An ability to successfully add numerical digits is a key goal of early mathematics education. But the mechanisms by which adults and children develop the skills to perform such arithmetical tasks remain poorly understood. Recently researchers have demonstrated robust evidence that humans have an inbuilt 'number sense' which supports approximate numerical operations. But, to date, the role that this system plays in the development of formal symbolic mathematical skills has been unclear. During this grant we conducted programme of experiments investigating number sense and its role in adults' (and in some cases childrens') arithmetic and mathematical performance.

You may wish to look at examples of the types of experiments that we run. If so, visit our Experimental Paradigms page.

Public Engagement Activities

During our work on this project we collected some data at the University of Nottingham's Summer Scientist Week, an outreach event where children visit the university and participate in behavioural experiments. At this event we presented information about our research to interested parents. Some of the posters we used as part of these presentations are available here and here.

Further details about the Summer Scientist Week can be found in the newsletter sent to all participants.


Our work was generously supported by the ESRC via grant RES-000-22-2981.


  • Nina Attridge, Mathematics Education Centre, Loughborough University.
  • Camilla Gilmore, Learning Sciences Research Institute, University of Nottingham.
  • Matthew Inglis, Mathematics Education Centre, Loughborough University.

Brief Summary

Two main findings have emerged from our work on this grant:

  • Childrens' approximate number system accuity (as measured by performance on nonsymbolic comparison tasks) is correlated with their formal mathematics acheivement (we replicated this finding of Halberda et al, using a concurrent testing design), however the same is not true of adults. We are currently engaged in follow-up work to study the pattern and nature of the decline in this relationship.
  • Although many tasks in the literature have been used to study the approximate number system, it is unclear whether these are measuring the same thing. We found that individuals' performances on nonsymbolic addition and comparison tasks do not correlate, a finding difficult to account for within current models of the approximate number system.

For more information about these findings, please see the papers and presentations below.

Tasks and Stimuli

We have produced a package of stimuli and experimental tasks that we used during this grant. If you are involved in numerical cognition research and would find these useful, please contact Camilla Gilmore.


Other outputs will be added to this site as they become available.


  • Gilmore, C., Attridge, N., & Inglis, M. (in press). Measuring the approximate number system. Quarterly Journal of Experimental Psychology. [preprint].
  • Inglis, M., Attridge, N., Batchelor, S., & Gilmore, C. (submitted). Non-Verbal Number Acuity Correlates with Symbolic Mathematics Achievement: But only in Children. Manuscript submitted for publication.
  • Attridge, N., Gilmore, C. & Inglis, M. (2010). Non-dyscalculic adults' use of the approximate number system in symbolic addition. Research in Mathematics Education, 12, 149-151. [journal version].
  • Attridge, N., Gilmore, C. K. & Inglis, M. (2010). Symbolic addition tasks, the approximate number system and dyscalculia. Proceedings of the British Society for Research into Learning Mathematics, 29(3). [pdf].


  • Attridge, N., Lay, K., Inglis, M., Gilmore, C., & Batchelor, S. (2011, July). The reliability of the Approximate Number System. Poster presented at Meeting of the Experimental Psychology Society, University of Nottingham. [pdf]
  • Attridge, N., Gilmore, C., Inglis, M. & Batchelor, S. (2010, April). Is non-symbolic 'number sense' related to formal mathematics ability in children and in adults? First Joint Conference of the Experimental Psychology Society and the Sociedad Espanola de Psicologia Experimental, Granada, Spain. [pdf].
  • Inglis, M., Gilmore, C. & Attridge, N. (2009, July). Reverse operational momentum in symbolic arithemtic. Cultural effects on the mental number line, University of York. [pdf].


  • Inglis, M., Attridge, N., & Gilmore, C. (2011, April). The Approximate Number System: What is it? And what is its role in mathematics education? Annual Conference of the Mathematical Association, Loughborough University.
  • Inglis, M. (2010, September). The Approximate Number System in adults. Advanced Mathematical Thinking Workshop, University of East Anglia.
  • Attridge, N. (2010, July). Is mathematical ability dependent on ‘number sense’? Mathematics Education Centre Workshop, Loughborough University.
  • Gilmore, C. (2010, June). The approximate number system in adults. Numerical Cognition Workshop, Universiteit Ghent, Belgium.
  • Attridge, N., Gilmore, C., Inglis, M. & Batchelor, S. (2010, June). The relationship between number sense and mathematical ability in children and in adults. Day Conference of the British Society for Research into the Learning of Mathematics, University of Nottingham.
  • Attridge, N. (2010, March). Is ‘number sense’ related to mathematical ability in adults? Research seminar, Learning Sciences Research Institute, University of Nottingham.
  • Gilmore, C. (2010, March). Children’s mapping between different representations of number. Research Seminar, Graduate School of Education, University of Bristol.
  • Gilmore, C. (2010, February). Children’s mapping between different representations of number. Research Seminar, Department of Psychology and Human Development, Institute of Education, London.
  • Gilmore, C. (2010, January). The nature of children’s numerical representations. Research Seminar, School of Psychology, University of York.
  • Attridge, N., Gilmore, C. K. & Inglis, M. (2009, November). Is non-symbolic "number sense" necessary for exact symbolic arithmetic?. Day Conference of the British Society for Research into the Learning of Mathematics, Loughborough University.

Related Papers

  • Gilmore, C.K. & Spelke, E. (2008). Children's understanding of the relationship between addition and subtraction. Cognition, 107, 932-945, [pdf].
  • Gilmore, C. K. & Inglis, M. (2008). Process- and object-based thinking in arithmetic. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojana & A. Sepulveda (Eds.), Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 73-80). Morelia, Mexico, [pdf].
  • Gilmore, C.K., McCarthy, S.E. & Spelke, E. (2007). Symbolic arithmetic knowledge without instruction. Nature, 447, 589-591, [journal pdf] [supplementary information pdf].