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This paper initially discusses recent changes in mathematics education and assessment in England and Wales against the background of research on mathematics performance and assessment. It then reports findings from qualitative research with 10–11 year olds undertaken with the object of exploring the validity of the pilot pencil and paper tests in mathematics developed as part of the assessment programme for the English and Welsh National Curriculum in 1993 and 1994. Fifteen children from across the ’ability‘ range were asked to work through a selection of items in the situation of an individual clinical interview. This enabled in-depth data to be collected about their interpretation of and performance on the items. This paper focuses in particular on items where the ambiguity of the boundary between everyday knowledge and mathematics might be expected to lead to problems for children in interpreting the tasks required of them by the test items. The results show that the nature of the items might well have prevented some of these children, in the context of a paper and pencil testing situation, from demonstrating mathematical capacities and understandings they seem to have possessed. Their initial performance does not always seem to have reflected their underlying competence as demonstrated in the extended interview. [ABSTRACT FROM AUTHOR]

This paper explores written calculation methods for division used by pupils in England (n = 276) and the Netherlands (n = 259) at two points in the same school year. Informal strategies are analysed and progression identified towards more structured procedures that result from different teaching approaches. Comparison of the methods used by year 5 (Group 6) pupils in the two countries shows greater success in the Dutch approach, which is based on careful progression from informal strategies to more structured and efficient procedures. This success is particularly notable for the girls in the sample. For the English pupils, whose written solutions largely involved the traditional algorithm, the discontinuity between the formal computation procedure and informal solution strategies presents difficulties. [ABSTRACT FROM AUTHOR]