Using the Van Hiele phases of instruction to design and implement a circle geometry teaching programme in a secondary school in Oshikoto region

A Namibian case study

Abstract

Despite my positive views of geometry as one of the most interesting topics in the mathematics curriculum, others find it rather complicated and sometimes unbearable to successfully complete a geometry course. It is a common phenomenon that secondary school students globally struggle with simple geometric problems and their thinking and reasoning are generally below average. Although difficulties in geometric thinking and reasoning are prevalent in global educational research, problems in geometric conceptualisation still prevail. It is therefore the aim of this paper to report on the case study research that was conducted to examine, analyse and report on the findings of the experiences of selected mathematics teachers when they used the Van Hiele phases of instruction in designing and implementing a Grade 11 circle geometry teaching programme. The sample consisted of three selected Grade 11 mathematics teachers from the school where the researcher taught. The findings of this research revealed that teachers used and implemented all the five Van Hiele phases of instruction in their lessons whilst navigating quite freely from one phase of instruction to the next, but also returned to the earlier phases for clarification and reinforcement in their teaching. Teachers also saw the phases of instruction as a good pedagogical tool or template for planning and presenting lessons. The majority of the learners followed the instructions and seemed to obtain the answers faster than expected.