Abstract
The article proposes the structure and content of the project of a children’s academy in the framework of additional mathematical education in «Fractal geometry for senior students». The system of building the educational process in the children’sacademy is described and a table of thematic planning for one academic year is given. The purpose of this article is to present a new form of the educational process with the use of design and research activities in the additional education of high school students through fractal geometry for implementation in educational organizations. The objectives of the article are to scientifically substantiate the need to include the humanitarian component in teaching fractal geometry; study of the theoretical foundations of fractal geometry in order to use it in additional mathematical education in the organization of design and research activities; description of the types of organization of mathematical activities and the identification of methodological techniques for students; development of a methodological apparatus, description of the design and research form of education.
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