ОСОБЕННОСТИ ИЗУЧЕНИЯ ОПРЕДЕЛИТЕЛЕЙ ПРИ ПОДГОТОВКЕ УЧИТЕЛЯ МАТЕМАТИКИ

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Modern educational technologies are associated with data-related accessibility to factual knowledge, computer-aided capabilities for its application in the course of solving problems, technological solutions in discussing various issues, etc. For that purpose, it is imperative to develop guidelines with regard to the features of the subject-matter expertise being generated among to-be mathematics teacher. According to the authors, the methodological nature of mathematical knowledge should become such a guideline. The article contains an analysis of the determinant theory studied in an algebra course in the process of mathematics teacher training. In the content of this section, the authors note two interpenetrating ideas of mathematics: constructivism and axiomatization. It is recommended to use this feature to organize the study of determinants in the course of mathematics teacher training. In the standard study of the theory of determinants, only a constructive definition of the concept of a determinant is usually used; on its basis, the properties of the determinant are proved and its applications are considered. The axiomatic approach to constructing the determinant theory is only mentioned as a possibility for structuring the content, if at all. The authors believe that the disregard of the axiomatic construction of the determinant theory makes it impossible to reveal the methodological essence of mathematical knowledge. This understanding is essential for prospective mathematics teachers. This is justified by the fact that their understanding of the fundamental principles of constructing mathematical knowledge is the basis for organizing their students’ mathematical learning activities. Therefore, the authors consider it appropriate to consider the axiomatic definition of the concept of determinant. The article schematically presents a program for studying the determinant theory, including a constructive approach to the concept of determinant and the construction of the determinant theory in line with the axiomatic method. The mutual use of the constructivism and axiomatization ideas in obtaining facts on the determinant theory is shown. The authors note that the implementation of the proposed approach to the study of determinants makes it possible to encourage students to do additional research in the determinant theory.