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Development of elementary numerical abilities: A neuronal model
 Journal of Cognitive Neuroscience
, 1993
"... Despite their lack of language, human infants and several animal species possess some elementary abilities for numerical processing. These include the ability to recognize that a given numerosity is being presented visually or auditorily, and, at a later stage of development, the ability to compare ..."
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Cited by 120 (15 self)
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Despite their lack of language, human infants and several animal species possess some elementary abilities for numerical processing. These include the ability to recognize that a given numerosity is being presented visually or auditorily, and, at a later stage of development, the ability to compare two numerosities and to decide which is larger. We propose a model for the development of these abilities in a formal neuronal network. Initially, the model is equipped only with unordered numerosity detectors. It can therefore detect the numerosity of an input set and can be conditioned to react accordingly. In a later stage, the addition of a shortterm memory network is shown to be sufficient for number comparison abilities to develop. Our computer simulations account for several phenomena in the numerical domain, including the distance effect and Fechner’s law for numbers. They also demonstrate that infants ’ numerosity detection abilities may be explained without assuming that infants can count. The neurobiological bases of the critical components of the model are discussed.
Beyond hemispheric dominance: Brain regions underlying the joint lateralization of language and arithmetic to the left hemisphere
 J. Cogn. Neurosci.,inpress
, 2009
"... & Language and arithmetic are both lateralized to the left hemisphere in the majority of righthanded adults. Yet, does this similar lateralization reflect a single overall constraint of brain organization, such an overall ‘‘dominance’ ’ of the left hemisphere for all linguistic and symbolic ope ..."
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Cited by 22 (6 self)
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& Language and arithmetic are both lateralized to the left hemisphere in the majority of righthanded adults. Yet, does this similar lateralization reflect a single overall constraint of brain organization, such an overall ‘‘dominance’ ’ of the left hemisphere for all linguistic and symbolic operations? Is it related to the lateralization of specific cerebral subregions? Or is it merely coincidental? To shed light on this issue, we performed a ‘‘colateralization analysis’ ’ over 209 healthy subjects: We investigated whether normal variations in the degree of left hemispheric asymmetry in areas involved in sentence listening and reading are mirrored in the asymmetry of areas involved in mental arithmetic. Within the language network, a regionofinterest analysis disclosed partially dissociated patterns of lateralization, inconsistent with an overall ‘‘dominance’’ model. Only two of these areas presented a lateralization during sentence listening and reading which correlated strongly with the lateralization of two regions active during calculation. Specifically, the profile of asymmetry in the posterior superior temporal sulcus during sentence processing covaried with the asymmetry of calculationinduced activation in the intraparietal sulcus, and a similar colateralization linked the middle frontal gyrus with the superior posterior parietal lobule. Given recent neuroimaging results suggesting a late emergence of hemispheric asymmetries for symbolic arithmetic during childhood, we speculate that these colateralizations might constitute developmental traces of how the acquisition of linguistic symbols affects the cerebral organization of the arithmetic network. &
Origins of Mathematical Intuitions  The Case of Arithmetic
 THE YEAR IN COGNITIVE NEUROSCIENCE
, 2009
"... Mathematicians frequently evoke their “intuition” when they are able to quickly and automatically solve a problem, with little introspection into their insight. Cognitive neuroscience research shows that mathematical intuition is a valid concept that can be studied in the laboratory in reduced parad ..."
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Cited by 15 (1 self)
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Mathematicians frequently evoke their “intuition” when they are able to quickly and automatically solve a problem, with little introspection into their insight. Cognitive neuroscience research shows that mathematical intuition is a valid concept that can be studied in the laboratory in reduced paradigms, and that relates to the availability of “core knowledge” associated with evolutionarily ancient and specialized cerebral subsystems. As an illustration, I discuss the case of elementary arithmetic. Intuitions of numbers and their elementary transformations by addition and subtraction are present in all human cultures. They relate to a brain system, located in the intraparietal sulcus of both hemispheres, which extracts numerosity of sets and, in educated adults, maps back and forth between numerical symbols and the corresponding quantities. This system is available to animal species and to preverbal human infants. Its neuronal organization is increasingly being uncovered, leading to a precise mathematical theory of how we perform tasks of number comparison or number naming. The next challenge will be to understand how education changes our core intuitions of number.
Nonsymbolic approximate arithmetic in children: Abstract addition prior to instruction
, 2008
"... Do children draw upon abstract representations of number when they perform approximate arithmetic operations? In this study, kindergarten children viewed animations suggesting addition of a sequence of sounds to an array of dots, and they compared the sum to a second dot array that differed from the ..."
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Cited by 15 (2 self)
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Do children draw upon abstract representations of number when they perform approximate arithmetic operations? In this study, kindergarten children viewed animations suggesting addition of a sequence of sounds to an array of dots, and they compared the sum to a second dot array that differed from the sum by 1 of 3 ratios. Children performed this task successfully with all the signatures of adults ’ nonsymbolic number representations: accuracy modulated by the ratio of the sum and the comparison quantity, equal performance for within and crossmodality tasks and for addition and comparison tasks, and performance superior to that of a matched subtraction task. The findings provide clear evidence for nonsymbolic numerical operations on abstract numerical quantities in children who have not yet been taught formal arithmetic.
