Tracking Grade 10 learners' geometric reasoning through folding back

Abstract

This article uses parts of qualitative data from the first author's study that focused on exploring Pirie and Kieren's process of folding back, revisiting previously held understandings of a concept for its extended understanding in order to solve the problem of enhancing Grade 10 learners' reasoning in geometry. In South Africa, secondary school leavers and pre-service teachers have difficulties in understanding geometric concepts and little is known about learners' geometric reasoning. Using teaching experiment methodology, we particularly tracked Grade 10 learners' geometric reasoning through folding back. We targeted two groups of learners from a class of 54 in which learners grouped themselves: the first group consisted of two members and the second group consisted of three members. The selection of learners was prompted by the manner in which the learners argued and questioned each other during four weeks of exploratory teaching. Data were collected through participant observations, where notes were taken and video recordings made in different sessions. We analysed the field notes and verbatim transcriptions of the video recordings using Polkinghorne's narrative analysis and analysis of narratives. Both the teacher's and the learners' interventions prompted effective folding back resulting in critical sharing of ideas. We thus argue that learners' effective folding back is a powerful tool to enhance their geometric reasoning.