The ESRC-RNID project has two aims: (1) to provide a large scale survey of deaf children's numeracy achievements in primary school, analysing the relationships between background variables and achievement; (2) to investigate longitudinally the connections between different aspects of numeracy achievement (number knowledge, spatial knowledge, knowledge of number facts, word problem solving) and cognitive competencies (the understanding of some logical principles; working memory) that are strong predictors of hearing children's mathematics achievements, after controlling for the effects of general intelligence. The focus of the project is on attainment at Key Stages 1 and 2.

Both aims will produce original contributions to knowledge. (1) A survey of deaf primary school children's mathematics is urgently needed.The last extensive U.K. survey of deaf children's mathematics achievement that described the attainments of school leavers was carried out by Wood et al. (1984) and showed that deaf children lag behind their hearing peers by 2 to 3.5 years in mathematics attainment.Due to changes in educational provision (e.g. access to BSL) and technology (use of computers and calculators), audiological interventions (better hearing aids and cochlear implants), and progress in knowledge of how deaf children learn, previous surveys may not reflect present achievements. The inclusion of data already available for the ALSPAC study would strengthen the database for this ESRC-RNID project. (2) Research on deaf children's mathematics learning (Nunes et al., 2008) shows that they underperform in mathematics in relation to their level of non-verbal intelligence; when non-verbal intelligence is controlled for, hearing children still perform significantly better than deaf children in a variety of measures of numeracy and cognitive competencies (logical reasoning and working memory). However, it is not known how well the cognitive measures predict deaf children's mathematics learning. This project will analyse whether these cognitive measures predict deaf children's mathematics learning longitudinally as well as they predict hearing children's learning (Nunes et al, 2007).Tymms et al. (2003) found that the school-entry measures that predict hearing children's performance in Year 2 do not predict the performance of profoundly deaf children. This may have been due to their small sample size. It would be very important to attempt to attempt to replicate and understand these results, if they are replicated.

The data available in ALSPAC would provide an initial analysis of some of these aspects, namely:

• the importance of background variables (SES and mother's education);
• the performance of deaf children in comparison to that of hearing children, controlling for SES and mother's education;
• the importance of age of diagnosis;
• the performance of deaf children in comparison to that of hearing children, controlling for cognitive factors (performance IQ and working memory)
• the connections between mathematical reasoning, working memory, knowledge of number facts and visual-spatial organisation and mathematics attainment.

The analysis of the connections between the cognitive factors and mathematics attainment would not be possible in terms of a longitudinal prediction because the children's Key Stage 1 results precede the focus@8 assessments, which contain the relevant cognitive variables, and there may be very few children with hearing loss taking Key Stage 2 assessments (often they are not included in these assessments).

It is likely that there are many more deaf children who have received cochlear implants currently in school than those included in the ALSPAC sample. A careful description of the mathematics attainment of children who did not receive an implant could be used at a later point by professionals interested in analysing the effects of implantation on children's attainment. If the report provides detailed information, it could be used in a meta-analysis for comparison with children who had cochlear implants.

Variables relevant for this analysis

The predictors relevant for this analysis are measures of SES and maternal education, age of diagnosis, and the cognitive measures, which include assessments of the children's:

a) mathematical reasoning (Year 4);

b) knowledge of arithmetic (a sub-test of the WISC);

c) working memory (backward digit span), short-term memory (non-word repetition and forward digit span) and attention (Coding and two Digit Span tasks from the WISC and the scale within the Strengths and Difficulties Questionnaire);

d) general intelligence (Weschler Intelligence Scale for Children: WISC);

e) Key Stage 1 and 2 Maths results.

These variables are included in the dataset which T. Nunes, P. Bryant and K. Sylva are currently analysing for a previously approved DCSF project, with the exception of the age of diagnosis of the child's hearing impairment. This information will be obtained from the earliest age at which there is an entry of hearing impairment for the child and compared to later entries (to avoid including children who had temporary impairments due to illness, for example).