The role of pedagogical content knowledge in preservice teachers’ choice of examples to create opportunities for learning analytical geometry in KwaZulu-Natal multilingual classrooms

Abstract

The study set to respond to calls for research in multilingual mathematics teacher training classrooms with the intention to advance the quality of mathematics preservice teachers (PSTs) content knowledge and improve mathematics education for school learners. In this qualitative study, the pedagogical content knowledge (PCK) of PSTs in one of the universities in the KwaZulu Natal Province in South Africa was explored. This was to understand how it guides their choice of examples for teaching analytical geometry in multilingual classrooms. Grade 11 analytical geometry lesson plans of 21 PSTs who had been given an analytical geometry test were analysed. The test was to investigate the PSTs content knowledge, which is a basis for PCK, and the lesson plans were analysed to examine the PSTs PCK from the way they structure their lesson objectives and choice of examples. Semi-structured verification interviews were conducted to follow up on both the test responses and lesson plan content, mainly the choice of examples. The domains and subdomains of the Shulman’s PCK born Mathematics Teacher’s Specialised Knowledge (MTSK) model and patterns of variation from the variation theory were used as the theoretical framework, which also guided the analytical framework. The study established that the PSTs had limited content knowledge, and PCK for teaching analytical geometry at Grade 11. The limited knowledge was seen in the way the PSTs relied on procedures for problem solving rather than conceptual understanding, and for this reason they chose procedural examples for teaching the topic. The study also found that the language of learning and teaching affects the PSTs ability to explain concepts in their problem solving, and this also affects their examples choice. Interview responses confirmed that the PSTs are not cognizant of the use of language in their example choice. Therefore, PSTs in multilingual teacher training must be explicitly taught to choose examples and consider learners in multilingual classrooms.