Encyclopedia of Clinical Neuropsychology

2018 Edition
| Editors: Jeffrey S. Kreutzer, John DeLuca, Bruce Caplan

Arithmetic Reasoning

  • J. Zhou
  • R. SandsEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-3-319-57111-9_1434


Numerical reasoning; Quantitative reasoning


Mathematical reasoning is the mathematical methodology of axiomatic reasoning, logical deduction, and formal inference.

Current Knowledge

Research in evolutionary genetics and neuroscience suggests important neurological differences between mathematical capacities that are evolutionary primitive (e.g., counting) and those (e.g., arithmetic) that are more culturally taught (Geary 1995). Empirical data demonstrate that mathematical reasoning and language are functionally and neuroanatomically independent, suggesting (a) there is a common and domain-general syntactic mechanism that underpins both language and mathematics, but that mathematical expressions can gain direct access to this system without translation into a language format, and (b) autonomous, domain-specific syntactic mechanisms exist for language and mathematics (Varley et al. 2005). Studies on sex differences provide evidence that mathematical reasoning...

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

References and Readings

  1. Geary, D. C. (1995). Reflections on evolution and culture in children’s cognition: Implications for mathematical development and instruction. American Psychologist, 50(1), 24–37.PubMedCrossRefGoogle Scholar
  2. Spelke, E. (2005). Sex differences in intrinsic aptitude for mathematics and science? American Psychologist, 60(9), 950–958.PubMedCrossRefGoogle Scholar
  3. Varley, R. A., Klessinger, N. J. C., Romanowski, C. A. J., & Siegal, M. (2005). Agrammatic but numerate. Proceedings of the National Academy of Science of the United States of America, 102, 3519–3524.CrossRefGoogle Scholar
  4. Zhou, Z. (2011). Mathematical reasoning. In J. S. Kreutzer, J. Deluca, & B. Caplan (Eds.), Encyclopedia of clinical neuropsychology. New York: Springer.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School PsychologyThe Chicago School of Professional PsychologyChicagoUSA
  2. 2.Legal Psychology (Psychology and Law), Neuropsychology, Clinical Psychology, The Chicago School of Professional PsychologyChicagoUSA