There is increasing interest in creating frameworks for online discussions to improve learning outcomes in higher education environments. Many of these frameworks rely on and promote argumentation-based "challenge" models as the primary mode of discourse. This study tested one existing framework, created by Gunawardena, Lowe, and Anderson (1997), with four small groups in an online higher education environment. Asynchronous discussion transcripts of the four groups as they completed goal-oriented tasks were analyzed for both what the groups talked about and how they created new knowledge together. Using computer-mediated discourse analysis techniques, the Gunawardena et al. (1997) categories were operationalized into functional moves to capture the knowledge construction process. Findings show that rather than a challenge model of argumentation discourse, participants engaged in a relationship-oriented discourse of connection. Educators should be aware of both models of discourse, challenge and connect, because emphasizing only argumentation before trust has been developed among members of the group could result in unproductive conflict.