This study addresses a pedagogical practice-based issue, that is, difficulties with eliciting student–student co-constructed oral interaction in the EFL classroom. The study was conducted with a bottom-up approach to pedagogical research through the close collaboration of teachers and researchers who were equal partners in the research team. It was observed that students often engage in parallel monologues or unauthentic question–response sequences when accomplishing oral activities; thus, the research team aimed to design tasks providing opportunities for meaningful, co-constructed talk. The research design involved an iteration of task design and classroom testing in three cycles, and the student–student interaction was analyzed using conversation analysis. Findings show that the divergent problem-based task designed in this process did elicit purposeful and collaborative oral interaction, as the students engaged in co-constructed talk by visibly attending to each other’s turns-at-talk and by formulating fitting turns that fostered the progressivity of the activity. The task also included artifacts (i.e., material objects), the manipulation of which played an important role in the emerging collaborative interaction. These findings suggest that the implementation of open-ended problem-based tasks can develop students’ interactional competence, while the use of artifacts can help students make their reasoning tangible and visually accessible.