This chapter analyzes the interaction of three students working on mathematics problems over several days in a virtual math team. Our analysis traces out how successful collaboration in a later session was contingent upon the work of prior sessions, and shows how representational practices are important aspects of these participants' mathematical problem solving. We trace the formation, transformation and refinement of one problem-solving practice-problem decomposition-and three representational practices-inscribe first solve second, modulate perspective and visualize decomposition. The analysis is of theoretical interest because it suggests that "situated cognition" is contingent upon not only the immediate situation but also the chronologically prior resources and associated practices; shows how inscriptions become representations for the group through an interactive process of interpretation; and sheds light on "group cognition" as an interactional process that is not identical to individual cognition yet that draws upon a dynamic interplay of individual contributions.Prior work in our laboratory at the University of Hawai'i and elsewhere has examined the importance of representational resources to collaborative learning, including experimental studies testing hypotheses concerning how given notations or environments can influence learning processes (Suthers & Hundhausen, 2003;Suthers et al., 2008) and ideographic analyses of how participants make use of representational affordances (Dwyer & Suthers, 2006;. In order to broaden our understanding to a greater diversity of representations and situations, we have begun to analyze data from other sources. Sharing of data and analyses across laboratories is an important strategy for advancing our field, as exemplified by this volume. At Gerry Stahl's recommendation, we selected for examination Team B's work in the VMT Spring Fest 2006, previously analyzed in Stahl (2007b) (now expanded in Chapter 26). In this sequence of four hour-long sessions, students address a breakdown in their understanding of how they solved a problem, making indexical references to inscriptions in a whiteboard as problem representations. The first major concern of this paper is to understand the role of representations in these students' problem solving.There is a convincing body of work showing that learning, problem solving and other group accomplishments are contingent upon the situation (e.g., Garfinkel, Medina, R., Suthers, D. D., & Vatrapu, R. (2009) Goodwin, 2000;Greeno, 2006;Koschmann, Stahl, & Zemel, 2007;Lave & Wenger, 1991). The second major concern of this paper is the claim that this situated contingency is not restricted to the immediate situation or bounded at some temporal threshold, but reaches into the past at successively larger granularities. As Blumer tells us, "any instance of joint action, whether newly formed or long established, has necessarily arisen out of a background of previous actions of the participants" (Blumer, 1969, p. 20). In computer-supported co...