Arriving at the starting point? Exploring a teacher's use of circular reasoning in a mathematics classroom

Abstract

The problem of poor content knowledge of mathematics teachers in South Africa has been so widely reported that such reports provoke little reaction. My study was set around the following question: How does a teacher with poor mathematics knowledge teach mathematics for understanding? The participant in the study was a teacher who was mediating an assessment task with a Grade 9 mathematics class. Data was generated from five classroom observations, as well as interviews with the teacher and students. The purpose of the study was to explore the ways in which her mathematics knowledge impacted on classroom interactions. It was found that because of the teacher's poor understanding of the concepts of ratio and number, she missed some key ideas and presented explanations that were convoluted and which involved circular reasoning. The analysis also revealed that the teacher's development was hampered by the stressful working conditions. The study recommends that school and education management teams should prioritise the creation of supportive environments within which teachers can be encouraged to learn from unsuccessful lessons.

Keywords:

• process-object understanding
• mathematics teacher knowledge
• ratio
• rational numbers