Did you know a student can copy a mathematically correct worked example and still get the homework wrong? The calculation might be flawless. The misunderstanding lies one step earlier: the example and the question do not have the same conditions.
Example matching means checking whether a model solution and a new task share the same goal, quantities, relationships and restrictions before borrowing the method. It is a practical way to learn from worked solutions without treating them as recipes. A familiar word does not guarantee a familiar mathematical structure.
Begin by diagnosing what the learner actually noticed
Before showing a solution, ask the child to read the question aloud, describe the goal and underline the words that govern the relationship. Then place the example beside the new task. Can the student name a condition that stayed the same and a condition that changed? If the answer is only “both questions say share”, the learner is matching surface words rather than meaning.
Some students understand the structure but copy a number inaccurately. Others choose a sensible method and make an arithmetic slip. Keep those difficulties distinct. The remedy for poor reading is not simply ten more calculations; the remedy for uncertain division is not another lecture about instructions.
Worked example: the same twelve stickers, two different rules
This is an invented teaching example, not a real student case. The textbook problem says: “Twelve stickers are shared equally among three students.” Divide 12 by 3. Each student receives 4 stickers. The word equally supplies the rule.
Now read: “Twelve stickers are shared between three students in the ratio 1 : 2 : 3.” A student who copies 12 ÷ 3 = 4 for everybody has ignored the new condition. The ratio does not mean equal shares.
- Count the total number of ratio parts: 1 + 2 + 3 = 6.
- Find the amount represented by one part: 12 ÷ 6 = 2 stickers.
- Give the students 1, 2 and 3 parts respectively: 2, 4 and 6 stickers.
- Independently check both requirements: 2 + 4 + 6 = 12, and 2 : 4 : 6 simplifies to 1 : 2 : 3.
Both problems involve sharing and division. Yet the first divides by the number of people to obtain equal shares; the second divides by the number of ratio parts. The distinction determines the method. A total check alone is insufficient: 4 + 4 + 4 is also twelve, but it violates the ratio.
A three-column comparison students can actually use
Draw three headings: “Worked example”, “My question” and “Important difference”. Compare what is being found, what information is supplied and what condition must be respected. If a difference changes the relationship, do not copy the steps unchanged. This takes less time than completing a page of corrections after choosing the wrong method.
The same technique works beyond Mathematics. A model English response may explain a character’s feelings; a new question may require evidence of a character’s change. A Science example might compare two temperatures; a new investigation may ask for a change in temperature. Similar appearance is a starting clue, not proof that the same answer is appropriate.
Teach in stages and gradually remove the example
- Model a comparison aloud. Circle “equally”, then underline “1 : 2 : 3”, and explain the effect of that difference.
- Offer two short problems that look alike but require different procedures. Ask the learner to choose and justify a method before calculating.
- Change the total to 18 stickers in the ratio 1 : 2 : 3. The correct shares are 3, 6 and 9; let the child reach that result without seeing the model.
- Give an unfamiliar problem and ask for a verbal explanation plus an independent check. The goal is choosing, adapting and checking, not just repeating a formula.
For parents, one useful question is: “What would have to be true for that example’s method to work here?” Teachers can ask pairs of students to defend different method choices, then examine the overlooked condition. In a small-group tutorial, observing where the learner first diverges from the correct reasoning makes the next explanation more targeted.
Mistakes to watch for
- Keyword shortcuts: “share” does not always mean divide into equal amounts.
- Copying every line: steps can be appropriate in one context but unsuitable in another.
- Checking only arithmetic: also check whether the numerical answer satisfies the original relationship.
- Rejecting valid alternatives: a different method can be sound if its assumptions and results are justified.
- Giving a hint too early: this can conceal whether the child could choose a method independently.
How parents and teachers can observe progress
Use three fresh questions on different days. Record whether the learner identifies the distinguishing condition, selects and explains the correct method, and checks the answer against all the question’s requirements. Record those three behaviours separately. A correct result with a copied procedure is less convincing evidence of transfer than a correct choice independently explained.
If the child keeps failing because earlier concepts are missing, follow the guide to mapping learning prerequisites. The Clementi Mathematics teaching guide demonstrates a diagnosis-first approach with explanation, progressive practice and independent checking. The emphasis here is not more homework for its own sake.
Frequently asked questions
Is it bad to copy a worked example when first learning?
No. Following a complete model can help a beginner notice the structure. The risk is continuing to copy without comparing conditions or understanding each decision. Support should be gradually reduced as understanding develops.
What if two different methods produce the same answer?
Check both methods against the question’s requirements. A correct result from an invalid assumption is fragile; two independently sound methods are useful, not a problem.
What can a parent ask in two minutes?
Ask what stayed the same, what changed and whether the change affects the solution. If the student can explain those three things, you have much better evidence than the neatness of the copied work.
The wider aim: transfer that survives a new question
Learning from examples should help students decide, not merely imitate. The habit of noticing conditions connects to the Core Aim of Education learning hub and the wider eduKate Education Hub. A good lesson ends when the learner can recognise both where a method applies and where it does not.