Comparison of quantities: Core and formatdependent regions as revealed by fMRI
 Cerebral Cortex
, 2012
"... The perception and handling of numbers is central to education. Numerous imaging studies have focused on how quantities are encoded in the brain. Yet, only a few studies have touched upon number mining: the ability to extract the magnitude encoded in a visual stimulus. This article aims to character ..."
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Cited by 6 (0 self)
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The perception and handling of numbers is central to education. Numerous imaging studies have focused on how quantities are encoded in the brain. Yet, only a few studies have touched upon number mining: the ability to extract the magnitude encoded in a visual stimulus. This article aims to characterize how analogue (i.e., disks and dots) and symbolic (i.e., positive and negative integers) formats influence number mining and the representation of quantities. Sixteen adult volunteers completed a comparison task while we recorded the blood oxygen leveldependent response using functional magnetic resonance imaging. The results revealed that a restricted set of specific subdivisions in the right intraparietal sulcus is activated in all conditions. With respect to magnitude assessment, the results show that 1) analogue stimuli are predominantly processed in the right hemisphere and that 2) symbolic stimuli encompass the analogue system and further recruit areas in the left hemisphere. Crucially, we found that polarity is encoded independently from magnitude. We refine the triplecode model by integrating our findings.
Development of quantitative thinking
 In
, 2012
"... For understanding development of quantitative thinking, the distinction between nonsymbolic and symbolic thinking is fundamental. Nonsymbolic quantitative thinking is present in early infancy, culturally universal, and similar across species. These similarities include the ability to represent and ..."
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Cited by 1 (1 self)
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For understanding development of quantitative thinking, the distinction between nonsymbolic and symbolic thinking is fundamental. Nonsymbolic quantitative thinking is present in early infancy, culturally universal, and similar across species. These similarities include the ability to represent and compare numerosities, the representations being noisy and increasing logarithmically with actual quantity, and the neural correlates of number representation being distributed in homologous regions of frontoparietal cortex. Symbolic quantitative thinking, in contrast, emerged recently in human history, differs dramatically across cultural groups, and develops over many years. As young children gain experience with symbols in a given numeric range and associate them with nonverbal quantities in that range, they initially map them to a logarithmicallycompressed mental number line and later to a linear form. This logarithmictolinear shift expands children’s quantitative skills profoundly, including ability to estimate positions of numbers on number lines, to estimate measurements of continuous and discrete quantities, to categorize numbers by
Parietal functional connectivity in numerical cognition. Cereb. Cortex 23, 2127–2135. doi: 10.1093/cercor/ bhs193
, 2013
"... The parietal cortex is central to numerical cognition. The right parietal region is primarily involved in basic quantity processing, while the left parietal region is additionally involved in precise number processing and numerical operations. Little is known about how the 2 regions interact during ..."
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The parietal cortex is central to numerical cognition. The right parietal region is primarily involved in basic quantity processing, while the left parietal region is additionally involved in precise number processing and numerical operations. Little is known about how the 2 regions interact during numerical cognition. We hypothesized that functional connectivity between the right and left parietal cortex is critical for numerical processing that engages both basic number representation and learned numerical operations. To test this hypothesis, we estimated neural activity using functional magnetic resonance imaging in participants performing numerical and arithmetic processing on dot arrays. We first found taskbased functional connectivity between a right parietal seed and the left sensorimotor cortex in all task conditions. As we hypothesized, we found enhanced functional connectivity between this right parietal seed and both the left parietal cortex and neighboring right parietal cortex, particularly during subtraction. The degree of functional connectivity also correlated with behavioral performance across individual participants, while activity within each region did not. These results highlight the role of parietal functional connectivity in numerical processing. They suggest that arithmetic processing depends on crosstalk between and within the parietal cortex and that this crosstalk contributes to one’s numerical competence.
Neuron Review Cultural Recycling of Cortical Maps
"... Part of human cortex is specialized for cultural domains such as reading and arithmetic, whose invention is too recent to have influenced the evolution of our species. Representations of letter strings and of numbers occupy reproducible locations within largescale macromaps, respectively in the lef ..."
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Part of human cortex is specialized for cultural domains such as reading and arithmetic, whose invention is too recent to have influenced the evolution of our species. Representations of letter strings and of numbers occupy reproducible locations within largescale macromaps, respectively in the left occipitotemporal and bilateral intraparietal cortex. Furthermore, recent fMRI studies reveal a systematic architecture within these areas. To explain this paradoxical cerebral invariance of cultural maps, we propose a neuronal recycling hypothesis, according to which cultural inventions invade evolutionarily older brain circuits and inherit many of their structural constraints.
Neuropsychologia 46 (2008) 2463–2475 Contents lists available at ScienceDirect
"... journal homepage: www.elsevier.com/locate/neuropsychologia Verbal numerosity estimation deficit in the context of spared semantic representation of numbers: A neuropsychological study of a patient ..."
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journal homepage: www.elsevier.com/locate/neuropsychologia Verbal numerosity estimation deficit in the context of spared semantic representation of numbers: A neuropsychological study of a patient