Radian π: Concept images evoked by quantitative representations of radian angle measure

Abstract

ABSTRACT This article investigates evoked concept images (CIs) of seven secondary preservice mathematics teachers (PMTs) as they interact with different types of representations of radian angle measure. A thematic analysis indicates that representations emphasizing quantitative aspects of angle measure evoke conceptions that are attuned to quantitative elements of radian angle measure. Specifically, quantitative representations evoked CIs relating the length of the arc subtending the angle to the radius. Non-quantitative representations evoked CIs of radian in terms of π or in relation to degrees, even when the representation did not contain angles in these measurements. To foster a quantitative understanding of radian angle measure, teachers and curriculum developers are encouraged to consider how visual representations might support students in conceptualizing radian angle measure quantitatively.