Students are expected to learn mathematics such that when they encounter challenging problems they will persist. Creating opportunities for students to persist in problem solving is therefore argued as essential to effective teaching and to children developing positive dispositions in mathematical learning. This analysis takes a novel approach to perseverance by conceptualizing it as collective enterprise among learners in lieu of its more conventional treatment as an individual capacity. Drawing on video of elementary school children in two US classrooms (n = 52), this paper offers: (1) empirical examples that define perseverance as collective enterprise; (2) indicators of perseverance for teachers (and researchers) to support (and study) its emergence; and (3) evidence of how the task, peer dynamics, and student-teacher interactions afford or constrain its occurrence. The significance of perseverance as collective enterprise and as an object of design in developing effective learning communities, is discussed.