Worked Example Effect

What it is

Most technical teaching follows one pattern: explain a method, then set problems and let students solve them. In 1988 Sweller argued that this is a poor way to build the knowledge that expert problem solving rests on. His reasoning was that a strategy such as means-ends analysis, in which the solver keeps comparing the current state with the goal and searching for a step that narrows the gap, uses up so much of a learner's limited working memory that little is left for noticing how the problem is built. A learner can finish a page of problems and still hold little that transfers.

A worked example removes the search. The student is shown a complete solution, step by step, and studies it. The attention that would have gone to finding the next move can go to the structure of the solution, which is what the later problems share.

Sweller and Cooper tested this in five experiments, reported in Cognition and Instruction in 1985. The first compared Year 9 pupils, Year 11 pupils and university mathematics students. The more experienced groups were better at recalling equations and at telling apart equations that look alike but call for different solution methods, which the authors took as evidence that experience builds richer mental representations of algebra. The other four experiments asked whether worked examples could help build those representations. The examples took less time to process, and students who then met similar problems solved them faster and made fewer mathematical errors.

The authors drew a cautious conclusion about what the students had learned. Novices, they proposed, store general algebra rules as a limited set of problem-specific schemas, and turning these into broader rules probably takes sustained practice across a wider range of problem types. The effect is therefore a statement about efficiency on problems of a familiar shape, not a claim that a handful of examples produces general mastery.

In the vocabulary the theory developed later, the effect is usually understood as a way of cutting load that the task does not require. That is our reading of how it fits the framework, not a statement taken from the 1985 paper.

In effect

The algebra experiments

The research case is the 1985 paper itself. Across experiments two to five, students given worked examples spent less time on them and then solved similar problems faster and with fewer mathematical errors than students who had practised conventionally. The advantage did not carry over to problems with a different structure. It is a result about algebra, about students at school and university level, and about problems of one kind.

A recipe with the steps shown

The following is an illustration, not a result from the studies above. A cook learning a technique for the first time usually does better watching it done in full, with each stage visible, than being handed the finished dish and a list of ingredients and left to work out the method. The finished dish gives the goal; the demonstration gives the path. The same applies to a new learner of a spreadsheet formula, a knitting pattern or a chess opening.

Onboarding that shows a finished case

Another illustration, drawn from product design rather than from research. A software tool can ask a new user to build a first project from a blank screen, or it can open on a completed sample project and let the user study how it was put together. The second approach follows the logic of the worked example. Whether it works for a particular product is an empirical question about that product's users, and the 1985 experiments do not answer it.

What it does not say

It does not say that practice is useless. Sweller and Cooper concluded that moving from problem-specific schemas to general rules probably takes sustained practice across a wider range of problem types, so examples and practice do different jobs.

It does not say the gains transfer. In the algebra experiments they were confined to problems with the same structure as the examples.

It does not say worked examples suit every learner. The expertise reversal effect, reviewed by Kalyuga and colleagues in 2003, reports that methods which help novices can lose their value, or hurt, with more experienced learners, so the effect should not be assumed for people who already know the method.

It does not supply a size. No effect sizes or sample figures are given here.

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