Number and comparison in early grade mathematics : learning from isiXhosa and English canonical texts

Ph.D.Abstract: Teaching early grade mathematics in a rural, no-fee, African language-dominant school, typical of South Africa’s mainstream education system, requires different skills and knowledge to teaching early grade mathematics in an urban, fee paying English-dominant school, typical of South Africa’s privileged education system. Part of the reason for the widely reported disparity between the two systems that make up South Africa’s education landscape is that the knowledge of “what works” is primarily embedded in the privileged education system. The location of this knowledge, together with an implicit assumption that this knowledge can successfully be transfer to and used within the mainstream system, has resulted in a paucity of research that examines the linguistic resources and pedagogical practices of the mainstream system. This is particularly true in relation to teaching and learning mathematics in rural, African language dominant schools. This study contributes to addressing this paucity by undertaking four inter-related studies on the constraints and affordances of teaching mathematics in rural schools in one African language, namely isiXhosa. In order to examine the constraints and affordances of teaching mathematics in rural isiXhosa-dominant classrooms, four studies, written and published as academic papers, were undertaken. These four papers make up the core of this study. I was the sole author on three of the papers, and first author (supported by my supervisor Nicky Roberts) on one paper titled, ‘Diversity of mathematical expression: The language of comparison in English and isiXhosa early grade mathematics texts’. Three of the papers focus on the constraints and affordances of teaching in isiXhosa and one focuses on the constraints and affordances of the pedagogical practice of relying heavily on one teaching source. Collectively the four papers provide an example of the kind of research that can be undertaken by an “outside specialist” who is not proficient in isiXhosa, but who is committed to doing research that is accountable to the majority of South African learners. As a study made up of four papers, there are a variety of different types of research questions. The first is an overarching research question which is answered by the collection of the four papers as a whole: ‘What research possibilities are available for an “outside specialist” wishing to build the education knowledge project in ways that are accountable to rural isiXhosa-dominant schools?’. The question at the centre of the study is: ‘What are the affordances and constraints of teaching early grade mathematics in rural isiXhosa-dominant classrooms, both in relation to the linguistic features of isiXhosa and the instructional practices of teachers?’ Each paper answers this central question by providing..