How do spatial representations enhance cognitive numerical processing?

  • 266 Accesses

  • 1 Citations


Several philosophical theories attempt to explain how actions performed in the world enhance cognitive processing: internalism, active externalism, and cognitive integration. The aim of this paper is to examine whether the use of spatial representations in arithmetic can shed light on this debate. Relying on philosophical analysis, on a discussion of empirical work in the cognitive neuroscience of number, and on a historical case study, I will show that spatial representations of number indicate an integration between internal and external cognitive processes.

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

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.

Fig. 1


  1. 1.

    This method is an alternative way of solving simultaneous linear equations, predating Gaussian elimination.


  1. Adams F, Aizawa K (2001) The bounds of cognition. Philos Psychol 14:43–64

  2. Barabashev AG (1997) In support of significant modernization of original mathematical texts (in defense of presentism). Philos Math 5:21–41

  3. Chemla K, Guo S (2004) Les neuf chapitres. Le classique mathématique de la Chine ancienne et ses commentaires. Dunod, Paris

  4. Clark A, Chalmers D (1998) The extended mind. Analysis 58:7–19

  5. Cohen Kadosh R, Walsh V (2009) Numerical representation in the parietal lobes: abstract or not abstract? Behav Brain Sci 32:313–328

  6. De Cruz H, De Smedt J (2010) The innateness hypothesis and mathematical concepts. Topoi 29:3–13

  7. De Cruz H, De Smedt J (in press) Mathematical symbols as epistemic actions. Synthese

  8. Dehaene S, Izard V, Spelke ES, Pica P (2008) Log or linear? Distinct intuitions of the number scale in western and Amazonian indigene cultures. Science 320:1217–1220

  9. Hart R (2010) The Chinese roots of linear algebra. Johns Hopkins University Press, Baltimore

  10. Menary R (2007) Cognitive integration: attacking the bounds of cognition. Palgrave, Basingstoke

  11. Siegler R, Ramani G (2008) Playing linear numerical board games promotes low-income children’s numerical development. Dev Sci 11:655–661

  12. Sparrow B, Liu J, Wegner D (2011) Google effects on memory: cognitive consequences of having information at our fingertips. Science 333:776–778

  13. Tudusciuc O, Nieder A (2007) Neuronal population coding of continuous and discrete quantity in the primate posterior parietal cortex. Proc Natl Acad Sci USA 104:14513–14518

Download references

Conflict of interest

This supplement was not sponsored by outside commercial interests. It was funded entirely by ECONA, Via dei Marsi, 78, 00185 Roma, Italy.

Author information

Correspondence to Helen De Cruz.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (MP4 2478 kb)

Supplementary material 1 (MP4 2478 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

De Cruz, H. How do spatial representations enhance cognitive numerical processing?. Cogn Process 13, 137–140 (2012).

Download citation


  • Spatial representations
  • Numerical cognition
  • Cognitive integration
  • Chinese algebra