Mental Arithmetic: A Componential Analysis of Speed‐of‐Processing Across Monolingual, Weak Bilingual, and Strong Bilingual Adults

Geary, David C.; Cormier, Pierre; Goggin, Judith P.; Estrada, Patricia; Lunn, Melanie C. E.

doi:10.1080/00207599308247184

Cited by 22 publications

(19 citation statements)

References 23 publications

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“…Thus, the fact that our two Chinese groups were fluently bilingual could be a factor in their better simple-arithmetic performance. Geary, Cormier, Goggin, Estrada, and Lunn (1993) found, however, that adults' simple addition and multiplication performance was not affected by degree of bilingualism. Another possible linguistic influence is that Mandarin uses a consistent system for constructing number names (e.g., 12 is ten two and 53 is five ten three), whereas English is more irregular (e.g., the teens words are quite idiosyncratic).…”

Section: Other Potential Sourcesmentioning

confidence: 65%

Cognitive arithmetic across cultures.

Campbell¹,

Xue²

2001

Journal of Experimental Psychology: General

427

606

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Canadian university students either of Chinese origin (CC) or non-Asian origin (NAC) and Chinese university students educated in Asia (AC) solved simple-arithmetic problems in the 4 basic operations (e.g., 3 + 4, 7 -3, 3 X 4, 12 •*• 3) and reported their solution strategies. They also completed a standardized test of more complex multistep arithmetic. For complex arithmetic, ACs outperformed both CCs and NACs. For simple arithmetic, however, ACs and CCs were equal and both performed better than NACs. The superior simple-arithmetic skills of CCs relative to NACs implies that extracurricular culture-specific factors rather than differences in formal education explain the simple-arithmetic advantage for Chinese relative to non-Asian North American adults. NAC's relatively poor simple-arithmetic performance resulted both from less efficient retrieval skills and greater use of procedural strategies. Nonetheless, all 3 groups reported using procedures for the larger simple subtraction and division problems, confirming the importance of procedural knowledge in skilled adults' performance of elementary mathematics.

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Section: Other Potential Sourcesmentioning

confidence: 65%

Cognitive arithmetic across cultures.

Campbell¹,

Xue²

2001

Journal of Experimental Psychology: General

427

606

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“…Previous arithmetic research involving bilinguals has produced mixed conclusions about the role of language in number-fact memory. Geary, Cormier, Goggin, Estrada, and Lunn (1993) found that simple addition and multiplication performance was not affected by degree of bilingualism, which led them to suggest that basic arithmetic facts might be stored in a single-abstract format. Nonetheless, speed of arithmetic in bilinguals is faster when problems are encoded or answers are produced in the preferred language (Frenck-Mestre & Vaid, 1993;Marsh & Maki, 1976;McClain & Shih Huang, 1982).…”

Section: Language and Arithmeticmentioning

confidence: 99%

Number Processing in Chinese-English Bilinguals

Campbell¹,

Kanz²,

Xue³

1999

Mathematical Cognition

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To investigate effects of surface notation on basic numerical skills we examined number naming, magnitude selection, and simple arithmetic performed by adult Chinese-English bilinguals born and educated in China. Stimuli were presented using either arabic (7 + 8) or "mandarin" ( symbols and participants were cued to respond either in English or Chinese. The naming task demonstrated that the mandarin characters were as easy to identify as the arabic digits, but for both arithmetic and magnitude selection there were faster RTs and fewer errors overall with arabic notation. Arabic notation also produced smaller problem-size effects in arithmetic and a smaller split effect in magnitude selection relative to mandarin notation. These results suggest that retrieval processes in the arithmetic and selection tasks were more efficient with arabic than mandarin stimuli. Arithmetic RTs were substantially slower with English than Chinese responses given either arabic or mandarin stimuli, but the English-language cost was greater with mandarin stimuli. The form of the Notation × Language RT interaction is consistent with language-specific Chinese and English number-fact stores ("arithmecons") that were differentially accessible as a function of notation. Naming RTs also presented a significant Notation × Language interaction due mainly to slow RTs to produce English number names for mandarin stimuli. These Notation × Language interactions are not easily reconciled with the standard version of McCloskey's (1992) model of number processing, which holds that numeral reading and arithmetic performance are based on a single, abstract-semantic code regardless of input or output conditions. Instead, the results suggest that different Notation × Language combinations were mediated by independent associative paths that varied in strength and efficiency as a function of prior experience.Requests for reprints should be sent to

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“…Here, we based our current experiment on previous work in complex arithmetic that showed that both adults and children had poorer performance on harder than on easier problems, whether difficulty of problems was defined on the basis of the size of operands, on involving carryover, or both (e.g., De Smedt, Holloway, & Ansari, 2011;Geary, Cormier, Goggin, Estrada, & Lunn, 1993;Geary, Widaman, Little, & Cormier, 1987;Green, Lemaire, & Dufau, 2007;Hodzik & Lemaire, 2011;Lemaire & Arnaud, 2008;Lemaire & Calliès, 2009;Widaman, Geary, Cormier, & Little, 1989). The present work aimed at replicating such problem difficulty effects on children's performance in complex arithmetic and at testing interactions of problem difficulty with other variables (i.e., children's age and strategies).…”

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confidence: 99%

Age-related changes in children’s strategies for solving two-digit addition problems

Lemaire

Brun

2018

J. Numer. Cogn.

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The present study investigated how elementary-school children solve two-digit addition problems (e.g., 34+68). To achieve this end, we examined age-related differences in children's strategy use and strategy performance. Results showed that (a) both third and fifth graders used a set of 9 strategies, (b) fifth-grade individuals used more strategies than third-grade individuals, (c) age-related differences in the size of strategy repertoire was partially explained by age-related differences in basic arithmetic fluency, (d) how often children used each available strategy changed with problem difficulty and children's age, as younger children tended to focus more on one or two strategies and older children used a wider range of strategies, (e) increased arithmetic performance with age varied with problem difficulty both when overall performance was analyzed and when analyses of performance was restricted to children's favorite strategy. The present findings have important implications for our understanding of how complex arithmetic performance changes with children's age and change mechanisms underlying improved performance with age in complex arithmetic.

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Mental Arithmetic: A Componential Analysis of Speed‐of‐Processing Across Monolingual, Weak Bilingual, and Strong Bilingual Adults

Cited by 22 publications

References 23 publications

Cognitive arithmetic across cultures.

Cognitive arithmetic across cultures.

Number Processing in Chinese-English Bilinguals

Age-related changes in children’s strategies for solving two-digit addition problems

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