The Role of Complexity of Representations in Engineering Students’ Engagement With a Mathematical Content: A Case Study of Eye-Tracking
摘要
Representations play a crucial role in the process of learning and communicating mathematics. Each representation carries its own inherent complexity, which can pose challenges for students as they engage with mathematical documents. The interest of the present case study is to explore how two engineering students attend to different representations (texts, figures, and formulae) of varying estimated complexity when engaging with the concept of double integrals. Eye-tracking methodology, combined with two interviews, was used to investigate students’ engagement with the topic. Their eye movement patterns were analysed in relation to the complexity of the representations, as judged by two experts, and triangulated with their self-reported experiences. In addition, a written test was administered to assess their understanding of the topic. The results suggest that both students’ engagement with figures was closely related to their estimated complexity, with longer fixations on more complex figures, though with some variations. In contrast, their engagement with texts and formulae did not align with the estimated complexity but instead reflected selective attention, as noted by the students in the interviews. Test results further revealed that this pattern of engagement was associated with a primarily procedural understanding of double integrals and difficulties conceptualizing their relation to Riemann sums. The study contributes to a more nuanced understanding of how students attend to mathematical representations of varying complexity, offering insights for both research and instructional practice.