Adaptive variability in children's conceptual models of division

Pooja G. Sidney, Julie F. Shirah, Jessica Blake, Amanda L. Kruczkowski

Research output: Contribution to journalArticlepeer-review


This study examined whether different types of commonly used mathematical tasks affect how children think about whole number division problems. Prior research suggested that children tend to rely on the partitive model to understand whole number division, which is likely problematic when students transition to learning about fraction division. We assessed variability in correct whole number division problem-solving strategies among 63 elementary school children (41.5% female, 58.5% male, 0% nonbinary/gender expansive; 69.2% White, 10.7% multiracial, 6.1% Black, 4.6% Latino, 3.3% other/unidentified, 6.1% preferred not to answer). Each participant was asked to demonstrate four whole number division problems in each of three contexts (within participants): objects, story problems, and number lines. Most children displayed understanding of multiple conceptual models of division, but strategies varied by context. Story problems elicited partitive models, number lines elicited quotative models, and objects elicited both. Finally, elementary school children used strategies adaptively. Number line representations may afford conceptual connections between earlier-learned whole number concepts and analogous later-learned fraction concepts, supporting the integration of children's whole number and fraction knowledge.

Original languageEnglish
Article number105743
JournalJournal of Experimental Child Psychology
StatePublished - Dec 2023

Bibliographical note

Funding Information:
The authors thank Caelin McManis, Sanjana Rahman, and Ashlyn Pechon for their help with strategy coding. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Publisher Copyright:
© 2023 Elsevier Inc.


  • Conceptual model
  • Mathematics development
  • Number line
  • Strategy variability
  • Whole number division

ASJC Scopus subject areas

  • Experimental and Cognitive Psychology
  • Developmental and Educational Psychology


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