Keyword: «functional and graphical line»

The functional and graphical line is one of the main lines of the mathematics curriculum and it is of fundamental importance. The results of various diagnostic work, the analysis of domestic and foreign studies indicate an insufficient development of the system of knowledge and skills among students in the field of mathematical functions. This actualizes the methodical search for effective didactic tools enriched with the capabilities of the digital environment to form the concept of function as a mathematical model of the surrounding world phenomena and to master the full range of skills of the functional and graphical line. The aim of the study is to identify techniques for the formation of basic concepts and skills of the functional graphical line among secondary school students and to identify digital tools for the implementation of these techniques. To achieve this goal, we applied the following methods: comparative analysis of psychological and pedagogical literature, dynamic mathematics programs, as well as neural networks that generate visual content; study of local history material, fiction, film and game industry; pedagogical observation; student questionnaires; diagnostic works and their analysis; graphical representation of data. Didactic techniques are based on the principle of the unity of components of students' mathematical training; methodological scheme for studying functions in secondary school; heuristic approach to teaching mathematics. Examples of the identified techniques implementation are given. Based on the survey and analysis of the results of diagnostic work, it is concluded that the motivation of secondary school students to study functions, the effectiveness of subject learning results, the development of research skills and mathematical creativity in the field of functional and graphical line is increased. The theoretical significance of the study is represented by the description of a set of didactic techniques for the formation of basic concepts and skills of the functional graphical line and digital tools for their implementation in accordance with the stages of studying functions. The practical significance of the research lies in the description of methodological aspects of the implementation of the identified didactic techniques in the educational process: "Graphics around us", "Functions in stories, movies and games", "Functions as models of real processes", "Anki memory card", "Slide is a bright spot", "Digital assistant", "Interactive assignments".