# Difference between revisions of "Worked examples"

Line 3: | Line 3: | ||

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

## Revision as of 21:43, 10 April 2007

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.