Linear Numerical Magnitude Representations Aid Memory for Single Numbers

Linear Numerical Magnitude Representations Aid Memory for Single Numbers Christopher J. Young (young.1202@osu.edu) Francesca E. Marciani (marciani.2@osu.edu) John E. Opfer (opfer.7@osu.edu) Department of Psychology, The Ohio State University, 1835 Neil Ave., 245 Psychology Building Columbus, OH 43210, USA Abstract important finding in this research is that the number of digits that can be accurately recalled at age 2 years is about 2, at age 5 about 4, at age 10 about 5, and among adults about 7 (+/- 2). Memory for numbers improves with age and experience. One source of this improvement may be children’s learning linear representations of numeric magnitude, but previous evidence for this hypothesis may have confounded memory span with linear numerical magnitude representations. To obviate the influence of memory span on numerical memory, we examined children’s ability to recall a single number after a delay, and the relation between recall and performance on other numeric tasks. Linearity of numerical performance was consistent across numerical tasks and was highly correlated with numerical memory. In contrast, recall of numeric information was not correlated with recall of colors. Results suggest that linear representations of numeric magnitudes aid memory for even single numbers. Representational Change Account Keywords: number representations; numerical estimation; memory Introduction Both in school and everyday life, children are presented with a potentially dazzling succession of numbers that they must remember. Some numbers must be remembered exactly, such as phone numbers and the answers to arithmetic problems (6 X 8 = 48). Others only need to be remembered approximately, such as the number of children in one’s class, the amount of money in one’s piggy bank, or the temperature forecast for tomorrow’s weather. When confronted with a series of numbers in either type of situation—e.g., a digit span task (Dempster, 1981) or a vignette (Brainerd & Gordon, 1994)—children’s memory for numbers is much poorer than adults’, and it improves greatly with age and experience. In this paper, we examine two theories attempting to explain this improvement in numerical memory—the working memory theory and the representational change theory—ancome d report on a novel memory task (memory for single numbers) that allowed us to test their predictions. Another proposal for the source of improvements in numerical memory came from a recent study by Thompson and Siegler (2010). They proposed that poor recall of numerical information could be partly traced to children’s developing representations of numerical magnitudes. Specifically, children’s representations of the magnitudes of symbolic numbers appear to develop iteratively, with parallel developmental changes occurring over many years and across many contexts (Opfer & Siegler, in press). Early in the learning process, numerical symbols are meaningless stimuli for young preschoolers. For example, 2- and 3-year- olds who count flawlessly from 1-10 have no idea that 6 > 4, nor do children of these ages know how many objects to give an adult who asks for 4 or more (Le Corre et al., 2006). As young children gain experience with the symbols in a given numerical range and associate them with non-verbal quantities in that range, they initially map them to a logarithmically-compressed mental number line (see Figure 1). Over a period that typically lasts 1-3 years for a given Working Memory Account There are at least two potential explanations for age- related improvements in children’s memory. The first proposal is that numerical information is better retained as children age because children’s working memory also improves, thereby leading to better verbatim memory for numerical information when more than one number is presented sequentially (Dempster, 1981). This idea has been highly influential, and it has led to the digit span task being used widely as a measure of working memory span. An Figure 1. Depiction of a logarithmically-compressed mental number line. Within this representation, differences among numeric values are represented as a function of the difference in the logarithms of the numbers to be represented. Thus, differences between 1 and 2 seem larger than between 5 and 6.