The processing of Arabic numbers is under cognitive control

Macizo, Pedro; Herrera, Amparo

doi:10.1007/s00426-012-0456-6

Cited by 30 publications

(57 citation statements)

References 18 publications

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“…Hence, the computational model predicts that also the comparison of decimal fractions should be under cognitive control modulating the relevance of tenth and hundredth digits. Regarding the tenth–hundredth compatibility effect, we would expect it to be more pronounced in a stimulus set with a smaller proportion of incompatible relative to compatible number pairs, as found by Macizo and Herrera (2013) for the case of two-digit numbers. Moreover, in the original computational model (Huber et al, 2013c) cognitive control was implemented to act locally on a trial-by-trial basis and, thereby, it was able to simulate the Gratton effect in two-digit number comparison.…”

Section: Discussionmentioning

confidence: 81%

“…It was able to account for the proportion congruity effect found by Macizo and Herrera (2013) and predicted a Gratton effect (Gratton et al, 1992) in two-digit number comparison. Hence, the computational model predicts that also the comparison of decimal fractions should be under cognitive control modulating the relevance of tenth and hundredth digits.…”

Section: Discussionmentioning

confidence: 95%

“…In a similar vein as for the relevance of tenth and hundredth digits, the computational model predicts that the influence of the number of digits should be smaller for higher proportions of incongruent trials. More specifically, the string length congruity effect should be larger in a condition with only 25% incongruent trials than in a condition with 75% incongruent trials (see Macizo and Herrera, 2013, for a similar proportion congruity manipulation on the unit-decade compatibility effect). Moreover, as cognitive control was implemented to act locally on a trial-by-trial basis, the computational model also predicts a Gratton effect for the string length congruity.…”

Section: Discussionmentioning

confidence: 99%

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Decimal fraction representations are not distinct from natural number representations â€“ evidence from a combined eye-tracking and computational modeling approach

Huber¹,

Klein²,

Willmes³

et al. 2014

Front. Hum. Neurosci.

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Decimal fractions comply with the base-10 notational system of natural Arabic numbers. Nevertheless, recent research suggested that decimal fractions may be represented differently than natural numbers because two number processing effects (i.e., semantic interference and compatibility effects) differed in their size between decimal fractions and natural numbers. In the present study, we examined whether these differences indeed indicate that decimal fractions are represented differently from natural numbers. Therefore, we provided an alternative explanation for the semantic congruity effect, namely a string length congruity effect. Moreover, we suggest that the smaller compatibility effect for decimal fractions compared to natural numbers was driven by differences in processing strategy (sequential vs. parallel). To evaluate this claim, we manipulated the tenth and hundredth digits in a magnitude comparison task with participants’ eye movements recorded, while the unit digits remained identical. In addition, we evaluated whether our empirical findings could be simulated by an extended version of our computational model originally developed to simulate magnitude comparisons of two-digit natural numbers. In the eye-tracking study, we found evidence that participants processed decimal fractions more sequentially than natural numbers because of the identical leading digit. Importantly, our model was able to account for the smaller compatibility effect found for decimal fractions. Moreover, string length congruity was an alternative account for the prolonged reaction times for incongruent decimal pairs. Consequently, we suggest that representations of natural numbers and decimal fractions do not differ.

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Section: Discussionmentioning

confidence: 81%

Section: Discussionmentioning

confidence: 95%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Decimal fraction representations are not distinct from natural number representations â€“ evidence from a combined eye-tracking and computational modeling approach

Huber¹,

Klein²,

Willmes³

et al. 2014

Front. Hum. Neurosci.

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“…Furthermore, it has been observed that contextual effects during the processing of two-digit numbers not only increase the compatibility effect (Macizo & Herrera, 2011a) but this effect can be reduced too. Macizo and Herrera (2013) focused on the compatibility effect with two-digit Arabic digits. To evaluate the adaptation to conflict, the authors manipulated the percentage of incompatible trials relative to the percentage of compatible trials (20, 50, 80 % incompatible trials).…”

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confidence: 99%

Conflict resolution in two-digit number processing: evidence of an inhibitory mechanism

Macizo

2015

Psychological Research

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We investigated the mechanism involved in conflict resolution when individuals processed two-digit numbers. Participants performed a comparison task in blocks of two trials. In the first trial, between-decade two-digit numbers were used in a compatible condition where the decade and the unit of one number were larger than those of the other number (i.e., 21-73) and an incompatible condition where the decade of one number was larger but the unit was smaller than those of the other number (i.e., 61-53). In the second trial, within-decade two-digit numbers were presented in a related condition where the numbers contained the units presented previously (i.e., 41-43) and an unrelated condition with units that did not appear before (i.e., 48-49). In the first trial, participants responded more slowly in incompatible trials relative to compatible trials. In the second trial, participants were slower in the related condition relative to unrelated trials only after incompatible trials. These results suggest that participants experienced conflict in the incompatible condition of first trial and that they inhibited irrelevant units to resolve conflict.

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“…For instance, when the proportion of incongruent trials in the Stroop task decreases, interference caused by them increases (MacLeod, 1991). Analogously in the multi-digit number comparison task, as the ratio of incompatible vs. compatible trials decreases, the unit-decade compatibility effect gets stronger (Macizo and Herrera, 2013; Huber et al, 2016). …”

Section: Attention and Conflict Monitoringmentioning

confidence: 99%

Bringing Back the Balance: Domain-General Processes Are Also Important in Numerical Cognition

et al. 2017

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The processing of Arabic numbers is under cognitive control

Cited by 30 publications

References 18 publications

Decimal fraction representations are not distinct from natural number representations â€“ evidence from a combined eye-tracking and computational modeling approach

Decimal fraction representations are not distinct from natural number representations â€“ evidence from a combined eye-tracking and computational modeling approach

Conflict resolution in two-digit number processing: evidence of an inhibitory mechanism

Bringing Back the Balance: Domain-General Processes Are Also Important in Numerical Cognition

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