The analysis of the problems of general mathematical education revealed a violation of continuity in the trajectory of its development in the middle school. The justification of measures for the development of spatial thinking of students establishes the feasibility of including a special module (based on geometric modeling of origami) in the content of additional professional education of teachers) as a "tool" for the development of spatial thinking and the eye-an important component of mathematical abilities. The results of the study are the following conclusions: - the educational environment with the use of origami is revealed as a complex of pedagogical conditions within the framework of the post-non-classical paradigm; - the synergetic nature and personal significance of the phenomenon of accompanying children's primary education with the practice of origami are revealed; - the substantiation of an economically feasible and rational pedagogical tool that contributes to the maintenance of the principle of continuity of mathematical education of a growing personality is given. Keywords: preschool and primary school age; psychological and pedagogical support; world view; existential- Ifl phenomenological; axiological; synergetic approaches; the line of general geometric education; additional education of children and teachers.