A Class with Mathematical Knowledge, a Cube: In the lack of control, what learning happens? What knowledge happens? What existing happens?

This article presents a cartography of lines in processes that take place in the inner development of a class, taking three questions – What learning happens? What knowledge happens? What existing happens? – and maintaining an alliance with the studies developed by Gilles Deleuze and Félix Guattari, especially when they assume problematic science and existence as processes engendered with an imageless or non-dogmatic thought. The cartography occurs close to events in classrooms of training courses for mathematics teachers. In experimentation with mathematics, a device – take control of it – drags mathematical knowledge and formative processes and sets, through a policy that affirms cognition as a living thing, a disturbance both in mathematical knowledge and in the beliefs or conceptions that one has of this field of knowledge. This device makes it possible to approach learning along with a state of affairs by making the event count by updating it through functions, that is the role of science in the production of thinking. Thus, in experimentation, knowledge takes place in disturbance, abolishing quick responses and anticipated models, even living with them. Finally, experimentation requests other ways of life and other worlds, in another ethics, in another aesthetics in processes of desubjectivation, of involution, causing the destruction of the model of Being a Mathematics teacher.