Investigating opportunities to learn grade ten algebra : a case studies of three Catholic secondary schools

Abstract

The purpose of this thesis is to investigate opportunities to learn (OTL) algebra by grade ten learners at three Catholic secondary schools in South Africa. Performance in mathematics is poor and is a great cause for concern. Despite the government’s effort to make education open and available to all, underperformance has continued among the black majority who were previously marginalised in the former regime. This thesis focuses on the OTL which are afforded learners who are given the chance to attend classes. This thesis met its aims through an extensive review of related literature and the implementation of practical research. The latter was carried out through case studies conducted in three schools where lessons were observed and interviews conducted with the respective teachers. Literature on how OTL mathematics are created is lacking in South Africa. Real OTL still needs to be created if the expected level of performance is to be achieved. The research produced a number of key findings: the learners were given the right to attend class but were subjected to different OTL, learning to convert within and between the different registers of representation of algebraic concepts is necessary to provide learners with OTL, it is not enough for learners to master certain facts and procedures, and learning is enhanced if the means to make the conversion necessary for concept building is developed and the OTL provided. The teacher’s approach influences the way OTL are realised and utilised by learners. The main conclusion drawn from this research is that the OTL afforded the grade ten learners were not the same and that different chances to make conversion within and between registers of representation of algebra concepts were given. Giving the teachers guidelines without expounding the meaning of specific terms such as ‘convert’ leaves gaps in their practices and results in some learners receiving adequate OTL and others not. This research argues for a more involved capacity building programme for in-service teachers to acquaint them with the expected learner-centred approaches to lesson delivery as well as familiarise them with the terminology used in defining terms in the syllabus.