One, two, three, four, nothing more: an investigation of the conceptual sources of the verbal counting principles. Corre, M. L. & Carey, S. Cognition, 105(2):395-438, 2007. doi abstract bibtex Since the publication of [Gelman, R., & Gallistel, C. R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.] seminal work on the development of verbal counting as a representation of number, the nature of the ontogenetic sources of the verbal counting principles has been intensely debated. The present experiments explore proposals according to which the verbal counting principles are acquired by mapping numerals in the count list onto systems of numerical representation for which there is evidence in infancy, namely, analog magnitudes, parallel individuation, and set-based quantification. By asking 3- and 4-year-olds to estimate the number of elements in sets without counting, we investigate whether the numerals that are assigned cardinal meaning as part of the acquisition process display the signatures of what we call "enriched parallel individuation" (which combines properties of parallel individuation and of set-based quantification) or analog magnitudes. Two experiments demonstrate that while "one" to "four" are mapped onto core representations of small sets prior to the acquisition of the counting principles, numerals beyond "four" are only mapped onto analog magnitudes about six months after the acquisition of the counting principles. Moreover, we show that children's numerical estimates of sets from 1 to 4 elements fail to show the signature of numeral use based on analog magnitudes - namely, scalar variability. We conclude that, while representations of small sets provided by parallel individuation, enriched by the resources of set-based quantification are recruited in the acquisition process to provide the first numerical meanings for "one" to "four", analog magnitudes play no role in this process.
@Article{Corre2007,
author = {Mathieu Le Corre and Susan Carey},
journal = {Cognition},
title = {One, two, three, four, nothing more: an investigation of the conceptual sources of the verbal counting principles.},
year = {2007},
number = {2},
pages = {395-438},
volume = {105},
abstract = {Since the publication of [Gelman, R., & Gallistel, C. R. (1978). The
child's understanding of number. Cambridge, MA: Harvard University
Press.] seminal work on the development of verbal counting as a representation
of number, the nature of the ontogenetic sources of the verbal counting
principles has been intensely debated. The present experiments explore
proposals according to which the verbal counting principles are acquired
by mapping numerals in the count list onto systems of numerical representation
for which there is evidence in infancy, namely, analog magnitudes,
parallel individuation, and set-based quantification. By asking 3-
and 4-year-olds to estimate the number of elements in sets without
counting, we investigate whether the numerals that are assigned cardinal
meaning as part of the acquisition process display the signatures
of what we call "enriched parallel individuation" (which combines
properties of parallel individuation and of set-based quantification)
or analog magnitudes. Two experiments demonstrate that while "one"
to "four" are mapped onto core representations of small sets prior
to the acquisition of the counting principles, numerals beyond "four"
are only mapped onto analog magnitudes about six months after the
acquisition of the counting principles. Moreover, we show that children's
numerical estimates of sets from 1 to 4 elements fail to show the
signature of numeral use based on analog magnitudes - namely, scalar
variability. We conclude that, while representations of small sets
provided by parallel individuation, enriched by the resources of
set-based quantification are recruited in the acquisition process
to provide the first numerical meanings for "one" to "four", analog
magnitudes play no role in this process.},
doi = {10.1016/j.cognition.2006.10.005},
keywords = {Awareness, Child, Comprehension, Concept Formation, Female, Humans, Language Development, Male, Mathematics, Preschool, Problem Solving, Verbal Behavior, 17331490},
}
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The present experiments explore proposals according to which the verbal counting principles are acquired by mapping numerals in the count list onto systems of numerical representation for which there is evidence in infancy, namely, analog magnitudes, parallel individuation, and set-based quantification. By asking 3- and 4-year-olds to estimate the number of elements in sets without counting, we investigate whether the numerals that are assigned cardinal meaning as part of the acquisition process display the signatures of what we call \"enriched parallel individuation\" (which combines properties of parallel individuation and of set-based quantification) or analog magnitudes. Two experiments demonstrate that while \"one\" to \"four\" are mapped onto core representations of small sets prior to the acquisition of the counting principles, numerals beyond \"four\" are only mapped onto analog magnitudes about six months after the acquisition of the counting principles. Moreover, we show that children's numerical estimates of sets from 1 to 4 elements fail to show the signature of numeral use based on analog magnitudes - namely, scalar variability. We conclude that, while representations of small sets provided by parallel individuation, enriched by the resources of set-based quantification are recruited in the acquisition process to provide the first numerical meanings for \"one\" to \"four\", analog magnitudes play no role in this process.","doi":"10.1016/j.cognition.2006.10.005","keywords":"Awareness, Child, Comprehension, Concept Formation, Female, Humans, Language Development, Male, Mathematics, Preschool, Problem Solving, Verbal Behavior, 17331490","bibtex":"@Article{Corre2007,\n author = {Mathieu Le Corre and Susan Carey},\n journal = {Cognition},\n title = {One, two, three, four, nothing more: an investigation of the conceptual sources of the verbal counting principles.},\n year = {2007},\n number = {2},\n pages = {395-438},\n volume = {105},\n abstract = {Since the publication of [Gelman, R., & Gallistel, C. R. (1978). The\n\tchild's understanding of number. Cambridge, MA: Harvard University\n\tPress.] seminal work on the development of verbal counting as a representation\n\tof number, the nature of the ontogenetic sources of the verbal counting\n\tprinciples has been intensely debated. The present experiments explore\n\tproposals according to which the verbal counting principles are acquired\n\tby mapping numerals in the count list onto systems of numerical representation\n\tfor which there is evidence in infancy, namely, analog magnitudes,\n\tparallel individuation, and set-based quantification. By asking 3-\n\tand 4-year-olds to estimate the number of elements in sets without\n\tcounting, we investigate whether the numerals that are assigned cardinal\n\tmeaning as part of the acquisition process display the signatures\n\tof what we call \"enriched parallel individuation\" (which combines\n\tproperties of parallel individuation and of set-based quantification)\n\tor analog magnitudes. Two experiments demonstrate that while \"one\"\n\tto \"four\" are mapped onto core representations of small sets prior\n\tto the acquisition of the counting principles, numerals beyond \"four\"\n\tare only mapped onto analog magnitudes about six months after the\n\tacquisition of the counting principles. Moreover, we show that children's\n\tnumerical estimates of sets from 1 to 4 elements fail to show the\n\tsignature of numeral use based on analog magnitudes - namely, scalar\n\tvariability. 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