This paper reports on a series of statistical analyses carried out on some of the National Curriculum tests in mathematics for . The tests for 11-year-olds are very high stakes, in that the results are published in a school-by-school basis in newspapers etc. The analyses were prompted by the suggestion (from governmental organisations) that the balance of the curriculum content in the mathematics tests should be changed to accommodate better the requirements of the government-initiated National Numeracy Strategy. The analyses were carried out on two datasets, involving nationally representative samples of 11-year-old pupils. The analyses reveal some interesting patterns of change in the overall outcomes when Handling Data questions were statistically replaced by Number items of various kinds and also some interesting changes at the individual level, which could potentially affect the Level outcomes of a significant number of children nationally. However, the final conclusion reached is that, given an appropriately sized and structured pool of items across the curriculum content areas, tests can be constructed which are of an appropriate level of difficulty and discrimination power and which still allow year-on-year calibration of the national standards in mathematics.

It is fair to say that the results of the 1995 TlMSS work proved something of a disappointment to both educationists and policy makers in England. In broad terms, in the 'Multiple Comparisons' analyses for mathematics, the English sample scores placed them 17 th out of 26 in the Population 1 comparisons (Year 5) and 25 th out of 41 in the Population 2 comparisons (Year 9). In science, the results were a little different, with the English sample being placed 8 th out of 26 in the Population 1 (Year 5) comparisons and 10th out of 41 in those for Population 2 (Year 9). The results for Year 4 and Year 8 were broadly similar. All figures used here are drawn from Keys et al., (1996) and Harris et al., (1997). The main findings as reported are summarised in more detail in Table 11.1 below, and further information is available in Keys (1999).Perhaps even more significantly, in the 'Test-curriculum matching' analyses (Keys et al., 1996 andHarris et al., 1997), an equally complex picture emerged. In these analyses, each country selected the questions most closely related to its curriculum and comparisons were made across several countries in terms of only these selected items. In mathematics, performance on this specially selected sub-set deemed most relevant to the mathematics curriculum in England showed the English sample to emerge as 8 th out of the nine countries included in the Population 1 analysis (Year 5) and 9 th out of eleven in the countries included in the Population 2 (Year 9) equivalent investigation. In science, the parallel analyses placed the English sample 6 th 233