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

Nosisi Feza,Paul Webb

doi:10.4102/pythagoras.v0i62.113

Abstract

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.

Highlights

There appears to be widespread realisation that teaching in mathematics in general has failed to overcome a number of cognitive barriers to learner understanding (Carpenter & Fennema, 1988; Kempa, 1993; Peterson, 1998)
A number of researchers in mathematical education assert that the instruction in geometry offered in South African schools is inadequate in terms of providing learners with the necessary skills needed to operate at the level of axiomatic thinking required for most high school courses (McAuliffe, 1999)
This study investigates whether a sample of grade seven learners who had recently completed their intermediate phase of schooling in previously disadvantaged primary schools meet both the assessment criteria for geometry as stated by the Intermediate Phase Revised National Curriculum Statement (Department of Education, 2002) and the requirements of Van Hiele thinking at level two

Summary

Introduction

There appears to be widespread realisation that teaching in mathematics in general has failed to overcome a number of cognitive barriers to learner understanding (Carpenter & Fennema, 1988; Kempa, 1993; Peterson, 1998). This study investigates whether a sample of grade seven learners who had recently completed their intermediate phase of schooling in previously disadvantaged primary schools meet both the assessment criteria for geometry as stated by the Intermediate Phase Revised National Curriculum Statement (Department of Education, 2002) and the requirements of Van Hiele thinking at level two This has been done in order to get an indication of the probable (but not generalisable) level of learners’ understanding in geometry at the end of their primary schooling and, as such, to raise teachers’ awareness of what may be reasonably expected of children who have come through previously disadvantaged South African primary schools. This study should make a contribution to our understanding of these children’s understanding of geometry after a period of learning in this context and, hopefully, provide some indicators of what is needed in order to successfully teach geometry to children in similar schools and social conditions

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Conclusion