The Development of Automaticity in Accessing Number Magnitude

Girelli, Luisa; Lucangeli, Daniela; Butterworth, Brian

doi:10.1006/jecp.2000.2564

Cited by 232 publications

(317 citation statements)

References 22 publications

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“…This means that a prerequisite for the automatic triggering of this procedure is the capacity to automatically convert digits into their analogical representations. However, it has been shown that, although the Arabic code is easily learnt and used by young children, the automatic access to analogue representations from digits does not seem to occur before age 9 or 10 (Girelli, Lucangeli, & Butterworth, 2000;Rubinsten, Henik, Berger, & Shahar-Shalev, 2002). This would explain why the developmental shift from algorithmic computing to direct retrieval has been described as occurring around these ages (Ashcraft & Fierman, 1982).…”

Section: Acquisitionmentioning

confidence: 99%

Fast automated counting procedures in addition problem solving: When are they used and why are they mistaken for retrieval?

2016

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a b s t r a c tContrary to a widespread assumption, a recent study suggested that adults do not solve very small additions by directly retrieving their answer from memory, but rely instead on highly automated and fast counting procedures (Barrouillet & Thevenot, 2013). The aim of the present study was to test the hypothesis that these automated compiled procedures are restricted to small quantities that do not exceed the size of the focus of attention (i.e., 4 elements). For this purpose, we analyzed the response times of ninety adult participants when solving the 81 additions with operands from 1 to 9. Even when focusing on small problems (i.e. with sums 610) reported by participants as being solved by direct retrieval, chronometric analyses revealed a strong size effect. Response times increased linearly with the magnitude of the operands testifying for the involvement of a sequential multistep procedure. However, this size effect was restricted to the problems involving operands from 1 to 4, whereas the pattern of response times for other small problems was compatible with a retrieval hypothesis. These findings suggest that very fast responses routinely interpreted as reflecting direct retrieval of the answer from memory actually subsume compiled automated procedures that are faster than retrieval and deliver their answer while the subject remains unaware of their process, mistaking them for direct retrieval from long-term memory.

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Section: Acquisitionmentioning

confidence: 99%

Fast automated counting procedures in addition problem solving: When are they used and why are they mistaken for retrieval?

2016

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“…Moreover, the distance and the size effects are believed to reflect a process that is derived from the mental number line (Moyer and Landauer, 1967). Hence, additional support for the suggestion that different dimensions interfere with each other as a result of a shared magnitude processing is given by the interaction of the size congruity effect with the distance effect (Cohen Kadosh and Henik, 2006;Cohen Kadosh et al, 2007e;Girelli et al, 2000;Henik and Tzelgov, 1982;Schwarz and Heinze, 1998;Schwarz and Ischebeck, 2003;Tzelgov et al, 1992), and the size effect (Pinhas et al, submitted for publication).…”

Section: Similar Effect Patterns With Different Kinds Of Quantity: Thmentioning

confidence: 99%

“…In the size congruity paradigm, children show a mutual interference between size and number starting at the end of first grade when they have to perform a magnitude comparison (Rubinsten et al, 2002). However, such a mutual interference is absent at the beginning of first grade (Girelli et al, 2000;Rubinsten et al, 2002). These results reflect the slow development of the automatic association between digits and the quantity they refer to (see Ansari et al, 2005, for the evolution of the neural basis of digits comparison in childhood).…”

Section: Evidence For Shared Mechanisms and Representations In Childrenmentioning

confidence: 99%

Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation

Kadosh

Lammertyn

Izard

2008

Progress in Neurobiology

332

304

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There is a current debate whether the human brain possesses a shared representation for various types of magnitude such as numerical quantities, physical size, or loudness. Here, we critically review evidence from chronometric, neuroimaging, developmental and comparative fields, and supplement it with a meta-analysis of the neuroimaging data. Together, based on such an integrative overview, we discuss limitations inherent in each approach, and the possibility whether shared, or distinct magnitude representation, or both representations exist. #

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“…Evidence of shared magnitude processing arises when the distance effects of different magnitudes interact. Among the most investigated is the interaction between physical and symbolic size, as depicted by the numerical Stroop paradigm (Girelli, Lucangeli, & Butterworth, 2000;Henik & Tzelgov, 1982). In this paradigm, participants are required to indicate either the numerically or physically larger digit (relevant dimension) within a pair, while the other (irrelevant) dimension varies, yielding congruent (e.g., 2 ) or incongruent (e.g., 4) conditions.…”

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confidence: 99%

Exploiting illusory effects to disclose similarities in numerical and luminance processing

Ranzini

Girelli

2012

Atten Percept Psychophys

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Recent studies have suggested that numerical and physical magnitudes are similarly processed by a generalized magnitude system. The present study investigates the number-luminance interaction, taking advantage of illusory effects in a cued line bisection task with numerical or nonnumerical flankers and varying levels of luminance. The results showed that both dimensions influenced bisection performance. Whereas numbers (Experiment 1) induced a systematic shift of the subjective midpoint toward the larger digit, luminance (Experiment 2) modulated the bisection performance toward the darker flanker. By combining these two illusions (Experiments 3 and 4), the two dimensions interfered with each other. This pattern of results suggests overlapping representations for physical and numerical magnitudes and highlights the value of illusory effects in cognitive research.

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The Development of Automaticity in Accessing Number Magnitude

Cited by 232 publications

References 22 publications

Fast automated counting procedures in addition problem solving: When are they used and why are they mistaken for retrieval?

Fast automated counting procedures in addition problem solving: When are they used and why are they mistaken for retrieval?

Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation

Exploiting illusory effects to disclose similarities in numerical and luminance processing

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