Make it count! Numerical development and the role of working memory

Abstract

Numbers play an important role in our lives. They are used to specify times, in planning activities, in money transfers and are intertwined with our daily activities. Therefore, it is important for children to understand the number words and number symbols that are so overwhelmingly present in their lives. Children have to learn that number symbols (‘3’) equal number words (‘three’) and that both match a set of objects (‘***’). These number-to-quantity connections are an important prerequisite of math performance. It has been frequently shown that the ability to solve addition or subtraction problems arises from the ability to understand that numbers are connected to a specific quantity. Not only in basic math skills but also in more advance math problems (for example in fractions) it has been shown that number-quantity connections play an important role. Little is known, however, about the development of number-to-quantity connections and important precursors. The aim of this dissertation was to unravel the processes that contribute to the development of number-to-quantity mapping skills. In this dissertation, the ability to make connections between number symbols and their corresponding quantities is referred to as ‘mapping’. According to a widely shared view, mapping skills originate from a specialized cognitive system in which numbers and the quantities they denote are spatially ordered from left to right with smaller quantities associated with the left side of the space and larger quantities with the right side of space, often referred to as the ‘mental number line’. It is assumed that this spatial ordering becomes more precise during development (Booth & Siegler, 2006; Durand, Hurme, Larkin, & Snowling, 2005; Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007; Holloway & Ansari, 2009; Siegler & Booth, 2004). An important debate in the recent literature concentrates on the origins of the spatial ordering of numbers and quantities. Some authors assume that the spatial ordering is a highly domain-specific phenomenon that is based on an innate system specifically dedicated to processing approximate non-symbolic quantity information (Dehaene, Bossini, & Giraux, 1993; Wood, Willmes, Nuerk, & Fischer, 2008). Others, however, suggest that a domain-general system for processing spatial information provides the fundament for the spatial representation of numbers and quantities (Henik, Leibovich, Naparstek, Diesendruck, & Rubinsten; 2011). In addition, several studies demonstrate that culturally acquired skills such as counting help children to order their knowledge about quantities, which eventually gives rise to the development of mapping skills (Helmreich et al., 2011; Noël & Rouselle, 2011; Opfer & Furlong, 2011). The present dissertation contributes to this debate by examining the longitudinal relations between mapping skills and domain-specific and domain-general precursors. The results of the different studies provide evidence consistent with the presupposition that mapping skills are not founded on an innate domain-specific system for ordering of quantities. Rather, the results suggest that mapping skills arise from the interplay of a domain-general ability for processing visual-spatial information and acquired symbolic skills that result from cultural learning, more specifically from-learning the verbal counting sequence