PRE-SERVICE TEACHERS’ UNDERSTANDING OF GEOMETRICAL DEFINITIONS AND CLASS INCLUSION: AN ANALYSIS USING THE VAN HIELE MODEL

The subject of teacher knowledge has been a key issue in mathematics education reform and the advent of information technology to the mathematics classroom does not make it less topical. This study sought to determine pre-service mathematics major teachers’ understanding of geometrical definitions and class inclusion using the van Hiele level model prior to their entry into a voluntary series of workshops designed to introduce them to activities involving the educational use of the Geometer’s Sketchpad, a dynamic geometry software package for mathematics teaching. A survey research design was used and sixteen out of the twenty pre-service teachers who were selected to take part in the workshop series took the baseline test which focused on the geometry of triangles and quadrilaterals that was going to be dealt with in the induction programme. The study reported here is therefore part of a larger study reported in Ndlovu (2004).

The results for this survey showed that participants had a higher van Hiele level of understanding geometrical definitions than class inclusion. These results were surprising for the same cohort and suggested that the levels in the van Hiele (1986) model were neither as discrete nor as autonomous as assumed by the model. This confirmed earlier findings by researchers such as Burger and Shaughnessy (1986). Overall, however, the participants’ understanding of the geometry of triangles and quadrilaterals was below expectations suggesting that even though the participants had passed their General Certificate of Education (GCE) Ordinary level mathematics examinations, some of them had regressed considerably in their understanding of the geometry in question. A recommendation is made that any efforts to reintroduce or consolidate Euclidean geometry in the school curriculum must take cognisance of the many teachers who might need comprehensive support in subject matter knowledge (SMK).

References:
[1] Burger WF, & Shaughnessy JM 1986. Characterising the van Hiele levels of development in geometry. Journal for Research in Mathematics Education , 17 (1), 31-48.
[2] Ndlovu M 2004. An analysis of teacher competencies in a problem-centred approach to dynamic geometry teaching. Unpublished MEd dissertation. Pretoria: University of South Africa.
[3] Van Hiele PM 1986. Structure and Insight. Orlando: Academic Press.