Student reasoning about graphs in different contexts

This study investigates university students’ graph interpretation strategies and difficulties in mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel (isomorphic) mathematics, physics, and other context questions about graphs, which were developed by us, were administered to 385 first-year students at the Faculty of Science, University of Zagreb. Students were asked to provide explanations and/or mathematical procedures with their answers. Students’ main strategies and difficulties identified through the analysis of those explanations and procedures are described. Student strategies of graph interpretation were found to be largely context dependent and domain specific. A small fraction of students have used the same strategy in all three domains (mathematics, physics, and other contexts) on most sets of parallel questions. Some students have shown indications of transfer of knowledge in the sense that they used techniques and strategies developed in physics for solving (or attempting to solve) other context problems. In physics, the preferred strategy was the use of formulas, which sometimes seemed to block the use of other, more productive strategies which students displayed in other domains. Students’ answers indicated the presence of slope-height confusion and interval-point confusion in all three domains. Students generally better interpreted graph slope than the area under a graph, although the concept of slope still seemed to be quite vague for many. The interpretation of the concept of area under a graph needs more attention in both physics and mathematics teaching.

Figure 1

An example of one set of parallel questions.

Figure 2

Overview of different strategies on slope questions and their frequencies (the number of students who used them).

Figure 3

Overview of student strategies on area questions and their frequencies (number of students who used them).

Figure 4

The response of one student to question CA1, indicating dimensional analysis which led student to the idea of multiplication. The variables on the axes of the graph are time and water level rate of change.

Figure 5

An example of student answer to question CA3, where student fitted a scale of velocities on the graph of acceleration vs time, and determined the velocity at $t=7\mathrm{s}$ as $15\mathrm{m}/\mathrm{s}$ from the initial velocity of $30\mathrm{m}/\mathrm{s}$.

Figure 6

Phi coefficients for each set of slope questions, indicating association of student answers to different combinations of questions (e.g., mathematics and physics, physics and other contexts, mathematics and other contexts).

Figure 7

Number of students on each set of questions who used same strategies in different combinations of domains.