Learning Science · A first practice and feedback cycle

Using an error to guide a revision

Treat an error as evidence to investigate, then practise the corrected reasoning.

Use the examples to connect this lesson with the earlier topics. No specialist equipment is needed.

After reading, you can

Distinguish likely error causes
Make and check a targeted revision

An answer is a clue

Two learners give the same wrong total. One selected the wrong numbers; the other selected correctly but made an arithmetic slip. Their answers look alike, but the next practice should differ. An error is evidence about an attempt, not a complete explanation of the learner.

First locate the earliest point at which the work diverges from a valid approach. Ask what the learner intended. Preserve correct parts: they can provide the foundation for repair. Avoid assuming every error reveals a deep misconception, or that every error is merely carelessness.

Repair the reason

If the learner added quantities that should be compared, demonstrate the relationship with a small case and ask them to choose the operation. If the method is sound but a digit was copied incorrectly, practise a checking routine. The revision should address the reason for the error, rather than only replace the final answer.

Then try a fresh case. Repeating the corrected answer can succeed through recent memory alone. A different example tests whether the learner can use the repaired idea. Keep the new case close enough that the relevant relationship remains clear.

Make error use constructive

Errors can guide learning when they are noticed, explained and corrected. They do not automatically become beneficial through repetition. In safety-critical tasks, use simulations or harmless materials for early practice and obtain competent supervision. The opportunity to learn never requires allowing preventable harm in the real task.

Ask the learner to state a checking question for future work. After a unit error, “Do these quantities use the same unit?” is more portable than “Remember the answer was two hundred.” The check should point to the relationship that caused the error and be rehearsed in a new relevant situation.

Worked example

Correcting a unit mistake

A learner says that 2 metres equals 20 centimetres. How can the error be repaired as a relationship?

Locate the relationship being used. The answer suggests a factor 10; ask the learner to show how many centimetres make 1 metre before assuming the cause.
Establish the metric relationship 1 m = 100 cm. Therefore 2 m = 2 × 100 cm = 200 cm, with the unit kept visible.
Use fresh checks: 3 m = 300 cm and half a metre = 50 cm. Ask why each follows from the same relationship rather than requesting the original answer again.

Two metres is 200 centimetres. The repair connects metres to centimetres through the factor 100 and tests whether the relationship works in new cases.

Two metres contain two hundred centimetres

Aligned scales show 0, 1 and 2 metres at the same positions as 0, 100 and 200 centimetres. Each small division is 10 centimetres. A short highlighted segment of 20 centimetres reaches only two small divisions, or 0.2 metres, rather than the two-metre endpoint.

Try it yourself

Think through each question before opening the answer.

Why inspect intermediate work?
Show the answer and reasoning
It helps distinguish a method error from a later slip and prevents practising the wrong remedy.
The same final answer can arise at different points. Finding the first mismatch shows whether to teach a relation, a method or an execution check.
Does erasing an error complete the learning?
Show the answer and reasoning
No. Explain the correction and test a new relevant case so the learner can use the repaired knowledge.
Erasure changes the page, not necessarily the learner’s method. Explain the relationship and use it in a different case to inspect whether the repair can guide future work.

What to carry forward

Locate the source of the mismatch.
Preserve what worked.
Correct the reasoning and check a fresh case.

References

Sources supporting the explanations and learning checks in this lesson.