Rural Teachers’ Teaching of Algebraic Functions Through a Commognitive Lens

Abstract

Rural contexts and their schools have continuously been overlooked by researchers of mathematics education in South Africa. This is despite the assumption that the educational landscape may vary markedly in rural areas compared to urban and township areas which have been solely researched in the post-apartheid dispensation. To address the dearth of mathematics education research located within South Africa's rural contexts, the study explored five Grade 10 rural mathematics teachers' discourses and approaches of teaching algebraic functions with five teachers from five different school sites. This qualitative multiple case study, using Sfard's commognitive theory, draws attention to rural mathematics teachers' classroom practices and views about the teaching of algebraic functions which is unexamined in the South African context. Three data generation tools were used to gain insight into teachers' discourses and approaches while teaching the topic. These are individual semi-structured interviews, classroom observations and Video-Stimulated Recall Interviews (VSRI). Research findings focus primarily on the data generated through classroom observations. To analyse the data, I use Sfard's commognitive theory to give meaning to teachers' classroom practices. Focusing on the distinction between two tenets of commognitive theory, ritual and explorative routines, the findings demonstrate that four participating teachers acted in an extremely ritualised way. The other teacher was more explorative in her classroom observable actions. The findings illuminate that teachers need to move more towards the participationist approach during teaching to enable them to think, observe, and communicate about mathematical objects that commognitively link more with explorative routines.

Keywords

• algebraic function
• commognitive framework
• rural
• discourse
• teaching
• rural teachers