Ordinal Processing of Numerical and Non-numerical Information

  • Dana Sury
  • Orly Rubinsten
Part of the Literacy Studies book series (LITS, volume 6)


Numerical knowledge requires representations of both quantities and ordinal relationships. Furthermore, the basic ability to judge and learn the ordinality of a sequence might be innately available to humans and animals. However, numerical ordinality processing has received much less research interest then quantity processing. In this chapter, we review the literature on ordinal processing, including the different definitions of numerical ordinality, the development of ordinal knowledge and unique effects related to ordinal task (e.g., the distance effect and the spatial numerical association of response codes (SNARC)). Additionally, we discuss cognitive and neurofunctional similarities and differences in processing numerical (ordinality and quantity) and non-numerical sequences. It is argued here that current studies are sometimes controversial and are not directly comparable because of the variance in task, stimuli and instructions that are used, but mainly because of different definitions. We conclude by describing a theoretical model of the neuro-cognitive representations which are required to process ordinal information and suggest ordinality as an additional core cognitive system. The model can contribute a framework for the new scientific field of ordinal processing.


Mental Number Line Transitive Inference Numerical Knowledge Developmental Dyscalculia Ordinal Information 
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.


  1. Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9, 278–291.PubMedCrossRefGoogle Scholar
  2. Binkofski, F., Amunts, K., Stephan, K. M., Posse, S., Schormann, T., Freund, H. J., Zilles, K., & Seitz, R. J. (2000). Broca’s region subserves imagery of motion: A combined cytoarchectonic and fMRI study. Human Brain Mapping, 11, 273–285.PubMedCrossRefGoogle Scholar
  3. Boysen, S. T., Berntson, G. G., Shreyer, T. A., & Quigley, K. S. (1993). Processing of ordinality and transitivity by chimpanzees. Journal of Comparative Psychology, 107(2), 208–215.PubMedCrossRefGoogle Scholar
  4. Brannon, E. M., & Roitman, J. D. (2003). Nonverbal representation of time and numbers in animals and human infants. In W. H. Meck (Ed.), Functional and neural mechanisms of interval timing (pp. 143–182). Boca Raton: CRC Press.Google Scholar
  5. Brannon, E. M., & Terrace, H. S. (1998). Ordering of the numerosities 1 to 9 by monkeys. Science, 282, 746–749.PubMedCrossRefGoogle Scholar
  6. Brannon, E. M., & Van de Walle, G. A. (2001). The development of ordinal numerical competence in young children. Cognitive Psychology, 43, 53–81.PubMedCrossRefGoogle Scholar
  7. Buckley, P. B., & Gillman, C. B. (1974). Comparisons of digits and dot patterns. Journal of Experimental Psychology, 103(6), 1131–1136.PubMedCrossRefGoogle Scholar
  8. Cantlon, J. F., Platt, M. L., & Brannon, E. M. (2009). Beyond the numbers domain. Trends in Cognitive Sciences, 13(2), 83–91.PubMedCrossRefGoogle Scholar
  9. Cohen Kadosh, R., Cole, N. B., Henik, A., Rubinsten, O., Mohr, H., Dori, H., et al. (2005). Are numbers special? The comparison systems of the human brain investigated by fMRI. Neuropsychologia, 43(9), 1238–1248.PubMedCrossRefGoogle Scholar
  10. Conson, M., Cinque, F., Barbarulo, A. M., & Trojano, L. (2008). A common processing system for duration, order and spatial information: Evidence from a time estimation task. Experimental Brain Research, 187(2), 267–274.CrossRefGoogle Scholar
  11. De Havia, M. D. & Spelke, E. S. (2010). Number-space mapping in human infants. Psychological Science, 21(5), 653–660.Google Scholar
  12. Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44(1–2), 1–42.PubMedGoogle Scholar
  13. Dehaene, S. (2009). Origins of mathematical intuitions: The case of arithmetic. Annals of the New York Academy of Sciences, 1156, 232–259.PubMedCrossRefGoogle Scholar
  14. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology, 122(3), 371–396.Google Scholar
  15. Dehaene, S., Naccache, L., Le Clec’H, G., Koechlin, E., Mueller, M., Dehaene-Lambertz, G., et al. (1998). Imaging unconscious semantic priming. Nature, 395, 597–600.PubMedCrossRefGoogle Scholar
