Building blocks of numerical cognition: The development of quantity-space mapping

Abstract

This dissertation focused on quantity-space mapping as a building block of numerical cognition. The aim was twofold: (1) to explore the early onset and development of quantity-space mapping, and (2) to analyze the relation between quantity-space mapping and numerical cognition. Quantity-space mapping refers to the ability to associate quantities or symbolic numbers with space. Two types of quantity-space mapping were studied in this dissertation: (1) associations between ordinalities and spatial directions, as measured by block counting, adding and subtracting, and (2) associations between quantities and spatial intervals, as measured by number line estimation. Chapter 2 reported on a study on the role of hand use in mapping ordinalities to spatial directions in 3.5-year-old children. It was found that the majority of the children mapped numbers to space from right to left in the counting task, and from left to right in the adding and subtracting tasks. The change in mapping direction across tasks can be explained by physical interaction between the body and the task: the starting point of block counting, adding and subtracting direction was related to the hand used to perform the task. Chapter 3 reported on a study on ordering strategies in mapping quantities to spatial intervals in 3.5- and 5-year-old children. It was found that performance on a non-symbolic number line estimation task builds on two types of ordering strategies: local ordering and global ordering. Local ordering refers to ordering of successively presented quantities and global ordering refers to the ordering of all quantities across the number line. In Chapter 4 it was found that the early development of mapping quantities to spatial intervals acts as a building block for the development of later (early) math skills. Mapping quantities to spatial intervals at age 3.5 years was related to mapping symbolic numerical to spatial intervals and counting skills at 5 years. In contrast, quantity comparison and enumerating skills at 3.5 years could not predict early math skills at 5 years. Chapter 5 showed that mapping quantities to spatial intervals is also related to mathematical difficulties. It was found that children with mathematical difficulties are less accurate and use different reference points in symbolic number line estimation than children without mathematical difficulties. This suggests that children with mathematical difficulties have problems with dynamic spatial processing of symbolic numbers; they are not able to use accurate spatial reference points for estimation. Together, the results of this dissertation suggest that quantity-space mapping is influenced by an interplay of situated, embodied and cultural/educational processes. The development of later numerical cognition builds on this early development of quantity-space mapping.