Translating between Graphs and Equations: The Influence of Context, Direction of Translation, and Function Type

We report on a study investigating the influence of context, direction of translation, and function type on undergraduate students' ability to translate between graphical and symbolic representations of mathematical relations. Students from an algebra-based and a calculus-based physics course were asked to solve multiple-choice items in which they had to link a graph to an equation or vice versa and explain their answer. The first part of the study focuses on the accuracy of the chosen alternative. Using a generalized estimating of equations (GEE) analysis we find that mathematics items are solved better than physics or kinematics items; that items starting from a graph are solved better than those starting from an equation; and that items on inversely proportional functions are the hardest for students. Quantitatively we see big differences in the number of correct answers between the algebra-based and calculus-based cohorts, but qualitatively the effects of the item variables on the accuracy are the same for both groups. The second part of the study focuses on students' argumentations for the chosen alternative. We observe that students use their physical knowledge 2 to even 3 times as much in kinematics items than in other physics items. When there is an effect of context on argument use, we observe that the use of an argument in a mathematics context differs significantly from the use of that argument in the physics and/or kinematics context. With regard to function type, students explain their choice of answer in items on inversely proportional functions with different arguments and fail more often to answer correctly. In general, the data also show that students from the calculus-based course use more mathematical arguments and score better on the items.