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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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& 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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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.
How 15 hundred is like 15 cherries: effect of progressive alignment on representational changes in numerical cognition
 Child Development
, 2010
"... How does understanding the decimal system change with age and experience? Second, third, sixth graders, and adults (Experiment 1: N = 96, mean ages = 7.9, 9.23, 12.06, and 19.96 years, respectively) made number line estimates across 3 scales (0–1,000, 0–10,000, and 0–100,000). Generation of linear e ..."
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How does understanding the decimal system change with age and experience? Second, third, sixth graders, and adults (Experiment 1: N = 96, mean ages = 7.9, 9.23, 12.06, and 19.96 years, respectively) made number line estimates across 3 scales (0–1,000, 0–10,000, and 0–100,000). Generation of linear estimates increased with age but decreased with numerical scale. Therefore, the authors hypothesized highlighting commonalities between small and large scales (15:100::1500:10000) might prompt children to generalize their linear representations to everlarger scales. Experiment 2 assigned second graders (N = 46, mean age = 7.78 years) to experimental groups differing in how commonalities of small and large numerical scales were highlighted. Only children experiencing progressive alignment of small and large scales successfully produced linear estimates on increasingly larger scales, suggesting analogies between numeric scales elicit broad generalization of linear representations. The ratio structure of the decimal system—where ‘‘1’ ’ denotes a quantity 1 ⁄10 of 10, ‘‘10’ ’ a quantity 1 ⁄10 of 100, ‘‘100’ ’ a quantity 1 ⁄10 of 1,000, and so forth—may apply to an infinity of numbers, but even over a lifetime, experience of symbolic num
All Numbers Are Not Equal: An Electrophysiological Investigation of Small and Large Number Representations
"... & Behavioral and brain imaging research indicates that human infants, humans adults, and many nonhuman animals represent large nonsymbolic numbers approximately, discriminating between sets with a ratio limit on accuracy. Some behavioral evidence, especially with human infants, suggests that the ..."
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& Behavioral and brain imaging research indicates that human infants, humans adults, and many nonhuman animals represent large nonsymbolic numbers approximately, discriminating between sets with a ratio limit on accuracy. Some behavioral evidence, especially with human infants, suggests that these representations differ from representations of small numbers of objects. To investigate neural signatures of this distinction, eventrelated potentials were recorded as adult humans passively viewed the sequential presentation of dot arrays in an adaptation paradigm. In two studies, subjects viewed successive arrays of a single number of dots interspersed with test arrays presenting the same or a different number; numerical range (small numerical quantities 1–3 vs. large numerical quantities 8–24) and ratio difference varied across blocks as continuous variables were controlled. An earlyevoked component (N1), observed over widespread posterior scalp locations, was modulated by absolute number with small, but not large, number arrays. In contrast, a later component (P2p), observed over the same scalp locations, was modulated by the ratio difference between arrays for large, but not small, numbers. Despite many years of experience with symbolic systems that apply equally to all numbers, adults spontaneously process small and large numbers differently. They appear to treat smallnumber arrays as individual objects to be tracked through space and time, and largenumber arrays as cardinal values to be compared and manipulated. &
The Neural Development of an Abstract Concept of Number
"... entities that can be represented by a numeral, a word, a number of lines on a scorecard, or a sequence of chimes from a clock. This abstract, notationindependent appreciation of numbers develops gradually over the first several years of life. Here, using functional magnetic resonance imaging, we ex ..."
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entities that can be represented by a numeral, a word, a number of lines on a scorecard, or a sequence of chimes from a clock. This abstract, notationindependent appreciation of numbers develops gradually over the first several years of life. Here, using functional magnetic resonance imaging, we examine the brain mechanisms that 6 and 7yearold children and adults recruit to solve numerical comparisons across different notation systems. The data reveal that when young children compare numerical values in symbolic and nonsymbolic notations, they invoke the same network of brain regions as adults including occipitotemporal and parietal cortex. However, children also recruit inferior frontal cortex during these numerical tasks to a much greater degree than adults. Our data lend additional support to an emerging consensus from adult neuroimaging, nonhuman primate neurophysiology, and computational modeling studies that a core neural system integrates notationindependent numerical representations throughout development but, early in development, higherorder brain mechanisms mediate this process. &
EXACT EQUALITY and SUCCESSOR FUNCTION: Two Key Concepts on the Path towards Understanding
, 2008
"... This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan or sublicensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express ..."
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This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan or sublicensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
On the descriptive value of loss aversion in decisions under risk. Available at SSRN: http://ssrn.com/abstract=1012022 Ert
 Psychological Review
, 2010
"... Previous studies of loss aversion in decisions under risk have led to mixed results. Losses appear to loom larger than gains in some settings, but not in others. The current paper clarifies these results by highlighting six experimental manipulations that tend to increase the likelihood of the behav ..."
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Cited by 9 (4 self)
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Previous studies of loss aversion in decisions under risk have led to mixed results. Losses appear to loom larger than gains in some settings, but not in others. The current paper clarifies these results by highlighting six experimental manipulations that tend to increase the likelihood of the behavior predicted by loss aversion. These manipulations include: (1) framing of the safe alternative as the status quo; (2) ensuring that the choice pattern predicted by loss aversion maximizes the probability of positive (rather than zero or negative) outcomes; (3) the use of high nominal (numerical) payoffs; (4) the use of high stakes; (5) the inclusion of highly attractive risky prospects that creates a contrast effect; and (6) the use of long experiments in which no feedback is provided and in which the computation of the expected values is difficult. In addition, the results suggest the possibility of learning in the absence of feedback: The tendency to select simple strategies, like “maximize the worst outcome ” which implies “loss aversion”, increases when this behavior is not costly. Theoretical and practical implications are discussed.
Exact Equality and Successor Function: Two Key Concepts
, 2016
"... (Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Izard, Véronique, Pierre Pica, Elizabeth S. Spelke, and StanislasDehaene. 2008. Exact equality and successor function: two key concepts ..."
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(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Izard, Véronique, Pierre Pica, Elizabeth S. Spelke, and StanislasDehaene. 2008. Exact equality and successor function: two key concepts on the path towards understanding exact numbers.