Problem solving in mathematical and everyday contexts : teachers' practices and knowledge. - Fonseca, Kathleen (My University, 2012)
The Revised National Curriculum requires that mathematics teachers make shifts in their pedagogical content knowledge about teaching non-routine problems. One of the shifts is to move from a traditional approach of teaching routine tasks to an approach which includes problem solving. Teaching non-routine problems develops flexible forms of knowledge, which allow learners to construct their own strategies and not merely follow steps shown to them by the teacher. In this study I explore what pedagogical content knowledge grade 6 teachers have about problem solving in everyday and mathematical contexts. A qualitative study was used to explore Grade 6 teachers’ pedagogical content knowledge about problem solving in these contexts. Data was collected by means of interviews and lesson observations. The study found variations in the teachers’ content knowledge but very similar pedagogical content knowledge among the teachers. Teachers have different understandings of teaching non-routine problems and they are faced with the challenge of how much to make knowledge accessible to their learners in order to lay a conceptual foundation to solve non-routine problems while not lowering the demands of the task. Teachers taught everyday context tasks differently to mathematical context tasks by focusing on the linguistic aspects of the tasks.
Keywords: Mathematics teachers; Problem solving