Encyclopedia of Animal Cognition and Behavior

Living Edition
| Editors: Jennifer Vonk, Todd Shackelford


Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-47829-6_1093-1

The study of arithmetical reasoning and numerical understanding has been a topic of interest for cognitive, developmental, and comparative psychologists for many decades. Questions of whether mathematical processes are innate and how they develop has led to many studies on children’s numerical capabilities, including studies designed to help outline the relationships between understanding quantities and numbers and the arithmetical transformations that can change those representations. One well-studied aspect of arithmetical competence in children is the process of addition (e.g., Carpenter et al. 1982). Addition is defined as the process or skill of calculating the total of two or more numbers or amounts. At a young age, children have already gained a simple understanding of the concept of “more” and “less” (Brush 1978), and then they learn to count. But, it is not until they get older that they come to appreciate addition, subtraction, and other operations. Studies with infants have...

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


  1. Beran, M. J. (2004). Chimpanzees (Pan troglodytes) respond to nonvisible sets after one-by-one addition and removal of items. Journal of Comparative Psychology, 118, 25–36.CrossRefPubMedGoogle Scholar
  2. Boysen, S. T., & Berntson, G. G. (1989). Numerical competence in a chimpanzee (Pan troglodytes). Journal of Comparative Psychology, 103, 23–31.CrossRefPubMedGoogle Scholar
  3. Brush, L. R. (1978). Preschool children’s knowledge of addition and subtraction. Journal for Research in Mathematics Education, 9, 44–54.CrossRefGoogle Scholar
  4. Cantlon, J. F., & Brannon, E. M. (2007). Basic math in monkeys and college students. PLoS Biology, 5, e328.CrossRefPubMedPubMedCentralGoogle Scholar
  5. Carpenter, T. P., Moser, J. M., & Romberg, T. A. (1982). Addition and subtraction: A cognitive perspective. Hillsdale: Erlbaum.Google Scholar
  6. Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 43–74.CrossRefPubMedGoogle Scholar
  7. Hanus, D., & Call, J. (2007). Discrete quantity judgments in the great apes (Pan paniscus, Pan troglodytes, Gorilla gorilla, Pongo pygmaeus): The effect of presenting whole sets versus item-by-item. Journal of Comparative Psychology, 121, 241–249.CrossRefPubMedGoogle Scholar
  8. McCrick, K., & Wynn, K. (2004). Large-number addition and subtraction by 9-month-old infants. Psychological Science, 15, 776–781.CrossRefGoogle Scholar
  9. Meck, W. H., & Church, R. M. (1983). A mode control model of counting and timing processes. Journal of Experimental Psychology. Animal Behavior Processes, 9, 320–334.CrossRefPubMedGoogle Scholar
  10. Olthof, A., Iden, C. M., & Roberts, W. A. (1997). Judgments of ordinality and summation of number symbols by squirrel monkeys (Saimiri sciureus). Journal of Experimental Psychology. Animal Behavior Processes, 23, 325–339.CrossRefPubMedGoogle Scholar
  11. Pepperberg, I. M. (2006). Gray parrot (Psittacus erithacus) numerical abilities: Addition and further experiments on a zero-like concept. Journal of Comparative Psychology, 120, 1–11.CrossRefPubMedGoogle Scholar
  12. Rugani, R., Fontanari, L., Simoni, E., Regolin, L., & Vallortigara, G. (2009). Arithmetic in newborn chicks. Proceedings of the Royal Society of London, 276, 2451–2460.CrossRefGoogle Scholar
  13. Rumbaugh, D. M., Savage-Rumbaugh, E. S., & Hegel, M. T. (1987). Summation in the chimpanzee (Pan troglodytes). Journal of Experimental Psychology. Animal Behavior Processes, 13, 107–115.CrossRefPubMedGoogle Scholar
  14. Wakeley, A., Rivera, S., & Langer, J. (2000). Can young infants add and subtract? Child Development, 71, 1525–1534.CrossRefPubMedGoogle Scholar

Authors and Affiliations

  1. 1.Georgia State UniversityAtlantaUSA

Section editors and affiliations

  • Mark Krause
    • 1
  1. 1.Southern Oregon UniversityAshlandUSA