Abstract:
The purpose of this study was to promote Grade 10 learners’ algebraic reasoning through the use of folding back as a teaching frame. Algebraic reasoning is a sine qua non for mathematical understanding and, as a result, no field of mathematics can escape its application. In this regard, it is regarded as a prerequisite for STEM careers. Nevertheless, the literature highlights learners’ challenges, errors, and limited understanding in the application of algebraic reasoning across various areas of mathematical knowledge. These challenges are often attributed to traditional teaching strategies characterised by teacher-centred approaches and limited opportunities for learners to actively participate in the construction of mathematical knowledge. Accordingly, this qualitative study employed an autoethnographic research design to explore how teaching framed by the notion of folding back can promote Grade 10 learners’ algebraic reasoning. The participants were 12 Grade 10 mathematics learners purposively sampled from a class of 22 learners who were exposed to four weeks of exploratory teaching. In line with folding back studies, data were collected through learning activities, video recordings, document analysis, and semi-structured interviews. Polkinghorne’s narrative analysis was utilised to explore how Grade 10 learners’ algebraic reasoning was promoted through folding back. The interpretations used to produce compelling narratives were informed by the theoretical framework of folding back, as outlined by Martin (2008). Consequently, information-rich interactions drawn from learners’ algebraic reasoning activities, where folding back was observed, were selected for analysis. Among other findings, the study revealed that learners improved their algebraic reasoning skills by evaluating their solutions within a folding back learning environment. In addition, the results showed that learners developed the ability to justify their thinking as they folded back across various layers of understanding. Furthermore, the study found that teacher and peer interventions provided Grade 10 learners with opportunities to explain, justify and refine their algebraic reasoning while the action of folding back allowed them to make sense of solutions in real-life financial mathematics context. However, the study also found that the implementation of folding back may be hindered by limited teacher availability, learners’ reluctance to engage in peer questioning, and difficulties in reaching a shared reasoning pathway. The findings therefore suggests that folding back is a valuable teaching approach for promoting Grade
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10 learners’ algebraic reasoning. In light of this, the study recommends that mathematics teachers adopt probing questions and create collaborative small-group interactions. In addition, future research should explore folding back in other mathematical topics and research the role of home language in folding back classrooms, as well as quantitatively measure its effect on learners’ achievement in mathematics.
