The development and assessment of counting-based cardinal number concepts

Arthur J. Baroody, Menglung Lai

Research output: Contribution to journalArticlepeer-review


The give-n task is widely used in developmental psychology to indicate young children’s knowledge or use of the cardinality principle (CP): the last number word used in the counting process indicates the total number of items in a collection. Fuson (1988) distinguished between the CP, which she called the count-cardinal concept, and the cardinal-count concept, which she argued is a more advanced cardinality concept that underlies the counting-out process required by the give-n task with larger numbers. One aim of the present research was to evaluate Fuson’s disputed hypothesis that these two cardinality concepts are distinct and that the count-cardinal concept serves as a developmental prerequisite for constructing the cardinal-count concept. Consistent with Fuson’s hypothesis, the present study with twenty-four 3- and 4-year-olds revealed that success on a battery of tests assessing understanding of the count-cardinal concept was significantly and substantially better than that on the give-n task, which she presumed assessed the cardinal-count concept. Specifically, the results indicated that understanding the count-cardinal concept is a necessary condition for understanding the cardinal-count concept. The key methodological implication is that the widely used give-n task may significantly underestimate children’s understanding of the CP or count-cardinal concept. The results were also consistent with a second aim, which was to confirm that number constancy concepts develop after the count-cardinal concept but before the cardinal-count concept.

Original languageEnglish (US)
Pages (from-to)185-205
Number of pages21
JournalEducational Studies in Mathematics
Issue number2
StatePublished - Oct 2022


  • Assessment
  • Cardinality principle
  • Counting concepts
  • Early childhood
  • Give-n task
  • Learning progression

ASJC Scopus subject areas

  • Education
  • General Mathematics


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