Counting Practice with Pictures, but not Objects, Improves Children's Understanding of Cardinality

Counting Practice with Pictures, but not Objects, Improves Children’s Understanding of Cardinality Lori A. Petersen (lpetersen@uchicago.edu) Department of Psychology, University of Chicago 5848 S. University Ave., Chicago, IL 60637 USA Nicole M. McNeil (nmcneil@nd.edu) Department of Psychology, University of Notre Dame 118 Haggar Hall, Notre Dame, IN 46556 USA Alice K. Tollaksen (atollaks@nd.edu) Department of Psychology, University of Notre Dame 118 Haggar Hall, Notre Dame, IN 46556 USA Alexander G. Boehm (aboehm@nd.edu) Department of Psychology, University of Notre Dame 118 Haggar Hall, Notre Dame, IN 46556 USA Casey J. Hall (chall7@nd.edu) Department of Psychology, University of Notre Dame 118 Haggar Hall, Notre Dame, IN 46556 USA Cristina Carrazza (Cristina.Carrazza.1@nd.edu) Department of Psychology, University of Notre Dame 118 Haggar Hall, Notre Dame, IN 46556 USA Brianna L. Devlin (Brianna.L.Devlin.13@nd.edu) Department of Psychology, University of Notre Dame 118 Haggar Hall, Notre Dame, IN 46556 USA Abstract When counting, the final word used to tag the final item in a set represents the cardinality, or total number, of the set. Understanding of this concept serves as a foundation for children’s basic mathematical skills. However, little is known about how the early learning environment can be structured to help children understand this important concept. The current study examined the effects of the representational status of to- be-counted items on preschoolers’ understanding of cardinality. Children (M age = 3 years, 6 months) were randomly assigned to receive counting practice with either physical objects or pictures over five practice sessions. Children’s counting skill and understanding of cardinality were assessed at pretest and posttest. Results revealed that only children in the picture condition increased their understanding of cardinality from pretest to posttest. These results suggest that picture books are better than physical objects at supporting children’s understanding of cardinality. Keywords: cognitive development; counting; learning; mathematics Counting is a foundational skill. It provides the basis for learning to add and subtract, as well as for other basic arithmetic skills (Aunio & Niemivirta, 2010; Fuson, 1988; Stock et al., 2009). According to the NCTM (2000), teaching young children to “count with understanding and recognize ‘how many’ in sets of objects” is one of the earliest ways to get them on the path toward developing a good number sense. Counting is also of theoretical interest because it is the first formal math system that young children learn, and it takes children a surprisingly long time to master it (Le Corre, et al., 2006; Sarnecka & Carey, 2008; Wynn, 1990). Research suggests that children go through a relatively predictable developmental progression as they construct an understanding of counting. First, they pass through the “one-” knower level, where they can reliably identify and give one object, but not more. Then several months later they become “two-” knowers and then “three-” knowers, and some studies have even found “four-” knowers (Le Corre et al., 2006). Finally, children become “cardinal principle” (or CP) knowers (Le Corre et al., 2006). Prior to this development, children construct understanding of the numbers “one,” “two,” and “three” quite slowly over the course of several months. In contrast, CP-knowers, seemingly all at once, develop understanding of any number