Agrammatic but numerate

Neuropsychologia, 2000

We report the case of a patient (ATH) who suered from aphasia, deep dyslexia, and acalculia, following a lesion in her left perisylvian area. She showed a severe impairment in all tasks involving numbers in a verbal format, such as reading aloud, writing to dictation, or responding verbally to questions of numerical knowledge. In contrast, her ability to manipulate nonverbal representations of numbers, i.e., Arabic numerals and quantities, was comparatively well preserved, as evidenced for instance in number comparison or number bisection tasks. This dissociated impairment of verbal and non-verbal numerical abilities entailed a dierential impairment of the four arithmetic operations. ATH performed much better with subtraction and addition, that can be solved on the basis of quantity manipulation, than with multiplication and division problems, that are commonly solved by retrieving stored verbal sequences. The brain lesion aected the classical language areas, but spared a subset of the left inferior parietal lobule that was active during calculation tasks, as demonstrated with functional MRI. Finally, the relative preservation of subtraction versus multiplication may be related to the fact that subtraction activated the intact right parietal lobe, while multiplication activated predominantly left-sided areas. 7

Brain and Cognition, 2013

and sharing with colleagues.

Neuroscience Letters, 2006

The main purpose of the present study was to learn how mathematical abilities are located and develop in the brain with respect to language. Mathematical abilities were assessed in six right-handed patients affected by aphasia following a lesion to their non-dominant hemisphere (crossed aphasia) and in two left-handed aphasics with a right-sided lesion. Acalculia, although in different degrees, was found in all cases. The type of acalculia depended on the type of aphasia, following patterns that have been previously observed in the most common aphasias resulting from left hemisphere lesions. No sign of right hemisphere or spatial acalculia (acalculia in left lateralised right-handed subjects) was detected. These results suggest that, as a rule, language and calculation share the same hemisphere. A primitive computational mechanism capable of recursion may be the precursor of both functions.

2012

Although there is evidence that exact calculation recruits left hemisphere perisylvian language systems, recent work has shown that exact calculation can be retained despite severe damage to these networks. In this study, we sought to identify a "core" network for calculation and hence to determine the extent to which left hemisphere language areas are part of this network. We examined performance on addition and subtraction problems in two modalities: one using conventional two-digit problems that can be easily encoded into language; the other using novel shape representations. With regard to numerical problems, our results revealed increased left fronto-temporal activity in addition, and increased parietal activity in subtraction, potentially reflecting retrieval of linguistically encoded information during addition. The shape problems elicited activations of occipital, parietal and dorsal temporal regions, reflecting visual reasoning processes. A core activation common to both calculation types involved the superior parietal lobule bilaterally, right temporal sub-gyral area, and left lateralized activations in inferior parietal (BA 40), frontal (BA 6/8/32) and occipital (BA 18) regions. The large bilateral parietal activation could be attributed to visuo-spatial processing in calculation. The inferior parietal region, and particularly the left angular gyrus, was part of the core calculation network. However, given its activation in both shape and number tasks, its role is unlikely to reflect linguistic processing per se. A possibility is that it serves to integrate right hemisphere visuo-spatial and left hemisphere linguistic and executive processing in calculation.

Journal of the …, 1999

The aim of this study was to investigate numerical difficulties in 50 patients with left hemispheric lesions. Aphasic patients were grouped according to their type of aphasia diagnosed by the Aachener Aphasia Test. The overall error rate in various transcoding and calculation tasks was clearly correlated with the severity of the language deficit, global aphasics being the most impaired patients. Broca's and Wernicke's aphasics scored similarly at the quantitative level, and amnesic aphasics were less impaired. Interestingly, qualitative analysis of the errors indicated that each group presented with specific difficulties, partially reflecting the nature of the language problems. In simple calculation, multiplication was found to be the most impaired operation, in particular in Broca's aphasics. This result supports the hypothesis that the retrieval of multiplication facts is preferentially mediated by verbal processing. Calculation procedures were mainly impaired in Wernicke's and global aphasics. (JINS, 1999, 5, 213-221.)

