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Impact of High Mathematics Education on the Number Sense
, 2012
"... In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) ..."
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In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) which develops later in life following the acquisition of symbolic number knowledge. The current study investigated the influence of high level math education on the ANS and the ENS. Our results showed that the precision of nonsymbolic quantity representation was not significantly altered by high level math education. However, performance in a symbolic number comparison task as well as the ability to map accurately between symbolic and nonsymbolic quantities was significantly better the higher mathematics achievement. Our findings suggest that high level math education in adults shows little influence on their ANS, but it seems to be associated with a better anchored ENS and better mapping abilities between ENS and ANS.
Natural Number and Natural Geometry
"... How does the human brain support abstract concepts such as seven or square? Studies of nonhuman animals, of human infants, and of children and adults in diverse cultures suggest these concepts arise from a set of cognitive systems that are phylogenetically ancient, innate, and universal across human ..."
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How does the human brain support abstract concepts such as seven or square? Studies of nonhuman animals, of human infants, and of children and adults in diverse cultures suggest these concepts arise from a set of cognitive systems that are phylogenetically ancient, innate, and universal across humans: systems of core knowledge. Two of these systems—for tracking small numbers of objects and for assessing, comparing and combining the approximate cardinal values of sets—capture the primary information in the system of positive integers. Two other systems—for representing the shapes of smallscale forms and the distances and directions of surfaces in the largescale navigable layout—capture the primary information in the system of Euclidean plane geometry. As children learn language and other symbol systems, they begin to combine their core numerical and geometrical representations productively, in uniquely human ways. These combinations may give rise to the first truly abstract concepts at the foundations of mathematics. For millenia, philosophers and scientists have pondered the existence, nature and origins of abstract numerical and geometrical concepts, because these concepts have striking features. First, the integers, and the figures of the Euclidean plane, are so intuitive to human adults that the systems underlying them are called “natural number ” and, by some, “natural geometry”
When time is space: Evidence for a mental time line
 Neuroscience and Biobehavioural Reviews
, 2012
"... (This is a sample cover image for this issue. The actual cover is not yet available at this time.) This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors i ..."
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(This is a sample cover image for this issue. The actual cover is not yet available at this time.) This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit:
Quantities, amounts, and the numerical core system
, 2012
"... Numerical cognition is essential to many aspects of life and arithmetic abilities predict academic achievements better than reading (Estrada et al., 2004). Accordingly, it is important to understand the building blocks of numerical cognition, the neural tissue involved, and the developmental traject ..."
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Numerical cognition is essential to many aspects of life and arithmetic abilities predict academic achievements better than reading (Estrada et al., 2004). Accordingly, it is important to understand the building blocks of numerical cognition, the neural tissue involved, and the developmental trajectories. In the last two decades research has made impressive strides forward in studying numerical cognition and brain mechanisms involved in arithmetic. This advance was marked by suggestions of a numerical core system that can be characterized as a set of intuitions for quantities innately available to humans (Brannon et al., 2006)
A Functional Measurement Study on Averaging
"... How to cite Complete issue More information about this article Journal's homepage in redalyc.org Scientific Information System ..."
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How to cite Complete issue More information about this article Journal's homepage in redalyc.org Scientific Information System
Journal of Experimental Child Psychology xxx (2012) xxxxxx Evidence from the preschool years
, 2012
"... a b s t r a c t Humans rely on two main systems of quantification; one is nonsymbolic and involves approximate number representations (known as the approximate number system or ANS), and the other is symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across d ..."
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a b s t r a c t Humans rely on two main systems of quantification; one is nonsymbolic and involves approximate number representations (known as the approximate number system or ANS), and the other is symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across development, recent studies with adolescents and schoolaged children point to individual differences in the precision of these representations that, importantly, have been shown to relate to symbolic math competence even after controlling for general aspects of intelligence. Such findings suggest that the ANS, which humans share with nonhuman animals, interfaces specifically with a uniquely human system of formal mathematics. Other findings, however, point to a less straightforward picture, leaving open questions about the nature and ontogenetic origins of the relation between these two systems. Testing children across the preschool period, we found that ANS precision correlated with early math achievement but, critically, that this relation was nonlinear. More specifically, the correlation between ANS precision and math competence was stronger for children with lower math scores than for children with higher math scores. Taken together, our findings suggest that earlydeveloping connections between the ANS and mathematics may be fundamentally discontinuous. Possible mechanisms underlying such nonlinearity are discussed.
Explaining school mathematics performance from symbolic and nonsymbolic magnitude processing: similarities and differences between typical and lowachieving children
, 2012
"... Abstract Magnitude processing is one of the most central cognitive mechanisms that underlie persistent mathematics difficulties. No consensus has yet been reached about whether these difficulties can be predominantly attributed to deficits in symbolic or nonsymbolic magnitude processing. To investi ..."
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Abstract Magnitude processing is one of the most central cognitive mechanisms that underlie persistent mathematics difficulties. No consensus has yet been reached about whether these difficulties can be predominantly attributed to deficits in symbolic or nonsymbolic magnitude processing. To investigate this issue, we assessed symbolic and nonsymbolic magnitude representations in children with low or typical achievement in school mathematics. Response latencies and the distance effect were comparable between groups in both symbolic and nonsymbolic tasks. The results indicated that both typical and low achievers were able to access magnitude representation via symbolic and nonsymbolic processing. However, low achievers presented higher error rates than typical achievers, especially in the nonsymbolic task. Furthermore, measures of nonsymbolic magnitude explained individual differences in school mathematics better than measures of symbolic magnitude when considering all of the children together. When examining the groups separately, symbolic magnitude representation explained differences in school mathematics in low achievers but not in typical achievers. These results suggest that symbolic magnitude is more relevant to solving arithmetic problems when mathematics achievement is particularly low. In contrast, individual differences in nonsymbolic processing appear to be related to mathematics achievement in a more general manner.
Order and Ordinality: The Acquisition of Cardinals and Ordinals in Dutch
, 2016
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OUP UNCORRECTED PROOF – FIRSTPROOFS, Sat Dec 22 2012, NEWGEN 1.3 Core Social Cognition
"... As a species, humans are distinguished by extraordinary capacities to learn and to socialize. A number of investigators of human cognitive development have proposed that these abilities are related: Our cognitive accomplishments are rooted in capacities and propensities for engaging with other peopl ..."
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As a species, humans are distinguished by extraordinary capacities to learn and to socialize. A number of investigators of human cognitive development have proposed that these abilities are related: Our cognitive accomplishments are rooted in capacities and propensities for engaging with other people, learning from them, and navigating the social world (Csibra & Gergely,
Philosophy of Mathematics: Making a Fresh Start
"... ABSTRACT: The paper distinguishes between two kinds of mathematics, natural mathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment ..."
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ABSTRACT: The paper distinguishes between two kinds of mathematics, natural mathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment of the method of mathematics, the notion of demonstration, the questions of discovery and justification, the nature of mathematical objects, the character of mathematical definition, the role of intuition, the role of diagrams in mathematics, and the effectiveness of mathematics in natural science.