The aim of the study is the development and experimental verification of the effectiveness of methods of formation of students’ constructive abilities. The objectives of the study are to study the operating part of the constructive skills of students; the definition of methodological features of formation of geometric concepts in the context of implementation of STEM education; selection of content of educational material and determination of methods for development of pupils’ constructive skills. The object of the study is the process of formation of students’ geometrical skills at geometry class in school. The subject of the study is the technique of formation of students’ constructive skills in the context of STEM education implementation. The research was carried out by means of analysis and generalization of data on the research problem based on the study of psycho-pedagogical and methodical literature, electronic resources, school practice and own teaching experience. Qualitative and quantitative analysis was conducted. The author developed methods and the system of learning tasks on geometry, aimed at developing of students’ constructive abilities, criteria of selection of students’ constructive activities in term of STEM education.