Abstract
<jats:p>This article considers the actual problem of development of the geometrical component of students' mathematical abilities, which is relevant not only for one national system of education, but as international monitoring studies (TIMSS, PISA, etc.) show in general and globally. The aim of the study is to identify personal characteristics (“geometric vision”, the ability of spatial representations, the role of students' intrinsic motivation, etc.) for use in the process of solving geometric problems. The technology was developed for use in the process of solving predominantly geometric problems, manifested in a personalized approach, prioritizing identified personal characteristics. As an example, a mathematical description of a stereometric problem is offered and its solution is analyzed in a psychological and pedagogical context, in the context of the development of the geometric component of students' mathematical abilities. The results of the analysis of theoretical and practical interpretation of the content, in the context of the problem under consideration, can serve as a basis for designing a modern model of teaching the younger generation: for building a model of development of the geometric component of their mathematical abilities and the technology of solving geometric problems (mainly stereometric), taking into account the priority tasks of secondary general education and federal working programmes of teaching the course ‘Geometry’.</jats:p>