Learning Science · Examples, guidance and growing independence
Learning from a worked example
Study a complete solution by tracing the decisions that turn a problem into an answer.
Use the examples to connect this lesson with the earlier topics. No specialist equipment is needed.
Back to the chapterAfter reading, you can
- Identify a worked example’s goal, steps and checks.
- Use example study to prepare for an independent problem.
The solution is material to investigate
A worked example presents a problem and a route to its solution. It can reduce the need for a beginner to search blindly among possible operations. This leaves attention available for understanding why the route works. But watching someone solve a problem is not the same as learning the relationships that make the solution possible.
Begin by identifying the known quantities, the goal and the conditions. Then inspect one meaningful step at a time. Ask what changed, why the change is allowed and how it moves toward the goal. If the example skips a step that you cannot reconstruct, fill the gap or request an explanation before treating the chain as understood.
Follow choices rather than copying marks
An example of calculating a percentage may begin by identifying the whole. This choice matters more than copying the subsequent multiplication. Compare the denominator with the question’s meaning: percentage of what? Note the decision point so that a new story does not leave you with an operation divorced from its purpose.
A good example includes a check appropriate to the task. Substitute an algebraic solution into the original equation, compare a numerical result with an estimate, or test whether a written argument actually supports its conclusion. A final answer displayed without such a check hides part of competent performance.
| Decision | 20% off 50 | 10% off 80 |
|---|---|---|
| Identify the original whole | 50 | 80 |
| Find the reduction | 0.20 × 50 = 10 | 0.10 × 80 = 8 |
| Find what remains | 50 − 10 = 40 | 80 − 8 = 72 |
Move from inspection to use
Close the solution and reconstruct its main steps, then solve a related problem with changed details. Return to the example when a specific gap appears. Alternating example study and problem solving allows each to reveal what the other has missed: examples supply a coherent route, while an attempt shows whether the learner can select and execute it.
Experiments with geometry tutoring found benefits from adding faded worked examples compared with a tutor-only condition. Such results concern particular tasks and learners. They do not mean that reading solutions is always superior to attempting problems, especially after the required relationships are familiar. Choose the balance using evidence from independent work.
Worked example
Finding a discounted price
What is the price after a 20% discount on 50 currency units, and why?
- A worked example asks for the price after a 20% discount on 50 currency units. It first identifies 50 as the whole. Twenty percent means 20 per hundred, so the discount is 0.20 × 50 = 10. Subtracting the discount gives 40. A reasonableness check notes that a reduction must produce a value below 50.
- The learner then answers a related question: a 10% discount on 80 leaves 72. They explain why calculating 10% of the discount amount would use the wrong whole. The second task checks the decision that matters, rather than whether the learner remembers the first example’s numbers.
The discount is 0.20 × 50 = 10 and the remaining price is 40. The percentage refers to the original 50, not to the discount amount.
Try it yourself
Think through each question before opening the answer.
What should you inspect before the first operation in a worked solution?
Show the answer and reasoning
Identify the goal, the given information and the assumptions.
These explain why a method is relevant before its steps are followed.
Why can copying every line still produce little independent learning?
Show the answer and reasoning
Copying may preserve symbols without requiring a decision or reason.
Reconstruct and apply the method to find out what you can use without the displayed route.
When should you return to the example during practice?
Show the answer and reasoning
Return to resolve an identified gap, such as choosing the whole or justifying a transformation.
Then attempt that choice again without copying.
What to carry forward
- Treat a worked solution as an explanation of choices.
- Follow example study with reconstruction and a related independent attempt.
References
Sources supporting the explanations and learning checks in this lesson.