Patterns of multiple representation use by experts and novices during physics problem solving

It is generally believed that students should use multiple representations in solving certain physics problems, and earlier work in PER has begun to outline how experts and novices differ in their use of multiple representations. In this study, we build on this foundation by interviewing expert and novice physicists as they solve two types of multiple representation problems: those in which multiple representations are provided for them and those in which the students must construct their own representations. We analyze in detail the types of representations subjects use and the order and manner in which they are used. Expert and novice representation use is surprisingly similar in some ways, especially in that both experts and novices make significant use of multiple representations. Some significant differences also emerge. Experts are more flexible in terms of starting point and move between the available representations more quickly, and novices tend to move between more representations in total. In addition, we find that an examination of how often and when multiple representations are used is inadequate to fully characterize a problem-solving episode; one must also consider the purpose behind the use of the available representations. This analysis of how experts and novices use representations sharpens the differences between the two groups, demonstrates analysis techniques that may be useful in future work, and suggests possible paths for instruction.

Figure 1

Four representations of the motion of a car (a snapshot from a Flash movie, a graph of position versus time, a graph of velocity versus time, and a written description). The students interviewed were required to make sets of these representations that all corresponded to the same motion.

Figure 2

The first four electrostatics problems solved in the interviews.

Figure 3

Electrostatics challenge problem and example solution.

Figure 4

The statement of the pulley problem given only to the expert group.

Figure 5

(Color online) Schoenfeld-style diagram for a novice student’s unsuccessful attempt at the electrostatics challenge problem. Note the lack of planning or analysis.

Figure 6

(Color online) Graph of a 202 novice’s representation use during their solution of the electrostatics challenge problem.

Figure 7

Sequence diagrams showing the order in which students used representations in two of their problem solutions. Above: A novice’s correct solution to the first of the electrostatics problems. Below: A solution where a novice student did not reach the correct answer. The complexity parameter is defined in the text.

Figure 8

(Color online) Three codings of novice Carrie’s attempted solution of the electrostatics challenge problem. Above, we have the representations used as a function of time. The middle graph shows how these representations were being used. On the bottom, we have the sequence of representations used. Some quick translations back and forth have been removed for clarity.

Figure 9

(Color online) Three codings of novice Sam’s successful solution of the electrostatics challenge problem.

Figure 10

(Color online) Three codings of expert Jim’s successful solution of the electrostatics challenge problem.

Figure 11

(Color online) Distribution of time spent in by experts and novices during their solutions to the electrostatics problems. The possibility of coding more than one behavior per interval leads to totals above 1.0. Error bars represent the standard error of the mean.

Figure 12

(Color online) Distribution of time spent in by experts during their solutions to the more challenging pulley problem. The distribution is similar to the expert distribution in the electrostatics problems of Fig. 11.