METHODS OF TEACHING SCIENTIFIC FOUNDATIONS OF THE FUNCTIONAL CONTENT LINE OF FUTURE MATHEMATICS TEACHERS

Introduction. The assimilation of the scientific foundations of the functional content line of the school course of mathematics by the future teachers of mathematics is a prerequisite for the formation of them, and subsequently by the pupils, which they will teach, the mathematical competence associated with the concept of function. Purpose. Proceeding from the stated the goal and the individual goals of the course of choice «Some issues of the school mathematics course from the point of view of higher», to present the teaching methods the theme «Onto mapping and functions in the school course mathematics», which is the scientific basis of the functional content line of the school mathematics course. Methods. Theoretical: analysis and comparison of spasial mathematical disciplines syllabuses of higher school and from mathematics curriculum for comprehensive school, content and approach near exposition of theoretical material in textbooks from this theme. Empirical: questioning (with the aim of determination of level of knowledge of students from the courses of mathematics of higher school). Results. The purpose of the teaching of this theme is to systematize the knowledge of students related to the concept of the function that underlies the modern school course of mathematics. The task of teaching the subject: 1) analysis of the school mathematics course from the point of view of fundamental mathematical ideas: correspondence, onto mapping, function; 2) to show of the evolution of the concept of «function», which plays a leading role in the course of modern mathematics school; 3) the disclosure of the role and place of the concepts of «function» and «mapping» in the school and university mathematics course; 4) promoting students' awareness of plural theoretical and logical aspects to the teaching this theme of the topic that relates to the theoretical foundations of mathematics school; 5) conducting of a comparative analysis of the definitions of general scientific concepts related to the function with the definitions of these concepts in the school mathematics course; 6) consideration of the basic elementary and elementary functions and their classes, classification of functions by their structure and properties; 7) elucidation of common approaches and features used in the study of elementary functions and their properties in the school course of mathematics and university courses «Mathematical analysis», «Higher mathematics». Originality. The author's teaching methods is proposed for the theme «Onto mapping and functions in the school mathematics», which is the scientific basis of the functional content line of the school mathematics course. This methodic contributes to the formation of mathematical and special competences of future teachers of mathematics. Conclusion. Methods of teaching scientific fundamentals of the functional content line presented in the article contributes forming to students of choice «Some issues of school mathematics course in terms of higher» of special competencies, which include: 1) the ability to demonstrate the basics of mathematical subjects, including «Mathematical analysis» and « Discrete mathematics «; 2) possession by professional mathematical language, the ability to speak properly and reasonably justify the position of «Introduction to Mathematical Analysis»; 3) understanding of the general cultural value of mathematics; 4) possession of content and methods of elementary mathematics; 5) understanding the logic of the development of the school's mathematics course. These competencies are one of type competencies that should have a student who obtains a degree 014.04. In Secondary Education (Mathematics).