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Responsive mathematics teaching is an instructional approach in which teachers encourage students to solve problems using whichever strategy they prefer. Research has examined the difficulties teachers may encounter in teaching responsively, yet little has characterized the especially high-stakes moments that bring responsive lessons to a halt, what we refer to as “critical junctures.” We examined 51 prospective elementary teachers’ reflections on the challenges they encountered in teaching a responsive lesson in rehearsal, as well as video of challenges that halted their lessons. We find that critical junctures involve stagnation or confusion for the teacher, students, or both. Critical junctures also vary in their criticality. As critical junctures were rarer than expected, teacher educators may need to introduce these into rehearsals.