3373

Russell Dudley-Smith & Jeremy Burke

philosophy of mathematics education

2016

30

Deleuze and Guattari , Dowling , Hjelmslev’s semiotics, liminality , recontextualisation , Rotman , Social Activity Method , mathematical subjectivity , semiotics in mathematics education research

Rotman has specified a triadic conception of the mathematical subject, drawing inspiration from Peirce’s semiotics. This paper interrogates Rotman’s discussion by imposing a different theoretical framework recontextualised by Dowling from Hjelmslev. The argument is that by separating out dimensions of expression and content a fully relational account of subjectivity can be achieved; one in which the necessary pedagogic paths and their difficulties in the formation of specialised subjects are specifiable with some texture. It is argued that to become subject requires moments of liminality; with all that this entails about the significance of ritualising action, and the perils of avoiding a necessary symbolic violence in education. The approach does not grant semiotic privilege to the discursive, so satisfying one of Rotman’s principle concerns: the embodied nature of subjectivity. The resulting framework is complementary to Rotman. It provides a basis for considering the apprenticeship and distribution of the subject in the socio-political context of mathematics education. It seeks to do this without falling back on an ontologised notion of the value of school mathematics in-itself – one conceived somehow to lie outside of its socio-cultural-historical instantiation. A connecting thread is the recontextualisation of Hjelmslev by Deleuze and Guattari, whose work is significant to a reading of Rotman. Yet the framework also offers distance from a current trend in the mathematics education literature: one in which the names, if not the substance, of Rotman, Deleuze and Guattari are heavily recruited to substitute, for a proper relationality, an (ultimately humanistic and liberatory) material ontology.