Persistence, context, and visual strategy of graph understanding: Gaze patterns reveal student difficulties in interpreting graphs

Linear functions are an essential part of school and university education. Nevertheless, this topic is challenging for many students—especially in STEM topics. In this article, we contribute to the understanding of learning difficulties in the context of mathematical and physical problems. Here, we present the results of an eye-tracking study on visual attention during the interpretation of linear graphs using the gaze-cued retrospective think-aloud (RTA) method. Gaze data of $N=131$ and interview data of $N=60$ grammar school students were recorded while solving items of a validated test instrument: pairs of items in a mathematical and kinematic context that are isomorphic, i.e., have similar surface features and require the same procedure to solve. We will show that the difficulties in interpreting the kinematic diagrams, which have already been identified in 9th-grade students, are still present in students in the entry phase of the upper secondary level. Further, students’ eye-tracking behavior differs significantly between mathematical and kinematic contexts. Triangulation of eye-tracking data with RTA data reveals context-dependent solution strategies—transfer from mathematics to physics is a major problem for students.

Figure 1

Isomorphic item pair no. 8 (IP8) from the original test instrument; on the left: mathematical context (M8), on the right: kinematic context (K8).

Figure 2

Positioning of the AOIs for the mathematics item M8 (left) and the kinematics item K8 (right).

Figure 3

Comparison of item difficulty level $P$ of all item pairs (IP) in the test instrument.

Figure 4

Exemplary gaze plots of one and the same student for the mathematical item (M8, left) and the kinematic item (K8, right). The circle with numbers (1, 2, 3, 4…) indicates the order of observation, i.e., where the student looked first (1), subsequently (2), and so on, until the position where the student looked last.

Figure 5

Diagram area of item K8 divided into AOIs 1–9. AOIs with significantly longer TVDs in item M8 than item K8 are marked in blue. AOIs with significantly longer TVDs in item K8 than item M8 are marked in red. Dotted lines indicate transitions between AOIs that appear significantly more often in item K8 than in the similar counterpart.

Figure 6

Frequency of solution strategies in the mathematics (M) and kinematics (K) context for item pair no. 8. The strategies “no strategy” (no strtg), “quot axis intercept” (quot axis int), “slope triangle,” and “other” were coded in the participants’ interview data.