How to Write Diagnostic Questions That Actually Reveal Misconceptions

A test question checks whether a child knows the answer. A diagnostic question does something more: it reveals exactly what a child who gets it wrong is thinking. The wrong answers are as designed as the right one.

The difference matters because teaching should respond to the specific misconception, not just to the fact of error.

The anatomy of a good diagnostic question

A well-designed multiple-choice diagnostic question has four answers: one correct, and three plausible distractors — each representing a specific, common misconception.

Example: *What is 0.3 + 0.45?*

A) 0.75 ✓ B) 0.48 (adding digits without regard to place value) C) 0.75, written as 0.075 (confusion between tenths and hundredths) D) 0.345 (concatenating rather than adding)

Each wrong answer tells you something different. B tells you the child hasn't understood decimal place value. C suggests confusion about column headings. D suggests the child is treating the digits as separate numbers rather than parts of the same quantity.

When you show this question to a class using show-me boards or ClassQuiz, you get a diagnostic map of the class in 60 seconds. You know who thinks what. Your next teaching decision is informed, not guesswork.

Common primary maths misconceptions to diagnose

**Fractions:** children who say 3/4 > 4/5 because '4 is bigger than 3'. Children who think 1/3 > 1/4 is wrong because '4 > 3'. The fraction-as-two-separate-numbers misconception is persistent and specific.

**Multiplication:** 'multiplication always makes bigger' — breaks at fractions and decimals less than 1. Specific diagnostic question: *What is 6 × 0.5?* with A) 3, B) 6.5, C) 30, D) 0.6.

**Algebra:** variable as abbreviation (n means 'number of apples', not a value that can vary). Students write n + n = 2n as n + n = n2. Specific and teachable.

Where to find good diagnostic questions

Diagnostic Questions (Craig Barton's platform at diagnosticquestions.com) has thousands of free, peer-reviewed diagnostic maths questions. Every question has data on which distractors most children choose — based on thousands of actual student responses. This data is invaluable.