Children's Use of Structure Mapping in Numerical Estimation

Children’s use of Structure Mapping in numerical estimation Jessica Sullivan (jsulliva@ucsd.edu) David Barner (barner@ucsd.edu) Department of Psychology University of California, San Diego Department of Psychology University of California, San Diego Abstract mappings. Structure Mappings (SM), in contrast, support estimation for larger numbers, and are formed by creating a single link between the verbal and nonverbal number systems on the basis of their shared structure (Gentner & Namy, 2006; Carey, 2009; Gentner, 2010). In particular, SM requires noticing the ordinal structure of each system – e.g., that the word “fifty” comes later in the count sequence than “forty”, and should therefore be used to label larger sets. As a result, each number word mapped through SM will be mapped in relation to all other mappings in the count list. These two mechanisms make distinct predictions regarding the effects of new learning experiences on existing mappings. In the case of ALM, changes to the mapping for one number word should have little effect on the mappings of other words, since they are mapped independently. For SM, in contrast, changes to any individual mapping in the system should have consequences for all other mappings. Evidence for ALM comes from the developmental literature, where it has been shown that young children learn the referents of number words sequentially (Wynn, 1990), and that even after learning the referents of many number words, some children still fail to demonstrate a structural knowledge of the relationship between the count list and numerical magnitudes (Lipton & Spelke, 2005; Le Corre & Carey, 2008; Barth et al., 2009). Additional evidence for ALMs come from research on adults that has shown that estimates for numerical magnitudes smaller than about 20 are not influenced by misleading feedback (Sullivan & Barner, 2010). Evidence for SM also comes from multiple lines of research. First, several studies have shown that providing adults with misleading feedback about an individual mapping or about the range of magnitudes being tested shifts estimation behavior for most of the number line, and especially for large numbers (Izard & Dehaene, 2008; Sullivan & Barner, 2010). This provides evidence that SM guides the mappings of relatively large number words to ANS representations of their referents. In the absence of misleading feedback, adults’ patterns of estimation are also influenced by the distribution of numbers being estimated (Sullivan, Juhasz, Slattery, & Barth, in press), suggesting that adults dynamically adjust their mappings in response to the estimates they have already made. There is also some evidence that children use structure mappings by at least the age of 7. Thompson and Opfer (2010) found that 2 nd graders can analogically extend knowledge about numbers with a familiar range (e.g., 1-100) to perform estimates for numbers within an unfamiliar ranges (e.g., 1-10,000). Taken How do young children connect number words to the magnitudes they represent? Here, we test whether 5- to 7- year-old children, like adults, use Structure Mappings (SM) to link number words and approximate magnitudes. We show that 6- and 7-year-olds’ number line estimates are recalibrated in response to the distribution of numbers being estimated, providing evidence for SM in these older children. We also find that 5-year-olds show improved estimation performance when given visual access to their previous estimates, suggesting that, while these youngest children do not use SM in some estimation tasks, they nonetheless understand the structural relationship between the count list and approximate magnitudes. Keywords: Language acquisition, number, approximate magnitudes, word learning, number words. Introduction Beginning in infancy, humans can represent the approximate numerical magnitude of sets using the Approximate Number System, or ANS (for review, see Dehaene, 1997). Upon learning the verbal count sequence, children gain access to another way to store and manipulate numerical information—the count list. The count list is a symbolic number system that allows for the precise representation of numerical quantities. These two systems become linked to each other early in development: Children in preschool and kindergarten provide bigger estimates for larger numbers, indicating an ability to map number words onto nonverbal numerical representations (Le Corre & Carey, 2007; Lipton & Spelke, 2005; Barth, Starr, & Sullivan, 2009). However, these early mappings are not stable, and change over development. Accuracy on estimation tasks improves with age, with counting ability, and with explicit training (Siegler & Opfer, 2003; Lipton & Spelke, 2005; Booth & Siegler, 2006; Le Corre & Carey, 2007; Ebersbach et al., 2008; Barth, et al., 2009; Mundy & Gilmore, 2009; Siegler & Ramani, 2009; Thompson & Opfer, 2010). However, while much is known about the developmental trajectory of estimation ability, surprisingly little is known about the learning mechanisms that children use to construct and refine mappings between number words and approximate magnitudes. Recent research has argued that adults rely on at least two distinct mechanisms for attaching number words to magnitudes (see Sullivan & Barner, 2010, for review). Associatively Learned Mappings (ALM) involve the creation of item-by-item links between individual words and magnitudes, resulting in many mutually independent