This paper analyzes two examples of whiteboard meetings from a college calculus-based introductory physics course taught using University Modeling Instruction. In this pedagogy, students work in small groups to create a solution to the same problem on 2' × 3' whiteboards. They then sit in a large circle with their whiteboards held facing in and conduct a student-led whole-class discussion ("board" meeting) to reach a consensus. One example is given of a conversation where students overcame sharp disagreements to eventually reach whole-class consensus and another example is given where they did not. We examine how social positioning contributed to students either successfully examining and resolving different ideas or failing to do so. Initial results from two different "board" meetings tentatively support the idea that meetings where "experts" soften their position by "hedging" more frequently are better able to overcome sharp initial disagreements to reach consensus on their own. Our analysis suggests that the way students position themselves in discussions may open or close the collaborative space to productive sense-making.