Eye-Tracking Data in the Exploration of Students' Engagement with Representations in Mathematics: Areas of Interest (AOIs) as Methodological and Conceptual Challenges.

In mathematics, and in learning mathematics, representations (texts, formulae, and figures) play a vital role. Eye-tracking is a promising approach for studying how representations are attended to in the context of mathematics learning. The focus of the research reported here is on the methodological and conceptual challenges that arise when analysing students' engagement with different kinds of representations using such data. The study critically examines some of these issues through a case study of three engineering students engaging with an instructional document introducing double integrals. This study reports that not only the characteristics of different types of representations affect students' engagement with areas of interests (AOIs), but also methodological decisions, such as how AOIs are defined, will be consequential for interpretations of that engagement. This shows that both technical parameters and the inherent nature of the representations themselves must be considered when defining AOIs and analysing students' engagement with representations. The findings offer practical considerations for designing and analysing eye-tracking studies when students' engagement with different representations is in focus.