Newborn infants perceive abstract numbers Izard, Véronique; Sann, Coralie; Spelke, Elizabeth S ...
Proceedings of the National Academy of Sciences - PNAS,
06/2009, Letnik:
106, Številka:
25
Journal Article
Recenzirano
Odprti dostop
Although infants and animals respond to the approximate number of elements in visual, auditory, and tactile arrays, only human children and adults have been shown to possess abstract numerical ...representations that apply to entities of all kinds (e.g., 7 samurai, seas, or sins). Do abstract numerical concepts depend on language or culture, or do they form a part of humans' innate, core knowledge? Here we show that newborn infants spontaneously associate stationary, visual-spatial arrays of 4-18 objects with auditory sequences of events on the basis of number. Their performance provides evidence for abstract numerical representations at the start of postnatal experience.
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 or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic.
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 evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms.
Representations of space, time, and number in neonates de Hevia, Maria Dolores; Izard, Véronique; Coubart, Aurélie ...
Proceedings of the National Academy of Sciences - PNAS,
04/2014, Letnik:
111, Številka:
13
Journal Article
Recenzirano
Odprti dostop
A rich concept of magnitude—in its numerical, spatial, and temporal forms—is a central foundation of mathematics, science, and technology, but the origins and developmental relations among the ...abstract concepts of number, space, and time are debated. Are the representations of these dimensions and their links tuned by extensive experience, or are they readily available from birth? Here, we show that, at the beginning of postnatal life, 0- to 3-d-old neonates reacted to a simultaneous increase (or decrease) in spatial extent and in duration or numerical quantity, but they did not react when the magnitudes varied in opposite directions. The findings provide evidence that representations of space, time, and number are systematically interrelated at the start of postnatal life, before acquisition of language and cultural metaphors, and before extensive experience with the natural correlations between these dimensions.
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 mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education.
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. By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction.
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 few inducer trials, in which participants are explicitly (and sometimes misleadingly) told that a given display contains 30 dots, is sufficient to calibrate their estimates on the whole range of stimuli. Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line.
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 representing the shapes of large‐scale, navigable surface layouts and of small‐scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems.
All humans, regardless of their culture and education, possess an intuitive understanding of number. Behavioural evidence suggests that numerical competence may be present early on in infancy. Here, ...we present brain-imaging evidence for distinct cerebral coding of number and object identity in 3-mo-old infants. We compared the visual event-related potentials evoked by unforeseen changes either in the identity of objects forming a set, or in the cardinal of this set. In adults and 4-y-old children, number sense relies on a dorsal system of bilateral intraparietal areas, different from the ventral occipitotemporal system sensitive to object identity. Scalp voltage topographies and cortical source modelling revealed a similar distinction in 3-mo-olds, with changes in object identity activating ventral temporal areas, whereas changes in number involved an additional right parietoprefrontal network. These results underscore the developmental continuity of number sense by pointing to early functional biases in brain organization that may channel subsequent learning to restricted brain areas.
Subitizing is the rapid and accurate enumeration of small sets (up to 3--4 items). Although subitizing has been studied extensively since its first description about 100 years ago, its underlying ...mechanisms remain debated. One hypothesis proposes that subitizing results from numerical estimation mechanisms that, according to Weber's law, operate with high precision for small numbers. Alternatively, subitizing might rely on a distinct process dedicated to small numerosities. In this study, we tested the hypothesis that there is a shared estimation system for small and large quantities in human adults, using a masked forced-choice paradigm in which participants named the numerosity of displays taken from sets matched for discrimination difficulty; one set ranged from 1 through 8 items, and the other ranged from 10 through 80 items. Results showed a clear violation of Weber's law (much higher precision over numerosities 1--4 than over numerosities 10--40), thus refuting the single-estimation-system hypothesis and supporting the notion of a dedicated mechanism for apprehending small numerosities.
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