Conceptual Correlates of Counting: Children’s Spontaneous Matching and Tracking of Large Sets Reflects Their Knowledge of the Cardinal Principle


  • Anna Shusterman
  • Pierina Cheung
  • Jessica Taggart
  • Ilona Bass
  • Talia Berkowitz
  • Julia A. Leonard
  • Ariel Schwartz


The acquisition of counting is a major milestone for children. A central question is how children’s non-verbal number concepts change as they learn to count. We assessed children’s verbal counting knowledge using the Give-N task and identified children who had acquired the cardinal principle (Cardinal Principle Knowers, or CP-knowers) and those who had not (Subset-Knowers, or SS-knowers). We compared their performance on two tests of nonverbal numerical cognition. We report comparable performance between SS- and CP-knowers for matching and tracking small sets of objects up to four, but disparate performance for sets between five and nine, with CP-knowers outperforming SS-knowers. These results indicate that the difference between CP- and SS-knowers extends beyond their knowledge of the verbal number system to their non-verbal quantitative reasoning. The findings provide support for the claim that children’s induction of cardinality represents a conceptual transition with concurrent, qualitative changes in numerical representation.