical competence, establishing zones for the students' nearest mathematical development, implementing a problem-based approach, and the teacher's personal stance. It was substantiated that the development of the above mentioned type of thinking involves the development of an innovative type of mathematics education, namely the developmental and reflective, and it was found out that its phased approach ensures the establishment of the content and structure of the main components of mathematical educational activity: problem – solving the problem – solving typical problems – logical progression from the abstract to the concrete (solving partial problems) – competency-based problem – solving the competency-based problem. Furthermore, it was determined that the execution of this educational technology is carried out within the context of heuristic conversation, a didactically balanced combination of reproductive and exploratory teaching methods, as well as the expedient application of the tools pertaining to dynamic Mathematics.