Psychological Research

, Volume 78, Issue 4, pp 539–548 | Cite as

Cognitive control in number magnitude processing: evidence from eye-tracking

  • S. Huber
  • A. Mann
  • H.-C. Nuerk
  • K. Moeller
Original Article


The unit-decade compatibility effect describes longer response times and higher error rates for incompatible (e.g., 37_52) than compatible (e.g., 42_57) number comparisons. Recent research indicated that the effect depends on the percentage of same-decade filler items. In the present study, we further examined this relationship by recording participants’ eye-fixation behaviour. In four conditions, participants had to compare item sets with different filler item types (i.e., same-decade and same-unit filler items) and different numbers of same-decade filler items (i.e., 25, 50, and 75 %). We found a weaker unit-decade compatibility effect with most fixations on tens in the condition with same-unit filler items. Moreover, the compatibility effect increased with the percentage of same-decade filler items which was accompanied by less fixations on tens and more fixations on units. Thus, our study provides first eye-tracking evidence for the influence of cognitive control in number processing.


Cognitive Control Compatibility Effect Filler Item Number Pair Mental Number Line 
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.



We thank Ian Mackenzie for proof-reading of the manuscript.


  1. Botvinick, M. M., Braver, T. S., Barch, D. M., Carter, C. S., & Cohen, J. D. (2001). Conflict monitoring and cognitive control. Psychological Review, 108, 624–652.PubMedCrossRefGoogle Scholar
  2. Botvinick, M. M., Cohen, J. D., & Carter, S. C. (2004). Conflict monitoring and anterior cingulate cortex: An update. Trends in Cognitive Sciences, 8, 539–546.PubMedCrossRefGoogle Scholar
  3. 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, 626–641.PubMedGoogle Scholar
  4. Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 43–74.PubMedCrossRefGoogle Scholar
  5. Ganor-Stern, D., Tzelgov, J., & Ellenbogen, R. (2007). Automaticity and two-digit numbers. Journal of Experimental Psychology: Human Perception and Performance, 33, 483–496.PubMedGoogle Scholar
  6. Hinrichs, J. V., Yurko, D. S., & Hu, J. (1981). Two-digit number comparison: Use of place information. Journal of Experimental Psychology: Human Perception and Performance, 7, 890–901.Google Scholar
  7. Kallai, A. Y., & Tzelgov, J. (2012). The place-value of a digit in multi-digit numbers is processed automatically. Journal of Experimental Psychology: Learning, Memory, and Cognition, 38, 1221–1233.PubMedGoogle Scholar
  8. Korvorst, M., & Damian, M. F. (2008). The differential influence of decades and units on multi-digit number comparison. The Quarterly Journal of Experimental Psychology, 61, 1250–1264.PubMedCrossRefGoogle Scholar
  9. Logan, G. D. (1980). Attention and automaticity in Stroop and priming tasks: Theory and data. Cognitive Psychology, 12, 523–553.PubMedCrossRefGoogle Scholar
  10. Macizo, P., & Herrera, A. (2008). The effect of number codes in the comparison task of two-digit numbers. Psicológica, 29, 1–34.Google Scholar
  11. Macizo, P., & Herrera, A. (2010). Two-digit number comparison: Decade-unit and unit-decade produce the same compatibility effect with number words. Canadian Journal of Experimental Psychology, 64, 17–24.PubMedCrossRefGoogle Scholar
  12. Macizo, P., & Herrera, A. (2011). Cognitive control in number processing: Evidence from the unit-decade compatibility effect. Acta Psychologica, 136, 112–118.PubMedCrossRefGoogle Scholar
  13. Macizo, P., & Herrera, A. (2012). The processing of Arabic numbers is under cognitive control. Psychological Research. doi: 10.1007/s00426-012-0456-6.
  14. 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.PubMedCrossRefGoogle Scholar
  15. Merkley, R., & Ansari, D. (2010). Using eye-tracking to study numerical cognition: the case of the numerical ratio effect. Experimental Brain Research, 206, 455–460.PubMedCrossRefGoogle Scholar
  16. 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.PubMedCrossRefGoogle Scholar
  17. 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.PubMedCrossRefGoogle Scholar
  18. Moeller, K., Klein, E., & Nuerk, H.-C. (2011). Three processes underlying the carry effect in addition–evidence from eye-tracking. British Journal of Psychology, 102, 623–645.PubMedCrossRefGoogle Scholar
  19. Moeller, K., Klein, E., & Nuerk, H.-C. (2013). Influences of cognitive control in numerical cognition–adaptation by binding for implicit learning. Topics in Cognitive Science, 5, 335–353.PubMedCrossRefGoogle Scholar
  20. Moyer, R. S., & Landauer, T. K. (1967). The time required for judgments of numerical inequality. Nature, 215, 1519–1520.PubMedCrossRefGoogle Scholar
  21. Notebaert, W., & Verguts, T. (2008). Cognitive control acts locally. Cognition, 106, 1071–1080.PubMedCrossRefGoogle Scholar
  22. 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
  23. 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, B25–B33.PubMedCrossRefGoogle Scholar
  24. Nuerk, H.-C., Weger, U., & Willmes, K. (2002). A unit-decade compatibility effect in German number words. Current Psychology Letters: Behavior, Brain, & Cognition, 2, 19–38.Google Scholar
  25. Nuerk, H. C., & Willmes, K. (2005). On the magnitude representations of two-digit numbers. Psychology Science, 47, 52–72.Google Scholar
  26. Poltrock, S. E., & Schwartz, D. R. (1984). Comparative judgement of multi-digit numbers. Journal of Experimental Psychology: Learning, Memory, and Cognition, 10, 32–45.Google Scholar
  27. Rayner, K., & Pollatsek, A. (1989). The psychology of reading. Englewood Cliffs: Prentice Hall.Google Scholar
  28. Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 83, 32–45.CrossRefGoogle Scholar
  29. Shepard, R. N., Kilpatrick, D. W., & Cunningham, J. P. (1975). The internal representation of numbers. Cognitive Psychology, 7, 82–138.CrossRefGoogle Scholar
  30. Tzelgov, J., Henik, A., & Berger, J. (1992). Controlling Stroop effects by manipulating expectations for color words. Memory & Cognition, 20, 727–735.CrossRefGoogle Scholar
  31. Verguts, T., & Notebaert, W. (2008). Hebbian learning of cognitive control: Dealing with specific and nonspecific adaptation. Psychological Review, 115, 518–525.PubMedCrossRefGoogle Scholar
  32. Verguts, T., & Notebaert, W. (2009). Adaptation by binding: a learning account of cognitive control. Trends in Cognitive Science, 13, 252–257.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Knowledge Media Research CenterTuebingenGermany
  2. 2.Department of PsychologyEberhard Karls UniversityTuebingenGermany

Personalised recommendations