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Magnitude representation in sequential comparison of two-digit numbers is not holistic either

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Abstract

There is accumulating evidence suggesting that two-digit number magnitude is represented in a decomposed fashion into tens and units rather than holistically as one integrated entity. However, recently, it has been claimed that this property does not hold for the case when two to-be-compared numbers are presented sequentially. In the present study, we pursued this issue in two experiments by evaluating perceptual as well as strategic aspects arising for sequential stimulus presentation in a magnitude comparison task. We observed reliable unit-decade compatibility effects indicating decomposed processing of tens and units in a magnitude comparison task with sequential presentation of the to-be-compared numbers. In particular, we found that both confounding low-level perceptual features and stimulus set characteristics determining cue validity of the units influenced the compatibility effect. Taken together, our results clearly indicate that decomposed representations of tens and units seem to be a general characteristic of multi-digit number magnitude processing, rather than an exception occurring under very specific conditions only. Implications of these results for the understanding of number magnitude representations are discussed.

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Fig. 1

Notes

  1. A percentage of about 85 % validity of the decade digit for the overall decision resembles the validity rates of cues in a standard Posner paradigm investigating processes of attention shifting/allocation (e.g., Posner et al. 1980; Posner and Cohen 1984 for a review).

  2. Please note that this argument also applies to the study of Zhang and Wang (2005), who also argued for a holistic representation of two-digit numbers when presented sequentially. In their study, only 13 % within-decade comparisons were included in the stimulus set. For Zhou et al. (2008) we could not infer the percentage of within-decade fillers, because the respective information was not reported.

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Acknowledgments

This research was funded in part by the German Research Foundation (DFG) for project 2 within the Research Group (Forschergruppe) Analyse und Förderung effektiver Lehr-Lern-Prozesse (FOR 738/2/) granted to Ulrike Cress and Hans-Christoph Nuerk supporting Korbinian Moeller. Additionally, part of this research was supported by a project in the ScienceCampus (WissenschaftsCampus) Tuebingen (Cluster 1/TP 1). We are grateful to Ian Mackenzie for language editing.

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Moeller, K., Klein, E., Nuerk, HC. et al. Magnitude representation in sequential comparison of two-digit numbers is not holistic either. Cogn Process 14, 51–62 (2013). https://doi.org/10.1007/s10339-012-0535-z

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