This article reports on regularities observed in learners’ preconceptions of reflective symmetry.
Literature suggests that the very existence of such regularities indicates a gap between what
learners know and what they need to know. Such a gap inhibits further understanding and
application, and hence needed to be investigated. A total of 235 Grade 11 learners, from 13
high schools that participate in the First Rand Foundation-funded Mathematics Education
project in the Eastern Cape, responded to a task on reflective symmetry. Our framework for
analysing the responses was based on the taxonomy of structure of the observed learning
outcome. The results indicated that 85% of learner responses reflect a motion understanding
of reflections, where learners considered geometric figures as physical motions on top of the
plane. While this understanding is useful in some cases, it is not an essential aspect of mapping
understanding, which is critical for application in function notations and other analytical
geometry contexts. We suggest that if this gap is to be closed, learners need to construct these
reflections physically so that they may think of reflections beyond motion.

doi: 10.15700/saje.v33n2a686