scholarly journals Grammatical morphology as a source of early number word meanings

2013 ◽  
Vol 110 (46) ◽  
pp. 18448-18453 ◽  
Author(s):  
A. Almoammer ◽  
J. Sullivan ◽  
C. Donlan ◽  
F. Marusic ◽  
R. Zaucer ◽  
...  
Keyword(s):  
Number Word ◽  
Word Meanings ◽  
Grammatical Morphology ◽  
Early Number

scholarly journals Do children's number words begin noisy?

2018 ◽  
Author(s):  
Katherine Wagner ◽  
Junyi Chu ◽  
David Barner
Keyword(s):  
Number System ◽  
Number Word ◽  
Approximate Number System ◽  
Word Meanings ◽  
Number Words ◽  
System P ◽  
Number Representations ◽  
Lively Debate ◽  
Early Number ◽  
Made In

How do children acquire exact meanings for number words like three or forty-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 findings generated by Wynn’s (1990, 1992) 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 (1) before children learn exact meanings for words like one, two, three, and four, they first acquire noisy preliminary meanings for these words, (2) there is no reliable evidence of preliminary meanings for larger meanings, and (3) Give-a- Number cannot be used to readily identify signatures of the approximate number system.

scholarly journals Ontogenetic origins of human integer representations

2019 ◽  
Author(s):  
Susan Carey ◽  
David Barner
Keyword(s):  
Number Word ◽  
Second Phase ◽  
Word Meanings ◽  
Hume’S Principle ◽  
Number Words ◽  
Number Representations ◽  
Exact Counting ◽  
Counting Algorithms ◽  
Numerical Magnitudes ◽  
Two Phases

Do children learn number words by associating them with perceptual magnitudes? Recent studies argue that approximate numerical magnitudes play a foundational role in the development of integer concepts. Against this, we argue that approximate number representations fail both empirically and in principle to provide the content required of integer concepts. Instead, we suggest that children’s understanding of integer concepts proceeds in two phases. In the first phase, children learn small exact number word meanings by associating words with small sets. In the second phase, children learn the meanings of larger number words by mastering the logic of exact counting algorithms, which implement the successor function and Hume’s principle (that 1-to-1 correspondence guarantees exact equality). In neither phase do approximate number representations play a foundational role.

scholarly journals Numerical morphology supports early number word learning: Evidence from a comparison of young Mandarin and English learners

2016 ◽  
Vol 88 ◽  
pp. 162-186 ◽  
Author(s):  
Mathieu Le Corre ◽  
Peggy Li ◽  
Becky H. Huang ◽  
Gisela Jia ◽  
Susan Carey
Keyword(s):  
Word Learning ◽  
English Learners ◽  
Number Word ◽  
Early Number

Preschool children master the logic of number word meanings

Cognition ◽  
2006 ◽  
Vol 98 (3) ◽  
pp. B57-B66 ◽  
Author(s):  
Jennifer S. Lipton ◽  
Elizabeth S. Spelke
Keyword(s):  
Preschool Children ◽  
Number Word ◽  
Word Meanings

scholarly journals Shape-shifting Davydov’s ideas for early number learning in South Africa

2020 ◽  
Author(s):  
Hamsa Venkat ◽  
Mike Askew ◽  
Samantha Morrison
Keyword(s):  
South Africa ◽  
South African ◽  
Teaching And Learning ◽  
Number Word ◽  
Assessment Data ◽  
Task Sequence ◽  
Early Grades ◽  
Early Number ◽  
Key Aspects ◽  
Directing Attention

AbstractIn this paper, we share details of a South African early grades’ number intervention informed by aspects of Davydov’s writing on early number teaching and learning. A key part of Davydov’s approach to early number teaching involves starting with attention to relationships between quantities rather than with counting. The Structuring Number Starters (SNS) intervention focused—over a nine-year period—on supporting early grades’ students to move beyond the calculating-by-counting approaches that are prevalent in South Africa. In attending to this focus, the intervention shifted increasingly towards an emphasis on relationships between quantities, though not in the same format or task sequence as advocated by Davydov. The contextual and cultural features that led to our adaptations—or shape-shifting—are highlighted in this paper. We interrogate key aspects of Davydov’s approaches to early number teaching in relation to key features typical of South African classroom mathematics teaching in order to understand the evolution of the SNS initiative. Quasi-longitudinal interview-based assessment data available from a cross-attainment sample of students in 2011, 2014 and 2018 indicate shifts over time from calculating-by-counting to calculating-by-structuring. These outcomes point to successes with moves into increasingly structured ways of working with early number, but suggest also that these successes may be contingent on some fluency with forward and backward number word sequences. The outcomes suggest that it is feasible to explore interventions directing attention to early number structure from the outset in larger scale studies.

The social and linguistic context of early number word use

1986 ◽  
Vol 4 (3) ◽  
pp. 269-288 ◽  
Author(s):  
Kevin Durkin ◽  
Beatrice Shire ◽  
Roland Riem ◽  
Robert D. Crowther ◽  
D. R. Rutter
Keyword(s):  
Number Word ◽  
Linguistic Context ◽  
Word Use ◽  
The Social ◽  
Early Number

Early understanding of number

2020 ◽  
Author(s):  
Pierina Cheung ◽  
Daniel Ansari
Keyword(s):  
Daily Basis ◽  
Cultural Practice ◽  
Number Word ◽  
Formal Schooling ◽  
Number Representation ◽  
Word Meanings ◽  
Quantitative Understanding ◽  
Human Capacity ◽  
Shed Light

We see, hear, and use numbers to communicate with other people on a daily basis. What are the origins of human capacity for representing number? How does our capacity for number representation develop? To shed light into these questions, three types of evidence, from infancy till age 5, will be reviewed in this chapter. Specifically, studies on 1) infants’ abilities to process nonsymbolic quantities, 2) children’s protracted learning of the first few number word meanings, and 3) how they may acquire a representation of number through learning the cultural practice of counting will be synthesized. Together, studies reveal that children have a rich quantitative understanding even prior to formal schooling.

scholarly journals Language, procedures, and the non-perceptual origin of number word meanings

2017 ◽  
Vol 44 (3) ◽  
pp. 553-590 ◽  
Author(s):  
DAVID BARNER
Keyword(s):  
Building Blocks ◽  
Independent Learning ◽  
Learning Problems ◽  
Number Word ◽  
Word Meanings ◽  
Number Words ◽  
Perceptual Representations ◽  
Children First ◽  
Positive Integers ◽  
Perceptual Systems

AbstractPerceptual representations of objects and approximate magnitudes are often invoked as building blocks that children combine to acquire the positive integers. Systems of numerical perception are either assumed to contain the logical foundations of arithmetic innately, or to supply the basis for their induction. I propose an alternative to this framework, and argue that the integers are not learned from perceptual systems, but arise to explain perception. Using cross-linguistic and developmental data, I show that small (~1–4) and large (~5+) numbers arise both historically and in individual children via distinct mechanisms, constituting independent learning problems, neither of which begins with perceptual building blocks. Children first learn small numbers using the same logic that supports other linguistic number marking (e.g. singular/plural). Years later, they infer the logic of counting from the relations between large number words and their roles in blind counting procedures, only incidentally associating number words with approximate magnitudes.

Partial knowledge of word meanings: The case for "knowing not"

1999 ◽  
Author(s):  
Janae N. Lockett ◽  
Wendelyn J. Shore
Keyword(s):  
Partial Knowledge ◽  
Word Meanings
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