Grade 12 rural mathematics teachers 'discourses during calculus lessons: a case of effective teachers in Qwa-Qwa, Free State Province, South Africa

Abstract

This study investigates the mathematical discourses of Grade 12 mathematics teachers in rural classrooms during Calculus lessons in Qwa-Qwa, Free State Province, South Africa. The selection of five teachers was based on their consistent achievement of an 80% pass rate in the National Senior Certificate mathematics assessment over a period of three years or more. Employing a qualitative research approach, the study utilised three primary data sources: unstructured classroom observations, semi-structured interviews, and Video-Stimulated Recall Interviews (VSRI). Framed as a multiple case study within the interpretivist paradigm, the research focused on the discourse practices of these teachers during their teaching of Calculus. Critical Discourse Analysis (CDA) served as the analytical framework, complemented by the Mathematics Discourse in Instruction (MDI) conceptual framework. The study reveals how the components of MDI—namely exemplification, explanatory talk, and learner participation—were effectively integrated into the teachers’ lessons to convey Calculus concepts. The findings indicate that these elements were not only present but were also skilfully utilised by the teachers. They initiated Calculus instruction by linking it to students' prior knowledge and potential career paths, employing visual aids to facilitate comprehension. However, some teachers did not sufficiently connect graphical and algebraic representations. The discourses observed included scaffolding of new knowledge and structured questioning, though these practices sometimes restricted more profound mathematical discussions. While visual aids, gestures, and exemplification were employed to clarify concepts, certain methods inadvertently led to misconceptions. Furthermore, although teachers promoted learner participation, their reliance on structured questioning often limited opportunities for independent reasoning. The findings highlight both effective instructional strategies and areas for improvement, particularly in promoting deeper conceptual understanding and addressing potential misunderstandings in Calculus.