Predictors of Success and Struggle in Mathematics: A Developmental Approach to Cognition and Affect

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Many children struggle with mathematics, and difficulties with fractions in particular can fuel anxiety, avoidance, and negative attitudes (Starling-Alves et al., 2023). These challenges often begin during primary school and, if unresolved, persist into later learning and everyday numeracy. Fraction difficulties are closely tied to mathematics anxiety: children who encounter persistent misconceptions may lose confidence, withdraw from participation, and develop lasting negative beliefs about their mathematical ability. To address these issues, we need a detailed understanding of how misconceptions and errors develop over time, how they shape children’s feelings about mathematics, and how they can best be refuted.

This PhD project will track the developmental trajectories of fraction understanding, attitudes, and mathematics anxiety across two years of primary school. It will investigate when misconceptions appear, how they change, which errors are most resistant to instruction, and how these factors interact with shifts in confidence and attitudes. A key strand of the project will involve designing and testing explanation types that directly address misconceptions, helping learners to understand both why an error occurred and how to approach the concept correctly. In addition, there will be opportunities to extend this work by examining fraction understanding, errors, and associated attitudes in adults.

The successful candidate will gain advanced training in the collection, analysis, and visualisation of longitudinal data, alongside experience working directly in school settings. They will also have the chance to collaborate internationally through the SPARK (Supporting Progress in Acquisition of Rational number Knowledge) Consortium, a global network of researchers dedicated to improving fraction learning and teaching.

Supervision will be provided by Dr Sabrina Burr and Dr Emma Blakey in the Sheffield Cognitive Development Lab. The project offers excellent opportunities for interdisciplinary training and international collaboration, equipping the candidate for a career in developmental psychology, education research, or applied intervention design.

As a member of the Sheffield Cognitive Development lab, the PhD researcher will be able to make use of our lab facilities, excellent links with local schools and families, stakeholders in the community and the expertise of the wider lab including staff and students. Please see our website for more information about the lab:

https://sites.google.com/sheffield.ac.uk/sheffieldcogdev/home