Children's Learning of the Compositional Number System

Abstract

The compositional system of natural numbers underlies our abilities to measure time, use money, and represent quantities. In the present dissertation, I examined how children master the compositional number system by (i) investigating the challenges that they face in learning it and (ii) evaluating game-based interventions to discern causal impacts of representations that facilitate their learning. In Chapter 2, I provide evidence using home-based games that training children’s innate numerical concepts does not support their learning of the symbolic number system taught in school. In Chapter 3, I provide evidence using cross-linguistic comparisons that the degree of transparency of number words in making the compositional rules of the number system explicit (e.g., “eleven” in English that translates to “ten one” in Mandarin) affects children’s counting skills. However, mastering the compositional number system is hard for children even when their language’s number words reveal its logic more transparently. In Chapters 4 and 5, I provide evidence using home-based games that training children’s understanding of the base-10 compositional number system, using multiple representations, successfully enhances their learning of it and the numerical concepts it supports. Crucially, some games in this dissertation were evaluated as a part of multifaceted school-based interventions that had distinct impacts on children’s math learning. This dissertation evaluated different components of the multifaceted interventions that could have accounted for their success. Together, this dissertation sheds light on children’s learning of the compositional number system and highlights the importance of smallscale home-based interventions conducted in synergy with large-scale school-based interventions to deepen our understanding of how children learn in their real-world environments.