Assessment standards, Van Hiele levels, and grade seven learners' understandings of geometry

A number of researchers in mathematical education assert that the instruction in geometry offered in South African schools is inadequate and that traditional teaching strategies do little to promote teachers understandings of their learners' levels of mathematical thought. Van Hiele specifically states that the inability of many teachers to match instruction with their learners' levels of geometrical understanding is a contributing factor to their failure to promote meaningful understandings in this topic. This study investigated whether a sample of grade seven learners in previously disadvantaged primary schools met both the assessment criteria for geometry as stated by the South African Revised National Curriculum Statement and the implied Van Hiele thinking levels. The data generated suggest that none of the 30 learners who participated in this study had attained these requirements and that language competency in general is a barrier to the attainment of higher levels of understanding amongst this group of second-language learners. It is suggested that not only Van Hiele Levels and Assessment Standards, but also learners' cultural background and their specific use of words in the vernacular context, need to be taken into consideration by teachers when developing learning programmes. Possible strategies to meet these requirements are suggested.