Context: Visuospatial abilities that derive from perception, for example, are not usually considered one of the mathematical abilities developed in the national school geometry curricula. Objective: This work aims to explore school practices that seek to guide the ways of being and acting of students in Chile. Design: This is done by mapping the geometry school curriculum to trace the system of reason that makes possible the fabrication of particular kinds of people. The study uses a Foucaultian toolbox to address school geometry as a technology of government that has power effects in shaping students' subjectivities. Data: School textbooks distributed by the Chilean Ministry of Education, MINEDUC, from the final six levels of school education (13 to 18 years) were analyzed. Data analysis: The school textbooks were explored, through discourse analysis, to map the connections between the activities proposed in the geometry units for each level in order to trace the paths that allow for guiding students’ ways of being and acting. Results: Evidence compiled from an analysis of current Chilean mathematics textbooks shows that geometry school practices are constructed to train the eye so that students conceive and experience space not through their senses but through reason and logic, which inserts students in the modern process of training scientific minds of the future.