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. The causes for such difficulties are also varied, though they tend to overlap: they include individual characteristics (e.g. unusual patterns of brain development); inadequate or inappropriate teaching; and lack of preschool home experience with mathematical activities and language. The type and extent of intervention needed to address arithmetical difficulties will depend in part on the nature and causes of these difficulties. For example, intervention is more necessary for children with persisting arithmetical difficulties than for those with temporary delays.
There have been several studies of arithmetical difficulties and their characteristics. As will be seen in the section on the history of individualized interventions, research has been carried out on arithmetical errors and faulty procedures since at least the 1920s. Many people experience difficulties with mathematics. For example, Bynner and Parsons (1997) gave some Basic Skills Agency literacy and numeracy tests to a sample of 37-year-olds from the National Child Development Study cohort (which had included all individuals born in Britain in a single week in 1958). The numeracy tests included such tasks as working out
change, calculating area, using charts and bus and train timetables, and working out percentages in practical contexts. According to the standards laid down by the Basic Skills Agency, nearly one-quarter of the cohort had 'very low' numeracy skills that would make everyday tasks difficult to complete successfully. This proportion was about four times as great as that classed as having very low literacy skills. Most of the adults with numeracy difficulties had already been experiencing difficulties with school mathematics at the age of 7.
The reasons for these people's mathematical difficulties are undoubtedly various. Some would have had insufficient or inappropriate instruction in mathematics. Some would have had learning difficulties affecting many subjects. There is no doubt, however, that some individuals experience learning difficulties that are relatively specific to mathematics. Several studies have investigated the prevalence of learning difficulties in mathematics.
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 score equal or below the mean for children two years younger. 143 of these children were located and receivedparental consent for further testing. This included the WISC-R IQ test, and reading and spelling tests standardized on 70 age-matched typically developing children. 3 children were excluded from the 'dyscalculic' group because they obtained IQ tests below 80. Of the 140 dyscalculic children, 75 were girls and 65 were boys, once again indicating an approximately equal gender distribution. Their IQs ranged from 80 to 129, with a mean of 98.2. They were assessed for symptoms of other learning problems. The researchers diagnosed 17% as dyslexic, and 26% as having symptoms of attention deficit hyperactivity disorder. They came from significantly lower socio-economic backgrounds than the children without dyscalculia. 42% had first-degree relatives with specific learning disabilities.
Bzufka, Hein and Neumarker (2000) studied 181 urban and 182 rural German third-grade pupils. They were given standardized school achievement tests of arithmetic and spelling. 12 children in each sample (about 6.6% of the whole population) performed above the 50th percentile in spelling, but below the 25th percentile in mathematics. When the urban and rural children were compared, they showed little difference in incidence of specific spelling or mathematics difficulties, but the urban children [who were on the whole of lower socioeconomic background] were far more likely than the rural children to have difficulty with
both (48.6% versus 3.3%).
Thus, the incidence of mathematical learning difficulties depends widely between studies, depending on the methods and criteria used. For example, they have used different IQ tests; different mathematics tests –which may be emphasizing quite different components; and different cut-off points for establishing deficit in both IQ and mathematics. Moreover, it has been pointed out (Mazzocco and Myers, 2002; Desoete, Roeyers and DeClercq, 2004) that findings about the incidence, nature and outcomes of mathematical difficulties may vary
considerably, depending on whether one uses criteria of discrepancy between mathematical performance and IQ, severity of mathematical weaknesses, or persistence of mathematical weaknesses. Given the marked differences in criteria between studies, it is perhaps inappropriate to focus too much on the exact numbers obtained. The main conclusion one can gain from most studies is that many children have difficulties with mathematics, and a significant number have relatively specific difficulties with mathematics.
Ultimately, the criteria for describing children as having 'mathematical difficulties' must involve not only test scores, but the children's educational and practical functioning in mathematics. Within the present educational system, it may be considered that children have some degree of mathematical difficulty; and that those who have failed to reach the above levels have quite marked mathematical difficulties.
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