Why Misconceptions Persist and How to Correct Them
By NeurofiED Editorial Team · Reviewed by NeurofiED Learning Science Team
NeurofiED resources are written for UK 11+ families and reviewed against the platform's retrieval practice, spacing, interleaving and feedback principles.
A calm five-step routine for uncovering a misconception, testing its boundary, rebuilding the concept and checking it on fresh English and Maths examples.
A misconception persists when a child’s explanation makes sense to them, even though it produces wrong answers outside a limited situation. Correct it by uncovering the idea, finding the part that is reasonable, showing a case where it fails, rebuilding the concept, and checking the new idea on a fresh example. Simply saying “wrong”, supplying a rule or collecting mistakes rarely reaches the belief underneath.
This is different from a slip. Writing 7 × 8 = 54 once, then immediately correcting it, may be an attention or recall error. Repeatedly insisting that multiplication must make a number larger is a misconception: a stable idea is driving a pattern of answers. The focus here is conceptual correction, not proofreading, behaviour points or a punitive error log.
Contents
What makes a misconception different
A wrong answer is evidence to investigate, not a complete diagnosis. Ask your child to explain the route before deciding what needs correcting.
Use three quick tests:
The Education Endowment Foundation (EEF) defines a mathematical misconception as an understanding that leads to a “systematic pattern of errors”. It notes that a limited idea can become a misconception when it is applied beyond the context where it works.[1] This matters because the child may not be guessing. They may be reasoning consistently from a rule that once seemed useful.
By contrast, a slip is local: a copied sign, a missed word or an isolated calculation error that the child can recognise and repair without re-teaching the concept. Treating every slip as a misconception wastes time; treating a misconception as carelessness leaves the underlying idea intact.
A five-step correction routine
1. Elicit the current idea
Begin with: “Talk me through how you decided.” Avoid leading questions. You need the child’s idea in their own words. Write a neutral sentence: “I think ___ because ___.” For example: “I think 3/8 + 2/8 = 5/16 because you add both numbers in a fraction.” Now you have an idea to examine, not a child to blame.
2. Find the partial truth
Ask where the rule does work. Multiplication by whole numbers greater than one often produces a larger positive number. When multiplying fractions, numerators and denominators are both multiplied. The mistaken rule is not nonsense; it has travelled too far.
The EEF guidance recommends considering how a misconception arose and exploring the “partial truth” beneath it and the circumstances where it no longer applies.[1] Naming that boundary is more useful than saying, “Never think that.”
3. Create a decisive contrast
Choose one example where the current idea works and one carefully matched case where it fails. Ask your child to predict both answers before calculating. A good contrast changes one important feature and keeps the rest simple. Say, “Let’s test the rule,” rather than setting a trap.
4. Rebuild the meaning
Use a representation, definition or sentence that explains why the correct relationship works. Do not jump straight from contradiction to a new slogan. A child can memorise “keep the denominator” without understanding that eighths remain eighths when quantities of eighths are combined.
Ask them to complete: “The old rule works when ___. It fails when ___. A better idea is ___.”
5. Revisit with fresh cases
Use a near match, a contrast where the old rule would give a different answer, and a short explanation or choice between examples and non-examples. The EEF guidance recommends uncovering and addressing misconceptions rather than avoiding them. It says counterexamples can challenge a belief, while pupils may still need time and support to develop a more robust conception.[1] One correct answer therefore closes the immediate conversation; it does not prove that the idea is secure.
Maths example: multiplication always makes bigger
Suppose a child says, “The answer must be more than 12 because multiplication makes numbers bigger.” Start with two predictions:
The first is 36, so the old idea appears to work. For the second, connect multiplication to “half of 12”. Six is less than 12. The operation has not changed; the size and meaning of the multiplier have.
A stronger replacement is: multiplying tells us how many times or what fraction of a quantity we take. Multiplying a positive number by more than 1 makes it larger; by 1 keeps it the same; and by a positive number below 1 makes it smaller.
