Skip to main content
SpringerLink
Log in

Processing multi-digit numbers: a translingual eye-tracking study

  • Original Article
  • Published:
Psychological Research Aims and scope Submit manuscript

Abstract

The present study aimed at investigating the underlying cognitive processes and language specificities of three-digit number processing. More specifically, it was intended to clarify whether the single digits of three-digit numbers are processed in parallel and/or sequentially and whether processing strategies are influenced by the inversion of number words with respect to the Arabic digits [e.g., 43: dreiundvierzig (“three and forty”)] and/or by differences in reading behavior of the respective first language. Therefore, English- and German-speaking adults had to complete a three-digit number comparison task while their eye-fixation behavior was recorded. Replicating previous results, reliable hundred-decade-compatibility effects (e.g., 742_896: hundred-decade compatible because 7 < 8 and 4 < 9; 362_517: hundred-decade incompatible because 3 < 5 but 6 > 1) for English- as well as hundred-unit-compatibility effects for English- and German-speaking participants were observed, indicating parallel processing strategies. While no indices of partial sequential processing were found for the English-speaking group, about half of the German-speaking participants showed an inverse hundred-decade-compatibility effect accompanied by longer inspection time on the hundred digit indicating additional sequential processes. Thereby, the present data revealed that in transition from two- to higher multi-digit numbers, the homogeneity of underlying processing strategies varies between language groups. The regular German orthography (allowing for letter-by-letter reading) and its associated more sequential reading behavior may have promoted sequential processing strategies in multi-digit number processing. Furthermore, these results indicated that the inversion of number words alone is not sufficient to explain all observed language differences in three-digit number processing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. Note that these results have to be treated with caution. In the stimulus set used, hundred-decade-compatibility was confounded with overall numerical distance. More precisely, hundred-decade compatible number pairs had, on average, a larger numerical distance than hundred-decade incompatible number pairs (419 vs. 349 respectively). As large overall numerical distance and compatible number pairs both lead to a better performance, it is not clear whether the more pronounced hundred-decade-compatibility effect can be attributed solely to the manipulation of hundred-decade-compatibility.

  2. As we are dealing with relative probabilities, the probability for fixating unit digits is identical to 1 – the combined probabilities of hundreds and tens being fixated which leads to identical statistics as presented for the univariate ANOVA run on relative TRT on the unit digit.

References

  • Bahnmueller, J., Moeller, K., Mann, A., & Nuerk, H. C. (2015). On the limits of language influences on numerical cognition—no inversion effects in three-digit number magnitude processing in adults. Frontiers in Psychology, 6, 1216.

    Article  PubMed  PubMed Central  Google Scholar 

  • Brysbaert, M. (1995). Arabic number reading: on the nature of the numerical scale and the origin of phonological recoding. Journal of Experimental Psychology: General, 124(4), 434.

    Article  Google Scholar 

  • Brysbaert, M., Fias, W., & Noël, M. P. (1998). The Whorfian hypothesis and numerical cognition: is ‘twenty-four’ processed in the same way as ‘four-and-twenty’? Cognition, 66(1), 51–77.

    Article  PubMed  Google Scholar 

  • Dehaene, S., Dupoux, E., & Mehler, J. (1990). Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance, 16(3), 626–641.

    PubMed  Google Scholar 

  • Frith, U., Wimmer, H., & Landerl, K. (1998). Differences in phonological recoding in German- and English-speaking children. Scientific Studies of Reading, 2, 31–54.

    Article  Google Scholar 

  • Göbel, S., Moeller, K., Pixner, S., Kaufmann, L., & Nuerk, H. C. (2014). Language affects symbolic arithmetic in children: the case of number word inversion. Journal of Experimental Child Psychology, 119, 17–25.

    Article  PubMed  Google Scholar 

  • Hartmann, M. (2015). Numbers in the eye of the beholder: what do eye movements reveal about numerical cognition? Cognitive Processing, 16(1), 245–248.

    Article  PubMed  Google Scholar 

  • Helmreich, I., Zuber, J., Pixner, S., Kaufmann, L., Nürk, H. C., & Möller, K. (2011). Language effects on children’s nonverbal number line estimations. Journal of Cross-Cultural Psychology, 42(4), 598–613.

    Article  Google Scholar 

  • Hinrichs, J. V., Yurko, D. S., & Hu, J. M. (1981). Two-digit number comparison: use of place information. Journal of Experimental Psychology: Human Perception and Performance, 7(4), 890.

