The Organization of Graphical, Narrative and Symbolic Interactions

In order to collaborate effectively in group discourse on a topic like mathematical patterns, group participants must organize their activities so that they have a shared understanding of the significance of their utterances, inscriptions and behaviors—adequate for sustaining productive interaction. Some methodologies applied in CSCL research—such as the widespread coding-and-counting quantitative analysis genre—systematically ignore the sequentiality of actions and thereby miss the implicit referencing, which is essential to shared understanding. The VMT Project attempts to capture and analyze the sequential organization of references and inter-relationships among whiteboard inscriptions, chat postings, mathematical expressions and other elements of virtual math team activities in order to understand the mechanisms of group cognition. Here, we report the results of a micro-ethnographic case study of collaborative math problem-solving activities mediated by the VMT multimodal online environment. We employ ethnomethodological conversation analysis techniques to investigate moment-to-moment details of the interaction practices through which participants organize their chat utterances and whiteboard actions as a coherent whole. In particular, we observe that the sequential construction of shared drawings and the deictic references that link chat messages to features of those drawings and to prior chat content are instrumental in the achievement of shared understanding (intersubjective reciprocity) among the team members. We characterize this foundational precondition of collaboration as the co-construction of an indexical field that functions as a common ground for group cognition. The integration of graphical, narrative and symbolic semiotic modalities in this manner also facilitates joint problem solving by allowing group members to invoke and operate with multiple realizations of their mathematical artifacts, a characteristic of deep learning of math.