Barry Cooper and Máiréad Dunne
Sociological approaches to assessment have taken a variety of forms. Broadly macro-structural perspectives have focused on the relations between the criteria for assessment, social selection and the wider, socio-economic context (for example, Bowles and Gintis, 1976). Broadly micro-structural perspectives have focused instead on the ways in which assessment outcomes are constructed within classrooms or testing contexts (for example, Mehan, 1973; Newman et al., 1989). Both of these approaches have produced important contributions to our understanding of the origins, the practice and the consequences of assessment. Notwithstanding their different emphases these authors have had many useful things to say about the relations between social structure, culture and the processes of meaning construction in the contexts in which assessment actually occurs. Bourdieu's work (for example, Bourdieu, 1974) on the nature of assessment practices in French higher education serves as an early example of work of this type. Turning to maths education, there has been a considerable body of research in recent years focusing on the ways in which the contexts within which mathematical problem-solving occurs can affect radically both the processes and the products of such cognitive activity (Nunes et al., 1993; Lave, 1988). In parallel, there has also been much research on children's 'failure' to take a 'realistic' perspective during mathematical problem-solving when it would seem appropriate to do so (for example, Säljö, 1991). Our recent research on maths assessment, on which we will draw here, is intended as a contribution to these relational and contextual approaches to the study of assessment in maths (for example, Cooper, 1998b; Cooper and Dunne, 2000; Dunne, 1994).
We will draw on our research programme on the assessment of the mathematical knowledge and understanding of 10-11- and 13-14-year-old children in England. This research was partly motivated by a concern that the national testing of children's mathematics mainly via 'realistically' contextualised items might have a variety of unintended consequences, especially for the validity of the assessment of working-class children's knowledge and understanding. Children are often required by 'realistic' test items to make quite subtle judgements about the relevance to the process of solution of their everyday knowledge and experience (Cooper, 1992, 1994). There are sociological grounds for expecting working-class children to find it more difficult to