Predictors of children's mathematical achievement: the role of the number line estimation task

Low levels of mathematics proficiency can have negative consequences at a personal and societal level. Given these negative effects, preventing poor mathematical proficiency is crucial. Mathematics learning difficulties are one of the reasons that can lead to low mathematics proficiency. Thus, the early identification of children presenting with mathematics learning difficulties and subsequent provision of additional supports are essential to ensure that children achieve their best possible learning outcomes. The overall aims of this thesis are to identify a domain-specific mathematical skill that best predicts later mathematics achievement (Aim 1) and understand how this skill relates to more complex mathematical skills (Aim 2).

In line with the first aim, a meta-analysis was conducted to identify which domain-specific skills in the first year of formal schooling can predict achievement in mathematics during the primary school years (Chapter 2). The meta-analysis was conducted to facilitate the selection of the specific mathematic skill that would be the focus for the remaining studies. However, inconclusive findings from this study meant that it was unreliable for this purpose. Other sources of information were used and led to choosing the number line estimation task as a good candidate for early identification (i.e., universal screening). The selection of the number line estimation task led to the further specification of the second aim into three specific aims: a)explore the relationship between performance on the number line estimation task and othermathematical skills in typically developing children, b) better understand how performance on the number line estimation task relates to growth in mathematical skills for children at risk of mathematics learning difficulties, c) explore the nature and mechanisms underlying the relationship between performance on the number line estimation task and other mathematical skills.

To address the first specific aim, Chapters 3 and 4 present studies based on secondary data analysis of a sample of Singaporean children in their last year of kindergarten. Chapter 3 uses a quantile regression approach to scrutinise the relationship between accuracy on the number line estimation task and mathematical reasoning. Chapter 4 analyses the patterns followed by children’s estimates on the number line task, and analysis of variance is used to determine their relationship to children’s mathematical performance.

To address the second specific aim, Chapter 5 presents a study based on secondary data analysis of a sample of Singaporean children who had been identified as being at risk of mathematics learning difficulties. The study explores the relationship between number line estimation (i.e., accuracy and estimation patterns) and mathematical achievement across the first two years of primary school using latent growth curve models and Bayesian analysis of covariance.

Finally, to address the third specific aim, Chapter 6 presents a multiple baseline case series design to examine the effect and mediators of a number line intervention on the calculation skills of Australian first grade children struggling with mathematics. The rationale for the study and the methodological design are presented. However, data collection could not be completed within the thesis timeframe.

The findings from this thesis support the number line estimation task as a possible candidate for the early identification of children with mathematics learning difficulties. The findings highlight that accuracy on the number line task predicts concurrent mathematical reasoning across the achievement spectrum, as well as growth in some mathematical skills for children at risk of presenting mathematics learning difficulties. Nonetheless, the findings from this thesis also highlight the need for a better understanding of some features of the number line task (e.g., the role of the number range, the fitting and interpretation of estimation patterns) before it can be fully implemented in the context of early identification.