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Related Experiment Video

Updated: Aug 30, 2025

Quantifying Learning in Young Infants: Tracking Leg Actions During a Discovery-learning Task
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Counting many as one: Young children can understand sets as units except when counting.

Theresa Elise Wege1, Bert De Smedt2, Camilla Gilmore1

  • 1Centre for Mathematical Cognition, Loughborough University, Loughborough LE11 3TU, UK.

Journal of Experimental Child Psychology
|September 1, 2022
PubMed
Summary

Young children often miscount sets by focusing on individual items instead of the set itself. This study shows that a developing understanding of counting principles, not just set identification, contributes to this common childhood counting error.

Keywords:
Abstraction principleCountingCounting principlesEarly learningNumerical cognitionUnitizing

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Area of Science:

  • Developmental Psychology
  • Cognitive Science
  • Early Childhood Education

Background:

  • Children commonly err in counting when presented with sets of items, often counting discrete elements instead of the sets.
  • Previous explanations suggest this error stems from an incomplete understanding of what constitutes a countable unit.
  • This points to a potential gap in children's conceptualization of units and their ability to abstract.

Purpose of the Study:

  • To investigate whether children's understanding of counting principles, beyond set identification, contributes to errors in counting sets.
  • To examine the role of the abstraction principle of counting in young children's counting mistakes.
  • To identify specific cognitive factors underlying the common error of counting discrete items instead of sets.

Main Methods:

  • An experiment was conducted with 4- and 5-year-old children (N=43).
  • Children's abilities to name sets, group items into sets, and establish one-to-one correspondences were assessed.
  • Performance was evaluated on tasks requiring the counting of sets as single units.

Main Results:

  • A significant number of children, despite successfully naming sets, grouping items, and creating correspondences, struggled to count sets as units.
  • This indicates that proficiency in set manipulation does not guarantee the ability to count sets abstractly.
  • The findings highlight a disconnect between set awareness and the application of counting principles.

Conclusions:

  • A nascent understanding of the abstraction principle of counting is a key factor contributing to children's errors when counting sets.
  • Children's difficulty lies not only in identifying units but also in applying abstract counting rules to these units.
  • Interventions should focus on developing children's understanding of abstract counting principles to address this common developmental error.