    Google Scholar 

  • Huber, S., Cornelsen, S., Moeller, K., & Nuerk, H. C. (2015). Toward a model framework of generalized parallel componential processing of multi-symbol numbers. Journal of Experimental Psychology. Learning, Memory, and Cognition, 41(3), 732–745.

    Article  PubMed  Google Scholar 

  • Huber, S., Moeller, K., Nuerk, H. C., & Willmes, K. (2013). A computational modeling approach on three-digit number processing. Topics in Cognitive Science, 5(2), 317–334.

    Article  PubMed  Google Scholar 

  • Klein, E., Bahnmueller, J., Mann, A., Pixner, S., Kaufmann, L., Nuerk, H.-C., & Moeller, K. (2013). Language influences on numerical development—inversion effects on multi-digit number processing. Frontiers in Psychology, 4, 480.

    Article  PubMed  PubMed Central  Google Scholar 

  • Korvorst, M., & Damian, M. F. (2008). The differential influence of decades and units on multidigit number comparison. The Quarterly Journal of Experimental Psychology, 61, 1250–1264.

    Article  PubMed  Google Scholar 

  • Macizo, P., Herrera, A., Román, P., & Martín, M. C. (2011a). Proficiency in a second language influences the processing of number words. Journal of Cognitive Psychology, 23(8), 915–921.

    Article  Google Scholar 

  • Macizo, P., Herrera, A., Román, P., & Martín, M. C. (2011b). The processing of two-digit numbers in bilinguals. British Journal of Psychology, 102(3), 464–477.

    Article  PubMed  Google Scholar 

  • Mann, A., Moeller, K., Pixner, S., Kaufmann, L., & Nuerk, H.-C. (2012). On the development of Arabic three-digit number processing in primary school children. Journal of Experimental Child Psychology, 113, 594–601.

    Article  PubMed  Google Scholar 

  • Meyerhoff, H. S., Moeller, K., Debus, K., & Nuerk, H.-C. (2012). Multi-digit number processing beyond the two-digit number range: a combination of sequential and parallel processes. Acta Psychologica, 140, 81–90.

    Article  PubMed  Google Scholar 

  • Mock, J., Huber, S., Klein, E., & Moeller, K. Insights into numerical cognition—considering eye-fixations in number processing and arithmetic. Psychological Research (in press).

  • Moeller, K., Fischer, M. H., Nuerk, H.-C., & Willmes, K. (2009). Sequential or parallel processing of two-digit numbers? Evidence from eye-tracking. The Quarterly Journal of Experimental Psychology, 62, 323–334.

    Article  PubMed  Google Scholar 

  • Moyer, R., & Landauer, T. (1967). Time required for judgements of numerical inequality. Nature, 215, 1519–1520.

    Article  PubMed  Google Scholar 

  • Noël, M. P., Fias, W., & Brysbaert, M. (1997). About the influence of the presentation format on arithmetical-fact retrieval processes. Cognition, 63(3), 335–374.

    Article  PubMed  Google Scholar 

  • Nuerk, H. C., Moeller, K., Klein, E., Willmes, K., & Fischer, M. H. (2011). Extending the mental number line. Zeitschrift für Psychologie/Journal of Psychology, 219(1), 3–22.

    Article  Google Scholar 

  • Nuerk, H. C., Weger, U., & Willmes, K. (2001). Decade breaks in the mental number line? Putting the tens and units back in different bins. Cognition, 82(1), B25–B33.

    Article  PubMed  Google Scholar 

  • Nuerk, H. C., Weger, U., & Willmes, K. (2002). A unit-decade compatibility effect in German number words. Current Psychology Letters: Behavior, Brain & Cognition, 7, 19–38.

    Google Scholar 

  • Nuerk, H. C., Weger, U., & Willmes, K. (2005). Language effects in magnitude comparison: small, but not irrelevant. Brain and Language, 92(3), 262–277.

    Article  PubMed  Google Scholar 

  • Pixner, S., Moeller, K., Hermanova, V., Nuerk, H.-C., & Kaufmann, L. (2011). Whorf reloaded: language effects on nonverbal number processing in first grade—a trilingual study. Journal of Experimental Child Psychology, 108, 371–382.

    Article  PubMed  Google Scholar 

  • Poltrock, S. E., & Schwartz, D. R. (1984). Comparative judgments of multidigit numbers. Journal of Experimental Psychology. Learning, Memory, and Cognition, 10, 32.

    Article  Google Scholar 

  • Ratcliff, R. (1993). Methods for dealing with reaction time outliers. Psychological Bulletin, 114(3), 510–532.

