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Psychological Research

, Volume 79, Issue 1, pp 95–103 | Cite as

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

  • Regina M. Reinert
  • Stefan Huber
  • Hans-Christoph Nuerk
  • Korbinian Moeller
Original Article

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.

Keywords

Number Line Unit Size Target Number Mental Number Line Number Magnitude 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Ashcraft, M. H., & Moore, A. M. (2012). Cognitive processes of numerical estimation in children. Journal of Experimental Child Psychology, 111, 246–267.PubMedCrossRefGoogle Scholar
  2. Barth, H. C., & Paladino, A. M. (2011). The development of numerical estimation: evidence against a representational shift. Developmental Science, 14, 125–135.PubMedCrossRefGoogle Scholar
  3. Berteletti, I., Lucangeli, D., Piazza, M., Dehaene, S., & Zorzi, M. (2010). Numerical estimation in preschoolers. Developmental Psychology, 46, 545–551.PubMedCrossRefGoogle Scholar
  4. Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 41, 189–201.CrossRefGoogle Scholar
  5. Cohen, D. J., & Blanc-Goldhammer, D. (2011). Numerical bias in bounded and unbounded number line tasks. Psychonomic Bulletin and Review, 18, 331–338.PubMedCentralPubMedCrossRefGoogle Scholar
  6. Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1, 83–120.Google Scholar
  7. Dehaene, S., & Cohen, L. (1997). Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex, 33, 219–250.PubMedCrossRefGoogle Scholar
  8. Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487–506.PubMedCrossRefGoogle Scholar
  9. Ebersbach, M., Luwel, K., Frick, A., Onghena, P., & Verschaffel, L. (2008). The relationship between the shape of the mental number line and familiarity with numbers in 5- to 9-year old children: evidence for a segmented linear model. Journal of Experimental Child Psychology, 99, 1–17.PubMedCrossRefGoogle Scholar
  10. Fuson, K. (1988). Children’s counting and concepts of cumber. New York: Springer.Google Scholar
  11. Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 43–74.Google Scholar
  12. Helmreich, I., Zuber, J., Pixner, S., Kaufmann, L., Nuerk, H.-C., & Moeller, K. (2011). Language effects on children’s mental number line: how cross-cultural differences in number word systems affect spatial mappings of numbers in a non-verbal task. Journal of Cross-Cultural Psychology, 42, 598–613.CrossRefGoogle Scholar
  13. Hollands, J. G., & Dyre, B. P. (2000). Bias in proportion judgments: the cyclical power model. Psychological Review, 107, 500–524.PubMedCrossRefGoogle Scholar
  14. Lee, K. M., & Kang, S. Y. (2002). Arithmetic operation and working memory: differential suppression in dual tasks. Cognition, 83, B63–B68.PubMedCrossRefGoogle Scholar
  15. Moeller, K., Fischer, M. H., Nuerk, H.-C., & Willmes, K. (2009a). Eye fixation behaviour in the number bisection task: evidence for temporal specificity. Acta Psychologica, 131, 209–220.PubMedCrossRefGoogle Scholar
  16. Moeller, K., Klein, E., Fischer, M. H., Nuerk H.-C., & Willmes, K. (2011b). Representation of multiplication facts: evidence for partial verbal coding. Behavioral and Brain Functions, 7:25.Google Scholar
  17. Moeller, K., & Nuerk, H.-C. (2011). Psychophysics of numerical representation: why seemingly logarithmic representations may rather be multi-linear. Zeitschrift für Psychologie/Journal of Psychology, 219, 64–70.CrossRefGoogle Scholar
  18. Moeller, K., Pixner, S., Kaufmann, L., & Nuerk, H.-C. (2009b). Children’s early mental number line: logarithmic or rather decomposed linear? Journal of Experimental Child Psychology, 103, 503–515.PubMedCrossRefGoogle Scholar
  19. Nuerk, H.-C., Geppert, B. E., van Herten, M., & Willmes, K. (2002). On the impact of different number representations in the number bisection task. Cortex, 38, 691–715.PubMedCrossRefGoogle Scholar
  20. Nuerk, H.-C., Moeller, K., Klein, E., Willmes, K., & Fischer, M. H. (2011). Extending the mental number line: a review of multi-digit number processing. Journal of Psychology, 219, 3–22.Google Scholar
  21. Nuerk, H.-C., Weger, U., & Willmes, K. (2001). Decade breaks in the mental number line? Putting tens and units back into different bins. Cognition, 82, B25–B33.PubMedCrossRefGoogle Scholar
  22. Opfer, J. E., & Siegler, R. S. (2007). Representational change and children’s numerical estimation. Cognitive Psychology, 55, 169–195.PubMedCrossRefGoogle Scholar
  23. Price, A. J. (2001). Atomistic and holistic approaches to the early primary mathematics curriculum for addition. In: M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th PME International Conference, 4, 73–80.Google Scholar
  24. Rusconi, E., Galfano, G., Speriani, V., & Umiltà, C. (2004). Capacity and contextual constraints on product activation: evidence from task-irrelevant fact retrieval. Quarterly Journal of Experimental Psychology, 57A, 1485–1511.CrossRefGoogle Scholar
  25. Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75, 428–444.PubMedCrossRefGoogle Scholar
  26. Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: evidence for multiple representations of numerical quantity. Psychological Science, 14, 237–243.PubMedCrossRefGoogle Scholar
  27. Slusser, E., Santiago, R., & Barth, H. (2013). Developmental change in numerical estimation. Journal of Experimental Psychology: General, 142, 193–208.CrossRefGoogle Scholar
  28. Spence, I. (1990). Visual psychophysics of simple graphical elements. Journal of Experimental Psychology: Human Perception and Performance, 16, 683–692.PubMedGoogle Scholar
  29. Sullivan, J., Juhasz, B., Slattery, T., & Barth, H. (2011). Adults’ number-line estimation strategies: evidence from eye movements. Psychonomic Bulletin and Review, 18, 557–563.PubMedCentralPubMedCrossRefGoogle Scholar
  30. Wood, G., Nuerk, H.-C., Moeller, K., Geppert, B., Schnitker, R., Weber, J., et al. (2008). All for one but not one for all: how multiple number representations are recruited in one numerical task. Brain Research, 1187, 154–166.PubMedCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Regina M. Reinert
    • 1
  • Stefan Huber
    • 2
  • Hans-Christoph Nuerk
    • 2
    • 3
  • Korbinian Moeller
    • 2
    • 3
  1. 1.Center for Disability and Integration (CDI-HSG)University of St. GallenSt. GallenSwitzerland
  2. 2.Knowledge Media Research CenterTüebingenGermany
  3. 3.Department of PsychologyEberhard-Karls University TüebingenTüebingenGermany

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