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Précis of "The number sense"
"... Number sense " is a shorthand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence sugg ..."
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Cited by 151 (21 self)
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Number sense " is a shorthand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domainspecific, biologicallydetermined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology between the animal, infant, and human adult abilities for number processing ; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higherlevel cultural developments in arithmetic emerge through the establishment of linkages between this core analogical representation (the " number line ") and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution.
NonVerbal Numerical Cognition: From the Reals to the Integers
, 2000
"... nthesis of these findings, the tension between the discrete and the continuous, which has been central to the historical development of mathematical thought, is rooted in the nonverbal foundations of numerical thinking, which, it is argued, are common to humans and nonverbal animals. In this view, ..."
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Cited by 56 (4 self)
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nthesis of these findings, the tension between the discrete and the continuous, which has been central to the historical development of mathematical thought, is rooted in the nonverbal foundations of numerical thinking, which, it is argued, are common to humans and nonverbal animals. In this view, the nonverbal representatives of number are mental magnitudes (real numbers) with scalar variability. Scalar variability means that the signals encoding these magnitudes are "noisy;" they vary from trial to trial, with the width of the signal distribution increasing in proportion to (scaled to) its mean. In short, the greater the magnitude, the noisier its representation. These noisy mental magnitudes are arithmetically processedadded, subtracted, multiplied, divided and ordered. Recognition of the importance of arithmetically processed mental magnitudes in the nonverbal representation of number has emerged from a convergence of results from human and animal studies. This is comparative
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.
A Neural Model of How the Brain Represents and Compares MultiDigit Numbers: Spatial and Categorical Processes
, 2003
"... Both animals and humans represent and compare numerical quantities, but only humans have evolved multidigit placevalue number systems. This article develops a Spatial Number Network, or SpaN, model to explain how these shared numerical capabilities are computed using a spatial representation of nu ..."
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Cited by 11 (5 self)
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Both animals and humans represent and compare numerical quantities, but only humans have evolved multidigit placevalue number systems. This article develops a Spatial Number Network, or SpaN, model to explain how these shared numerical capabilities are computed using a spatial representation of number quantities in the Where cortical processing stream, notably the inferior parietal cortex. Multidigit numerical representations that obey a placevalue principle are proposed to arise through learned interactions between categorical language representations in the What cortical processing stream and the Where spatial representation. Learned semantic categories that symbolize separate digits, as well as place markers like `ty,' `hundred,' and `thousand,' are associated through learning with the corresponding spatial locations of the Where representation. Such WhattoWhere auditorytovisual learning generates placevalue numbers as an emergent property, and may be compared with other examples of multimodal crossmodality learning, including synesthesia. The model quantitatively simulates error rates in quantification and numerical comparison tasks, and reaction times for number priming and numerical assessment and comparison tasks. In the Where cortical process, transient responses to inputs are integrated before they activate an ordered spatial map that selectively responds to the number of events in a sequence and exhibits Weber law properties. Numerical comparison arises from activity pattern changes across the spatial map that define a `directional comparison wave.' Variants of these model mechanisms have elsewhere been used to explain data about other Where stream phenomena, such as motion perception, spatial attention, and target tracking. The model is compared wi...
Are numerical impairments syndrome specific? Evidence from Williams syndrome and Down’s syndrome
 Journal of Child Psychology and Psychiatry
, 2006
"... syndrome ..."
Developmental neuroscience of time and number: implications for autism and other neurodevelopmental disabilities
 FRONTIERS IN INTEGRATIVE NEUROSCIENCE
, 2012
"... ..."