Short answer
Do not choose between examples and problems as if one should replace the other. For a new skill, study one complete example, explain why each step is valid, complete a partially worked problem, and then solve a similar problem without guidance. Check the result, classify the error, and fade support as you become accurate. Finish with a transfer problem whose surface details differ.
What to remember
- A worked example is useful when you study the decisions, not only the finished steps.
- Self-explanation exposes gaps that passive copying can hide.
- Partially worked problems create a bridge to independent performance.
- A transfer problem checks whether you learned the method rather than the page layout.
Diagnose what is missing before adding more problems
A learner can fail for different reasons: the underlying concept is unclear, the procedure is unfamiliar, or the learner cannot recognize when the procedure applies. Ten more identical problems may rehearse a procedure without fixing a concept or selection gap.
Before starting, name the smallest uncertainty. If you cannot explain the meaning of a variable, return to the concept. If you know the concept but lose the sequence, study a worked solution. If you can follow the solution but cannot begin a new problem, practice choosing and initiating the method.
Use example, explain, complete, solve
Study one complete example
Annotate the cue, goal, and decision at each step. Keep the example small enough that you can see the whole reasoning chain.
Explain it with the solution covered
Reconstruct why each step follows from the previous one. If you can repeat a line but cannot justify it, uncover only the relevant part.
Complete a faded example
Use a similar problem with one or more steps removed. Fill the gaps before checking the model solution.
Solve and transfer
Solve one related problem unaided, then try another with different surface details. Explain why the same method still applies—or why it does not.
Self-explain the decisions instead of narrating the ink
Useful self-explanation answers questions such as: what goal does this step achieve, which principle permits it, what alternative would fail, and how would the step change if one condition changed? Research on worked examples found that prompts supporting sophisticated self-explanations can foster transferable knowledge.
The goal is not a single magic script. Ask only the questions that reveal the structure of this problem. A concise explanation you can reproduce is more useful than a long annotation copied from the page.
Review the error, then return to the right rung
- Concept error: revisit the definition, representation, or prerequisite.
- Selection error: compare two similar problems and identify the deciding cue.
- Procedure error: return to the exact step in a worked example, then retry.
- Careless execution error: correct it and solve one fresh item without adding a new lesson.
- Transfer error: vary the context while keeping the underlying structure visible afterward.
Common questions
How many worked examples should I study before practicing?
There is no universal number. Start with one clear example, attempt a faded or similar problem, and let the error tell you whether you need another example or independent practice.
Is copying a worked solution useful?
Copying may slow you down enough to notice details, but it does not demonstrate that you can select or reproduce the reasoning. Cover the solution and explain or complete it from memory.
When should I stop using examples?
Fade guidance as soon as you can accurately explain and apply the steps. Keep examples available for targeted correction rather than rereading them before every problem.
Sources and method
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- Institute of Education Sciences: Organizing Instruction and StudyOfficial practice guide supporting alternation between worked solutions and problems to solve.
- Renkl et al. (1998), Contemporary Educational PsychologyOriginal research on example variability, elicited self-explanations, and transferable knowledge.
