Concept images and concept definitions of seventh-grade middle school students regarding the concept of angle

Abstract

Angle is a fundamental concept that students need to learn correctly, as it is one of the building blocks of geometry and is embedded in many geometry topics. This study aimed to determine seventh-grade middle school students’ concept definitions and concept images of angle, as well as the ways in which they associated their concept definitions with their concept images. Adopting a qualitative research method, a form consisting of 23 open-ended questions was prepared by taking into account most of the angle-related learning outcomes up to the seventh grade. The form was administered to 168 seventh-grade students attending two state middle schools; after the written data were analysed, clinical interviews were conducted using the same form with 9 participants selected through criterion sampling. The data were analysed using qualitative data analysis and interpreted within Tall and Vinner’s concept image-concept definition framework. The findings showed that the participants held incorrect or incomplete images of angle and largely produced their personal concept definitions from their concept images. The participants could not define angle formally, confused angle with angle measure, and mostly emphasised the measure-related aspect of angle. They also had difficulty using the concept of angle in problem situations. The results point to the importance of learning environments in which the dynamic and static aspects of angle are associated and in which everyday-life contexts and dynamic geometry tools are used.