Causal role of spatial-attentional mechanisms in solving arithmetical problems: Behavioural and neuropsychological evidence

Objectives: Recent findings suggest that mental arithmetic involves shifting attention on a mental continuum where numbers would be ordered from left to right, from small to large numbers, with addition and subtraction causing rightward or leftward shifts respectively. Neuropsychological data showing that brain-damaged patients with left neglect experience difficulties in solving subtraction but not addition problems support this hypothesis. However, the reverse dissociation is needed to establish the causal role of spatial attention in mental arithmetic. Method: We conducted a case study a 65-year-old left brain-damaged patient (JPB), exhibiting right unilateral visuo-spatial and representational neglect, was tested with various numerical tasks including numerical comparison, arithmetic problem solving and numerical interval bisection. Results: In numerical comparison, JPB showed a selective response latency increase when judging numbers larger than the references while his performance was normal for smaller numbers. In the arithmetic task, JPB was impaired in solving addition but not subtraction problems. In contrast, performance in number bisection suggests greater difficulties in keeping track of small numbers than large numbers. Conclusion: These results establish a double dissociation between subtraction and addition solving in patients with left vs. right neglect, and demonstrate clear evidence that attentional mechanisms are crucial for mental arithmetic. We suggest that attention shifts are involved whenever a number is represented relative to another on a mental continuum, be it during numerical comparison or arithmetic problem solving. His performance in numerical interval bisection indicates that this task measures other processes than those involved in number comparison and mental arithmetic