Enhancing mathematics pedagogical content knowledge in Grade 9 class using problem based learning
Mceleli, Bedeshani Moses
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This study was aimed at designing a strategy to enhance mathematics pedagogical content knowledge (PCK) of teachers teaching Grade 9 learners using a problem-based learning (PBL) approach. PCK is the blending of content and pedagogy into how particular topics are presented to learners. Four components of PCK, namely understanding of learners’ misconceptions, understanding of content knowledge for teaching, understanding of pedagogical knowledge and understanding of curriculum knowledge were used to define a knowledge base needed for teaching mathematics. Furthermore, in the context of this study, PBL was used to enhance the above-mentioned PCK components through coordinated teams. PBL is defined as a learner-centred instructional method that utilizes real problems as a primary pathway for learning that develops learners’ ability to analyse ill-structured problems to strive for a meaningful solution. The study focused on how to enhance Grade nine mathematics teachers’ PCK using problem-based learning. It explored the challenges that teachers face when teaching Grade nine mathematics in terms of mathematics pedagogical content knowledge (MPCK). These challenges included, but were not limited to the non-existence of a coordinated team to enhance MPCK for teaching the Grade nine curriculum; poor follow-up of learners’ misconceptions; insufficient lesson preparation; insufficient use of curriculum materials when teaching; no integration of assessment and lesson facilitation; non-implementation of a learner-centred approach and poor mathematical knowledge for teaching. The study generated a strategy to respond to these challenges. However, the major challenge was that the knowledge base needed for teaching mathematics is contextually bound and complex. Therefore, the study adopted Critical Emancipatory Research (CER) as a theoretical lens for the study, mainly due to its critical commitment to confront social oppression and challenge well-established ways of thinking that frequently limit teachers’ potential. In this study, CER enabled co-researchers and I to consciously work together towards mastering critically challenging and changing systems that routinely oppress them. Through CER the study embraced multiple perspectives and negotiated meaning in formulating a strategy to respond to the identified challenges. Guided by an epistemological stance that embraces the value of welcoming subjective views on knowledge production, participatory action research (PAR) created a platform for participants who later became co-researchers to engage in knowledge production activities with equality and tolerance of contrasting views. Through problem-based learning workshops (PBLW), anchored in PAR methodology, a team of eight Grade nine mathematics teachers, their classes, a principal, a mathematics subject advisor and I worked together at the research sites. The research team collectively identified challenges that teachers faced, and enacted negotiated solutions to improve the wisdom of practice when teaching Grade nine mathematics. The generated data comprised photos, video recordings, audio recordings, learners’ scripts, co-researchers’ reflections, and lesson plans. Data were analysed using Critical Discourse Analysis (CDA). To understand the deeper meaning of the personal and subjective accounts of co-researchers’ lived experiences in teaching mathematics, data were analysed and interpreted at three levels of CDA, namely text, discursive practice and social structure. Through CDA the study analysed problems experienced by teachers who teach mathematics. This was done for the purpose of proposing possible solutions and strategies that might be developed, adopted and adapted to effectively address the problems that teachers experienced. Finally, to sustain the formulated strategy to enhance MPCK during and beyond the duration of the study, the conducive conditions for the strategy were investigated and enacted. The study further analysed and presented possible ways to circumvent threats and risks that could derail successful implementation of the strategy. The study was transformative in nature, which created the opportunity to operationalise and evaluate the success of the strategy prior to it being considered for recommendation. In conclusion, the study findings are revealed, indicators of success are identified, and recommendations are made. Some of the findings were that teachers worked in silos; their lessons were inadequately prepared; mathematics manipulatives were not judiciously utilized as the classroom discourse was teacher centred, starting with demonstration first and assessment later. Lastly, teachers’ knowledge gap regarding mathematics knowledge for teaching resulted in a learning cul-de-sac.