Studies on children's understanding of counting examine when and how children acquire the cardinal principle: the idea that the last word in a counted set reflects the cardinal value of the set. Using Wynn's (1990) Give‐N Task, researchers classify children who can count to generate large sets as having acquired the cardinal principle (cardinal‐principle‐knowers) and those who cannot as lacking knowledge of it (subset‐knowers). However, recent studies have provided a more nuanced view of number word acquisition. Here, we explore this view by examining the developmental progression of the counting principles with an aim to elucidate the gradual elements that lead to children successfully generating sets and being classified as CP‐knowers on the Give‐N Task. Specifically, we test the claim that subset‐knowers lack cardinal principle knowledge by separating children's understanding of the cardinal principle from their ability to apply and implement counting procedures. We also ask when knowledge of Gelman & Gallistel's (1978) other how‐to‐count principles emerge in development. We analyzed how often children violated the three how‐to‐count principles in a secondary analysis of Give‐N data (
- NSF-PAR ID:
- 10278121
- Date Published:
- Journal Name:
- Frontiers in Psychology
- Volume:
- 12
- ISSN:
- 1664-1078
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract N = 86). We found that children already have knowledge of the cardinal principle prior to becoming CP‐knowers, and that understanding of the stable‐order and word‐object correspondence principles likely emerged earlier. These results suggest that gradual development may best characterize children's acquisition of the counting principles and that learning to coordinate all three principles represents an additional step beyond learning them individually. -
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Abstract When asked to explain their solutions to a problem, children often gesture and, at times, these gestures convey information that is different from the information conveyed in speech. Children who produce these gesture‐speech “mismatches” on a particular task have been found to profit from instruction on that task. We have recently found that some children produce gesture‐speech mismatches when identifying numbers at the cusp of their knowledge, for example, a child incorrectly labels a set of two objects with the word “three” and simultaneously holds up two fingers. These mismatches differ from previously studied mismatches (where the information conveyed in gesture has the potential to be integrated with the information conveyed in speech) in that the gestured response contradicts the spoken response. Here, we ask whether these contradictory number mismatches predict which learners will profit from number‐word instruction. We used the
Give‐a‐Number task to measure number knowledge in 47 children (M age = 4.1 years,SD = 0.58), and used theWhat's on this Card task to assess whether children produced gesture‐speech mismatches above their knower level. Children who were early in their number learning trajectories (“one‐knowers” and “two‐knowers”) were then randomly assigned, within knower level, to one of two training conditions: a Counting condition in which children practiced counting objects; or an Enriched Number Talk condition containing counting, labeling set sizes, spatial alignment of neighboring sets, and comparison of these sets. Controlling for counting ability, we found that children were more likely to learn the meaning of new number words in the Enriched Number Talk condition than in the Counting condition, but only if they had produced gesture‐speech mismatches at pretest. The findings suggest that numerical gesture‐speech mismatches are a reliable signal that a child is ready to profit from rich number instruction and provide evidence, for the first time, that cardinal number gestures have a role to play in number‐learning. -
Humans are unique in their capacity to both represent number exactly and to express these representations symbolically. This correlation has prompted debate regarding whether symbolic number systems are necessary to represent large exact number. Previous work addressing this question in innumerate adults and semi-numerate children has been limited by conflicting results and differing methodologies, and has not yielded a clear answer. We address this debate by adapting methods used with innumerate populations (a “set-matching” task) for 3- to 5-year-old US children at varying stages of symbolic number acquisition. In five studies we find that children’s ability to match sets exactly is related not simply to knowing the meanings of a few number words, but also to understanding how counting is used to generate sets (i.e., the cardinal principle). However, while children were more likely to match sets after acquiring the cardinal principle, they nevertheless demonstrated failures, compatible with the hypothesis that the ability to reason about exact equality emerges sometime later. These findings provide important data on the origin of exact number concepts, and point to knowledge of a counting system, rather than number language in general, as a key ingredient in the ability to reason about large exact number.more » « less
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Cascadilla Press (Ed.)The morphosyntactic information in grammatical number marking may be a useful cue for children in the process of acquiring number words. A language with dual marking, like Slovenian, may help children to bootstrap the meaning of the word “two” by drawing their attention to sets of two as a referent of language. If the dual marker indeed facilitates number learning, then we hypothesized that “two” should be acquired earlier in populations exposed to the dual marker; the dual should be learned before “two”; and knowledge of the dual form should be correlated with knowledge of “two”. We tested these hypotheses by having Slovenian and English-speaking children complete the Give-a-Number and Give-Morphology tasks. We analyzed the Give-Morphology in a new way, using stricter criteria to determine that children “know” the morphological markers than simple percent correct. In this sample, Slovenian children exposed to the dual marker did not show evidence of knowing “two” (i.e., being 2-knowers) at very young ages or earlier than English-speaking children. Knowledge of the dual marker did not precede nor correlate with the acquisition of “two”; indeed, the dual form was only acquired after the singular and plural. These analyses were conducted using an open data set with more Slovenian 2-knowers, yielding similar results. These findings present challenges for the view that grammatical number plays a role in number acquisition. This theory requires articulation about how a dual-marked language can facilitate number acquisition if children do not notice or learn the dual form. The information in grammatical number marking may be a useful cue for children in the process of acquiring number words. A language with dual marking, like Slovenian, may help children to bootstrap the meaning of the word “two” by drawing their attention to sets of two as a referent of language. If the dual marker indeed facilitates number learning, we hypothesized that “two” should be acquired earlier in populations exposed to the dual marker; the dual should be learned before “two”; and knowledge of the dual form should be correlated with knowledge of “two”. We tested these hypotheses by having Slovenian and English-speaking children complete the Give-a-Number and Give-Morphology tasks. We analyzed the Give-Morphology in a new way, using stricter criteria to determine that children “know” the morphological markers than simple percent correct. In this sample, Slovenian children exposed to the dual marker did not show evidence of knowing “two” (i.e., being 2-knowers) at very young ages or earlier than English-speaking children. Knowledge of the dual marker did not precede nor correlate with the acquisition of “two”. Indeed, the dual form was acquired only after the singular and plural. Parallel analyses were also conducted using an open data set with more Slovenian 2-knowers, yielding similar results. These findings present challenges for the claim that grammatical number plays a role in number acquisition. Specifically, this theory requires better articulation about how a dual-marked language can facilitate number acquisition if children do not notice or learn the dual form.more » « less
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Abstract How do children acquire exact meanings for number words like
three orforty‐seven ? In recent years, a lively debate has probed the cognitive systems that support learning, with some arguing that an evolutionarily ancient “approximate number system” drives early number word meanings, and others arguing that learning is supported chiefly by representations of small sets of discrete individuals. This debate has centered around the findings generated by Wynn's (, ) Give‐a‐Number task, which she used to categorize children into discrete “knower level” stages. Early reports confirmed Wynn's analysis, and took these stages to support the “small sets” hypothesis. However, more recent studies have disputed this analysis, and have argued that Give‐a‐Number data reveal a strong role for approximate number representations. In the present study, we use previously collected Give‐a‐Number data to replicate the analyses of these past studies, and to show that differences between past studies are due to assumptions made in analyses, rather than to differences in data themselves. We also show how Give‐a‐Number data violate the assumptions of parametric tests used in past studies. Based on simple non‐parametric tests and model simulations, we conclude that (a) before children learn exact meanings for words like one, two, three, andfour, they first acquire noisy preliminary meanings for these words, (b) there is no reliable evidence of preliminary meanings for larger meanings, and (c) Give‐a‐Number cannot be used to readily identify signatures of the approximate number system.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/fpsyg.2021.703598
