Subdomains of early number sense and their relation to mathematics learning and achievement

Abstract

Early understanding of number, number relations, and number operations helps to set children’s learning trajectories in mathematics throughout the elementary years (Jordan et al., 2009). The present dissertation includes three studies that probed young children’s understanding of the interrelated subdomains of number sense and their relation to mathematics learning. In the first study, cross-sequential samples of pre-K, kindergarten, and first-graders (n =150 at each grade level) were assessed on their knowledge of number, number relations, and number operations and formal mathematics achievement a year later. Multiple regression analyses demonstrated that all subdomains of number sense explained a significant amount of variance in future mathematics achievement at each grade level when controlling for the other subdomains and background variables. However, unconditional quantile regression analyses showed that the relative predictive relationships were sometimes contingent upon level of mathematics achievement. ☐ The second study explored pre-K children’s (N = 48) understanding that numbers can be broken apart into smaller number partners using two domino tasks in varying contexts of representation and set size. Items with non-symbolic referents and smaller set sizes were easier for children than those with symbolic referents and larger set sizes. Increased accuracy on number partners tasks was associated with increased age, suggesting that number partners understanding is developing during the pre-K year. Furthermore, identifying non-symbolic number partners for a target value was related to conventional arithmetic knowledge. Future work is needed to assess these relationships in a population of children from a wider array of SES levels and ethnic diversity. ☐ The third study was aimed at exploring how the children in Study 2 (N = 46) used the number subdomain abilities of counting and subitizing as strategies for identifying non-symbolic number partners. Children adaptively used observable counting strategies to identify larger partners. Within-child comparisons of accuracy and strategy-use suggested that number partners identification may develop before symbolic addition skill, but future research is needed to unpack the relationship between the two abilities. ☐ The findings of these studies highlight the importance of all three subdomains of early number sense for mathematics achievement outcomes and add to knowledge of how specific number competencies relate to each other in the early years. This research lays important groundwork for the future development of number sense instructional activities for the pre-K classroom. That is, learning more about what children know about number and how it relates to later achievement can help guide the creation of activities that build meaningful knowledge of number from the very start.