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  1. Manuela Piazza, Pierre Pica, Véronique Izard, Elizabeth Spelke & Stanislas Dehaene (2013). Education Enhances the Acuity of the Nonverbal Approximate Number System. Psychological Science 24 (4):p.
    All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics education. (...)
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  2. Véronique Izard, Pierre Pica, Danièle Hinchey, Stanislas Dehane & Elizabeth Spelke (2011). Geometry as a Universal Mental Construction. In Stanislas Dehaene & Elizabeth Brannon (eds.), Space, Time and Number in the Brain. Oxford University Press.
  3. Pierre Pica, Véronique Izard, Elizabeth Spelke & Stanislas Dehaene (2011). Flexible Intuitions of Euclidean Geometry in an Amazonian Indigene Group. PNAS 23.
    Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that (...)
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  4. Elizabeth Spelke, Sang Ah Lee & Véronique Izard (2010). Beyond Core Knowledge: Natural Geometry. Cognitive Science 34 (5):863-884.
    For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for (...)
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  5. Stanislas Dehaene, Véronique Izard, Pierre Pica & Elizabeth Spelke (2009). Response to Comment on "Log or Linear? Distinct Intuitions on the Number Scale in Western and Amazonian Indigene Cultures&Quot;. Science 323 (5910):38.
    The performance of the Mundurucu on the number-space task may exemplify a general competence for drawing analogies between space and other linear dimensions, but Mundurucu participants spontaneously chose number when other dimensions were available. Response placement may not reflect the subjective scale for numbers, but Cantlon et al.'s proposal of a linear scale with scalar variability requires additional hypotheses that are problematic.
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  6. Manuela Piazza & Veronique Izard (2009). What is an (Abstract) Neural Representation of Quantity? Behavioral and Brain Sciences 32 (3-4):348-349.
    We argue that Cohen Kadosh & Walsh's (CK&W's) definitions of neural coding and of abstract representations are overly shallow, influenced by classical cognitive psychology views of modularity and seriality of information processing, and incompatible with the current knowledge on principles of neural coding. As they stand, the proposed dichotomies are not very useful heuristic tools to guide our research towards a better understanding of the neural computations underlying the processing of numerical quantity in the parietal cortex.
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  7. Véronique Izard & Stanislas Dehaene (2008). Calibrating the Mental Number Line. Cognition 106 (3):1221-1247.
    Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a (...)
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  8. Véronique Izard, Stanislas Dehaene, Pierre Pica & Elizabeth Spelke (2008). Response to Nunez. Science 312 (5803):1310.
    We agree with Nuñez that the Mundurucu do not master the formal propreties of number lines and logarithms, but as the term "intuition" implies, they spontaneously experience a logarithmic mapping of number to space as natural and "feeling right.".
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  9. Véronique Izard, Pierre Pica, Elizabeth S. Spelke & Stanislas Dehaene (2008). Exact Equality and Successor Function: Two Key Concepts on the Path Towards Understanding Exact Numbers. Philosophical Psychology 21 (4):491 – 505.
    Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by (...)
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  10. Véronique Izard, Pierre Pica, Elizabeth Spelke & Stanislas Dehaene (2008). The Mapping of Numbers on Space : Evidence for a Logarithmic Intuition. Médecine/Science 24 (12):1014-1016.
  11. Pierre Pica, Stanislas Dehaene, Elizabeth Spelke & Véronique Izard (2008). Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures. Science 320 (5880):1217-1220.
    The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic (...)
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  12. Stanislas Dehaene, Véronique Izard, Cathy Lemer & Pierre Pica (2007). Quels Sont les Liens Entre Arithmétique Et Langage ? Une Étude En Amazonie. In Jean Bricmont & Julie Franck (eds.), Cahier Chomsky. L'Herne.
  13. Stanislas Dehaene, Véronique Izard, Pierre Pica & Elizabeth Spelke (2006). Core Knowledge of Geometry in an Amazonian Indigene Group. Science 3115759:381-384.
    Does geometry constitute a core set of intuitions present in all humans, regardless of their language or schooling? We used two nonverbal tests to probe the conceptual primitives of geometry in the Mundurukú, an isolated Amazonian indigene group. Mundurukú children and adults spontaneously made use of basic geometric concepts such as points, lines, parallelism, or right angles to detect intruders in simple pictures, and they used distance, angle, and sense relationships in geometrical maps to locate hidden objects. Our results provide (...)
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  14. Stanislas Dehaene, Véronique Izard, Pierre Pica & Elizabeth Spelke (2006). Examining Knowledge of Geometry : Response to Wulf and Delson. Science 312 (5778):1309-1310.
    La connaissances noyau de la géométrie euclidienne est liée au raisonnement déductif et non à la reconnaissance de motifs perceptuels.
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  15. Pierre Pica, Cathy Lemer, Véronique Izard & Stanislas Dehaene (2005). Quais São Os Vinculos Entre Aritmética E Linguagem ? Um Estudo Na Amazonia. Revista de Estudos E Pesquisas 2 (1):199-236.
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  16. Pierre Pica, Cathy Lemer, Véronique Izard & Stanislas Dehaene (2004). Exact and Approximate Arithmetic in an Amazonian Indigene Group. Science 306 (5695):499-503.
    Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 (...)
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