1An Analysis of the Geometric Understanding of Grade 9 Pupils Using Fuys et al.’s Interpretation of the Van Hiele Theory

The performance of Grade 9 pupils on a written geometry test was analysed using the van Hiele descriptors constructed by Fuys, Geddes, Lovett and Tischler (1988). On the basis of this analysis, three pupils were selected to be the subjects of case studies in which their geometric understanding was explored further. This paper reports on two of the three case studies, focusing on the problems encountered during the analysis and on the initial conclusions regarding the use of this particular interpretation of the van Hiele theory. The Context Dissatisfaction with the secondary school geometry curriculum and poor pupil performance in geometry have been the topic of many discussions in mathematics education over the past decades. During 1997 the Geometry Working Group at Malati has been attempting to reconceptualise the teaching and learning of geometry. It is felt that if this is to be done and if changes to the geometry curriculum are to be proposed, a means to understand the geometric thinking of learners is required. The Group has found the van Hiele model of thinking (see below), and particularly the interpretation of this theory proposed by Fuys, Geddes, Lovett and Tischler (1988), useful in providing a framework in which to work and for designing geometry activities which are to be trialed in 1998. For as Usiskin (1982) points out, the theory not only provides an explanation of why pupils have problems, but also suggests a remedy for these problems