Laurie Edwards Ornella Robutti Janete Bolite Frant

The goal of the Working Session is to deepen the investigation of mathematical thinking, learning, and communication by considering the variety of modalities involved in the production of mathematical ideas. These modalities include gesture, speech, written inscriptions, and physical and electronic artefacts. The central purpose will be to examine how basic communicative modalities such as gesture and speech, in conjunction with the symbol systems and social support provided by culture, are used to construct mathematical meanings. In addition, the role of unconscious conceptual mappings such as metaphors and blends will be investigated in relation to gesture and the genesis of mathematical concepts. Relevant theoretical and empirical work has been carried within cognitive linguistics (Lakoff & Núñez, 2000), semiotics (Radford, 2002) and psychology (McNeill, 1992). Themes and questions to be addressed include:
• How do gestures relate to speech, writing (eg, of formulas), drawing, graphing and other modalities of expression?
• How do gestures condense/manage information during social interaction?
• How are conceptual metaphors and blends involved in students’ cognitive processes while learning and doing mathematics, in different settings?
• How do gestures and unconscious conceptual mechanisms relate to external representations and technologies used in mathematical activity?
The Working Session will consist primarily of small groups working together to: (1) make progress in answering one of the above (or a related) question; and (2) engage in collaborative analysis of videotaped or other data showing the use of various modalities in mathematical activity.
Fauconnier, G. & Turner, M. (2002). The way we think: Conceptual blending and the mind's hidden complexities. New York: Basic Books.
Lakoff, G. & R. Nunez (2000). Where mathematics comes from. NJ: Basic Books.
McNeill, D. (1992) Hand and mind: What gestures reveal about thought. Chicago: Chicago University Press.
Radford, L. (2002). The seen, the spoken and the written: A semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics 22,2, 14-23.

Notes from SubGroups