Children’s early understanding of the successor function

Children learn the cardinalities of the first numbers one, two, three and four before they learn how counting tracks cardinality for all numbers. It may be that when children start to understand counting, they also discover how numbers relate to one another in a structured number system. Do children who understand that the cardinality of a set is the last number assigned after counting each item (cardinal principle knowledge) also understand that each number represents the cardinality of the set created by adding one to an empty set for every count it takes to reach that number (a recursive understanding of the successor function)? We tested this by assessing children’s early recursive understanding of the successor function in relation to their cardinality knowledge. Children who were not yet cardinal principle knowers already demonstrated a recursive understanding of the successor function within the limits of their cardinality knowledge. Our findings suggest that children have some structural knowledge of the number system before learning how counting tracks cardinality. We discuss how continued counting practice may eventually allow children to expand this knowledge across all numbers.