Cardinality principle understanding: the role of focusing on the subitizing ability

Veena Paliwal, Arthur J. Baroody

Research output: Contribution to journalArticlepeer-review


The cardinality principle (CP) is a conceptual basis of counting collections meaningfully and provides a foundation for understanding other key aspects of numeracy, such as the successor principle or counting-on to determine sums. Unfortunately, little research has focused on how best to teach the CP. One suggestion is that modeling the CP should be done with small collections children can subitize—that is, immediately recognize the total without counting. The present study was designed to investigate the following key, not fully resolved, questions: Is subitizing level associated with CP knowledge and is a particular level of subitizing critical for achieving the CP? Does fostering children’s subitizing ability improve CP knowledge? Which approach to modeling the CP with subitizable collections is most efficacious in promoting the CP and its transfer? Eighty 2- to 5-year-old participants first received instruction designed to promote the ability to subitize collections from 1 to 5. Subitizing instruction alone resulted in 31 participants learning the CP. The remaining 49 participants were randomly assigned to one of three CP interventions: count-first, label-first, and count-only. All interventions involved collections participants could subitize. Results revealed that the participants who could subitize at least three achieved partial success on the CP task. Those who could subitize four and were in the count-first intervention achieved general success on the CP task. The findings underscore the need for early childhood educators and parents to build on subitizing ability to teach the CP.

Original languageEnglish (US)
Pages (from-to)649-661
Number of pages13
JournalZDM - Mathematics Education
Issue number4
StatePublished - Aug 1 2020


  • Cardinality principle
  • Early numeracy
  • Meaningful counting
  • Subitizing

ASJC Scopus subject areas

  • Education
  • General Mathematics


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