The teacher’s perspective on the separation between conjecturing and proving in high school geometry classrooms

Inside the discipline, mathematical work consists of the interplay between stating and refining conjectures and attempting to prove those conjectures. However, the mathematical practices of conjecturing and proving are traditionally separated in high school geometry classrooms, despite some research showing that students can successfully navigate the interplay between the two. In this manuscript, we share perspectives from secondary mathematics teachers regarding what conjecturing and proving look like in geometry classrooms and possible rationales for why they are separated. We document that from the teachers’ perspective, the activities of conjecturing and proving have different goals, draw on different resources, and require different actions from students. In teachers’ eyes, these differences necessitate the separation of conjecturing and proving. By understanding teachers’ perspectives on the activities of conjecturing and proving, we can better consider the constraints of the classroom environment and possibly design activities in which conjecturing and proving could be reunited to allow students a more authentic mathematical experience.