How Students 'See' Boxplots: New Evidence for Extrafoveal Information Processing

Boxplots are powerful statistical representations—but they are also notoriously difficult to learn. A well-documented issue is that students often rely on misleading heuristics, such as treating the box area as proportional to frequency. Eye-tracking research has begun to uncover why such errors occur by examining how students visually process boxplots. In our new paper in ZDM – Mathematics Education, we investigated a question that has so far received little attention: Do students sometimes process key boxplot features simultaneously, using extrafoveal vision?

Have a look at the paper, written by Martin Abt, Anselm Strohmaier, myself, and Wim Van Dooren, at: https://doi.org/10.1007/s11858-025-01758-0

To explore this, we presented university students with comparison tasks involving boxplots in two visual arrangements: a stacked layout with close spatial proximity, and a diagonal layout with larger distances between features. Based on eye-tracking scenes such as those in the paper, we analyzed transitions and fixations on schema-relevant areas—medians, quartiles, and critical values.

Our goal: to determine whether close proximity supports simultaneous perception of information.

The results show clear evidence for this in the median schema: when boxplots appeared close together, students made fewer transitions and fewer fixations on the medians, indicating that they were able to perceive both medians at once. This supports the idea that learners do not always process statistical graphics sequentially—sometimes they take in relational information holistically.

For the box schema, findings partially aligned with this pattern; for the area schema, no signs of extrafoveal processing emerged. Together, these patterns suggest that lines (like quartiles and medians) may be processed extrafoveally, whereas areas may not—an insight with methodological and instructional implications.

These findings highlight that the spatial arrangement of statistical graphics can shape how students extract information. This matters not only for interpreting eye-tracking studies but also for instructional design: layout choices may support or hinder learners’ conceptual understanding of variability and distribution. By better understanding how students perceive visual information, we can design statistical representations—and learning environments—that make complex ideas more accessible.