Worked examples

Worked examples are a kind of example involving step-by-step solutions to problems typically presented in textual, graphical, video, or face-to-face format. Worked examples sometimes provide explanations of each step and sometimes withhold them so as to encourage student self-explanation.

A worked example is a problem plus the steps leading up to its solution. For instance, if the problem is "Solve 12+2*x=15 for x" then one worked example is:

In order to solve 12+2*x=15 for x, we write
 2*x = 15-12
 2*x = 3
   x = 3/2
   x = 1.5

There are 4 steps in this worked example solution.

A large body of literature, much due to John Sweller (see relevant references below) and his cognitive load theory, has investigated the benefits of interleaving worked examples with problem-solving practice. Such interleaving seems to provide a good balance of assistance between assistance-giving examples and assistance-withholding problems.

A worked example is sometimes called a "model", particularly when presented by expert in face-to-face or video format. Such a demonstration is the first step in the model-scaffold-face approach recommended by Collins et al. (1989).

For illustrative studies see the Renkl et al. study of faded worked-out examples in geometry and the McLaren et al. study of interleaved worked examples in Chemistry. A number of other studies involving manipulations in the distribution of, presentation of, or supporting instruction around worked examples can be found in the Coordinative Learning and Interactive Communication clusters.

References

• Collins, A., Brown, J. S., & Newman, S. E. (1989). Cognitive apprenticeship: Teaching the craft of reading, writing and mathematics. In L. B. Resnick (Ed.), Knowing, learning and instruction: Essays in honor of Robert Glaser (pp. 453-494). Hillsdale, NJ: Lawrence Erlbaum Associates.
• Sweller, J. (1999). Instructional design in technical areas. Australian Council for Education Press.
• Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2, 59–89.
• Trafton, J. G., & Reiser, B.J. (1993). The contributions of studying examples and solving problems to skill acquisition. In M. Polson (Ed.), Proceedings of the Fifteenth annual conference of the Cognitive Science Society (1017-1022). Hillsdale, N.J.: Erlbaum.
• Ward, M., & Sweller, J. (1990). Structuring effective worked examples. Cognition and Instruction, 7, 1-39.
• Zhu, X., & Simon, H. A. (1987). Learning mathematics from examples and by doing. Cognition and Instruction, 4(3), 137-166.