Visual perception of numerosity in infancy.

Loosbroek, Erik van; Smitsman, Ad W.

doi:10.1037/0012-1649.26.6.911.b

Cited by 144 publications

(55 citation statements)

References 29 publications

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“…For example, objects differentiated by movement patterns may sway quantity attention toward discrete number. Several infant habituation/dishabituation studies that employ stimulus movement during the habituation phase find infants have an awareness of discrete number despite controls for overall area (45)(46).…”

Section: Discussionmentioning

confidence: 99%

Sometimes area counts more than number

Hurewitz

Gelman

Schnitzer

2006

Proc. Natl. Acad. Sci. U.S.A.

208

210

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Using an interference paradigm, we show across three experiments that adults' order judgments of numbers, sizes, or combined area of dots in pairs of arrays occur spontaneously and automatically, but at different speeds and levels of accuracy. Experiment 1 used circles whose sizes varied between but not within arrays. Variation in circle size interfered with judgments of which array had more circles. Experiment 2 used displays in which circle size varied within and between arrays. Between-array differences in the amount of ''circle stuff'' (area occupied by circles) interfered with judgments of number. Experiment 3 examined whether variation in number also interferes with judgments of area. Interference between discrete and continuous stimulus dimensions occurred in both directions, although it was stronger from the continuous to the discrete than vice versa. These results bear on interpretations of studies with infants and preschoolers wherein subjects respond on the basis of continuous quantity rather than discrete quantity. In light of our results with adults, these findings do not license the conclusion that young children cannot represent discrete quantity. Absent data on attentional hierarchies and speed of processing, it is premature to conclude that infant and child quantity processes are fundamentally different from that of adults.attention ͉ child development ͉ estimation ͉ interference ͉ quantity T he capacity to represent both discrete and continuous quantity is found in both humans and nonhuman animals (1-3). Discrimination functions in animals and humans yield similar variability signatures for different dimensions of quantification (time, number, distance, and size), suggesting the use of a common representational format across species (4-7) and domains (discrete vs. continuous quantity).Questions of when in development different quantitative dimensions are represented and how these representations interact have become important issues in research on the development of numerical cognition in humans. On one view, preverbal numerical representations like those found in nonhuman animals are present at a very early age and form the basis for children's later numerical accomplishments, such as counting and the understanding of arithmetic operations (ordination, addition, and subtraction). Consistent with this view are reports that infants discriminate numerically small sets of one to three items (8-10), and larger pairs, like 8 vs. 16 (11). They also respond appropriately to the effects of addition and subtraction (12) and show intermodal numerical matching (13) and intermodal addition (14).The alternative view is that the ability to represent number (discrete quantity) appears late in development. On this view, infants' behavior in ostensibly numerical experiments is controlled by variation along covarying nonnumerical continuous dimensions of the stimuli (15). Discrete displays span various lengths, and the items cover varying amounts of surface or occupy varying volumes. Studies designed to investig...

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Section: Discussionmentioning

confidence: 99%

Sometimes area counts more than number

Hurewitz

Gelman

Schnitzer

2006

Proc. Natl. Acad. Sci. U.S.A.

208

210

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“…This only happens as a result of the integration of two conceptual systems, via language. The first system enables infants to apprehend small, exact numerosities (Starkey & Cooper, 1980;Strauss & Curtis, 1981;Van Loosbroek & Smitsman, 1990) and the other enables them to grasp large, approximate numerosties (Xu & Spelke, 2000). This is what Sarnecka and Gelman call the Approximate Numerosities/Bootstrapping (ANB) view which they describe as follows: "According to this view, children do not think about large, exact numerosities until an understanding of cardinality and the linguistic counting system makes such abstraction readily available (Carey, 2001).…”

Section: Developmental Backgroundmentioning

confidence: 99%

The semantics and acquisition of number words: integrating linguistic and developmental perspectives

Musolino

2004

Cognition

104

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This article brings together two independent lines of research on numerally quantified expressions, e.g. two girls. One stems from work in linguistic theory and asks what truth conditional contributions such expressions make to the utterances in which they are used -in other words, what do numerals mean? The other comes from the study of language development and asks when and how children learn the meaning of such expressions. My goal is to show that when integrated, these two perspectives can both constrain and enrich each other in ways hitherto not considered. Specifically, work in linguistic theory suggests that in addition to their 'exactly n' interpretation, numerally quantified NPs such as two hoops can also receive an 'at least n' and an 'at most n' interpretation, e.g. you need to put two hoops on the pole to win (i.e. at least two hoops) and you can miss two shots and still win (i.e. at most two shots). I demonstrate here through the results of three sets of experiments that by the age of 5 children have implicit knowledge of the fact that expressions like two N can be interpreted as 'at least two N' and 'at most two N' while they do not yet know the meaning of corresponding expressions such as at least/most two N which convey these senses explicitly. I show that these results have important implications for theories of the semantics of numerals and that they raise new questions for developmental accounts of the number vocabulary. q

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“…The numbers increase considerably for larger arrays (adapted from Mandler and Shebo 1982). very early age, human babies exhibit a variety of cognitive capacities that are preconditions for numerical competence. For instance, at three or four days, a baby can discriminate between collections of two and three items (Antell and Keating 1983), and under certain conditions, infants can even distinguish three items from four (Strauss and Curtis 1981;van Loosbroek and Smitsman 1990). By four and a half months, babies exhibit behaviors that can be interpreted as having some basic understanding of "simple arithmetic," as in "one plus one is two" and "two minus one is one" (Wynn 1992).…”

Section: Numerosity Discrimination and Cognitive Preconditions For Numentioning

confidence: 99%

Numbers and Arithmetic: Neither Hardwired Nor Out There

Núñez

2009

Biol Theory

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What is the nature of number systems and arithmetic that we use in science for quantification, analysis, and modeling? I argue that number concepts and arithmetic are neither hardwired in the brain, nor do they exist out there in the universe. Innate subitizing and early cognitive preconditions for numberwhich we share with many other species-cannot provide the foundations for the precision, richness, and range of number concepts and simple arithmetic, let alone that of more complex mathematical concepts. Numbers and arithmetic, and mathematics in general, have unique features-precision, objectivity, rigor, generalizability, stability, symbolizability, and applicability to the real world-that must be accounted for. They are sophisticated concepts that developed culturally only in recent human history. I suggest that numbers and arithmetic are realized through precise combinations of non-mathematical everyday cognitive mechanisms that make human imagination and abstraction possible. One such mechanism, conceptual metaphor, is a neurally instantiated inference-preserving cross-domain mapping that allows the conceptualization of abstract entities in terms of grounded bodily experience. I analyze how the inferential organization of the properties and "laws" of arithmetic emerge metaphorically from everyday meaningful actions. Numbers and arithmetic are thus-outside of natural selection-the product of the biologically constrained interaction of individuals with the appropriate cultural and historical phenotypic variation supported by language, writing systems, and education.

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Visual perception of numerosity in infancy.

Cited by 144 publications

References 29 publications

Sometimes area counts more than number

Sometimes area counts more than number

The semantics and acquisition of number words: integrating linguistic and developmental perspectives

Numbers and Arithmetic: Neither Hardwired Nor Out There

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