An analysis of pre-service mathematics teachers’ geometric thinking and classroom discourse using a commognitive lens.

Abstract

Learning geometry equips learners with cognitive skills such as visualisation, critical thinking, spatial reasoning and problem-solving abilities, that are necessary for learning mathematics in general. However, geometry is noted to be difficult for learning as well as teaching. An investigation of this difficulty, especially with teachers, will help address its teaching and learning. The purpose of this study was to analyse pre-service teachers’ geometric thinking and classroom discourse using the commognitive lens. The study was guided by three objectives, which were to analyse the pre-service teachers' discursive thinking in geometry; the nature of their routine thinking in solving the geometric tasks, and how these informed their classroom geometric discourse. The study aligned itself to the qualitative approach and was underpinned by the interpretivist research paradigm. Eight pre-service teachers who were second-year university students and had taken geometry as part of their programme modules, participated in the study. The study site was conveniently selected, whilst the participants were selected on purposively. Geometry worksheet (test), interview and classroom observation, were used to generate written, verbal (oral) response, and visual data in relation to the study objectives. The data was analysed using the themes of the commognitive framework. The results show that both literate and colloquial word use were found in the discourses of the pre-service teachers. Many participants in Group A used more literate words to define and explain geometric concepts and how they solved the geometry problems, than the participants in Group B, who used both literate and colloquial words. Also, the routine solution strategies of many in Group A showed more of an explorative way of thinking compared to those in Group B, who demonstrated more of a ritualised way of thinking. In addition, multiple solutions to tasks were found by many of Group A participants than those in Group B. Generally, many of the study participants demonstrated limited geometric thinking. Misconceptions were evident in the discourses of some pre-service teachers in both groups. Other key findings from the classroom observation were that, many participants in Group A demonstrated an explorative instruction that is characterised by developing learner understanding and using different kinds of visual mediators as compared to participants in Group B, whose classroom geometric discourse was ritualised in nature. In other words, their teaching was more procedure-driven than conceptual. The study concludes that many of the PSTs possess limited geometric thinking. In addition, those who possessed good geometric thinking were more capable of engaging learners in explorative instruction compared to those with limited geometric thinking. These findings may have an influence on mathematics teacher educators’ efforts to develop teaching competence among pre-service teachers.