Check 20 × 4 = 80, 20 × 1 = 20 and 20 × 1/4 = 5. Ask: “Which part of the multiplier predicts whether the result is larger, equal or smaller?” That tests the concept rather than recall of one answer.
Maths example: adding fractions
A child writes 2/7 + 3/7 = 5/14. Their partial truth may be that multiplication of fractions combines both top and bottom numbers. Test the addition claim with meaning: two sevenths plus three sevenths means two pieces of size one seventh plus three more pieces of the same size. There are five pieces, each still one seventh, so the sum is 5/7.
Contrast “2 apples + 3 apples = 5 apples” with “2 sevenths + 3 sevenths = 5 sevenths”. The unit stays the same when like quantities are added. Then use a non-example: 1/2 + 1/3 cannot become “2 fifths”, because halves and thirds are not the same-sized unit. Express them using a common unit: 3/6 + 2/6 = 5/6.
Fresh checks:
English example: every -ing word is a verb
Compare:
A child may label painting as a verb in both because it ends in -ing. The ending is a useful clue, but position and job in the sentence matter too. In the first, was painting tells us what Maya was doing. In the second, the painting names a thing and can be replaced by the picture.
Rebuild the idea: identify what the word is doing in this sentence; do not classify it from its ending alone. Try “The children are building a shelter” and “The building has a red door”, then ask your child to write one sentence of each kind. This English example is an editorial application of the correction routine; the EEF source is specifically guidance about Maths teaching.
How to check whether the idea has changed
Look for reasoning across varied examples, not a recited phrase. Ask your child to predict, explain why the old rule is tempting, identify its boundary, solve a fresh case, and create an example and non-example.
If they can answer only the original question, return to meaning. If they can explain but make an isolated arithmetic slip, correct it briefly without reopening the entire concept. If the same conceptual explanation returns, use a different representation or simpler contrast rather than repeating the same wording more loudly.
Parent actions
Keep any note task-focused: “Check what the multiplier means” is useful. “Careless again” is neither an explanation nor a next step.
Common mistakes
Correcting before listening
If you supply the explanation immediately, you may fix the answer without discovering the child’s model.
Giving a replacement slogan
“Never add denominators” may produce the next answer, but it does not explain units or what to do when denominators differ.
Choosing a complicated counterexample
A counterexample should expose one relationship. Large numbers or several unfamiliar steps hide what caused the conflict.
Turning correction into surveillance
A public chart of recurring failures, penalty or long correction sheet changes the task from understanding an idea to avoiding embarrassment. Keep the conversation specific, calm and finite.
Calling every error a misconception
A typo, forgotten sign or single uncertain answer needs a proportionate response. Look for a stable explanation and repeated pattern before teaching a conceptual correction.
Adjustment cues
Frequently asked questions
Should I show the correct answer first?
Usually, ask for the child’s reasoning first. If the task is inaccessible or distress is rising, model a simpler case and invite comparison.
How many examples are enough?
There is no fixed number in the approved guidance. Use enough variation to see whether the rebuilt idea travels beyond the teaching example, then stop.
Should we keep an error book?
Only if it records compact, useful ideas and next checks. Do not use it as a scorecard of failures.
Does one correct answer mean the misconception has gone?
Not necessarily. Ask for an explanation and a fresh contrasting case. The EEF guidance cautions that richer conceptions may take time and support.[1]
Is this routine only for Maths?
The cited guidance and formal definition here concern Maths. The practical questions can also organise a careful English discussion, but this article does not claim that the same evidence tested the home English routine.
Next step
Use the routine on one idea from recent English or Maths work: elicit, find the partial truth, contrast, rebuild and revisit. To understand the broader principles behind NeurofiED’s learning approach, see the science.
Source
[1] Education Endowment Foundation, Improving Mathematics in Key Stages 2 and 3: https://educationendowmentfoundation.org.uk/education-evidence/guidance-reports/maths-ks-2-3
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