Levels of thought in geometry of pre-service mathematics educators according to the van Hiele model

Abstract

This study aimed to investigate the level of understanding of Euclidian geometry, in terms of theoretical knowledge as well as its problem-solving application, in pre-service mathematics education (PME) students at the University of Pretoria. In order to do so, a one group pre-test/ post-test procedure was conducted around an intensive geometry module, and a representational group of students was interviewed before and after the module to discuss their high school experiences of learning geometry and to analyse their attitudes towards the subject. The van Hiele Theory of Levels of Thought in Geometry was used as the theoretical framework for this study. The PME students in this study, prior to their completion of the geometry module, lacked the content knowledge, skills and insight in Euclidian geometry that is expected at matric level (Level 3). The pre-test results revealed that half the group could only be classified as being on Level 0. By the time the post-test was written, 60% of the group had moved onto Level 1 as their maximum competence level. This implies that these students were all brought to greater insight by the teaching they received during the geometry module. However, the overall improvement in the group as revealed in the post-test results, consisted of an upward movement of only one level. Therefore, the geometry module offered did not bring about sufficient improvement for these students to be able to teach geometry adequately (Level 3 is required). The students who were interviewed for this study uniformly expressed their dislike or fear of Euclidian geometry in general, but described the positive change in their attitude during the course of the module because of the way it was presented. Training of students for a career as mathematics educators which includes an in-depth van Hiele-based geometry module would facilitate the acquisition of insight and relational understanding.