# Worked example principle

## Description of principle

"In courses that are teaching new tasks, learning time can be saved by replacing some practice problems with worked examples" (Clark & Mayer, 2004, p. 177). In addition, most studies comparing interleaved worked examples and problems with all problmes have also shown improved learning outcomes, including robust learning outcomes.

### Examples

Imagine instead of giving students a typical homework or seatwork assignment involving 8 problems, you give them an assignment where every other problem comes with a complete worked out solution. The even numbered items would be usual problems, like the following algebra problem:
Solve 12 + 2x = 15 for x

The odd numbered problems, come with solutions, like this:
Below an example solution to the problem:
“Solve 12 + 2x = 15 for x”
Study each step in this solution, so that you can better solve the next problem on your own:

12+2x = 15
2x = 15-12
2x = 3
x = 3/2
x = 1.5

Which approach, asking for solutions to

all 8 problems or interleaving 4 examples with 4 problems, will be lead to better student learning? You might think that the 8 problems require more work or that students might ignore the examples and thus, the 8 problems would lead to more learning. But, much research has shown that students typically learn more deeply and more easily from the second approach, when examples are interleaved between problems.

Teachers often think so many examples “give it away” or that students will not pay attention to the example. But, by having problems in between students are motivated to pay more attention to the example so as to prepare for the next problem or to resolve a question from the past problem. The problems break a students’ “illusion of knowing” (see the meta-cognition recommendation) that might otherwise lead them to skim the example and believe it is obvious.

It is important that students spend time actively engaged in learning and in genuine problem solving and reasoning. However, an emphasis on “learn by doing” is sometimes taken too far and students end up with homework problems or projects that are beyond their means. In such cases, they may spend much unproductive study time struggling without success. This time is often not only wasted but may increase a students’ frustration with the subject-matter and lead to unjustified feelings of not being good at math or science particularly. In contrast, during example study, students can focus their attention on understanding the principles underlying the examples instead of simply on finishing the problem. In early learning, the thought that goes simply into trying to solve the problem seems to distract students from trying to understand the principles underlying the solution.

Notice that in the example above, explanations for each step are not provided. It is best when students provide these explanations themselves and, while more research is needed, providing explanations can sometimes distract students doing so themselves and in other cases seems to provide no additional enhancement in student learning.

In whole classroom situation a teacher might implement this recommendation by going back and forth between a classroom or small group discussion around an example solution followed by small groups or individuals solving a problem (just one!) on their own. Then back to example study, for instance, by having students present their solutions and having others attempt to explain the steps (see the self-explanation recommendation). Now back to a second problem.

By giving the students frequent opportunities to study examples in between problem solving, students can more easily and more deeply acquire the big ideas, key concepts, or key principles that we want them to learn. With greater understanding, students will do better on harder problems in the future that require them to transfer these key concepts beyond the problems just like those they have seen before.

## Experimental support

There is a lot of evidence for the effectiveness of learning from worked examples.  As an example, in one study twelve geoametry problems were used.  In the conv

entional group the learners solved all twelve peoblems as practice.  In the worked examples group, the learners received eight problems already worked out to study and then four problems to solve as practice.  Students in the worked examples group spent significantly less time studying and scored higher on a test than did those in the conventional group.  Furthermore, the worked examples group scored higher not only on test problems similar to those used during practice but also on different types of problems requiring application of the principles taught (Paas, 1992).  The investigators conclude that "training with partly or completely worked-out problems leads to less effort-demanding and better transfer performance and is more time efficient" (p. 433).  In fact, in one study, the use of worked examples allowed learners to complete a three-year mathematics course in two years (Zhu and Simon, 1987).  Positive effects of worked examples have been reported in a variety of cources teaching well-defined problems, including algebra, geometry, statistics, and programming.

## Theoretical rationale

(These entries should link to one or more learning processes.)

"Working memory has a limited capacity that becomes inefficient when having to retain even a few items.  If the only way to build job-relevant skills is to perform many practice exercises, working memory can become overloaded by the mental work required to complete these exercises.  However, iflimited working memory resources could be used to study worked examples and build new knowledge from them, some of this labor- intensive effort could be bypassed.  Worked examples are more efficient for learning new tasks because they reduce the load in working memory, thereby allowing the learner to learn the steps in problem solving."

Clark, Mayer, 2004 (pp178-179)

## References

Clark, R. C., & Mayer, R. E. (2003). e-Learning and the Science of Instruction : Proven Guidelines for Consumers and Designers of Multimedia Learning. San Francisco: Jossey-Bass.

Paas, F. (1992). Training strategies for attaining transfer of problem solving skill in statistics: A cognitive load approach. Journal of Educational Psychology, 84, 429–434.

Zhu, X., & Simon, H. A. (1987). Learning mathematics from examples and by doing. Cognition and Instruction, 4(3), 137-166.