How are young children developing number sense, post national numeracy strategy

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University London.This thesis examines number sense in primary mathematics. I begin by presenting literature to demonstrate how a cognitive definition of number sense, dominates understandings of mathematical development. I argue that this has influenced fixed-ability practices in mathematics (e.g. Boaler, 1997; Marks, 2014) presenting number-sense as a natural ability. I outline the political landscape and explore data which demonstrates that mathematics education systematically disadvantages some people (Zevenbergen, 2001). After reviewing mathematics learning from a range of theoretical perspectives, I demonstrate a gap in the literature: a sociological exploration of number sense in primary school and illustrate the need to examine school structures and their implications for equitable outcomes for all children. To address this gap I have employed Bourdieusian tools of habitus, field and capital, to explore number sense development. Through ethnographic methods in Year 4 classrooms, I examine how number sense positions children in the field of primary mathematics. This research was undertaken during the first year of statutory implementation of the National Curriculum (DfE, 2013) allowing insight into the lived experiences of children at this time. My findings show that facts, fluency and flexibility are key ways children demonstrate their number sense. Through rapid recall of facts children are seen by their teachers, peers and themselves as ‘able’ at mathematics, leading to explicit reproduction of social class, as these facts are usually learned at home. Similarly, a demand for fluency has led to a focus on procedural accuracy with calculation. Based on this, children are sorted into ability groups magnifying infinitesimally small differences between them (Bourdieu, 1986). Finally, children demonstrate flexibility through different calculation strategies; however, lessons usually rehearse single methods, hiding this key mathematical practice. Each aspect of number sense differentiates children, advantaging those with middle-class habitus and therefore reproducing educational inequalities