Chapter 5: Embodied Mathematical Communication and the Visibility of Graphical Features

In the cognitive science and mathematics education literature on graphs and graph-related skills (interpretation, production), it is assumed that certain features (e.g., slope, height) inherently stand out implying that those asked to interpret a graph are assumed to be addressing the sense of these features. The epitome of this approach can be seen from cognitive science research that proposes mental models that include iconic images of the graphs in the human brain (neurons). On the other hand, there are a number of studies among scientists that show how the visibility of graphical features itself is the outcome of a collective process, which elaborates what it is that can be seen objectively. In this chapter, I investigate, using a method grounded in conversation analysis and ethnomethodology, how graphical features become visible and objective by analyzing the work of pairs of scientists asked to interpret in-field and out-of-field graphs. The pairs have been chosen over individual think-aloud sessions because, in attempting to complete the requested task, the participants make available for one another what is required to remain aligned in solving the problem at hand. The study shows that perception includes an essentially passive (rather than intentional) element, where features have to be understood as given to the individual. Any initially individual way of seeing a feature becomes objectively available in and for the community through the embodied communication involving (deictic, iconic) gestures, body orientations, and prosody. For both features of the graph interpretation sessions, the products are better understood as emergent rather than as the outcomes of intentional processe. The purpose of this chapter then is to articulate how graphs and graphical features progressively come to be visible in and through sequentially produced bodily and embodied communication (talk, gestures, body orientations, prosody).