Eye-Tracking Insights into Students' Cognitive Processes when Interpreting Graphs in Real-World Contexts

The digital age is characterized by the ubiquity of large and complex data sets. Graphs are a powerful means of making data and the underlying phenomena from economics, the environment, society, and other areas of life accessible. The interpretation of graphs is therefore a key ability for meeting the demands of the digital age. However, research findings show that interpreting graphs requires complex cognitive processes and poses considerable difficulties for learners. Typical errors, such as the graph-as-picture error, or difficulties such as establishing the connection between the data and the real-world context, illustrate that the cognitive processes involved in interpreting graphs with real-world reference, called contextual graphs, have not yet been sufficiently investigated and understood.
This thesis, therefore, examines how learners interpret contextual graphs based on selected aspects. Eye tracking is used as a research method. Eye tracking has proven beneficial in mathematics education research because it can provide insights into cognitive processes during task completion, especially when working with representations. At the same time, however, previous research has shown that the interpretation of eye movements is methodologically challenging. Another aim of this work is therefore to identify the potential of eye tracking as a methodological tool in the domain of graph interpretation.
To address these aims, two studies were conducted: a methodologically oriented case study with two university students and an empirically oriented main study with nineteen ninth-grade students. In both studies, participants worked on tasks to interpret graphs in different contexts. These covered various requirement levels, and some addressed typical errors and difficulties. The participants’ eye movements were recorded while they worked on the tasks. Finally, stimulated recall interviews were conducted in which they were asked to explain their cognitive processes during the original task situation using a video showing their eye movements and containing all their utterances.
The two studies have resulted in five publications so far: the three journal articles and two conference papers are presented and summarized in this dissertation. Furthermore, their connection is explained based on three overarching research questions.
To integrating these publications in a coherent manner and interpreting their findings with regard to the three overarching research questions, the thesis first addresses the theoretical and methodological foundations underlying the analysis of eye-movement data. Central to the latter discussion is the eye-mind hypothesis, which is a widely used as a theoretical basis for interpreting peoples’ gaze behavior. Its applicability to the domain of graph interpretation is critically discussed in this thesis. It shows the extent to which eye movements actually correspond to cognitive processes, what eye movement patterns are typical for certain task levels, and what cognitive processes they indicate. This research thus contributes to increasing the validity of gaze data interpretation. The papers also illustrate how eye movements can be used to characterize the approaches used by students when interpreting contextual graphs. In addition, the sub-studies present different, partly novel analysis methods that address existing interpretative challenges and open up new possibilities for gaining insights into how learners interpret contextual graphs.
Regarding the interpretation of contextual graphs, the work provides in-depth insights into two selected aspects. First, it identifies the approaches that students use when they capture the change in graphs, as well as key factors influencing the use of different approaches. Second, a model is developed and applied that categorizes the approaches used when comparing graphs with realistic images–a task in which the graph-as-picture error occurs particularly frequently. The findings revealed causes of this widespread error, which also opened up starting points for individual support for students. In addition, the role of the real-world context in the interpretation of graphs is determined in more detail, which has proven to be a significant influencing factor in the use of different approaches.
Overall, this work not only contributes to the methodological advancement of eye tracking in mathematics education research and demonstrates the potential of the method, particularly in the domain of graph interpretation, but also deepens the understanding of the cognitive processes underlying the interpretation of contextual graphs. The findings show which approaches are used for different types of tasks, which factors influence them, and how widespread errors such as the graph-as-picture error arise. The thesis thus provides new empirically based insights into the particular challenges of interpreting contextual graphs and the role of real-world context, and thus opens up opportunities for individual student support in the classroom and valuable further research.