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We conceptualize referencing as a primary means of establishing intersubjective meaning and, therefore, as an important consideration in supporting collaborative learning. What we call group cognition is a discourse-centered analysis of the interactional basis of collaborative knowledge building, establishing common ground and co-constructing shared meaning. This epistemological perspective has methodological, technological and pedagogical implications. It directs empirical analysis toward the manifold forms of referencing that constitute small-group communication. Studies of how students actually make sense of, adapt and adopt referential affordances in computational media are used to inform the design of educational software environments. In particular, we are developing an online service for groups of people to discuss mathematical themes. This paper looks at how a group of students used methods of referencing to co-construct geometric objects in a chat room with graphical referencing tools.