ON THE UNIFORM APPROACH TO THE ALGEBRAIC EXPRESSIONS IDENTICAL TRANSFORMATIONS STUDY IN THE COURSE OF ALGEBRA AND THE BEGINNINGS OF ANALYSIS

Abstract

Formulation of the problem. The article reveals the author's methodical approach to the study of algebraic expressions in the course of algebra and the beginnings of analysis in a senior professional school. Since this approach is recommended for studying irrational, trigonometric, exponential, and logarithmic expressions, it is called the only generalized one.

Materials and methods. According to this approach, it is recommended to study each type of algebraic expression in four stages: preparatory, basic, practical, and applied. Each of the stages is naturally consistent with the elements of the didactic cycle, which is considered as a consolidated unit of the educational process for the study of a specific educational topic of the algebra course and the beginnings of analysis. At the preparatory stage, attention should be focused on practical needs that prompt consideration of the specified expressions, historical information about the solution of problematic issues by the efforts of mathematicians of different times, the meaning and definition of the expression under consideration, etc., should be reported. At the basic level, the basic identical equalities are studied, at the practical level, the skills and abilities to perform transformations of expressions are formed, and at the applied level, the application of the acquired knowledge, skills and abilities is demonstrated when solving applied problems, where these expressions are used as mathematical models.

Results. The content of the unified generalized approach is clearly illustrated by the author in the article on the example of studying the topic "Trigonometric expressions and their transformations" (21 hours). It is clear that the content of each of the stages depends on the type of expressions to be studied, but the methodical scheme (guideline rule) is the same.

Conclusions. As the approbation of the mentioned approach showed, its practical use is less time-consuming compared to traditional approaches: it is effective, modern, more informative, implements the applied orientation of mathematics education, and deserves attention and use during the teaching of algebra and the beginnings of analysis in high school.