Abstract
The significance of the problem under study is due to the fact that the methodology of teaching students -future mathematics teachers of scientific knowledge is based on the idea of projecting the activities of a mathematics teacher with scientific knowledge on the process of studying the educational material of a school mathematics course.It includes the target (learning outcomes), substantive (pithy component systems), as well as processural (teaching methods and means) components.In this case, the main means of teaching students -future mathematics teachers is a system of tasks, the execution of which contributes to the formation of scientific knowledge, models the work of a mathematics teacher in the study of mathematical allegations.This article identifies the problems of designing and developing the content of elective courses in the system of higher pedagogical education, the psychological and pedagogical factors of students' assimilation of the content of educational (scientific) material in the study of elective disciplines determined, the theoretical foundations of designing the content of educational materials are determined, pithy meaningful components of elective courses based on the principles and criteria of pedagogical didactics have been developed, complementing the existing system of pithy components of mathematical disciplines, a methodology for the development and use of substantial components is proposed, the possibility of realizing their basic functions to form professional knowledge and skills of students -future mathematics teachers is justified, the basic requirements for designing the content of the educational material of elective disciplines are determined.