The stakes of movement: A dynamic approach to mathematical thinking

Abstract

Standard approaches to thinking in the mathematics curriculum depict it as the result of some stable constructions in the mind of the person, constructions that are the results of individual efforts in the mind of subjects or of collective efforts that are then appropriated by and into the mind of individuals. Such work does not appreciate what Vygotsky actually said about thought: that it is one part of a self-moving flow that relates to another part, speaking, without that one can be reduced to the other or the whole. Grounded in the works of Châtelet, Badiou and others, we exhibit the movement of thinking in a case study of graphing. In our account, there is a primacy of the Saying and drawing over their traces, the Said and the graph.

Keywords:

• movement
• thinking
• communicating
• flow
• unit analysis

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Mathematical physicists concretely use the idea of virtual displacements of a system to develop its mathematical description. They may take an arbitrary trajectory and then stipulate that the system will be in such a state that the virtual forces orthogonal to the movement disappear.

2. The sense of the Proto-Indo-European root per includes “going through”; this sense is carried over into English words such as experience, peril, performance and peregrination. Experience and performance, therefore, literally index processes of going through, undergoing and being imperiled.

3. See, e.g., http://www.manhattanarts.com/tag/marcel-duchamp/.

Additional information

Funding

A joint grant from the Natural Sciences and Engineering Research Council and the Social Sciences and Humanities Research Council of Canada (#412-1999-1007) supported the data collection for this article.

Notes on contributors

Wolff-Michael Roth

Wolff-Michael Roth is Lansdowne Professor of Applied Cognitive Science at the University of Victoria. He researches knowing and learning across the lifespan, drawing on a wide range of methods and theoretical frameworks. His most recent work is concerned with knowing, learning, assessment and development among airline pilots and airline companies as learning organizations. His most recent books include First-Person Method: For a Rigorous Approach to the Study of Living/Lived Experience (Sense, 2012), Passibility: At the Limits of the Constructivist Metaphor (Springer, 2011) and Geometry as Objective Science in Elementary School Classrooms: Mathematics in the Flesh (Routledge, 2011).

Jean-François Maheux

Jean-François Maheux is an associate professor in the Mathematics Department of the University du Québec à Montréal. His research interests are in primary and secondary mathematics education, and concern questions of the mobility of thought, ethics and epistemology in researching, teaching and learning with or without technology.