for the learning of mathematics

an international journal of mathematics education

Wolff-Michael Roth - Vol. 30 Num. 2 (2010)
 Incarnation: radicalizing embodiment of mathematics


As the end result of metaphysics, the Kantian and constructivist mind is not present in the world but withdrawn into the netherworld of its representations and constructions. First phenomenology then the embodied cognition research showed how there could be no cognition without the human body. There is something unsatisfying and lacking, however, in the concept of the body, which undermines the very effort to ground (mathematical) knowledge differently than in the private cogitations of the isolated mind. The purpose of this paper is to argue for a more radical approach to the conceptualization of mathematical knowledge that is grounded in dialectical materialist psychology (as developed by Lev Vygotsky), materialist phenomenology (as developed by Maine de Biran and Michel Henry), and phenomenological sociology (Bourdieu). Most essentially, the approach rests on a shift from the material body to the flesh. The close relation between cognition and the world is possible only when there is flesh, whereas material bodies are insufficient condition for mind to emerge. In this phenomenological reflection on the conditions of geometrical knowing, I draw on a concrete example from a second-grade classroom, which I consider from the perspectives of different conceptualizations of mathematical knowing.