In mathematics classrooms, educators encourage both creativity and collaboration. In the current study we investigated the dialogical moves that made up the interactions of three groups of post high-school students who worked on an open-ended mathematics task. The aim of this study was to characterize collective strategic pathways that can lead to different creativity products, and the possible impact of leadership styles and dialogical moves on those pathways. Collective "strategic" flexibility was defined as the number of strategies used by the group. Three strategy paths were found, namely, a disjointed strategy path, an emerging strategy path, and a straightforward strategy path. Dialogical moves such as asking for help, receiving clarifications, and explicating strategies, led to fluency. Elaborating mathematical explanations led to originality. Strategic flexibility was supported by evaluating strategies. Group leadership styles also contributed to varying amounts of cooperation and collaboration, in turn furthering different aspects of creativity. Findings indicated that cooperative collectives can lead to original unpredictable solutions. When a group is more collaborative, collective strategic flexibility may increase. When there is a mix, and students collaborate in a way that ensures that all can contribute, then collective fluency is promoted.