Reasoning, including arithmetical reasoning, can be carried out in many ways. Two broad categories that are often discussed with regard to individual differences are verbal and spatial reasoning. Information can be represented,manipulated and analysed in words; it can also be represented, manipulated and analysed in terms of visual-spatial imagery.
A number of researchers have investigated the issue of whether arithmetical skills are particularly associated with verbal or spatial reasoning and/or with discrepancies between the two. The factor analytic studies used to construct the IQ scales have consistently placed the Arithmetic subtest (one which emphasizes word problem solving) within the Verbal scale. However it has sometimes been suggested that spatial difficulties are particularly associated with difficulties in arithmetical reasoning. Rourke (1993; Strang and Rourke,1983) proposed that verbal weaknesses lead to memory difficulties and that nonverbal weaknesses lead to logical difficulties.
We know that children with developmental arithmetic disorders can show selective deficits in specific arithmetical components, which can parallel the deficits found in brain damaged patients. Some children experience arithmetic disorders as part of genetic syndromes, or early acquired brain damage. Though such causes are rare, there appears to be a genetic component to many developmental arithmetical problems that are not caused by specific syndromes.All of this would suggest a physiological, probably brain based contribution to developmental arithmetical deficits (this does not mean that they are caused exclusively by physiological factors). There is evidence for an association in some groups of children between arithmetical deficits and reduced size of the left parietal lobe
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