The nature of geometry instruction and observed learning-outcomes opportunities in Nigerian and South African high schools

Abstract

The purpose of this qualitative case study involving six secondary school teachers was to obtain insight into how geometry is taught in selected Nigerian and South African high schools. It also aimed, by making use of the van Hiele model of geometry instruction, to elucidate what possible learning opportunities observed instructional methods could offer learners in the subject. The sample comprised three mathematics teachers from Nigeria and three mathematics teachers from South Africa, all of whom were selected using purposive sampling techniques. Instructional activities in six geometry classrooms were recorded on videotape. The van Hiele learning phases provided the framework for data analysis. The findings of this study indicate that observed teaching methods in geometry classrooms in the participating schools offer learners scant opportunity to learn geometry. In comparative and relative terms, however, the observed instructional methods in geometry classrooms within the South African subsample offer greater opportunities for the learners to learn geometry than observed teaching methods in geometry classrooms within the Nigerian subsample. The tentative conclusion drawn is that learners whose instructional experiences align approximately with the van Hiele phases of learning demonstrate a better understanding of geometric concepts than their counterparts whose geometry classroom instructional experiences deviate significantly from the van Hiele model. Certain images of teaching evident in the videotaped lessons are discussed and some recommendations offered.