Do students appropriate the problems, making them their own? Are they the right problems, those designed for learning? These issues are particularly important in game-based learning where one may ask if students learn or play. This paper aims to present the first draft of a model for students' problem appropriation. It is based on both theoretical and empirical grounds. To build our model of appropriation we first articulate two sources: Bakhtin's (1981) Philosophy of Language and Brousseau's (1997) Theory of Didactical Situations. Secondly, we analyse data with two grids of analysis, one from the Cooperative Problem-solving model (Baker, 2002) to describe students' interactions and one built from our model to identify indicators of students' problem appropriation. The study occurs in recent implementation of serious game Laboratorium of Epidemiology© (Ney and Balacheff, 2008) in a Biostatistics course (Grenoble Medicine School, France). This game was inspired by Moher's (2006) Concept of Embedded Phenomena. Our database includes students' interactions, productions, and computer trails. Results and discussion set up relations between cooperative problem-solving and individual problem appropriation from which will emerge a model for group problem appropriation.