Development of Synthesis as a General Logical Method of Cognition in the Process of Teaching Mathematics of Students and Future Teachers

Abstract

General logical cognitive actions form the basis of almost all cognitive methods. This determines the necessity of their purposeful formation in the process of subject teaching. A special role in the development of cognitive methods belongs to mathematics, in the process of teaching which these actions manifest themselves in the most explicit form. In the article we consider the formation of synthesis as a basic general logical method. The purpose of our study is to develop approaches to the organization of subject-based teaching aimed at the formation and development of synthetic thinking of school students and teacher education students. The methodology of the research is the theory of funding of logical constructions, developed on the basis of the concept of funding in education (V. D. Shadrikov, E. I. Smirnov). The results of the study. Examples demonstrating the main types of synthesis in mathematics learning are considered. These types include: synthesis as a leading action in the construction a mathematical model and synthesis as a representation of a logically justified solution to a problem. The problems of synthesis implementation by students in the process of solving mathematical problems are analyzed. The specificity of educational tasks that contribute to the formation of synthetic thinking is studied. The role of combinatorial tasks as tasks with prevailing logical component in the formation of synthetic thinking of students is described. In conclusion, on the basis of the theory of funding, the typification of types of synthesis in school mathematical education is proposed.