Radical embodiment and semiotics: toward a theory of mathematics in the flesh

The idea that mathematical knowledge is embodied is increasingly taking hold in the mathematics education literature. Yet there are challenges to the existing conceptualizations: There tend to be breaks between (a) the living and experienced body (flesh) and linguistic forms of thought, (b) individual and collective forms of knowing, and (c) the material body and the source of intentionality. Grounded in material phenomenology, we theorize the living body as semiotic expression that not only grounds thought but also leads to its development. We provide a detailed case study that elucidates the three ways in which the living body serves as sign for the growth of a second-grade student's geometric understanding and the other bodies he interacts with.