Preservice Mathematics Teachers’ Proportional Reasoning: The Case of Angle Measure Conversions

This study explored preservice mathematics teachers’ (PMTs’) use of proportional reasoning given a situation that involves relating degrees to radian angle measure. Five PMTs participated in a semi-structured task-based interview to solve conversion questions from degrees to radians. Thematic analysis of the transcripts showed PMTs using and connecting various proportional reasoning concepts to describe angle measure in radians when given the measure in degrees. The PMTs also justified using memorized facts and calculations for efficiency and practicality. Findings suggest that conversion questions elicit meanings that are attuned to proportional reasoning concepts. I conclude that PMTs’ meanings for the relationship between degrees and radians are complex and not limited to memorization. Mathematics teacher educators can support PMTs by building on proportional reasoning in situations involving conversion between degrees and radians to encourage them to move beyond memorized facts and calculations.