Re-visiting the competence/performance debate in the acquisition of the counting principles

Corre, Mathieu Le; Walle, Gretchen A. Van de; Brannon, Elizabeth M.; Carey, Susan

doi:10.1016/j.cogpsych.2005.07.002

Cited by 262 publications

(354 citation statements)

References 52 publications

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“…Consider three data sets: Japanese and English data contributed by our own labs (from Barner, Libenson, Cheung, & Takasaki, in press;Barner, Chow, & Yang, 2009), Japanese, Russian, and English data from Sarnecka and colleagues (Sarnecka et al, 2007) and English data from LeCorre et al (2006; see Appendix I for details about subjects and procedures for each study). For each data set, we performed an analysis in which we asked how often children who were non-knowers gave one object when asked for one, how often one-knowers gave two for two, and how often two-knowers gave three for three.…”

Section: Early Numeral Meanings and Implicaturementioning

confidence: 99%

Inference and exact numerical representation in early language development

Barner

Bachrach²

2010

Cognitive Psychology

161

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How do children as young as 2 years of age know that numerals, like one, have exact interpretations, while quantifiers and words like a do not? Previous studies have argued that only numerals have exact lexical meanings. Children could not use scalar implicature to strengthen numeral meanings, it is argued, since they fail to do so for quantifiers (Papafragou & Musolino, 2003). Against this view, we present evidence that children's early interpretation of numerals does rely on scalar implicature, and argue that differences between numerals and quantifiers are due to differences in the availability of the respective scales of which they are members.Evidence from previous studies establishes that (1) children can make scalar inferences when interpreting numerals, (2) children initially assign weak, non-exact interpretations to numerals when first acquiring their meanings, and (3) children can strengthen quantifier interpretations when scalar alternatives are made explicitly available.

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Section: Early Numeral Meanings and Implicaturementioning

confidence: 99%

Inference and exact numerical representation in early language development

Barner

Bachrach²

2010

Cognitive Psychology

161

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“…Gelman and Gallistel (1978) see Treacy (2001) observed that students with disability have innate understanding of counting procedure. Le Corre et al (2006) confirmed that students with disability have developed verbal counting procedural knowledge before the development of conceptual knowledge. They maintained further that these students had higher average levels on one on one correspondence principle than females.…”

Section: Counting Proceduresmentioning

confidence: 64%

Examine Counting Procedure among Students with Mild Intellectual Disability: A Case of Penang Malaysia

Taibat¹,

Ahmad²,

Ghazali³

2013

IES

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This study investigates counting procedure in number counting based on gender among students with mild intellectual disability. Quantitative approach was used for testing counting procedure in number counting among these students. The samples for the study comprise fifteen male and fifteen female students with intellectual disability. Descriptive statistics and T-test were used in analyzing the data. It was revealed from the result of the study that students with mild intellectual disability showed understanding of counting procedure in number counting. However, the results of the study showed that these students have difficulty in number counting using abstraction principle and order irrelevance principle. It was shown that there was no significant difference between males and females in number counting when applying counting procedure.

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“…Studies using the Give-N task have shown that children's performance moves through a predictable series of levels, called number-knower levels (e.g., Condry & Spelke, 2008;Le Corre & Carey, 2007;Le Corre et al, 2006;Negen & Sarnecka, 2012;Sarnecka & Gelman, 2004;Sarnecka & Lee, 2009Slusser, Ditta, & Sarnecka, 2013;Slusser & Sarnecka, 2011;Wynn, 1990Wynn, , 1992b. These number-knower levels are found in children acquiring number systems not only in English, but also in Arabic, Japanese, Mandarin Chinese, Russian, Slovenian, and even among the Tsimane', a farming and foraging society in rural Bolivia (Almoammer et al, 2013;Barner, Libenson, Cheung, & Takasaki, 2009;Li, Le Corre, Shui, Jia, & Carey, 2003;Piantadosi, Jara-Ettinger, & Gibson, 2014;Sarnecka, Kamenskaya, Yamana, Ogura, & Yudovina, 2007).…”

Section: Acquiring a System Of Representation For Exact Numbersmentioning

confidence: 99%

“…or, 'But the frog wanted six applesRunning head: LEARNING TO REPRESENT EXACT NUMBERS 10 can you fix it so there are six?') the children point to the apples and recite the number list correctly, but do not use the result of their counting to fix the set (Le Corre, Van de Walle, Brannon, & Carey, 2006;Sarnecka & Carey, 2008).…”

Section: Acquiring a System Of Representation For Exact Numbersmentioning

confidence: 99%

Learning to represent exact numbers

Sarnecka

2015

Synthese

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This article focuses on how young children acquire concepts for exact, cardinal numbers (e.g., three, seven, two hundred, etc.). I believe that exact numbers are a conceptual structure that was invented by people, and that most children acquire gradually, over a period of months or years during early childhood. This article reviews studies that explore children's number knowledge at various points during this acquisition process. Most of these studies were done in my own lab, and assume the theoretical framework proposed by Carey (2009). In this framework, the counting list ('one,' 'two,' 'three,' etc.) and the counting routine (i.e., reciting the list and pointing to objects, one at a time) form a placeholder structure. Over time, the placeholder structure is gradually filled in with meaning to become a conceptual structure that allows the child to represent exact numbers (e.g., There are 24 children in my class, so I need to bring 24 cupcakes for the party.) A number system is a socially shared, structured set of symbols that pose a learning challenge for children. But once children have acquired a number system, it allows them to represent information (i.e., large, exact cardinal values) that they had no way of representing before.

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Re-visiting the competence/performance debate in the acquisition of the counting principles

Cited by 262 publications

References 52 publications

Inference and exact numerical representation in early language development

Inference and exact numerical representation in early language development

Examine Counting Procedure among Students with Mild Intellectual Disability: A Case of Penang Malaysia

Learning to represent exact numbers

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