Concept gesture and concept definition in mathematics with particular reference to sequences and limits

Concept image and concept definition, among the most utilised constructs in mathematics education research, emerged in a period characterised by cognitive theories of learning aimed at explaining individual students’ mathematical constructions. Acknowledging learning theories that have since developed, and in particular those that emphasise the bodily dimensions of mathematical thinking, in this article we propose concept gesture as a construct that foregrounds the role of the body in mathematical teaching and learning, while expanding on the notions of concept image and concept definition. We illustrate the construct by examining some of a lecturer’s mathematical gestures in a first-year university analysis lecture, focusing specifically on those that convey conceptual meaning in relation to the concepts of sequence and limit. We discuss how concept gestures, understood within an embodied perspective, can productively enrich the concept image/definition framework, and suggest practical, theoretical, empirical, and methodological implications.