A study on cognition: invention, learning and Mathematical Instruction

This paper proposes a dialogue between the notion of invention andmathematical instruction, mainly, the mathematics classroom. The discussion is based upon an episode of fi eld research, carried out in the Cartography method in a public school in Juiz de Fora/MG. Around this episode, two discourses are articulated about cognition and learning: the Conceptual Field Theory, by Gérard Vergnaud, andthe Semantic Field Model, by R mulo Lins. The invention crosses both discourses transversally, creating possibilities of thinking learning as a co-production of self-world.