Development of Mathematical Understanding

Cognition, Perception, and Language

4. Conceptual Understanding and Achievements

  1. David C. Geary

Published Online: 1 JUN 2007

DOI: 10.1002/9780470147658.chpsy0218

Handbook of Child Psychology

Handbook of Child Psychology

How to Cite

Geary, D. C. 2007. Development of Mathematical Understanding. Handbook of Child Psychology. II:4:18.

Author Information

  1. Department of Psychological Sciences, University of Missouri, Columbia, Missouri, USA

Publication History

  1. Published Online: 1 JUN 2007


The chapter reviews research on infants' and children's developing mathematical competencies—from the ability to determine sizes of small sets to the solving of word problems. A brief summary of the history of research in the area is provided in the first section, and reviews of contemporary research are provided in the second section. The latter includes reviews of research and debate on infants' and preschool children's early quantitative abilities. These include infants' sensitivity to the quantity of sets of objects and sensitivity to additions and subtractions from these sets. Debates revolve around whether these abilities are primarily quantitative and whether they are inherent. The review in the second section continues with preschool children's emerging counting competencies and their application of these in contexts that involve simple arithmetic. Next, children's developing mathematical competencies in school are reviewed. The topics include arithmetic concepts, base-10 knowledge, fractions, estimation, arithmetical operations, and arithmetical problem solving. The second section concludes with discussion of potential mechanisms of change, that is, the mechanisms that underlie developmental and school-based learning in these quantitative areas, although the presented model is potentially related to change in other domains. The discussions include consideration of potentially evolved as well as culturally specific areas of mathematical competency and development.


  • arithmetic;
  • culture;
  • evolution;
  • mathematical development;
  • problem solving;
  • quantity