What works with worked examples: Extending self-explanation and analogical comparison to synthesis problems

The ability to solve physics problems that require multiple concepts from across the physics curriculum—“synthesis” problems—is often a goal of physics instruction. Three experiments were designed to evaluate the effectiveness of two instructional methods employing worked examples on student performance with synthesis problems; these instructional techniques, analogical comparison and self-explanation, have previously been studied primarily in the context of single-concept problems. Across three experiments with students from introductory calculus-based physics courses, both self-explanation and certain kinds of analogical comparison of worked examples significantly improved student performance on a target synthesis problem, with distinct improvements in recognition of the relevant concepts. More specifically, analogical comparison significantly improved student performance when the comparisons were invoked between worked synthesis examples. In contrast, similar comparisons between corresponding pairs of worked single-concept examples did not significantly improve performance. On a more complicated synthesis problem, self-explanation was significantly more effective than analogical comparison, potentially due to differences in how successfully students encoded the full structure of the worked examples. Finally, we find that the two techniques can be combined for additional benefit, with the trade-off of slightly more time on task.

Figure 1

The experimental design used in each of the three experiments. Experiments 2 and 3 used the same target synthesis problem.

Figure 2

An example synthesis worked example (a), the corresponding single concept worked examples (b), and the target synthesis problem (c).

Figure 3

Distributions of student score on target synthesis problem by treatment condition.

Figure 4

Proportion of students in each condition demonstrating recognition of centripetal acceleration and energy conservation. Error bars are standard errors.

Figure 5

An example synthesis problem provided as a worked example (a), corresponding single concept problems (b), and the target synthesis problem (c).

Figure 6

Proportion of students in each condition demonstrating recognition of Faraday’s law, Ohm’s law, and magnetic force on the target synthesis problem. Error bars are standard errors.

Figure 7

Proportion of students in each condition who employed the correct solution structure on the target synthesis problem. Error bars are standard errors.

Figure 8

Proportion of students in each condition demonstrating recognition of Faraday’s law, Ohm’s law, and magnetic force on the target synthesis problem. Error bars are standard errors.

Figure 9

Proportion of students in each condition demonstrating the correct general solution structure on the target problem. Error bars are standard errors.

Figure 10

Box plot of student time spent on training by condition.