Grade 8 and 9 township learners’ response to a problem-based mathematics extension programme
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A need to nurture learners so that they are ready for the demands of the future suggests the need for a re-evaluation of traditional teaching approaches that tend to be teacher-centred and promote rote learning and routine drill procedures. In contrast, learner-centred problem-based teaching approaches are aimed at enabling learners to think critically, regulate their own learning, shift the boundaries of their own capabilities and be more receptive to meaningful and long-lasting learning. However, skilful guidance and scaffolding from the teacher is a key determining factor for the success of such an approach. It is, therefore, unsurprising that, in South African schools, particularly in the townships, where teachers’ mathematics pedagogical and content knowledge is known to be low, problem-based teaching is rarely practiced. Further, the cognitively taxing and time-consuming problem-based teaching approach seems incompatible with training for high-stakes examinations, which is prevalent in this context. Little is known about the way learners in this context respond to problem-based extension programmes. To contribute to filling this gap in the literature, I conducted this research using a case study design informed by the pragmatic paradigm and the framework for integrated methodology. A mixed methods research design comprising qualitative and quantitative data and using inductive analysis to produce rich, detailed accounts of learners’ responses, was used. This was done to investigate how 27 Grades 8 and 9 learners responded cognitively and affectively to a problem-based mathematics extension programme that lasted two hours a day for five days. The learners were selected by applying non-probability purposive sampling. Triangulation and peer examination were used to strengthen validity and reliability. Data analysis was inductive, iterative and pragmatic, and guided by the research questions. Content analysis was performed using existing codes from Carlson and Bloom's (2005) multidimensional problem-solving framework to code the various data sources using NVivo software. This was followed by thematic analysis, in which themes were derived inductively from the coded data in answer to the research questions. This was done in the form of five assertions. I assert that the learners employed resources, many of which were incorrect, and displayed a diverse repertoire of heuristics, but generally needed to be prompted. Furthermore, across the intervention period, the learners responded to the teacher’s modelling of monitoring by increasingly posing Why and How questions but appeared unable to apply these questions to direct engagement in iterative problem-solving. Additionally, the learners engaged in the first three phases of the problem-solving process, but showed no engagement in the checking phase, nor were mathematical intimacy and integrity evident, although strong affective responses throughout the programme were visible. This study is not representative of Grades 8 and 9 South African learners at township schools; therefore, subsequent studies are needed to explore the extent to which the study could be generalisable to the broader population and more typical contexts. The significance of this study is that it demonstrates that it is possible to conduct problem-based extension programmes effectively to engage at least a sub-population of South African township learners both cognitively and affectively. A rich description of this programme is provided to serve as a model for the creation of similar programmes.