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Inscriptions becoming representations

This paper 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 shows how inscriptions become representations for the group through a historical trajectory of negotiation. This result is of theoretical interest because it shows how the practices underlying group cognition are contingent upon not only the immediate situation but also the chronologically prior resources and associated practices.