Chapter 11: Blending across Modalities in Mathematical Discourse

When people engage in face-to-face discourse about mathematical topics, they deploy a variety of communicative modalities, including at least speech, gesture, and various forms of symbolic and diagrammatic marking on paper or blackboards. These modalities are not parallel streams: To be parallel means to never meet, but speakers mix these streams constantly, coordinating distinct representational resources in a fine-grained way within a single, shared, and meaning-laden space, and it’s in this space that communication and thinking are performed. There are even cases where the apparent boundaries between modalities break down entirely. To understand mathematical discourse, then, it’s not enough to examine individual meaningful actions—single utterances, gesture strokes, and so forth. We also need to understand the structure of the space in which they occur and how this structure is built, maintained, and manipulated through communicative acts. In this chapter, I’ll examine this question through a series of examples drawn from a corpus of naturalistic video recordings of upper division and graduate mathematics students working together in small groups to complete their assigned homework in topology and abstract algebra (Smith, 2003).