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Siegel & Ryan (1989) reported that children with specific arithmetical learning difficulties (ALD) were impaired if they had to retain temporary information concurrently with counting visual arrays, but not if the concurrent operations were non-mathematical. This selective deficit was attributed to an impaired arithmetical working memory system. In the present study 15 children aged eight to nine with ALD were compared with 15 normally achieving controls. Experiment 1 examined performance on a number of tasks assessing span for information storage during concurrent operations. The results confirmed that children with ALD are impaired on concurrent span only when the operations involve counting and showed that this holds independently of the visuospatial or auditory-verbal characteristics of the task. Experiment 2 went on to investigate the possibility that children with ALD might be impaired at counting or retaining temporary information when each is assessed in isolation. The ALD group tended to count more slowly than controls and had lower auditory digit spans. It is argued that these deficits can account for the selective impairment of ALD children on concurrent counting span, without appealing to a special, arithmetical working memory system. Possible interpretations of the cognitive deficits associated with ALD and their implications for the ability to perform arithmetical skills are discussed.