Reflecting geometrical shapes: approaches of primary students to reflection tasks and relations to typical error patterns

Abstract

Students' issues dealing with reflection tasks, especially with inclined mirror lines, are widely known. Previous research conducted with primary school students mainly focussed on task difficulty and students' outcomes, especially their errors of reflection. Little is known about which not obviously sustainable understanding of reflection leads to what kind of errors. To address this issue, the purpose of this study is to explore which approaches students use in their solution finding processes when dealing with reflection tasks. We also investigated whether there was a relationship between the students' approaches and correct or incorrect solution products. This article discusses a task-based interview study focussing on approaches used in the students' solution process of four reflection tasks. To gather data, 42 interviews with students at the end of primary school in Germany were conducted. For the analysis, a category system with the categories ``properties of reflection,'' ``holistic approaches,'' ``gestures and actions illustrating the process of reflection,'' and ``mental images illustrating the process of reflection,'' was developed and validated. We observed that there is a relation between the approaches used by the students during their process of solving reflection tasks and their solution products. The observed relationship between the approaches applied during the solution processes and the solutions themselves leads to the assumption that the approaches the students used reveal varying degrees of mathematical understanding of reflection. As emphasized in the discussion of the results, it is important to take a differentiated look on the students' solution products and the importance of adequate instruction methods.