    Article  PubMed  Google Scholar 

  • Rau, A. K., Moll, K., Snowling, M. J., & Landerl, K. (2015). Effects of orthographic consistency on eye movement behavior: German and English children and adults process the same words differently. Journal of Experimental Child Psychology, 130, 92–105.

    Article  PubMed  Google Scholar 

  • Rayner, K. (1998). Eye movements in reading and information processing: 20 years of research. Psychological Bulletin, 124(3), 372–422.

    Article  PubMed  Google Scholar 

  • Rayner, K., & Pollatsek, A. (1989). The psychology of reading. Englewood Cliffs: Prentice Hall.

    Google Scholar 

  • Scheerer-Neumann, G. (2006). Das Lesen lernen (wollen). Wie das Eintauchen in die Welt der Buchstaben gelingt (Learning to read. How immersion in the world of letters works). Grundschulunterricht, 5, 16–20.

    Google Scholar 

  • Seymour, P. H. K., Aro, M., & Erskine, J. M. (2003). Foundation literacy acquisition in European orthographies. British Journal of Psychology, 94, 143–174.

    Article  PubMed  Google Scholar 

  • Shaki, S., & Fischer, M. H. (2008). Reading space into numbers—a cross-linguistic comparison of the SNARC effect. Cognition, 108, 590–599.

    Article  PubMed  Google Scholar 

  • Shaki, S., Fischer, M. H., & Petrusic, W. M. (2009). Reading habits for both words and numbers contribute to the SNARC effect. Psychological Bulletin and Review, 16, 328–331.

    Article  Google Scholar 

  • Whelan, R. (2008). Effective analysis of reaction time data. The Psychological Record, 58(3), 475–482.

    Google Scholar 

  • Wilkinson, G. S., & Robertson, G. J. (2006). Wide range achievement test (WRAT4). Lutz: Psychological Assessment Resources.

    Google Scholar 

  • Wimmer, H., & Goswami, U. (1994). The influence of orthographic consistency on reading development: word recognition in English and German children. Cognition, 51(1), 91–103.

    Article  PubMed  Google Scholar 

  • Ziegler, J., & Goswami, U. (2005). Reading acquisition, developmental dyslexia, and skilled reading across languages: a psycholinguistic grain size theory. Psychological Bulletin, 131(1), 3–29.

    Article  PubMed  Google Scholar 

  • Ziegler, J., Perry, C., Jacobs, A., & Braun, M. (2001). Identical words are read differently in different languages. Psychological Science, 12(5), 379–384.

    Article  PubMed  Google Scholar 

  • Zuber, J., Pixner, S., Moeller, K., & Nuerk, H.-C. (2009). On the language specificity of basic number processing: transcoding in a language with inversion and its relation to working memory capacity. Journal of Experimental Child Psychology, 102, 60–77.

    Article  PubMed  Google Scholar 

Download references

Acknowledgments

Julia Bahnmueller and Stefan Huber were supported by the Leibniz-Competition Fund (SAW-2014-IWM-4) providing funding to Elise Klein. Korbinian Moeller and Hans-Christoph Nuerk were principal investigators at the LEAD Graduate School [GSC1028], a project of the Excellence Initiative of the German federal and state governments.

Author information

Authors and Affiliations

  1. Neurocognition Laboratory, Leibniz-Institut für Wissensmedien, Schleichstraße 6, 72076, Tübingen, Germany

    Julia Bahnmueller, Stefan Huber, Hans-Christoph Nuerk & Korbinian Moeller

  2. Section Diagnostics and Cognitive Neuropsychology, Department of Psychology, Eberhard Karls University Tuebingen, Schleichstraße 4, 72076, Tübingen, Germany

    Julia Bahnmueller, Hans-Christoph Nuerk & Korbinian Moeller

  3. Department of Psychology, University of York, Heslington, York, YO10 5DD, UK

    Silke M. Göbel

Authors
  1. Julia Bahnmueller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefan Huber
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hans-Christoph Nuerk
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Silke M. Göbel
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Korbinian Moeller
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Julia Bahnmueller.

Ethics declarations

Ethical approval

All procedures performed in this study were in accordance with the ethical standards of the ethics committee of the Department of Psychology, University of York (UK) and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Conflict of interest

The authors declare that they have no actual or potential conflicts of interest concerning this work.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bahnmueller, J., Huber, S., Nuerk, HC. et al. Processing multi-digit numbers: a translingual eye-tracking study. Psychological Research 80, 422–433 (2016). https://doi.org/10.1007/s00426-015-0729-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00426-015-0729-y

Keywords

Search

Navigation