Students’ conceptions of reflection: Opportunities for making connections with perpendicular bisector

•We studied conceptions of reflection related to the use of perpendicular bisector.•We found five conceptions of reflection in students’ work on three problems.•Students used perpendicular bisector in their operations or as a control structure.•Teachers can build upon students’ implicit uses of perpendicular bisector.•Informed by students’ conceptions, instruction can build on students’ prior knowledge.

Given the current emphasis on the use of transformations for the teaching and learning of geometry, there is opportunity to consider how students’ understanding of geometric transformations can be used to build connections with interrelated concepts. We designed a sequence of three problems, collectively referred to as “the pottery lesson,” to elicit evidence of students’ understanding of reflections. We asked: What conceptions of reflection did students use while working on the pottery lesson? How did students’ work on a sequence of problems requiring reflecting create opportunities for establishing connections between reflections and perpendicular bisector? We identified opportunities for the use of perpendicular bisector to shift between an operation of students’ work and a measure of control. The characterization of students’ conceptions of reflection, and students’ related use of perpendicular bisector, provide a resource for the teaching of these concepts to build upon students’ prior knowledge to promote learning.