- Popkewitz (2008) has studied the effects of education and educational sciences into the constitution of the cosmopolitan citizen of Modernity in the USA during the 20th century. Cosmopolitanism refers to the ‘Enlightenment’s hope of the world citizen whose commitments transcended provincial and local concerns with ideal values about humanity’ (p. 1). The school mathematics curriculum is a powerful technology of the self. The technologies of the self are the techniques that human beings have historically developed in practice to understand themselves as human. These technologies:

- In the case of the schools, children and teachers that we have been working with, the existence of a deficit discourse on the students who live in the misery belt of Bogotá is an expression of the effective use of the tools of mathematics educational technologies not only to teach children mathematics, but also to create a clear position of exclusion for them. Teachers collectively constructed the class 703 − Grade 7, group 3 − as those who ‘have low values’, ‘have little interest in their learning, especially in the learning of mathematics’ and:

- According to the Colombian Curricular Guidelines (National Ministry of Education of Colombia [MEN], 1991), the mathematics curriculum in secondary schools should promote notions of space in Euclidean geometry and to a lesser extent in projective geometry. The curricular contents tend to be reduced to the establishment of geometric figures and their properties. In Euclidean geometry, space is constructed on the grounds of the reflection on the properties of geometrical shapes, made evident through the use of ruler and compasses. Combined with the Cartesian coordinate system, it allows one to think about space as a system of positions that can be described in a precise and uniform way (Gálvez, 1985). Projective geometry invites an active exploration of tridimensional space in an external or imagined reality, and through the representation of solid objects in space. The guidelines describe the cognitive processes that children need to attain as a result of the teaching of central notions of Euclidean and projective geometry in defining space:

- In each nodal point a series of activities combined different mathematical notions related to space as well as many other topics of the curriculum. However, the mathematical activity was always carried out allowing connections to the students’ experiences in the family, in the school and in the locality. For example, in the first nodal point ‘Who am I?’ students were asked to write a story about themselves in their family. Jeimy, one of the students, wrote: