DIDACTIC CONDITIONS FOR THE DEVELOPMENT OF SPATIAL IMAGINATION IN THE PROCESS OF GEOMETRIC TRAINING OF FUTURE MATHEMATICS TEACHERS

Abstract

Summary. The article examines the features of the formation of spatial imagination in students in the context of modern training of future mathematics teachers. Its key importance in the process of studying geometric disciplines is substantiated. It is determined that spatial imagination is an important cognitive ability that ensures successful operation with imaginary geometric images.

The purpose of the work is to theoretically substantiate and develop a methodological mechanism for the formation of spatial imagination of future mathematics teachers during the teaching of geometry in higher education institutions.

The methodological basis of the study is: an analysis of scientific and pedagogical sources regarding the features of the development of students' spatial thinking; the method of analytical transformations applied for studying methods of specifying spatial lines within higher mathematics; the generalization method to derive a universal definition of a line; the comparison method to identify differences between continuous and discrete languages ​​in geometry.

Research results. The main problem of teaching geometric disciplines in higher education institutions is the dominance of the abstract-deductive approach, which causes a loss of connection with the primary clarity of geometric images. An effective way to overcome this problem is to implement the principle of complementarity. In this context, the intra-subject integration of continuous and discrete languages ​​is considered as a key condition for the development of spatial imagination of future mathematics teachers.

Originality. A mechanism for forming students' ability to operate with spatial images during the study of differential geometry has been developed. The development of spatial imagination is considered as a teacher-controlled transition between complementary codes of information perception. Based on topological notions of homeomorphism (as a deformation without breaks and gluings), synthetic definitions of a curve are generalized.

Conclusions and prospects for further research. Prospects for further research in solving the following didactic problems are outlined: cognitive transition, methodological formalism, underestimation of pragmatics and spatial adaptation when teaching geometric disciplines.