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The acquisition of English number marking: the singular/plural distinction
 Language Learning and Development
, 2006
"... We present data from a preferential looking method to investigate when infants have mapped singular and plural markers in English onto the semantic distinction between singleton sets and sets with more than 1 individual. Twenty to 36monthold children heard sentences that marked number in 1 of 2 w ..."
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Cited by 19 (6 self)
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We present data from a preferential looking method to investigate when infants have mapped singular and plural markers in English onto the semantic distinction between singleton sets and sets with more than 1 individual. Twenty to 36monthold children heard sentences that marked number in 1 of 2 ways: (a) redundantly with verb morphology, lexical quantifiers, and noun morphology (“Look, there ARE SOME blicketS”/“Look, there IS A blicket”) or (b) only with noun morphology (“Look at the blicketS”/“Look at the blicket”). Twentyfourmonthold infants, but not 20monthold infants, looked at the screen that matched the carrier sentence with respect to singular–plural distinction when number was expressed on the verb, on the noun, and with quantifiers. Detailed lookingtime analyses suggest that the arrays begin to be differentiated on the child’s hearing are or is. Twentyfourmontholds failed when number was marked on the noun alone, whereas 36montholds sucCorrespondence should be addressed to Sid Kouider, Laboratoire de Sciences Cognitives et
Mathematical cognition
 In
, 2005
"... Mathematics is a system for representing and reasoning about quantities, with arithmetic as its foundation. Its deep interest for our understanding of the psychological foundations of scientific thought comes from what Eugene Wigner called the unreasonable efficacy of mathematics in the natural scie ..."
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Cited by 14 (2 self)
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Mathematics is a system for representing and reasoning about quantities, with arithmetic as its foundation. Its deep interest for our understanding of the psychological foundations of scientific thought comes from what Eugene Wigner called the unreasonable efficacy of mathematics in the natural sciences. From a formalist perspective, arithmetic is a symbolic game, like tictactoe. Its rules are more complicated, but not a great deal more complicated. Mathematics is the study of the properties of this game and of the systems that may be constructed on the foundation that it provides. Why should this symbolic game be so powerful and resourceful when it comes to building models of the physical world? And on what psychological foundations does the human mastery of this game rest? The first question is metaphysical—why is the world the way it is? We do not treat it, because it lies beyond the realm of experimental behavioral science. We review the answers to the second question that experimental research on human and nonhuman animal cognition suggests.
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;
Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation
, 2008
"... ..."
Representations of the magnitudes of fractions
 Journal of Experimental Psychology: Human Perception and Performance
, 2010
"... We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and den ..."
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Cited by 4 (0 self)
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We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and denominators as separate whole numbers. However, atypical characteristics of the presented fractions might have provoked the use of atypical comparison strategies in that study. In our 3 experiments, university and community college students compared more balanced sets of singledigit and multidigit fractions and consistently exhibited a logarithmic distance effect. Thus, adults used integrated, analog representations, akin to a mental number line, to compare fraction magnitudes. We interpret differences between the past and present findings in terms of different stimuli eliciting different solution strategies.
Correspondence: Computational Modeling of Numerical Cognition
"... Numerical cognition has been studied in both human and animal species for a long time. However, the computational basis of number representation and numerical skills has received very little attention, as compared with the computational basis of language processing, for example, reading (see Zorzi, ..."
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Cited by 2 (0 self)
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Numerical cognition has been studied in both human and animal species for a long time. However, the computational basis of number representation and numerical skills has received very little attention, as compared with the computational basis of language processing, for example, reading (see Zorzi, 2004, for a review). In general, computational modeling is a powerful tool in cognitive
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. &
Core systems in human cognition
"... Abstract: Research on human infants, adult nonhuman primates, and children and adults in diverse cultures provides converging evidence for four systems at the foundations of human knowledge. These systems are domain specific and serve to represent both entities in the perceptible world (inanimate ma ..."
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Abstract: Research on human infants, adult nonhuman primates, and children and adults in diverse cultures provides converging evidence for four systems at the foundations of human knowledge. These systems are domain specific and serve to represent both entities in the perceptible world (inanimate manipulable objects and animate agents) and entities that are more abstract (numbers and geometrical forms). Human cognition may be based, as well, on a fifth system for representing social partners and for categorizing the social world into groups. Research on infants and children may contribute both to understanding of these systems and to attempts to overcome misconceptions that they may foster.
Infants Make Quantity Discriminations for Substances
"... Infants can track small groups of solid objects, and infants can respond when these quantities change. But earlier work is equivocal about whether infants can track continuous substances, such as piles of sand. Experiment 1 (N = 88) used a habituation paradigm to show infants can register changes in ..."
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Cited by 1 (1 self)
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Infants can track small groups of solid objects, and infants can respond when these quantities change. But earlier work is equivocal about whether infants can track continuous substances, such as piles of sand. Experiment 1 (N = 88) used a habituation paradigm to show infants can register changes in the size of piles of sand that they see poured from a container when there is a 1to4 ratio. Experiment 2 (N = 82) tested whether infants could discriminate a 1to2 ratio. The results demonstrate that females could discriminate the difference but males could not. These findings constitute the youngest evidence of successful quantity discriminations for a noncohesive substance and begin to characterize the nature of the representation for noncohesive entities. Infants have the ability to discriminate numerical quantities in the 1st year of life. We know that they can represent both the number of individuals in a
Neuroimaging Unit
"... Children’s sense of numbers before formal education is thought to rely on an approximate number system based on logarithmically compressed analog magnitudes that increases in resolution throughout childhood. Schoolage children performing a numerical estimation task have been shown to increasingly r ..."
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Children’s sense of numbers before formal education is thought to rely on an approximate number system based on logarithmically compressed analog magnitudes that increases in resolution throughout childhood. Schoolage children performing a numerical estimation task have been shown to increasingly rely on a formally appropriate, linear representation and decrease their use of an intuitive, logarithmic one. We investigated the development of numerical estimation in a younger population (3.5 to 6.5yearolds) using 0–100 and 2 novel sets of 1–10 and 1–20 number lines. Children’s estimates shifted from logarithmic to linear in the small number range, whereas they became more accurate but increasingly logarithmic on the larger interval. Estimation accuracy was correlated with knowledge of Arabic numerals and numerical order. These results suggest that the development of numerical estimation is built on a logarithmic coding of numbers—the hallmark of the approximate number system—and is subsequently shaped by the acquisition of cultural practices with numbers.