Interactional achievement of shared mathematical understanding in a virtual math team

Learning mathematics involves specific forms of social practice. In this paper, we describe socially situated, interactional processes involved with collaborative learning of mathematics in a special online collaborative learning environment. Our analysis highlights the methodic ways group members enact the affordances of their situation (a) to visually explore a mathematical pattern, (b) to co-construct shared mathematical artifacts, (c) to make visible the meaning of the construction, (d) to translate between graphical, narrative and symbolic representations and (e) to coordinate their actions across multiple interaction spaces, while they are working on open-ended math problems. In particular, we identify key roles of referential and representational practices in the co-construction of deep mathematical group understanding. The case study illustrates how mathematical understanding is built and shared through the online interaction.