Cortex, 1997

We describe two acalculic patients, one with a left subcortical lesion and the other with a right inferior parietal lesion and Gerstmann's syndrome. Both suffered from "pure anarithmetia": they could read arabic numerals and write them to dictation, but experienced a pronounced calculation deficit. On closer analysis, however, distinct deficits were found. The subcortical case suffered from a selective deficit of rote verbal knowledge, including but not limited to arithmetic tables, while her semantic knowledge of numerical quantities was intact. Conversely the inferior parietal case suffered from a category-specific impairment of quantitative numerical knowledge, particularly salient in subtraction and number bissection tasks, with preserved knowledge of rote arithmetic facts. This double dissociation suggests that numerical knowledge is processed in different formats within distinct cerebral pathways. We suggest that a left subcortical network contributes to the storage and retrieval of rote verbal arithmetic facts, while a bilateral inferior parietal network is dedicated to the mental manipulation of numerical quantities. 220 Stanislas Dehaene and Laurent Cohen

We report the case of a patient (ATH) who suered from aphasia, deep dyslexia, and acalculia, following a lesion in her left perisylvian area. She showed a severe impairment in all tasks involving numbers in a verbal format, such as reading aloud, writing to dictation, or responding verbally to questions of numerical knowledge. In contrast, her ability to manipulate nonverbal representations of numbers, i.e., Arabic numerals and quantities, was comparatively well preserved, as evidenced for instance in number comparison or number bisection tasks. This dissociated impairment of verbal and non-verbal numerical abilities entailed a dierential impairment of the four arithmetic operations. ATH performed much better with subtraction and addition, that can be solved on the basis of quantity manipulation, than with multiplication and division problems, that are commonly solved by retrieving stored verbal sequences. The brain lesion aected the classical language areas, but spared a subset of the left inferior parietal lobule that was active during calculation tasks, as demonstrated with functional MRI. Finally, the relative preservation of subtraction versus multiplication may be related to the fact that subtraction activated the intact right parietal lobe, while multiplication activated predominantly left-sided areas.

Psychophysiology, 2006

Anterior negativities obtained during sentence processing have never been unambiguously reported in the mathematical domain. The reason for this might be that the tasks explored in the mathematical domain have been far from resembling those typically yielding language-related anterior negativities. To test this hypothesis, we explored three mathematical aspects: Order-relevant information, a parenthesis indicating the onset of an embedded calculation, and violations of the type of symbol displayed. Results yielded parieto-occipital instead of frontal negativities. Late posterior positivities were also found, largely comparable to linguistic P600 in topography, but dissociable in functional terms. Our data suggest that language-related anterior negativities may indeed reflect language-specific resources of the human brain and support recent claims that language and mathematical domains are more independent than previously thought.

NeuroImage, 2012

Written mathematical notation conveys, in a compact visual form, the nested functional relations among abstract concepts such as operators, numbers or sets. Is the comprehension of mathematical expressions derived from the human capacity for processing the recursive structure of language? Or does algebraic processing rely only on a language-independent network, jointly involving the visual system for parsing the string of mathematical symbols and the intraparietal system for representing numbers and operators? We tested these competing hypotheses by scanning mathematically trained adults while they viewed simple strings ranging from randomly arranged characters to mathematical expressions with up to three levels of nested parentheses. Syntactic effects were observed in behavior and in brain activation measured with functional magnetic resonance imaging (fMRI) and magneto-encephalography (MEG). Bilateral occipito-temporal cortices and right parietal and precentral cortices appeared as the primary nodes for mathematical syntax. MEG estimated that a mathematical expression could be parsed by posterior visual regions in less than 180 ms. Nevertheless, a small increase in activation with increasing expression complexity was observed in linguistic regions of interest, including the left inferior frontal gyrus and the posterior superior temporal sulcus. We suggest that mathematical syntax, although arising historically from language competence, becomes "compiled" into visuo-spatial areas in well-trained mathematics students.