Exploring Grade 10 teachers’ mathematical discourses during Euclidean geometry lessons in Johannesburg East District, South Africa

Abstract

The current study sought to investigate the mathematical discourses used by Grade 10 teachers during Euclidean geometry lessons. To explore and understand teachers’ classroom discourses during Euclidean geometry lessons, I researched with four Grade 10 mathematics teachers from Johannesburg East District in Gauteng, South Africa representing multiple cases. I espoused Adler and Ronda’s Mathematical Discourse in Instruction (MDI) framework to investigate and understand the classroom discourses the four teachers used during the lessons on Euclidean geometry. Within a qualitative research approach, I used semi-structured interviews, unstructured classroom observations, and video-stimulated recall interviews (VSRI) to generate data for the study. I used content analysis in relation to the MDI framework to analyse teachers' discourses and make summative judgments about their teaching of geometry concepts which allowed me to classify and categorise data in order to identify patterns and variances from the three data sources. The components of MDI were used to summarize the recorded lessons and all interviews were transcribed verbatim. The lessons were chunked into series of episodes, and I selected episodes that allowed for a detailed analysis of teachers’ discourses using the component of MDI. I make sense of teachers' MDI and the rationale for the specific discourses they restricted while teaching by analysing the teaching shifts that took place in each chosen episode using the data they supplied via semi-structured interviews and VSRI. The findings demonstrate that the four components of Mathematical Discourse in Instruction influenced each other during teachers’ Euclidean geometry lessons. The teachers did not provide explanatory talk during the lessons, instead they used questions-and-answer discourse to get learners to name and legitimate Euclidean geometry concepts and principles. Learners’ participation in all the observed lessons was limited to providing one-word answers and teachers did not prompt learners to provide justifications for their thinking.