Neuropsychologia 40 (2002) 1786–1793 Are multiplication facts implemented by the left supramarginal and angular gyri? Natasja J. van Harskamp, Peter Rudge, Lisa Cipolotti * Department of Neuropsychology, National Hospital for Neurology and Neurosurgery, Queen Square, London WC1N 3BG, UK Received 11 September 2001; received in revised form 11 February 2002; accepted 15 February 2002 Abstract A patient with presumed cerebral vasculitis showed preserved single digit multiplication facts and impaired single digit subtraction facts. Her ability to comprehend and manipulate numerical quantities was intact. Detailed analysis of her MRI-scan revealed a lesion involving the left parietal lobe including the supramarginal gyrus up to the intraparietal sulcus and extending posteriorly to involve part of the angular gyrus. This finding contradicts a previous report by Lee [Ann. Neurol. 48 (2000) 657] suggesting that these areas are critical for multiplication. In addition, this case contradicts the predicted association between subtraction and quantity manipulation, proposed by Dehaene’s triple-code model [Cortex 33 (1997) 219]. © 2002 Elsevier Science Ltd. All rights reserved. Keywords: Dyscalculia; Gerstmann syndrome; Selective multiplication preservation; Subtraction impairment; Supramarginal and angular gyri 1. Introduction Following acquired brain lesions, patients may present with a selective impairment in the retrieval of arithmetical facts. This impairment can be highly selective and involve only one particular type of operation. For example, pa- tients have been described with a selective impairment for multiplication with entirely or better preserved ability to solve addition and subtraction problems (e.g. [6,18]). These highly selective difficulties have led to the formulation of different theoretical models depicting the underlying organ- isation of arithmetical facts in memory. One of the most in- fluential proposals is the triple-code model of Dehaene and Cohen [6]. This model depicts both the functional as well as the neuro-anatomical architecture underlying arithmetical facts. At a functional level, it is proposed that multiplication facts require rote verbal memory. In contrast, according to this model, subtraction requires the manipulation of in- ternal quantity representations. The status of addition is more ambiguous. The authors claimed that many simple addition problems are underpinned by a verbal code like multiplication. However, more complex addition problems ∗ Corresponding author. Tel.: +44-207-829-8793; fax: +44-207-813-2516. E-mail addresses: n.harskamp@ion.ucl.ac.uk (N.J. van Harskamp), l.cipolotti@ion.ucl.ac.uk (L. Cipolotti). are solved through the manipulation of internal quantity rep- resentations (e.g. back-up strategies such as counting) like subtraction [4]. The triple-code model makes explicit predictions con- cerning: (1) the possible patterns of dissociation between operations; and (2) the relationships between subtraction and general quantity manipulation. First, the model pre- dicts that “... it should not be possible to have a selective impairment of addition relative to multiplication and sub- traction ... ”([5], p. 1427). This is because an impairment in addition should be a consequence of a deficit either in the verbal or in the quantity code. This should inevitably result in an additional impairment either in multiplication or in subtraction. Secondly, the model predicts that a severe im- pairment of subtraction should always entail a more general impairment of quantity manipulation [5]. This is because subtraction problems are thought to be solved through ma- nipulation of quantities rather than accessing to rote verbal memory. Brain-damaged patients with striking dissociations among different types of operations have recently challenged the functional analysis proposed by the triple-code model. In particular, van Harskamp and Cipolotti [18] reported two patients who are not in good accord with the two pre- dictions discussed earlier. One of the two patients (FS) showed a selective impairment of addition. In sharp con- trast, his multiplication and subtraction were well preserved. 0028-3932/02/$ – see front matter © 2002 Elsevier Science Ltd. All rights reserved. PII:S0028-3932(02)00036-2