The article reveals the problem of applying figurative thinking in the process of studying the fundamental concepts of mathematical analysis. The fundamental concepts of mathematical analysis include: real number, function, limit of a function at a point, continuity of a function. The article reflects the content of student's ideas about fundamental mathematical concepts of mathematical analysis, the possibility of actualization of student's pre-scientific ideas. The regularities of development

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... of pupil's visual images of mathematical notions are specified. The findings are based on studies of students' ideas about mathematical concepts. The types of images of mathematical concepts are disclosed: geometric, symbolic, artistic. The essence of stages of formation of fundamental mathematical concepts is characterized: the stage of "worldly" representations, the stage of monomodal mathematical representations, the stage of complex representations, the conceptual stage, the conceptual stage. The possibilities of using various forms of mathematical notions' representation are specified. The schemes demonstrating the interrelation of mathematical concepts and ideas in a school mathematics course are given. At presentation of a theoretical material the picked up examples which illustrate use of figurative thinking of pupils at studying of fundamental concepts of the mathematical analysis in a course of mathematics are applied expediently.