The relevance of this article is due to the need of the modern school to find a way to develop mathematical giftedness, and this can only be implemented through education taking into account the interests, inclinations and specific development of younger schoolchildren. To solve this problem, you revealed the structural components of the mathematical giftedness of junior schoolchildren, motivational-value, operational-technological, co-gnitive, reflexive, the stages, methods and diagnostics of the matte-mathematical giftedness of a junior schoolboy were determined. The concept of "mathematical giftedness of a junior schoolboy" is specified because mathematical giftedness is sometimes not correctly interpreted, denoting it as a high ste-ste of the functional and potential capabilities of a junior schoolboy within the framework of academic performance, stages, methods and diagonal-sticks of the mathematical giftedness of a junior schoolboy are determined. Analysis of the results of the experiment proves that the development of the mathematical giftedness of younger schoolchildren will be effective if specially developed stages are implemented, methods for the development of mathematical giftedness aimed at the development of the following components of mathematical giftedness: motivational-value, operational-technological, cognitive, reflexive components. Practical material contributes to the development of educational programs for the development of mathematical giftedness among younger schoolchildren.