Abstract:
This thesis presents the findings of a project that explored the ways in which primary school children developed understandings about mathematics, mathematical 'learning' and 'knowing' and themselves as learners of mathematics. The research aimed to describe the children's mathematical learning environments, to explore the ways in which children made meaning about mathematics through social interactions within these environments, and to identify elements of these environments that appeared to enhance or inhibit the children's learning of mathematics. Located within the body of literature that takes a sociocultural view of teaching and learning, the study adopted the theoretical framework of symbolic interactionism because of its usefulness in explaining how, through the social interactions of everyday life, an individual constructs and reconstructs personal versions of 'reality', including a sense of identity. Through this lens, familiar objects, routine events and everyday language surrounding the teaching and learning of mathematics were examined for their significance to young learners. The concept of the sociomathematical world was created and developed to describe the mathematical environment of the child as positioned within wider social networks. The sociomathematical world of the child was seen as the world of everyday life, the arena in which the child, through regular and routine interactions with others, negotiated meanings about, and made personal sense of, mathematics. The research focussed on ten case study children - four girls and six boys - all attending different schools, and selected randomly from the primary schools in the Wellington region of New Zealand. For three years, from the beginning of their third year at school to the end of their fifth, the children were regularly interviewed and observed in their classrooms. Other key participants in their sociomathematical worlds were also interviewed, including families, teachers, principals, and classmates. Evidence of teaching and learning was also gathered from children's books and assessment records, and linked to local and global curriculum documentation. A cumulative picture was compiled of the mathematical teaching and learning environments of these ten children. Originally intended to be presented as separate biographies, the data were instead collated and reported according to the four distinctive recurring themes that emerged from the findings: the emphasis of speed in mathematics teaching and learning; identification and differentiation based on socially constructed perceptions of mathematical 'ability'; the establishment of 'doing maths' as solo written work; the presentation of mathematics as consisting of 'correct' and non-negotiable facts and procedures. These dominant approaches to teaching and learning of mathematics were found to conform to deeply entrenched traditions, in which the learner was viewed as the passive recipient of, rather than an active participant in, education in general and mathematics education in particular. It was found that these taken-for-granted pedagogical cultures were not explicitly supported by the official curriculum. Marked negative effects of these common teaching practices were commonly observed: alienation, marginalisation and impoverished learning. These impacts were experienced in varying forms and at varying times, by all the case study children, suggesting that changed views of mathematics and of mathematical teaching and learning are needed if the learning potential of all children is to be fully realised.
