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. See the worked example principle. 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.

Sample 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.
• Hilbert, T., Schworm, S., & Renkl, A. (2004). Learning from worked-out examples: The transition from instructional explanations to self-explanation prompts. In P. Gerjets, J. Elen, R. Joiner, & P. Kirschner (Eds.), Instructional design for effective and enjoyable computer-supported learning (pp. 184-192). Tübingen: Knowledge Media Research Center.
• Schworm, S., & Renkl, A. (2006). Computer-supported example-based learning: When instructional explanations reduce self-explanations. Computers & Education, 46, 426-445
• Schworm, S. & Renkl, A. (2002). Learning by solved example problems: Instructional explanations reduce self-explanation activity. In W. D. Gray & C. D. Schunn (Eds.), Proceeding of the 24th Annual Conference of the Cognitive Science Society (pp.816-821). Mahwah, NJ: Erlbaum
• 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.