Experts' structuring processes of equations that can be solved with varying efficiency: An analysis of gaze paths with eye-tracking

Solving equations is fundamental to algebra yet remains a persistent challenge in mathematics teaching and learning. Drawing on a semiotic-pragmatic framework, we argue that algebraic equations lack inherent structure; instead, solvers must actively impose their own personal structure, a process known as 'structuring'. Using eye-tracking, we analysed gaze patterns of student teachers solving equations with varying efficiency. Adaptive experts showed global relating, characterised by rapid transitions between subexpressions of both sides of the equation, and hierarchical structuring, enabling faster solutions. In contrast, routine experts exhibited local relating, marked by sequential processing, longer fixations and increased cognitive load, leading to slower and less accurate performance. These findings provide insights into the cognitive strategies of equation solving and offer implications for instructional approaches that promote more effective equation solving.