In the context of the sociocultural approach, the authors studied the problem of the development of the students' conceptual mental structures in the process of geometry teaching. An educational activity for the development of a generalized ability to solve geometry construction problems in electronic educational environment served as a development means. The objective of the research is to introduce a characteristic of the technology for the formation of the students' generalized ability to solve geometry construction problems in electronic educational environment focusing on the development of conceptual mental structures. The key factor is the transition from the content-based mathematics teaching to instrument and value-based one, which corresponds to the transformation of the content sphere of mathematical knowledge into procedural and contextual. Construction problems introduce fundamentally new for an adolescent form of activity. This kind of work makes it possible to transform declarative knowledge that provides an understanding of educational material into procedural, providing mastering and application of geometric concepts. In addition, value-based knowledge is developed, providing the value positions experience and creating conditions for the formation of the axiological sphere of the student's personality. The statistical data analysis confirmed the hypothesis that the student's general proficiency in solving geometry construction problems in terms of socio-culturally oriented education influences positively the development of conceptual mental structures.