Studying Virtual Math Teams

Abstract

This chapter introduces a theoretical framework for analyzing collaborative problem solving in chats, based on the concept of polyphony and Bakhtin’s theory of dialog. Polyphony, a notion taken from music theory, may be considered as a general model for interaction and creativity by a group of people (“voices,” in an extended sense) following patterns of counterpoint. As Bakhtin emphasized, polyphony may occur in texts; we will show that it can occur in problem-solving chat texts. One of the features of polyphonic music is its potential development of complex architectures starting from a given theme. Polyphonic structuring of dialogs may transform the interaction into a “thinking device”: Different voices jointly construct a melody (story or solution), sometimes adopting different positions and then generating, idenepsying or solving dissonances (unsound, rickety stories or solutions). Polyphony consists of several “horizontal,” longitudinal melody lines that are “vertically,” transversally integrated. Similarly, in chats, the continuations of utterances are tied together over time providing a melodic line. Simultaneously, they are coordinated with the utterances of others, maintaining the integration toward unity across various themes and variations that sometimes can introduce differences. This chapter also proposes software tools for the visualization of the polyphonic weaving in chats. These tools idenepsy and visualize the explicit and implicit links among utterances, and may determine or visualize the contributions of each participant in a chat.