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Multiplication facts and the mental number line: evidence from unbounded number line estimation

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Abstract

A spatial representation of number magnitude, aka the mental number line, is considered one of the basic numerical representations. One way to assess it is number line estimation (e.g., positioning 43 on a number line ranging from 0 to 100). Recently, a new unbounded version of the number line estimation task was suggested: without labeled endpoints but a predefined unit, which was argued to provide a purer measure of spatial numerical representations. To further investigate the processes determining estimation performance in the unbounded number line task, we used an adapted version with variable units other than 1 to evaluate influences of (i) the size of a given unit and (ii) multiples of the units as target numbers on participants’ estimation pattern. We observed that estimations got faster and more accurate with increasing unit sizes. On the other hand, multiples of a predefined unit were estimated faster, but not more accurately than non-multiples. These results indicate an influence of multiplication fact knowledge on spatial numerical processing.

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Notes

  1. Please note that the results did not change substantially when using the absolute estimation error in pixels (instead of the relative measure of units) as the dependent variable.

  2. Please note that the constant working window of about 10 we observed was not driven by the fact that 10 was the largest unit in the experiment. As recommended by Marc Brysbaert we conducted a control experiment in which 46 participants performed an unbounded number line estimation task with units 7 and 13 in a paper–pencil version of the task. Importantly, statistical evaluation of the resulting working windows indicated that it did not differ between unit size 7 and 13 [9.41 vs. 9.76, respectively, t(45) = 1.07, p = 0.32)] as well as from the mean working window over all unit sizes observed in the main experiment [unit size 7: t(45) = 0.43, p = 0.67; unit size 13: t(45) = 0.84, p = 0.41].

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Author information

Authors and Affiliations

  1. Center for Disability and Integration (CDI-HSG), University of St. Gallen, Rosenbergstrasse 51, 9000, St. Gallen, Switzerland

    Regina M. Reinert

  2. Knowledge Media Research Center, Tüebingen, Germany

    Stefan Huber, Hans-Christoph Nuerk & Korbinian Moeller

  3. Department of Psychology, Eberhard-Karls University Tüebingen, Tüebingen, Germany

    Hans-Christoph Nuerk & Korbinian Moeller

Authors
  1. Regina M. Reinert
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  2. Stefan Huber
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  3. Hans-Christoph Nuerk
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  4. Korbinian Moeller
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Corresponding author

Correspondence to Regina M. Reinert.

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  1. Please note that multiples are indicated in italics

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Reinert, R.M., Huber, S., Nuerk, HC. et al. Multiplication facts and the mental number line: evidence from unbounded number line estimation. Psychological Research 79, 95–103 (2015). https://doi.org/10.1007/s00426-013-0538-0

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  • DOI: https://doi.org/10.1007/s00426-013-0538-0

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