Abstract
In this paper we study the mathematical body as an assemblage of human and non-human mathematical concepts. We argue that learners’ bodies are always in the process of becoming assemblages of diverse and dynamic materialities. Following the work of the historian of science Karen Barad, we argue that mathematical concepts must be considered dynamic material, and we suggest a “pedagogy of the concept” that animates concepts as both logical and ontological. We draw on the philosopher of mathematics Gilles Châtelet in order to pursue this argument, elaborating on the way that mathematical concepts partake of the mobility of the virtual, while learners, in engaging with this mobility, enter a material process of becoming. We show how the concept of virtuality allows us to look at mathematical concepts in school curriculum in new ways.
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Notes
See for instance the 2012 special issue of the Journal of the Learning Sciences 21(2).
Cutler and MacKenzie borrow the use of the term from Deleuze, who nicely leverages this mathematical concept to talk about processes of determination in which relations are more ontologically primitive than relata.
The simultaneous functioning we are describing here might evoke for readers a comparison with the process/content distinction made in the NCTM Standards. An important difference, however, is that the same concept (parity, in this case) partakes of both the content and the process. Moreover, when functioning on the ontological level, parity has much greater precision and power than process strands such as representation, communication and visualization.
In this he follows the scholastic tradition of contrasting extension—that being the interval actually travelled and its duration in time—with intension—that being its quickness, slowness or “lateness” (Châtelet, 2000, p. 38). As odd as this distinction might seem to modern readers, it is used by Châtelet to disrupt the privileging of position over motion, and to try and imagine motion as the ontogenetic force by which position (or extension) comes into being.
In referring to “iteration,” Châtelet means the kind of mechanical repeated juxtaposition of numbers that characterizes addition and subtraction (and some conceptions of multiplication).
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de Freitas, E., Sinclair, N. New materialist ontologies in mathematics education: the body in/of mathematics. Educ Stud Math 83, 453–470 (2013). https://doi.org/10.1007/s10649-012-9465-z
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DOI: https://doi.org/10.1007/s10649-012-9465-z