The authors investigated the microlevel processes of collaborative reasoning in heterogeneous peer dyads working on an open-design task in elementary geometry. Special attention was paid to the nature of student social interaction, problem-solving strategies, and mathematical language and how they shape collaborative problem-solving processes. Qualitative case-based analyses of 3 focal dyads reveal that collaborative reasoning was supported by equal participation in social interaction, consisting of joint negotiation of problem-solving strategies and active conceptualization and visualization of the situation. Challenges to collaboration were manifested in the existence of divergent strategies and verbal conceptualizations where negotiation did not lead to the construction of a shared understanding. In summary, the study demonstrates the power of microlevel process analyses in revealing the interpersonal dynamics of collaborative reasoning and shows how those dynamics mediate the learning opportunities in peer interactive dyads. (Contains 1 figure and 12 tables.)