Systems of linear equations and the theory of divisibility in the structure of mathematical competence of a chemistry teacher

Abstract

This article is dedicated to the analysis of the role of linear algebraic models and related divisibility theory issues in the mathematical activity of a chemistry teacher. The work has investigated the place and informational-logical connections of linear algebraic models in the system of mathematical competence of a chemistry teacher and has justified its significance. Examples from the school chemistry course have been given, where systems of linear algebraic equations have been actively used both over the field of real numbers and over the ring of integers. Various scenarios for solving problems, in fact reduced to linear algebraic models, have been illustrated. Such tasks have included classic problems with many reagent components as well as setting coefficients in complex chemical equations. The advantages and disadvantages of synthetic methods using chemical reasoning and formal algebraic methods have been analyzed. It has been substantiated that the teacher needed to understand the mathematical essence of the corresponding models to generate any solution and guide the students' corresponding work. The possibility of applying the basics of number theory in teaching chemistry has been shown. An analysis of the possession of relevant mathematical skills of working chemistry teachers has been conducted. Approaches were developed to improve the level of chemistry teachers’ skills of solving and analyzing systems of linear equations with real and integer variables in the conditions of postgraduate pedagogical education of teachers. The results, obtained in the work, have shown the need for an analysis of mathematics curricula in pedagogical and classical universities, sections related to linear algebra, as well as the introduction of the basics of number theory into mathematics curricula. The need to introduce mathematical training into the system of advanced training of chemistry teachers has been proven. Possible further research on this topic is related to the active implementation of blocks of linear algebraic models into the courses of advanced training of chemistry teachers and further analysis of their effectiveness