Student understanding of graph slope and area under a graph: A comparison of physics and nonphysics students

Previous studies have identified physics students’ difficulties with graph slope and area under a graph in different contexts. In this study we compared physics and nonphysics (psychology) students’ understanding of graphs; i.e., we evaluated the effects of concept (graph slope vs area under graph), type of question (qualitative vs quantitative), and context (physics vs finance) on their scores, strategies, and eye-tracking data. All students solved questions about graph slope better than the questions about area under a graph. Psychology students scored rather low on the questions about area under a graph, and physics students spent more time on questions about area under a graph than on slope questions, indicating that understanding of area under a graph is quite a difficult concept that seems unlikely to develop spontaneously. Generally, physics students had comparable scores on the qualitative and quantitative questions, whereas psychology students solved qualitative questions much better. As expected, students’ scores and eye-tracking measures indicated that problems involving physics context were easier for physics students since they typically had higher scores and shorter total and axes viewing times for physics than finance questions. Some physics students may have transferred the concepts and techniques from physics to finance because they typically scored better than psychology students on the finance questions that were novel for both groups. Analysis of student strategies showed that physics students mostly relied on strategies learned in physics courses, with strong emphasis on the use of formulas, whereas psychology students mostly used common-sense strategies, as they did not know the physics formulas. The implications of the results for teaching and learning about graphs in physics courses are also discussed.

Figure 1

Example of definition of AOIs for one test item.

Figure 2

(a) Average scores of physics students on the qualitative and quantitative questions about graph slope and area under a graph. (b) Average scores of psychology students on the qualitative and quantitative questions about graph slope and area under a graph. The error bars represent 1 standard error of the mean (SEM).

Figure 3

Average scores of physics and psychology students in the context of physics and finance on the qualitative and quantitative questions about graph slope and area under a graph. The error bars represent 1 SEM.

Figure 4

(a) Average total viewing time of physics students on the qualitative and quantitative questions about graph slope and area under a graph. (b) Average total viewing time of psychology students on the qualitative and quantitative questions about graph slope and area under a graph. The error bars represent 1 SEM.

Figure 5

Average total viewing time of physics and psychology students in the context of physics and finance on the qualitative and quantitative questions about graph slope and area under a graph. The error bars represent 1 SEM.

Figure 6

Average viewing time of physics and psychology students on the AOIs Question, Graph, and Multiple choice. The error bars represent 1 SEM.

Figure 7

Average viewing time on the AOI Axes of the physics and psychology students in the context of physics and finance on the qualitative and quantitative questions about graph slope and area under a graph. The error bars represent 1 SEM.