When the Classroom Floor Becomes the Complex Plane: Addition and Multiplication as Ways of Bodily Navigation

Abstract

In this article we contribute a perspective on mathematical embodied cognition consistent with a phenomenological understanding of perception and body motion. It is based on the analysis of 4 selected episodes in 1 session of an undergraduate mathematics class. The theme of this particular class session was the geometric interpretation of the addition and multiplication of complex numbers. On the basis of these episodes, the article examines 2 conjectures: (a) The mathematical insights developed by an individual or a group are expressed in and constituted by perceptuo-motor activity, and (b) the learning of mathematical ideas is shaped in nondeterministic ways by the setting or learning environment.