The study is funded by the Economic and Social Research Council, and I presented part of it at the British Psychological Society Development Section Conference last month.
The study involves a detailed investigation of the arithmetical and other cognitive strengths and weaknesses of six to nine-year-old children, and also of adults. So far, nearly 100 children have been studied. It is clear that there are often discrepancies between different arithmetic-related abilities : notably, there are children (about a quarter of those in the present study) who are much better at arithmetical reasoning than at calculation.
The results of this study so far show one highly significant difference between children with and without such a discrepancy between reasoning and calculation. This difference was that children with such a discrepancy appear significantly more likely also to show a marked unevenness in general cognitive abilities, as demonstrated by a wide scatter of scores between and within different standardised tests (for example, between verbal and performance IQ scores on the WISC).
So far, there does not seem to be any single consistent pattern of unevenness. One likely hypothesis that might explain at least part of this phenomenon is that teaching in schools, especially in a highly structured subject such as arithmetic, is geared toward children who do have a relatively uniform pattern of abilities. Those who do not may fall behind and this is likely to affect calculation more than arithmetical reasoning, which may be less dependent on school instruction.
One of the main conclusions stated in my conference paper was, indeed, as follows: "My findings of uneven patterns of arithmetical ability and of a relationship between these and generally uneven cognitive patterns may suggest that a Mathematics Recovery programme, similar in principle to Reading Recovery, might help to ameliorate numeracy problems. One might expect it to work best if introduced at the relatively early stages of arithmetical development."
Department of Experimental Psychology
University of Oxford
South Parks Road