Representational task formats and problem solving strategies in kinematics and work

Previous studies have reported that students employed different problem solving approaches when presented with the same task structured with different representations. In this study, we explored and compared students’ strategies as they attempted tasks from two topical areas, kinematics and work. Our participants were 19 engineering students taking a calculus-based physics course. The tasks were presented in linguistic, graphical, and symbolic forms and requested either a qualitative solution or a value. The analysis was both qualitative and quantitative in nature focusing principally on the characteristics of the strategies employed as well as the underlying reasoning for their applications. A comparison was also made for the same student’s approach with the same kind of representation across the two topics. Additionally, the participants’ overall strategies across the different tasks, in each topic, were considered. On the whole, we found that the students prefer manipulating equations irrespective of the representational format of the task. They rarely recognized the applicability of a “qualitative” approach to solve the problem although they were aware of the concepts involved. Even when the students included visual representations in their solutions, they seldom used these representations in conjunction with the mathematical part of the problem. Additionally, the students were not consistent in their approach for interpreting and solving problems with the same kind of representation across the two topical areas. The representational format, level of prior knowledge, and familiarity with a topic appeared to influence their strategies, their written responses, and their ability to recognize qualitative ways to attempt a problem. The nature of the solution does not seem to impact the strategies employed to handle the problem.

Figure 1

Kinematic task with graphical format requesting qualitative solution.

Figure 2

Kinematic task with graphical format requesting quantitative solutions.

Figure 3

Force-position graph requesting qualitative solution.

Figure 4

Pressure-volume graph requesting a quantitative solution.

Figure 5

Example of qualitative solution when interpreting kinematic equation.

Figure 6

Example of qualitative solution when interpreting the acceleration-time graph.

Figure 7

Use of equations only to solve for quantitative solutions from motion graphs.

Figure 8

Use of “qualitative” approach and equations to solve for quantitative solutions from motion graphs.

Figure 9

Inclusion of a diagram which was ignored when dealing with equations.

Figure 10

Example of description when interpreting the force-position equation.

Figure 11

Example of explanation when interpreting the force-position graph.

Figure 12

Use of quantitative approach to solve for a quantitative solution from force-position equation.

Figure 13

Inclusion of diagrams which were used in conjunction with equations.