  16. Delazer, M., & Butterworth, B. (1997). A dissociation of number meanings. Cognitive Neuropsychology, 14, 613–636.CrossRefGoogle Scholar
  17. Duncan, E. M., & McFarland, C. E. (1980). Isolating the effects of symbolic distance and semantic congruity in comparative judgments: an additive-factors analysis. Memory & Cognition, 8(6), 612–622.CrossRefGoogle Scholar
  18. Feigenson, L. (2007). The equality of quantity. Trends in Cognitive Sciences, 11, 185–187.PubMedCrossRefGoogle Scholar
  19. Feigenson, L., Carey, S., & Hauser, M. (2002). The representations of underlying infants’ choice of more: Object files versus analog magnitude. Psychological Science, 13, 150–156.PubMedCrossRefGoogle Scholar
  20. Feigenson, L., Dehaene, L., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314.PubMedCrossRefGoogle Scholar
  21. Fias, W., Lammertyn, J., Caessens, B., & Orban, G. A. (2007). Processing of abstract ordinal knowledge in the horizontal segment of the intraparietal sulcus. The Journal of Neuroscience, 27(33), 8952–8956.PubMedCrossRefGoogle Scholar
  22. Franklin, M. S., & Jonides, J. (2008). Order and magnitude share a common representation in parietal cortex. Journal of Cognitive Neuroscience, 21(11), 2114–2120.CrossRefGoogle Scholar
  23. Franklin, M. S., Jonides, J., & Smith, E. E. (2009). Processing of order information for numbers and months. Memory & Cognition, 37(5), 644–654.CrossRefGoogle Scholar
  24. Fulbright, R. K., Manson, S. C., Skudlarski, P., Lacadie, M. C., & Gore, C. J. (2003). Quantity determination and the distance effect with letters, numbers, and shapes: A functional MR imaging study of number processing. American Journal of Neuroradiology, 24, 193–200.PubMedGoogle Scholar
  25. Gevers, W., Reynvoet, B., & Fias, W. (2003). The mental representation of ordinal sequences is spatially organized. Cognition, 87, 87–95.CrossRefGoogle Scholar
  26. Holloway, I. D., & Ansari, D. (2008). Special section: The development of mathematical cognition: Domain-specific and domain-general changes in children’s development of number comparison. Developmental Science, 11(5), 644–649.PubMedCrossRefGoogle Scholar
  27. Ischebeck, A., Heim, S., Siedentopf, C., Zamarian, L., Schocke, M., Kremser, C., et al. (2008). Are numbers special? Comparing the generation of verbal materials from ordered categories (months) to numbers and other categories (animals) in an fMRI study. Human Brain Mapping, 29, 894–909.PubMedCrossRefGoogle Scholar
  28. Jacob, N. S., & Nieder, A. (2008). The ABC of cardinal and ordinal number representations. Trends in Cognitive Sciences, 12(2), 41–43.PubMedCrossRefGoogle Scholar
  29. Kaufmann, L., Vogel, S. E., Starke, M., Kremser, C., & Schocke, M. (2009). Numerical and non-numerical ordinality processing in children with and without developmental dyscalculia: Evidence from fMRI. Cognition Development, 24, 486–494.CrossRefGoogle Scholar
  30. Lewkowicz, D. J., & Berent, I. (2009). Sequence learning in 4-month-old infants: Do infants represent ordinal information? Child Development, 80, 1811–1823.PubMedCrossRefGoogle Scholar
  31. Maess, B., Koelsch, S., Gunter, T. C., & Friederici, A. D. (2001). Musical syntax is processed in the area of Broca: An MEG study. Nature Neuroscience, 4, 540–545.PubMedGoogle Scholar
  32. Moretti, R., Torre, P., Antonello, R. M., Cazzato, G., & Bava, A. (2002). Rivastigmine in subcortical vascular dementia: An open 22-month study. Journal of Neurological Sciences, 203(204), 141–146.CrossRefGoogle Scholar
  33. Moyer, R. S., & Landauer, T. K. (1967). Time required for judgments of numerical inequality. Nature, 215, 1519–1520.PubMedCrossRefGoogle Scholar
  34. Nieder, A. (2005). Counting on neurons: The neurobiology of numerical competence. Nature Reviews Neuroscience, 6, 1–14.CrossRefGoogle Scholar
  35. Nuerk, H. C., Kaufmann, L., Zoppoth, S., & Willmes, K. (2004). On the development of the mental number line: More, less, or never holistic with increasing age? Developmental Psychology, 40(6), 1199–1211.PubMedCrossRefGoogle Scholar
