The development of arithmetical abilities

Butterworth, Brian

doi:10.1111/j.1469-7610.2004.00374.x

Cited by 532 publications

(468 citation statements)

References 90 publications

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“…However, irrespective of the research tradition, our reading of the literature reveals three distinct but related perspectives. The first, preverbal number sense (Butterworth 2005;Ivrendi 2011;Lipton and Spelke 2005), reflects those number insights that are innate to all humans and comprises an understanding of small quantities in ways that allow for comparison. For example, "6-month-olds can discriminate numerosities with a 1:2 but not a 2:3 ratio, whereas 10-month-old infants also succeed with the latter" (Feigenson et al 2004, p. 307).…”

Section: What Is Number Sense?mentioning

confidence: 99%

Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

Andrews

Sayers

2014

Early Childhood Educ J

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It is known that an appropriately developed foundational number sense (FONS), or the ability to operate flexibly with number and quantity, is a powerful predictor of young children's later mathematical achievement. However, until now not only has FONS been definitionally elusive but instruments for identifying opportunities for children to acquire its various components have been missing from the classroom observation tools available. In this paper, drawing on a constant comparison analysis of appropriate literature, we outline the development of an eight dimensional FONS framework. We then show, by applying this framework to three culturally diverse European grade one lessons, one English, one Hungarian and one Swedish, that it is both straightforwardly operationalised and amenable to cross cultural analyses of classroom practice. Some implications are discussed.

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Section: What Is Number Sense?mentioning

confidence: 99%

Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

Andrews

Sayers

2014

Early Childhood Educ J

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“…Besides the important emphasis on a number representation (Butterworth, 1999;2005;Noël & Rouselle, 2011), studies focus on executive functioning as well (Bull & Scerif, 2001;D'Amico & Passolunghi, 2009;De Weerdt, Desoete & Roeyers, 2012). Research has shown that inhibition is predictive for mathematical abilities and necessary in math performance for the active suppression of immature or incorrect strategies (Bull & Scerif, 2001).…”

Section: Behavioral Inhibition In Children With Mathematical Disabilimentioning

confidence: 99%

Behavioral inhibition in children with learning disabilities

Weerdt

Desoete

Roeyers

2013

Research in Developmental Disabilities

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Children with reading disabilities (RD, n = 17), mathematical disabilities (MD, n = 22), combined reading and mathematical disabilities (RD+MD, n = 28) and control peers (n = 45) were tested on behavioral inhibition with a Go/no-go task in a picture, letter and digit-modality. In contrast to children without RD, children with RD made significantly more commission errors on alphanumeric (letter and digit) modalities compared to the non-alphanumeric picture modality. As compared to children without MD, children with MD made as much commission errors on the picture modality as on the letter modality. No significant interaction-effect was found between RD and MD. These results can be considered as evidence for behavioral inhibition deficits related to alphanumeric stimuli in children with RD but not in children with MD.

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“…Others propose instead that children are born with a few innate principles, which are sufficient to generate natural-number concepts. On these accounts the number system of one's culture may provide convenient labels for number concepts, but it does not provide the concepts themselves (Butterworth, 2005;Butterworth, Reeve, Reynolds, & Lloyd, 2008;Leslie, Gelman, & Gallistel, 2008). Still another view holds that children learn number concepts by constructing the axioms that define the natural numbers (Rips, Bloomfield, & Asmuth, 2008).…”

Section: Running Head: Learning To Represent Exact Numbersmentioning

confidence: 99%

“…A completely different account from Carey's (2009) is put forth by nativists (Butterworth, 2005;Leslie et al, 2008) who argue that the basis for all natural-number concepts is innate. According to this view, number concepts do not need to be 'constructed' at all, because they are automatically generated by the mind.…”

Section: Leslie Et Al's Nativist Argumentmentioning

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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The development of arithmetical abilities

Abstract: The evidence broadly supports the idea of an innate specific capacity for acquiring arithmetical skills, but the effects of the content of learning, and the timing of learning in the course of development, requires further investigation.

Cited by 532 publications

References 90 publications

Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

Identifying Opportunities for Grade One Children to Acquire Foundational Number Sense: Developing a Framework for Cross Cultural Classroom Analyses

Behavioral inhibition in children with learning disabilities

Learning to represent exact numbers

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