The use and effects of a CSCL-tool are not always predictable from the properties of the tool alone, but depend on how that tool is appropriated. This paper presents the findings from a case study about the appropriation of a graphical shared workspace. When students are presented with a new tool they may encounter competing constraints and multiple possibilities for interacting with it. We argue that during critical events the students make choices, and in order to collaborate, coordinate these choices as a group. We study appropriation by looking into the ways in which small groups organize their contributions during a computer-mediated argumentative discussion. The results of our study illustrate how certain principles for organization emerge from an implicit negotiation of conventions, with mutual influence between the students and the tool.