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Précis of "The number sense"
"... Number sense " is a shorthand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence sugg ..."
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Cited by 151 (21 self)
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Number sense " is a shorthand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domainspecific, biologicallydetermined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology between the animal, infant, and human adult abilities for number processing ; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higherlevel cultural developments in arithmetic emerge through the establishment of linkages between this core analogical representation (the " number line ") and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution.
Differential Contributions of the Left and Right Inferior Parietal Lobules to Number Processing
 Journal of Cognitive Neuroscience
, 1999
"... We measured cerebral activation with functional magnetic resonance imaging at 3 Tesla while eight healthy volunteers performed various number processing tasks known to be dissociable in brainlesioned patients: naming, comparing, multiplying, or subtracting single digits. The results revealed the ac ..."
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Cited by 45 (15 self)
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We measured cerebral activation with functional magnetic resonance imaging at 3 Tesla while eight healthy volunteers performed various number processing tasks known to be dissociable in brainlesioned patients: naming, comparing, multiplying, or subtracting single digits. The results revealed the activation of a circuit comprising bilateral intraparietal, prefrontal, and anterior cingulate components. The extension and lateralization of this circuit was modulated by task demands. The intraparietal and prefrontal activation was more important in the right hemisphere during the comparison task and in the left hemisphere during the multiplication task and was intensely bilateral during the subtraction task. Thus, partially distinct cerebral circuits with the dorsal parietal pathway underlie distinct arithmetic operations.
Number processing in pure alexia: the effect of hemispheric asymmetries and task demands
 Neurocase
, 1995
"... The relative sparing of arabic numerals, in patients who failto read words or even letters, is a classical feature of pure alexla orlglnallyobserved by Dejerlne (Comptes Rendus des Seances de la Societé de la Biologie1892;4: 6190).Wereport a study of number processlng abilities ln two patients sUff ..."
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Cited by 23 (11 self)
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The relative sparing of arabic numerals, in patients who failto read words or even letters, is a classical feature of pure alexla orlglnallyobserved by Dejerlne (Comptes Rendus des Seances de la Societé de la Biologie1892;4: 6190).Wereport a study of number processlng abilities ln two patients sUfferlngfrom typical pure alexla. Our main flndlngwas that number Identificationperformance varled considerably wlthtask demands. Both patients could name pairs of digits, when they were engaged ln a simple namlng task or for the purpose of magnitude comparlson. ln contras " they frequently misldentifledthe very same digits when treating them as the components of multldlgltnumerals, or as the operands of addition problems. Withtwodlgitnumerals, a slmilar dissociation was shown between excellent comparison and severely impalred readlng aloud. Flnally,the variation of performance withtask demands was shown not to prevail withspelledout numerals. These findings conflrm that some patients withpure alexla are able to process up to a semantic level symbolicstimuli that they cannot read aloud.Wespeculate that both hemispheres possess effective digit~dentiflcationabilitles, whlch are differenth:Ïlly called on depending on the task.
DC: Mathematics and learning disabilities
 J Learn Disabil
"... Between 5 % and 8 % of schoolage children have some form of memory or cognitive deficit that interferes with their ability to learn concepts or procedures in one or more mathematical domains. A review of the arithmetical competencies of these children is provided, along with discussion of underlyin ..."
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Cited by 19 (4 self)
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Between 5 % and 8 % of schoolage children have some form of memory or cognitive deficit that interferes with their ability to learn concepts or procedures in one or more mathematical domains. A review of the arithmetical competencies of these children is provided, along with discussion of underlying memory and cognitive deficits and potential neural correlates. The deficits are discussed in terms of three subtypes of mathematics learning disability and in terms of a more general framework for linking research in mathematical cognition to research in learning disabilities. The breadth and complexity of the field of mathematics make the identification and study of the cognitive phenotypes that define mathematics learning disabilities (MLD) a formidable endeavor. In theory, a learning disability can result from deficits in the ability to represent or process information in one or all of the
Understanding dissociations in dyscalculia: A brain imaging study of the impact of number size on the cerebral networks for exact and approximate calculation
, 2000
"... Neuropsychological studies have revealed different subtypes of... ..."
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Cited by 13 (1 self)
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Neuropsychological studies have revealed different subtypes of...
Moving along the number line: Operational momentum in nonsymbolic arithmetic. manuscript submitted for publication
, 2006
"... Can human adults perform arithmetic operations with large approximate numbers, and what effect, if any, does an internal spatial–numerical representation of numerical magnitude have on their responses? We conducted a psychophysical study in which subjects viewed several hundred short videos of sets ..."
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Cited by 6 (4 self)
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Can human adults perform arithmetic operations with large approximate numbers, and what effect, if any, does an internal spatial–numerical representation of numerical magnitude have on their responses? We conducted a psychophysical study in which subjects viewed several hundred short videos of sets of objects being added or subtracted from one another and judged whether the final numerosity was correct or incorrect. Over a wide range of possible outcomes, the subjects ’ responses peaked at the approximate location of the true numerical outcome and gradually tapered off as a function of the ratio of the true and proposed outcomes (Weber’s law). Furthermore, an operational momentum effect was observed, whereby addition problems were overestimated and subtraction problems were underestimated. The results show that approximate arithmetic operates according to precise quantitative rules, perhaps analogous to those characterizing movement on an internal continuum. Human adults possess an ability to estimate and manipulate approximate numerical magnitudes, which has been termed number sense (Dehaene, 1997). This ability appears to be largely independent of language and other symbol systems, since it is present in both infants (Xu & Spelke, 2000) and other animal species (Brannon & Roitman, 2003;
The problemsize effect in mental addition: Developmental and crossnational trends
 Mathematical Cognition
, 1996
"... Across two experiments, the magnitude of the problemsize effect in mental addition was examined for kindergarten and elementary school children, as well as adults, from mainland China and the United States. In North American samples, the problemsize effect represents the finding that arithmetic pr ..."
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Cited by 6 (1 self)
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Across two experiments, the magnitude of the problemsize effect in mental addition was examined for kindergarten and elementary school children, as well as adults, from mainland China and the United States. In North American samples, the problemsize effect represents the finding that arithmetic problems consisting of largervalued numbers (e.g. 8+7) take longer to solve and are more error prone than are problems consisting of smallervalued numbers (e.g. 2+3). This standard finding was found for the kindergarten, elementary school, and adult samples from the United States. For the Chinese children, the problem size effect was evident in kindergarten and at the beginning of first grade. However, the effect had disappeared at the end of first grade and had reversed (i.e. largervalued addition problems were solved more quickly than smallervalued problems) by the end of third grade. However, the standard problemsize effect “reappeared ” for the Chinese adults. The results are interpreted in terms of theoretical models of the nature of the memory representation for arithmetic facts and in terms of the mechanisms that govern the development of these representations. In the nearly 25 years since Groen and Parkman’s (1972) seminal study of the mental processes underlying the solution of simple addition problems, cognitive arithmetic has emerged as a vibrant area of research. Scientists in this area have mapped the cognitive processes and neurological correlates that govern the mental solution of simple and complex arithmetic problems and have extended these basic findings to more applied issues, such as