https://ir.unisa.ac.za/handle/10500/6440 2026-08-11T12:55:44Z 2026-08-11T12:55:44Z Kwankye, Emmanuel https://ir.unisa.ac.za/handle/10500/32744 2026-07-28T07:34:46Z 2025-07-30T00:00:00Z

Grade 9 learners’ understanding of algebraic expressions: A case of a selected high school in Frances Baard District in the Northern Cape Kwankye, Emmanuel Mathematics underachievement is a global challenge, with South Africa also experiencing a decline in skills consistent with international trends. This study aimed to explore the understanding of algebraic expressions amongst Grade 9 learners. The study was inspired by the fact that learners in the Northern Cape usually demonstrate dismal performance in algebraic expressions. When learners lack strong algebraic skills, it can reduce their confidence and achievement in further education and training, restricting access to careers in Science and Engineering. This study draws on Skemp’s theory of understanding to help explain and make sense of the phenomenon of poor performance in algebraic expression. The study adopted a qualitative case study research approach in which 40 learners from a selected school in the Frances Baard District, Northern Cape in South Africa, participated. Test and semi-structured interviews were used to collect data. The findings of the study revealed that learners lack the fundamental concepts or pre-requisite knowledge in algebraic expression. They also lack relational understanding in algebraic expressions and moreover, their mathematical connection abilities were very low. The implications of this study include but are not restricted to, the need for teachers to pay special attention, monitor, document and carefully examine learners’ misconceptions and conceptual gaps when teaching algebraic expression. There is also a need for learners to be exposed to appropriate, practical and real life-scenarios during the teaching and learning of algebraic expressions to make the content more simple, realistic, engaging and understandable. These stated implications should be regarded in view of some of the limitations of this research, including the small sample size, limited time and resources.

2025-07-30T00:00:00Z Tlhako, Malose Alsin https://ir.unisa.ac.za/handle/10500/32722 2026-08-06T07:34:39Z 0026-01-01T00:00:00Z

Promoting grade 10 learners’ algebraic reasoning through folding back: an autoethnographic perspective Tlhako, Malose Alsin 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 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.

0026-01-01T00:00:00Z Tlhako, Malose Alsin https://ir.unisa.ac.za/handle/10500/32721 2026-07-08T10:17:34Z 2026-01-01T00:00:00Z

Promoting grade 10 learners’ algebraic reasoning through folding back: an autoethnographic perspective Tlhako, Malose Alsin 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 v 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.

2026-01-01T00:00:00Z Nchabeleng, Meta https://ir.unisa.ac.za/handle/10500/32508 2026-06-30T11:34:56Z 2026-02-01T00:00:00Z

Grade 4 rural teachers’ pedagogical approaches of teaching geometric patterns in Sekhukhune East District, Limpopo Province, South Africa Nchabeleng, Meta This study explored the pedagogical approaches employed by Grade 4 teachers in the Sekhukhune East District when teaching geometric patterns, using Shulman’s Pedagogical Reasoning and Action (PRA) framework as an analytical lens for understanding how teachers conceptualise, transform, and enact mathematical content in real classroom settings. Through a qualitative multiple-case study design involving five teachers, the research employed non-participatory and unstructured classroom observations, Video-Stimulated Recall Interviews (VSRIs) and Semi-structured Individual Interviews. One or two episodes per teacher were purposively selected to allow for rich, close-up analysis of the teachers’ pedagogical approaches. These data were examined using a custom set of PRA-aligned recognition rules that captured teachers’ actions in relation to content comprehension, transformation of representations, instructional discourse, formative assessment, reflection, and pedagogical growth. The cross-case findings reveals that despite working in resource-constrained rural classrooms, all five teachers enacted pedagogical approaches that foregrounded the structural features of geometric patterns. Teachers consistently relied on concrete and contextual representations, such as matchsticks, coloured chalks, learners’ bodies, and familiar artefacts to make abstract concepts visible and accessible. They emphasised structural awareness by intentionally directing learners to identify growth rules, examine repeating units, analyse colour or shape changes, and predict future terms. Lessons were characterised by high levels of learner participation through demonstrations, board work, and group-constructed patterns, with teachers using probing, reasoning-eliciting questions to drive conceptual engagement and support generalisation. Formative assessment was embedded throughout teaching processes as teachers responded to learner thinking in real time, used misconceptions as learning opportunities, and encouraged peer validation of correctness. The study contributes methodologically by operationalising PRA through recognition rules that made teachers’ reasoning visible in empirical classroom analysis, particularly in relation to stabilising structure and transforming content. The findings carry implications for practice, suggesting the need for purposeful use of representations, structured questioning, and multilingual mediation; for policy, highlighting the need for resource provision and PRA-aligned professional development; and for future research, calling for expanded studies on pattern pedagogy, language, and longitudinal development of algebraic thinking. The study offers a nuanced understanding of how rural Grade 4 teachers navigate the teaching of geometric patterns and shows that meaningful, cognitively rich mathematics teaching can be enacted even in challenging contexts.

2026-02-01T00:00:00Z