Unpacking Conceptual and Procedural Meanings for Radian Angle Measure Through a Curricular Sequence: Henry’s Case

Abstract

Researchers report that preservice mathematics teachers (PMTs) conceptualize radian angle measure in terms of π using memorization and calculational strategies. In this report, I unpack the mathematical meanings of one PMT, Henry (pseudonym), as he engaged in a series of three task-based interviews involving radian angle measure. Through engagement and reflection on these tasks, I describe shifts in Henry’s meanings for radian by characterizing the amalgamation between procedural and conceptual meanings. Henry’s initial meanings for radian involved procedural strategies with an emphasis on memorized special angles written in terms of π. In response, the subsequent task-based interviews aimed at gaining more insight into Henry’s meanings and to challenge his dependence on the procedural strategies. An analysis of Henry’s strategies in the second and third interviews suggests shifts in his meanings for radian angle measure to include conceptual generalizations. I conclude by highlighting how tasks can be designed to build and support conceptual meanings.