This study provides analyses of the conversations when university students work in small groups solving context-rich physics problems. We constructed context-rich, open-ended physics problems related to everyday life situations that lack some information required to solve and complete the tasks. The students' ownership of learning, their actions of choice and control, was analyzed in two dimensions: group and individual. Conversation analyses and flowcharts of the conversation were constructed from the complete transcripts of three groups. The theoretical framework for student ownership of learning demonstrated that it was possible to show that even if students have group ownership of the task, the individual student ownership of learning is not self-evident. The study also demonstrates the methodological power and value of the flowchart to identify conversation patterns in the groups that were effective in the search for exploratory talks and individual questions. We discuss implications for teacher development to enhance group work.