Comparison of university students’ understanding of graphs in different contexts

This study investigates university students’ understanding of graphs in three different domains: mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel mathematics, physics, and other context questions about graphs were developed. A test consisting of these eight sets of questions (24 questions in all) was administered to 385 first year students at University of Zagreb who were either prospective physics or mathematics teachers or prospective physicists or mathematicians. Rasch analysis of data was conducted and linear measures for item difficulties were obtained. Average difficulties of items in three domains (mathematics, physics, and other contexts) and over two concepts (graph slope, area under the graph) were computed and compared. Analysis suggests that the variation of average difficulty among the three domains is much smaller for the concept of graph slope than for the concept of area under the graph. Most of the slope items are very close in difficulty, suggesting that students who have developed sufficient understanding of graph slope in mathematics are generally able to transfer it almost equally successfully to other contexts. A large difference was found between the difficulty of the concept of area under the graph in physics and other contexts on one side and mathematics on the other side. Comparison of average difficulty of the three domains suggests that mathematics without context is the easiest domain for students. Adding either physics or other context to mathematical items generally seems to increase item difficulty. No significant difference was found between the average item difficulty in physics and contexts other than physics, suggesting that physics (kinematics) remains a difficult context for most students despite the received instruction on kinematics in high school.

Figure 1

Questions $P\mathrm{\text{−}}S2$, $M\mathrm{\text{−}}S2$, and $C\mathrm{\text{−}}S2$: an example of a set of parallel slope items.

Figure 2

Item-person map. $M$ denotes the mean of each distribution; $S$ denotes 1 standard deviation, and $T$ 2 standard deviations from the mean. Each “#” represents 3 students and each “.” less than 3 students.

Figure 3

Average difficulties of slope and area items in three different domains ($M$ stands for mathematics without context, $P$ for physics, $C$ for other contexts). All values are in logit. Error bars indicate the combined uncertainties of each average value computed as $\mathrm{CE}=({\mathrm{SEM}}^2+{\mathrm{SE}}^2{)}^{1/2}$, where SEM is standard error of the mean and SE is the average Rasch standard error.

Figure 4

Average difficulties of items in different domains (mathematics without context, physics, other contexts). All values are in logit. Error bars indicate the combined uncertainties of each average value computed as $\mathrm{CE}=({\mathrm{SEM}}^2+{\mathrm{SE}}^2{)}^{1/2}$ where SEM is standard error of the mean and SE is the average Rasch standard error of items in the domain.