Textbook representations of radian angle measure: The need to build on the quantitative view of angle

Abstract

AbstractEmpirical studies of angle, angle measure, and radian angle measure have primarily focused on documenting students' and teachers' conceptions. Representations of angle measure have the potential to inform and build on these conceptions. To gain insight into the concept of radian angle measure from a curricular perspective, I investigated the representations of radian angle measure in eight widely used U.S. high school mathematics textbooks. The data for this study are the 20 figures and the 8 definitions of radian angle measure in the textbooks. Inductive content analysis was used to identify the frequency of observable characteristics in the representations. Textbook figures of radian angle measure most frequently focus on a one‐radian angle. Textbook figures also demonstrated radian angle measures in terms of π, in standard position, even when the Cartesian‐coordinate plane was not in the figure. The frequently used characteristics of radian representations could inadvertently reinforce a qualitative concept of angle, instead of fostering the quantitative attributes of radian angle measure. Moving forward, analyzing conceptions that are evoked by the frequently used representations of radian angle measure could build a link between evidence from this study and studies of learning.