Multimodal Semiotics of Mathematics Teaching and Learning
Sicoli, Mark A
The practice of mathematics education is fundamentally multimodal. It incorporates not only talk and embodied action, but also technical notation and diagrams, brought into discourse through verbal and gestural reference. As this interplay of semiotic systems arises in interaction, it can be interpreted by analyzing sequences of talk, writing, and gesture, but a better understanding requires an ethnographic perspective to contextualize interaction with reference to its physical surroundings, institutional setting, and enduring relationships within the community. Thus, classroom interaction is best understood as a multimodal ecology in which micro-level discursive practices, the history of a community, and the biographies of its members mutually influence and determine one another.Beginning from the ecological perspective on classroom interaction, this dissertation presents an analysis of observations and video recordings collected during a semester’s multi-site ethnographic fieldwork with both a middle school math class for English learners and a quasi-remedial college calculus section. To model how any perceptible feature of the environment may be taken as meaningful, I draw on the semiotic theory of C. S. Peirce, not only in interpreting observational data, but as an organizing principle, as the analysis moves from qualities, to particular instances, to recurring patterns. First, I consider the ontological status of mathematical notation as a quality of interaction, investigating its capacity for representing continuous phenomena. Second, I take up actually occurring sequences of interaction, showing how students’ participation in conversational repair offers insights into ideologies of classroom authority and mathematical knowledge. Third, I address students’ and teachers’ identities in the classroom as social perceptions that are constructed and recognized through patterns of interaction. Each area of inquiry is then reconsidered to identify semiotic affordances that are made available in classroom interaction, and to explicate problems of practice that prevent students from seeing themselves as successful mathematics learners. The problems I identify are similar to those addressed by mathematics education researchers in the learning sciences, so I conclude by proposing a future research trajectory combining linguistic anthropology, the learning sciences, and classroom teaching practice.
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