Young children’s understanding of angles in a dynamic geometry environment

Angle is an important topic in geometry. It is a concept that children find challenging to learn, in part because of its multifaceted nature. The purpose of this study is to understand how children’s thinking about angles evolves as they participate in a classroom setting featuring the use of a dynamic geometry environment (DGE) in which the concept of angle as turn was privileged, a concept that does not require a quantitative dimension. Three research questions were proposed for the study, addressing respectively: (1) the different conceptions of angles developed by the children; (2) contributions of the DGE (The Geometer’s Sketchpad) to children’s developing conceptions of angles; (3) the kinds of discourse in which children engage. The participants in the study were 20 kindergarten/grade 1 children (aged 5-6) along with their class teacher. The data consist of video recordings of nine classroom sessions around angles conducted by the class teacher. Sfard’s (2008) commognitive framework was used to analyse the data focusing mainly on her four characteristics of mathematics discourse, which are word use, visual mediators, routines, and narratives. The children’s gestures were also taken as a significant aspect of their discourse. This study highlights the importance of gestures and motion in children’s developing conceptions of angles. It presents implications of considering young children’s embodied forms of communications along with their verbal communication for understanding their mathematical thinking. Extending prior research on children’s difficulties in unifying static and dynamic conceptions of angles, this study provides one way of establishing a relationship between angle-as-turn and angle-as-shape conceptions.