It is well known that individual differences in arithmetical performance are very marked in both children and adults (Dowker, 1998). For example, British studies separated by 20 years, and by radical changes in mathematics education, have revealed a gap of about seven years in 'mathematics age' between the highest and lowest achievers in an average class of 10- or 11-year-olds (Cockcroft, 1982; Brown, Askew, Rhodes et al, 2002). Individual differences in arithmetic among children of the same age are consistently found to be large in most countries that have been studied. The average level of performance tends to be higher in Pacific Rim countries (TIMSS, 1996), though individual differences are high in these countries as well (Schmidt, McKnight, Cogan, Jackwerth and Huang, 1999). In all countries that have been studied, a significant number of children have real difficulty in mathematics (TIMSS, 1996).
Children's numeracy difficulties can take several forms. Some children have difficulties with many academic subjects, of which arithmetic is merely one; some have specific delays in arithmetic, which will eventually be resolved; and some have persisting, specific problems with arithmetic. It is the latter group for whom the term 'dyscalculia' may most appropriately be used.
The incidence and characteristics of dyscalculia
The term 'developmental dyscalculia', implying a specific disorder of mathematical learning, appears to have been popularised by Kosc (1974, 1981); though there was some earlier research on related problems (Kinsbourne and Warrington, 1963).
Kosc (1981) estimated that the incidence of developmental dyscalculia is approximately 6%. Some later studies appear to concur with this, while others suggest a higher or lower figure.
Lewis, Hitch and Walker (1994) studied 1056 unselected 9-to 10-year-olds English children (the entire age group within a particular, socially highly heterogeneous, local education authority; excluding only those assessed as having severe general learning difficulties). They were given the Ravens Matrices IQ test; Young's Group Mathematics Test; and Young's Spelling and Reading Test. 1.3% of the sample had specific arithmetical difficulties, defined as an arithmetic scaled score of 85 or below despite a Ravens IQ score of 90 or above. A further 2.3% had difficulties in both reading and arithmetic (scaled scores of 85 or below in both the reading and arithmetic tests) despite a Ravens IQ score of 90 or above. Thus, the prevalence of arithmetic difficulties in children of normal IQ was 3.6%. The children with arithmetical difficulties were equally divided as to gender.
Other studies have given a figure closer to Kosc's suggested 6%. Gross-Tsur, Manor and Shalev (1996) assessed the incidence of dyscalculia in a cohort of 3029 Israeli 11- to- 12-year-olds. The 600 children who scored in the lowest 20% on a standardized city-wide arithmetic test were selected for further testing. 555 were located and given an individualized arithmetic test battery previously constructed and standardized by the authors. This included reading, writing and comparing numbers; comparing quantities; simple calculations; and more complex (multi-digit) calculations. 188 children or 6.2% of the total were classified as having dyscalculia, using the criterion of a ...