Number‐Concept Acquisition and General Vocabulary Development

Negen, James; Sarnecka, Barbara W.

doi:10.1111/j.1467-8624.2012.01815.x

Cited by 100 publications

(103 citation statements)

References 29 publications

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“…Children acquire the concept faster if they know more words, even if those words are in no way related to the numbers (Negen and Sarnecka, 2012). This evidence supports the above argument.…”

Section: An Empirical Reason For Conceptual Autonomysupporting

confidence: 83%

Are the Natural Numbers Fundamentally Ordinals?

Assadian

Buijsman

2018

Philos Phenomenol Research

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There are two ways of thinking about the natural numbers: as ordinal numbers or as cardinal numbers. It is, moreover, well-known that the cardinal numbers can be defined in terms of the ordinal numbers. Some philosophies of mathematics have taken this as a reason to hold the ordinal numbers as (metaphysically) fundamental. By discussing structuralism and neo-logicism we argue that one can empirically distinguish between accounts that endorse this fundamentality claim and those that do not. In particular, we argue that if the ordinal numbers are metaphysically fundamental then it follows that one cannot acquire cardinal number concepts without appeal to ordinal notions. On the other hand, without this fundamentality thesis that would be possible. This allows for an empirical test to see which account best describes our actual mathematical practices. We then, finally, discuss some empirical data that suggests that we can acquire cardinal number concepts without using ordinal notions. However, there are some important gaps left open by this data that we point to as areas for 1 future empirical research.With just a little reflection it is clear that there are two roles which the natural numbers play. First of all, they can function as cardinal numbers. The natural numbers can be used to specify the number of objects falling under a concept. This is the role in which they appear when a number is given in answer to the question 'how many Fs are there?'. Second, the natural numbers can function as ordinal numbers. In this case they specify the position of an item in an ordering, for example, to say that a particular person finished third. If one wants to be even more explicit that the same number is used in such a case, consider that the same thing can be said with 'this person ended up being number three'. Rather than giving the size of a set, ordinal numbers give the position, and so answer questions of the form 'which F is this?'.The dual role of the natural numbers has long been known, just as it has long been known that it is possible to define cardinal numbers in terms of ordinal numbers. Cantor (1883) introduced the necessary machinery for defining a cardinal number based on an ordinal number in a well-ordering. According to Cantor (1895) the 'general concept' of a cardinal number, "arises from [a set] M when we make abstraction of the nature of its various elements m and of the order in which they are given [...] Since every single element m, if we abstract from its nature,

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Section: An Empirical Reason For Conceptual Autonomysupporting

confidence: 83%

Are the Natural Numbers Fundamentally Ordinals?

Assadian

Buijsman

2018

Philos Phenomenol Research

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“…A strong correlation between the child's vocabulary and the knowledge of number words was found in a study by Negen and Sarnecka (2012).…”

Section: Cardinalitymentioning

confidence: 97%

“…Negen & Sarnecka, 2012) indicate the expressive vocabulary as an important predictor for numerical competence. Negen and Sarnecka (2012) also found an important correlation between the child's vocabulary and the knowledge of number words. The expressive vocabulary is the best linguistic predictor for mathematic competencies.…”

Section: Vocabulary and Phonological Awarenessmentioning

confidence: 99%

Early Predictors for Basic Numerical and Magnitude Competencies in Preschool Children—Are They the Same or Different regarding Specific Subgroups?

Pixner¹,

Kraut²,

Dresen³

2017

PSYCH

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Basic numeric competencies in early childhood are found to be good predictors for later mathematical achievement. Therefore, it is of broad interest how specific predictors in early childhood, which are held responsible for a better arithmetic development later on, can be found. Our study aims to conduct more information to this topic and hence to extract factors that can already predict the basic numerical and magnitude competencies in preschool. Based on a sample of 188 preschoolers from 26 different kindergartens throughout Tyrol, we wanted to prove whether the factors of phonological awareness, counting abilities, fine motor skills, visual-spatial perception, motoric coordination as well as the children's age, their gender or handedness may be considered as possible predictors for later mathematic skills. Our data analysis revealed that only phonological awareness, counting abilities and children's visual-spatial perception pose significant predictors specifically for the basic numerical and magnitude competencies in preschoolers. In a second step, we tested whether these predictors are the same or different regarding two subgroups from our sample including children with different requirements. We found that children with different skills (concerning phonological awareness) might choose different strategies to acquire new competencies; therefore, different predictors are relevant for basic numerical and magnitude competencies. Regarding over all arithmetic competencies it is equal which predictor leads to basic numerical and magnitude competencies, children's performance did not differ.

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“…Of course, different children reach this milestone at different times, but in a sample of cardinal principle sometime between 34 and 51 months old. That is, any time from a couple of months before their third birthday to a couple of months after their fourth birthday (Negen & Sarnecka, 2012;Sarnecka & Carey, 2008;Sarnecka & Gelman, 2004;Sarnecka et al, 2007;Sarnecka & Lee, 2009;Slusser et al, 2013;Slusser & Sarnecka, 2011). Children from lowerincome backgrounds come to understand cardinality significantly later, at age 4 or older (Fluck & Henderson, 1996;Jordan & Levine, 2009).…”

Section: Acquiring a System Of Representation For Exact Numbersmentioning

confidence: 99%

“…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%

Learning to represent exact numbers

Sarnecka

2015

Synthese

Self Cite

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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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Number‐Concept Acquisition and General Vocabulary Development

Cited by 100 publications

References 29 publications

Are the Natural Numbers Fundamentally Ordinals?

Are the Natural Numbers Fundamentally Ordinals?

Early Predictors for Basic Numerical and Magnitude Competencies in Preschool Children—Are They the Same or Different regarding Specific Subgroups?

Learning to represent exact numbers

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