Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article


Doctor of Philosophy




Ansari, Daniel


The principal aim of this thesis was to examine the correlates of children’s math achievement. Studies 1 and 2 provided insights regarding the relation between children’s learning of symbolic numbers and math achievement. Study 3 examined the relation between math anxiety and math achievement.

There is currently significant debate regarding the role that the approximate, non-verbal number ability (approximate number system) plays in the development of children’s understanding of symbolic numbers. In particular, there exists much discussion regarding whether children’s approximate number ability predicts later symbolic number ability (the mapping account) or the other way around (the refinement account). Study 1 compared the theoretical predictions of these two developmental accounts over three timepoints in children from senior kindergarten to grade 1 (N=622). Results suggest that symbolic number ability consistency predicts later approximate number ability and math achievement, supporting the refinement account.

Emergent research findings suggest that there may be heterogeneity in the developmental trajectory children undergo when learning symbolic numbers. Study 2 examined the degree to which the theoretical predictions laid out by the mapping and refinement accounts adequately describe the whole population using the same sample as in study 1. Results suggest that children’s developmental trajectories are remarkably homogenous, however, there is considerable heterogeneity regarding the speed in which children progress through levels of development. Taken together, results from studies 1 and 2 suggest that the refinement account best describes children’s symbolic number development, and that a vast majority of students follow the same developmental path.

Using three international studies of student achievement, study 3 uses multilevel modelling to examine the degree to which the level of math anxiety in children’s immediate cultural and educational contexts could predict their math achievement over and above their own math anxiety. Results suggest that math anxiety in the education environment predicts math achievement. However, there are significant between-country differences in the strength of this contextual effect of math anxiety. These results bring into question the generalizability of existing research findings and suggest that children’s cultural and educational contexts must be taken into account for a complete description of the relation.

Summary for Lay Audience

Math achievement in early childhood has been shown to be an important factor for success in school, career advancement, and overall well-being. Consequently, there is great interest in understanding the underlying factors that contribute to improving children’s math achievement. The current thesis contributes to this goal by examining two factors that affect math achievement: 1) the process in how children initially learn numerical symbols (e.g., Arabic numbers, spoken numbers, etc.), 2) children’s anxiety towards doing math problems.

Research over the past decades has revealed that, even as infants, children possess an innate cognitive system that can perceive numerical quantities (approximate number system). Using data from 622 children, study 1 investigates whether children’s approximate number system predicts their understanding of numerical symbols, or is it the other way around. Results suggest that increased understanding in children’s understanding of numerical symbols not only refines and improves children’s approximate number system, but also predicts math achievement.

Study 2 examines the degree to which all children (or only some groups of children) undergo the developmental process as described in Study 1. Results indicate that virtually all children undergo the same developmental process, but they progress through these developmental levels at different speeds. Together, results from studies 1 and 2 suggest that recognizing and using symbolic numbers is an important skill that predicts future math achievement, and virtually all children undergo the same developmental process.

Using three international studies of achievement, study 3 asks whether anxiety towards mathematics in one’s peer group could affect one’s math achievement. In other words, this study asks whether there would be a difference in a child’s math achievement if his or her classmates have high average math anxiety versus low average math anxiety. Results suggest that higher levels of peer’s math anxiety are associated with a reduction in one’s own math achievement. However, this effect is only observed in approximately half the countries. This research inspires future studies to examine why there might be these between-country differences.

Together, the current thesis provides new insights into the ways different early childhood factors contribute to influencing children’s math achievement.

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Available for download on Tuesday, August 01, 2023