Defining radian: provoked concept definitions of radian angle measure

Abstract

ABSTRACT Despite the use of axiomatic definitions for mathematical concepts, scholars struggle to produce a single definition of angle that does not have some limitations. Textbooks’ treatment of angle and its measure reflects this multifaceted nature of the angle concept while informing the different ways learners conceive of these concepts. In this study, I investigated the concept definitions provoked by textbook representations (e.g. diagrams) of radian angle measure. Seven prospective mathematics teachers (PMTs) participated in a think-aloud semi-structured interview and defined radian angle measure through examining six diagrams. A thematic analysis of concept definitions indicated that interacting with different representations provoked various concept definitions. Some provoked concept definitions focused on defining one radian. Other definitions indicated different quantitative operations (e.g. iteration, partitioning, proportionality). To provide learners opportunities to conceptualise radian angle measure quantitatively, teachers and curriculum developers are encouraged to incorporate multiple representations of radian angle measure into instructional materials.