Arithmetic knowledge in semantic dementia: is it invariably preserved?

There is accumulating evidence of preserved arithmetic knowledge in semantic dementia (SD), contrasting with patients' striking impairment in other domains of semantic memory. This important finding exemplifies domain specificity in the breakdown of semantic memory and supports notions of the functional independence of semantic number knowledge. Nevertheless, evidence for preserved arithmetic knowledge in SD comes largely from single case studies. It is not known whether such preservation is a universal finding, or whether it persists irrespective of disease severity. The present study examined performance of 14 SD patients, varying in the severity of their semantic impairment, on tasks assessing knowledge of arithmetic signs, and on single-digit and multi-digit calculation problems, permitting evaluation of fact retrieval and use of procedures. SD patients performed generally well compared to 10 healthy controls on tests of addition and subtraction. However, abnormalities were elicited, which were not explained by education or hemispheric side of atrophy, but increased as a function of semantic severity. Patients had difficulty identifying arithmetic signs. They used increasingly basic, inflexible strategies to retrieve multiplication table 'facts', and in multi-digit calculations they made procedural errors that pointed to a failure to understand the differential weighting of left and right hand columns. The pattern of responses and error types mirrors in reverse that found in children as they acquire arithmetic competence, and suggests a progressive degradation in conceptual understanding of arithmetic. Longitudinal study of two SD patients demonstrated an association between semantic decline and impaired arithmetic performance. The findings challenge the notion of arithmetic knowledge as a totally separate semantic domain and suggest that the temporal lobes play an important role in arithmetic understanding.