Content line "Functions" of the school mathematics course and the peculiarities of its study in secondary school

Abstract

The article reveals the important circumstances and peculiarities of the study of the content line "Functions" in the school mathematics course. Among the circumstances is a different interpretation of the concept of function: in the basic school, the function is considered (classical approach) as a dependence between variables, and in the senior profile as a correspondence (modern, modern definition) between the elements of two sets. This leads to different schemes for studying the properties of a function and constructing its graph.

It is noted that the content line "Functions" is the leading line of the school course of algebra, algebra and the beginnings of analysis. It is the basis for studying equations, inequalities, identical transformations of algebraic expressions, the beginnings of probability theory, geometric quantities (area of a figure, volume of a body, surface area of a body, etc.). It starts in grade 7 and is taught in three stages: Stage 1 - grades 7-9. The main purpose of studying functions is to justify the study of linear, quadratic, fractional rational equations and inequalities, identical transformations of single terms, polynomials and fractional expressions, to teach how to use them as mathematical models in the study of physics, solving practical and applied problems; Stage 2 - grades 10-11, when basic elementary functions and their important properties (increasing, decreasing, periodicity, continuity) are studied. The main goal of the course is to teach students to solve irrational, trigonometric, and exponential equations and inequalities, transform corresponding algebraic expressions, and create graphs of the glass