“I’m Stuck”

When teaching a responsive mathematics lesson, teachers urge students to solve problems using whichever strategy they prefer. This instructional approach has many merits for students’ learning and mathematical dispositions, yet remains rare. Prior research has described the challenges of responsive mathematics teaching, but little has focused on the especially high-stakes moments in responsive lessons that engender notable confusion, threaten to derail the lesson, and may prevent responsive teaching from becoming commonplace—what we refer to as “critical juncture.” We examined the critical junctures that prospective elementary teachers encountered in video-recorded lesson rehearsals and described in written reflections. Critical junctures varied in their criticality, with the most critical ones involving substantial confusion that was difficult to resolve. We present a set of criteria and a criticality continuum that teachers may consult in learning to notice and respond to critical junctures, thereby contributing to efforts to make responsive mathematics teaching more commonplace.