  36. Paulsen, D. J., & Neville, H. J. (2008). The processing of non-symbolic numerical magnitudes as indexed by ERPs. Neuropsychologia, 46(10), 2532–2544.PubMedCrossRefGoogle Scholar
  37. Paulsen, D. J., Woldorff, M. G., & Brannon, A. B. (2010). Individual differences in nonverbal number discrimination correlate with event-related potentials and measures of probabilistic reasoning. Neuropsychologia, 48, 3687–3695.PubMedCrossRefGoogle Scholar
  38. Pavese, A., & Umiltà, C. (1998). Symbolic distance between numerosity and identity modulates Stroop interference. Journal of Experimental Psychology. Human Perception and Performance, 24, 1535–1545.PubMedCrossRefGoogle Scholar
  39. Restle, F. (1970). Theory of serial patterns learning: Structural trees. Psychological Review, 77, 481–495.CrossRefGoogle Scholar
  40. Rubinsten, O., & Sury, D. (2011). Processing ordinality and quantity: The case of developmental dyscalculia. PloS One, 6(9), e24079.PubMedCrossRefGoogle Scholar
  41. Rugani, R., et al. (2007). Rudimental numerical competence in 5-day-old domestic chicks (Gallus gallus): Identification of ordinal position. Journal of Experimental Psychology. Animal Behavior Processes, 33, 21–31.PubMedCrossRefGoogle Scholar
  42. Sekuler, R., & Mierkiewicz, D. (1977). Children’s judgments of numerical inequality. Child Development, 48, 630–633.CrossRefGoogle Scholar
  43. Shepard, N. R. (2001). Perceptual-cognitive universals as reflections of the world. Behavioral and Brain Science, 24, 581–601.Google Scholar
  44. Suanda, S. H., Tompson, W., & Brannon, E. M. (2008). Changes in the ability to detect ordinal numerical relationships between 9 and 11 months of age. Infancy, 13, 308–337.PubMedCrossRefGoogle Scholar
  45. Turconi, E., & Seron, X. (2002). Dissociation between order and quantity meaning in a patient with Gerstmann syndrome. Cortex, 38, 911–914.CrossRefGoogle Scholar
  46. Turconi, E., Jemel, B., Rossion, B., & Seron, X. (2004). Electrophysiological evidence for differential processing of numerical quantity and order in humans. Cognitive Brain Research, 21, 22–38.PubMedCrossRefGoogle Scholar
  47. Turconi, E., Campbell, J. I. D., & Seron, X. (2006). Numerical order and quantity processing in number comparison. Cognition, 98, 273–285.PubMedCrossRefGoogle Scholar
  48. Van Opstal, F., Verguts, T., Orban, G. A., & Fias, W. (2007). A hippocampal-parietal network for learning an ordered sequence. NeuroImage, 40, 333–341.PubMedCrossRefGoogle Scholar
  49. Van Opstal, F., Gevers, W., De Moor, W., & Verguts, T. (2008). Dissecting the symbolic distance effect: Comparison and priming effects in numerical and non-numerical orders. Psychonomic Bulletin & Review, 15, 419–425.CrossRefGoogle Scholar
  50. Van Opstal, F., Fias, W., Peigneux, P., & Verguts, T. (2009). The neural representation of extensively trained ordered sequences. NeuroImage, 47(1), 367–375.PubMedCrossRefGoogle Scholar
  51. Verguts, T., & Fias, W. (2004). Representation of number in animals and humans: A neural model. Journal of Cognitive Neuroscience, 16(9), 1493–1504.PubMedCrossRefGoogle Scholar
  52. Verguts, T., & Van Opstal, F. (2005). Dissociation of the distance effect and size effect in one-digit numbers. Psychonomic Bulletin & Review, 12(5), 925–930.CrossRefGoogle Scholar
  53. Vigliocco, G., Vinson, D. P., Damian, M. F., & Levelt, W. (2002). Semantic distance effects on object and action naming. Cognition, 85(3), 61–69.CrossRefGoogle Scholar
  54. Wood, G., Willmes, K., Nuerk, H. C., & Fischer, M. H. (2008). On the cognitive link between space and number: A meta-analysis of the SNARC effect. Psychology Science Quarterly, 50(4), 489–525.Google Scholar
  55. Zorzi, M., Prifitis, K., & Umilta, C. (2002). Brain damage: Neglect disrupts the mental number line. Nature, 417, 138–139.PubMedCrossRefGoogle Scholar
  56. Zorzi, M., Di Bono, M. G., & Fias, W. (2010). Distinct representations of numerical and non-numerical order in the human intraparietal sulcus revealed by multivariate pattern recognition. NeuroImage, 57, 674–680.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Edmond J. Safra Brain Research Center for the Study of Learning Disabilities, Department of Learning DisabilitiesUniversity of HaifaHaifaIsrael

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