Examining primary school teachers’ understanding of teaching geometry through the problem solving approach in Swaziland.
Ndlandla, Sibusiso Sandile.
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In this study, I examined primary teachers’ understanding of teaching geometry through the problem solving approach, using Ball, Thames and Phelps’s (2008) mathematical knowledge for teaching (MKT) framework as a lens, focusing on the knowledge of content and students (KCS) and knowledge of content and teaching (KCT) domains. I collected data in two phases. In the first phase, 34 participants who had been purposefully sampled completed an open-ended questionnaire with tasks adapted from Manizade and Mason (2011), which extracted their MKT in the two domains of decomposing and recomposing the area of polygons. In the second phase, I collected data using lesson observations, semi-structured interviews and lesson plan analysis from two participants, who volunteered from the initial 34, in their respective schools. The results showed that the participants had limited understanding of teaching geometry through the problem solving approach. The participants demonstrated procedural understanding in most of aspects used to describe MKT in this study. Notably, most participants could not identify the important mathematical ideas necessary for comparing the areas of the parallelogram and the triangle. In addition, they could not identify the misconception in the questionnaire associated with decomposing and recomposing the triangle into a parallelogram to compare their areas. Moreover, during the lesson observations, the participants could not demonstrate most of the practices associated with teaching by means of the problem solving approach, demonstrating instead traditional instructional practices consistent with their descriptions in the open-ended questionnaire and the semi-structured interview. The participants cited the language used in problems, learners’ abilities and attitude, their own knowledge and the advantages of the problem solving approach as the factors influencing their conceptions of teaching geometry through the problem solving approach. Arising from these results, I recommend that primary school teachers need to be empowered with knowledge in the relevant aspects of MKT that would enable them to teach geometry through the problem solving approach.