Characterizing Instructor Gestures in a Lecture in a Proof-Based Mathematics Class

Researchers have increasingly focused on how gestures in mathematics aid in thinking and communication. This paper builds on Arzarello's (2006) idea of a "semiotic bundle" and several frameworks for describing individual gestures and applies these ideas to a case study of an instructor's gestures in an undergraduate abstract algebra class. We describe the role that the semiotic bundle plays in shaping the potential meanings of gestures; the ways gestural sets create complex relationships between gestures; and the role played by polysemy and abstraction. These results highlight the complex ways in which mathematical meanings--both specific and general--are expressed in gesture, and to highlight the integrated nature of elements of the semiotic bundle.