Theorizing embodiment in the mathematics classroom – Elizabeth de Freitas, Nathalie Sinclair (2012)

http://www.esri.mmu.ac.uk/mect/papers_11/deFreitasSinclair.pdf

Rather than considering the diagram or gesture to be a mere representation of a concept, the authors (via the work of Gilles Chatelet and Humean tradition) view these as embodied acts that form and alter interactions with the outside world. The body extends to include tools, groups and institutions. The paper explicates the ideas of Chatelet at length, which is useful as the book they reference is hard to find, and explore the diagram as an act of ‘cutting out’ with reference also to Deleuze. The ‘hinge-horizon’ is a point or line where the plane is overridden and a different encoding allows for things such as the infinite to be suggested, eg. perspectival drawing.

The authors experiment with dynamic diagrams, as opposed to the finished, static images in textbooks, and engage students in a diagramming task which was considered an end in itself, and discuss what they learn of students’ interpretations, noting a subjectivity in some.

…the work of Châtelet challenges educators to reconsider the power of student diagramming as a disruptive and innovative practice that sheds light on the very nature of mathematical agency.

The mathematical subject comes into being (is always becoming) as an assemblage of material/social encounters. The mathematics student must make a composite or assemblage with the physicality of the film, paper, pencil, etc. in order to be constituted as a subject
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