Influence of Characteristics of Two-dimensional Figures on the Identification of Axial Symmetry-An Analysis on Tasks Solutions

Abstract

Symmetry is an important mathematical topic. Its understanding can already be developed at primary school age. Yet little is known about learning processes concerning the development of understanding axial symmetry or about students' conceptions and misconceptions when they are confronted with axial symmetry. Error analyses can provide an initial basis for drawing conclusions on the understanding of symmetry and be a good starting point for mathematics education. This study analyzes the influence of characteristics of two-dimensional figures (e.g. slope of the axis of reflection, symmetry of the figure itself) on students' performance in distinguishing axial symmetrical from non-axial symmetrical figures and drawing the correct axis of reflection. Moreover, the study identifies typical student errors with respect to the characteristics of axial symmetry tasks, especially for rotationally symmetrical figures. The test consists of 18 items to identify and draw symmetry axes in two-dimensional figures. The study was carried out with third class students (n=212). It turns out that special characteristics of axial symmetry tasks influence the amount of correct solutions and provoke typical student mistakes. The results point out some misconceptions on axial symmetry which can either be used in further research or in teaching practice as a foundation for further qualitative analyses of students' answers.