Flexible and unique representations of two-digit decimals

Zhang, Li; Chen, Min; Lin, Chongde; Szűcs, Dénes

doi:10.1016/j.actpsy.2014.06.002

Cited by 4 publications

(4 citation statements)

References 30 publications

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“…In contrast, decimal comparison is much less studied and while some studies have examined magnitude based processing (Kallai & Tzelgov, 2014;Zhang, Chen, Lin, & Szucs, 2014), to my knowledge, none have explicitly contrasted whole vs. rational distance effects in this notation. Decimals are a ripe area for future research as the stimuli space affords greater opportunities for orthogonalizing distance dimensions.…”

Section: Magnitude Representations Of Symbolic Rational Number Quantitiesmentioning

confidence: 99%

Probing the neural basis of rational numbers: The role of inhibitory control and magnitude representations

Rosenberg‐Lee

2021

Heterogeneous Contributions to Numerical Cognition

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Rational numbers, such as fractions, decimals and percentages, are a persistent challenge in the mathematics curriculum. An underappreciated source of rational number difficulties are whole number properties that apply to some, but not all, rational numbers. I contend that mastery of rational numbers involves refining and expanding whole number representations. Behavioral evidence for the role inhibitory control and magnitude-based processing of rational numbers support this hypothesis, although more attention is needed to task and stimuli selection, especially among fractions. In the brain, there is scant evidence on the role of inhibitory control in rational number processing, but surprisingly good correspondence, in the parietal lobe, between the handful of neuroimaging studies of rational numbers and the accumulated whole number literature. Decimals and discrete nonsymbolic representations are fruitful domains for probing the neural basis role of whole number interference in rational number processing.

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Section: Magnitude Representations Of Symbolic Rational Number Quantitiesmentioning

confidence: 99%

Probing the neural basis of rational numbers: The role of inhibitory control and magnitude representations

Rosenberg‐Lee

2021

Heterogeneous Contributions to Numerical Cognition

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“…Only recently, research in numerical cognition investigated the processing of decimal numbers in adults (Cohen, 2010; DeWolf, Grounds, Bassok, & Holyoak, 2014; Ganor-Stern, 2013; Huber, Klein, Willmes, Nuerk, & Moeller, 2014a; Iuculano & Butterworth, 2011; Kallai & Tzelgov, 2014; Varma & Karl, 2013; Zhang, Chen, Lin, & Szűcs, 2014). Findings are inconsistent so far, indicating that decimal numbers and natural numbers either share or differ in processing characteristics.…”

Section: Decimal Numbersmentioning

confidence: 99%

A general model framework for multisymbol number comparison.

Huber

Nuerk

Willmes

et al. 2016

Psychological Review

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Different models have been proposed for the processing of multisymbol numbers like two- and three-digit numbers but also for negative numbers and decimals. However, these multisymbol numbers are assembled from the same set of Arabic digits and comply with the place-value structure of the Arabic number system. Considering these shared properties, we suggest that the processing of multisymbol numbers can be described in one general model framework. Accordingly, we first developed a computational model framework realizing componential representations of multisymbol numbers and evaluated its validity by simulating standard empirical effects of number magnitude comparison. We observed that the model framework successfully accounted for most of these effects. Moreover, our simulations provided first evidence supporting the notion of a fully componential processing of multisymbol numbers for the specific case of comparing two negative numbers. Thus, our general model framework indicates that the processing of different kinds of multisymbol integer and decimal numbers shares common characteristics (e.g., componential representation). The relevance and applicability of our model goes beyond the case of basic number processing. In particular, we also successfully simulated effects from applied marketing and consumer research by accounting for the left-digit effect found in processing of prices. Finally, we provide evidence that our model framework can be integrated into the more general context of multiattribute decision making. In sum, this indicates that our model framework captures a general scheme of separate processing of different attributes weighted by their saliency for the task at hand. (PsycINFO Database Record

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“…Using the automatic processing paradigm where the numerical magnitude of decimals is task irrelevant, Kallai and Tzelgov (2014) showed that decimals are not represented well enough to be automatically activated as integers. In addition, three studies observed a smaller compatibility effect for decimals than for integers (Huber, Klein et al, 2014;Varma & Karl, 2013;Zhang et al, 2014).…”

mentioning

confidence: 99%

“…In contrast to abundant studies of fractions, only a few studies have investigated the mental representation of decimals (Cohen, 2010;Huber, Klein, Willmes, Nuerk, & Moeller, 2014;Kallai & Tzelgov, 2014;Varma & Karl, 2013;Zhang, Chen, Lin, & Szűcs, 2014). These studies have addressed whether the representation of decimals is similar to that of multidigit integers by examining the distance effect and/or the compatibility effect.…”

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confidence: 99%

Common magnitude representation of fractions and decimals is task dependent

Zhang

Fang

Gabriel

et al. 2016

Quarterly Journal of Experimental Psychology

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Although several studies have compared the representation of fractions and decimals, no study has investigated whether fractions and decimals, as two types of rational numbers, share a common representation of magnitude. The current study aimed to answer the question of whether fractions and decimals share a common representation of magnitude and whether the answer is influenced by task paradigms. We included two different number pairs, which were presented sequentially: fraction-decimal mixed pairs and decimal-fraction mixed pairs in all four experiments. Results showed that when the mixed pairs were very close numerically with the distance 0.1 or 0.3, there was a significant distance effect in the comparison task but not in the matching task. However, when the mixed pairs were further apart numerically with the distance 0.3 or 1.3, the distance effect appeared in the matching task regardless of the specific stimuli. We conclude that magnitudes of fractions and decimals can be represented in a common manner, but how they are represented is dependent on the given task. Fractions and decimals could be translated into a common representation of magnitude in the numerical comparison task. In the numerical matching task, fractions and decimals also shared a common representation. However, both of them were represented coarsely, leading to a weak distance effect. Specifically, fractions and decimals produced a significant distance effect only when the numerical distance was larger.

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Flexible and unique representations of two-digit decimals

Cited by 4 publications

References 30 publications

Probing the neural basis of rational numbers: The role of inhibitory control and magnitude representations

Probing the neural basis of rational numbers: The role of inhibitory control and magnitude representations

A general model framework for multisymbol number comparison.

Common magnitude representation of fractions and decimals is task dependent

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