Ways of thinking about axial symmetry: a study on the nature of misconceptions and difficulties of upper secondary school students

The aim of this paper is to investigate upper secondary school students’ difficulties and misconceptions related to axial symmetries, the nature of these misconceptions, and students’ ways of thinking about axial symmetry. We wondered to what extent students refer to figural rather than conceptual aspects in identifying figures symmetrical with respect to an axis. A multiple-choice questionnaire with a request for justification of answers was designed and administered to upper school students. A qualitative data analysis, carried out according to the Fischbein’s Theory of Figural Concepts, seems to show that the misconception related to conflating symmetry with congruence seems to be the most common one, and it emerges from students’ answers that refer to to both conceptual and figural aspects. Moreover, in this paper, we identify and describe other students’ misconceptions, namely: evaluating the distance of a point from a line, conflating the reflection with the reflected object, estimating the distance of a point from a line with respect to the “horizontal” or “vertical” direction. This research shows that some misconceptions of primary and middle school students seem to persist even in upper secondary school students as well. Some educational implications from this study are also discussed in the paper.