Making sense of numbers: early mathematics achievement and working memory in primary school children

Abstract

This dissertation aimed to investigate symbolic and non-symbolic number sense in relation to each other, to working memory, and to mathematics performance through the testing of (longitudinal) associations and training effects. These aims were achieved through a series of eight studies, with four different methodologies: meta-analyses aggregated previously reported associations between constructs and explored sources of variation. Short studies indexed the factor structure of number sense and the predictive role of working memory for number sense. Longitudinal studies were used to model development of number sense and mathematics performance, and explore the dynamic pattern of reciprocal associations. Training studies, finally, were used to investigate which assets of number sense and working memory could be trained, and how this impacted related constructs. The dissertation allows three main conclusions to be drawn. First, working memory capacity can be used to predict both number sense and formal mathematical skill, as evident from the reported meta-analyses, but the contribution of various working memory components differs depending on the domain of numerical skills assessed, the way in which working memory is assessed, and various other methodological decisions. Second, number sense can be divided into symbolic number sense (working with verbal and written number symbols) and non-symbolic number sense (working with quantities such as dots and line lengths), both of which are predictive of skill growth in number sense at a later age. Both factors can be predicted using concurrent working memory measures, but not by the same sets of working memory components. Symbolic and non-symbolic number sense are affected by training activities in discordant ways: symbolic number sense can be trained effectively in kindergarten, but there is only limited support for the notion that non-symbolic number sense van be trained in a similar way. Third, number sense is a consistent predictor of mathematical skill, but this relation is bidirectional: although number sense measures at one point in time can predict mathematics performance at a later point in time, mathematics performance can also predict number sense longitudinally. This indicated that insights associated with mathematics performance can be used to fine-tune a child’s understanding of number. Recommendations for future research include in increased focus on the dynamic relations between number sense, mathematics achievement, and working memory, more specific scrutiny of the roles of non-symbolic and symbolic number sense as latent constructs, and investigation of the relative merits of training specific assets of number sense, rather than the overarching skill. In sum, this dissertation contributes in an important way to current understandings of children’s number sense, its relations to mathematics and working memory, and the possibilities to facilitate these skills at an early age.