Children’s early understanding of the successor function

<p dir="ltr">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.<br><br><b>Non-Technical Summary</b></p><h4><b>Background</b></h4><p dir="ltr">Learning the meaning of the number system is a challenge for young children. They must discover how counting gives information about the number of objects in a set (cardinal principle) and how adding one item to a set is associated with moving one place along the count sequence (successor function).</p><h4><b>Why was this study done?</b></h4><p dir="ltr">Learning this takes many months and the processes which underlie it are as yet unknown. We developed a new task that sheds light on this development.</p><h4><b>What did the researchers do and find?</b></h4><p dir="ltr">Three- and four-year-old children were asked to create sets of different numbers of objects in two conditions. In one version of the task children could see the whole set of objects at the same time and this gave us insight into children’s understanding of the cardinal principle. In the other version they could only see one object at a time and this gave us insight into children’s understanding of the successor function. We found that most young children’s understanding of the cardinal principle and the successor function were equivalent. In other words, if they could create a set of up to two objects when the objects were visible then they could also create a set of up to two objects when they could only see one at a time.</p><h4><b>What do these </b><b>findings</b><b> mean?</b></h4><p dir="ltr">This suggests that understanding of cardinality is not a pre-requisite of understanding the successor function and that learning the meaning of the number system is a continuous and progressive process.</p>