Dissociations in numerical abilities revealed by progressive cognitive decline in a patient with semantic dementia

This study describes a 3-year follow-up investigation of the deterioration of number abilities in a semantic dementia patient (IH). A few studies have previously reported the decline of number knowledge in patients with degenerative disorders, although almost never in semantic dementia (Diesfeldt, 1993; Girelli, Luzzatti, Annoni, & Vecchi, 1999; Grafman, Kempen, Rosenberg, Salazar, & Boller, 1989). These studies described the change of the patients' performance mainly in terms of increased errors in number tasks. On the other hand, dissociations between different types of number abilities, or different arithmetical operations, have been reported in patients with focal lesions. In the present investigation, the cognitive basis of number processing was revealed throughout the patient's cognitive decline. Two major results emerged from a longitudinal study: First, the patient's conceptual knowledge of arithmetic was well preserved despite severe impairment of nonarithmetic conceptual knowledge. Second, the patient's progressive decline revealed patterns of dissociations between different number abilities. These were between ( 1) multiplication and other arithmetical operations, which particularly emerged in the use of algorithms; ( 2) impaired knowledge of number facts and procedures on one hand, and conceptual knowledge of arithmetic on the other; and ( 3) different types of transcoding skills. The implications of these dissociations for the cognitive architecture of number processing are discussed.