Education, Skills & Policy · 3 min read

Error Analysis: What Mistakes Can Tell Us

By Dishantra Editorial · Published 13 September 2026 · Reviewed 13 September 2026

Education, Skills & Policy · Learning & Mathematics

Use the working to decide what to discuss, rather than treating every incorrect answer alike.

Two students can give the same incorrect answer for different reasons. One may misread a number; another may use a rule that does not apply. A third may understand the method but make a calculation slip. The answer alone cannot tell us which happened. Asking ‘Can you show me how you reached this?’ keeps the discussion connected to evidence.

Consider the statement 1/2 + 1/3 = 2/5. It may come from adding the top numbers and then the bottom numbers. Before supplying a procedure, ask whether the result is reasonable. Adding a positive third to a half must give more than a half, yet 2/5 is less than a half. This check identifies a problem without requiring the correct calculation first.

Next, show both amounts in sixths of the same whole. One half equals three sixths and one third equals two sixths, so their sum is five sixths. The denominator names the unit being counted. The explanation matters because replacing 2/5 with 5/6 without understanding the units leaves the original rule unexamined.

Discussing a fictional worked mistake can make the conversation less personal. Ask what the writer did, where the reasoning stopped fitting the quantities and how to repair it. Then offer a fresh example to see whether the explanation is usable. Avoid labelling a student from one response: an error is information to explore, not a complete account of their understanding.

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