Practical advice

Mathematics and mathematical reasoning

Find where understanding breaks down before increasing the amount of practice.

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Look beyond the final answer

Ask the pupil to represent a quantity with objects or a drawing, explain a calculation and judge whether an answer is reasonable. Distinguish number sense, place value, fact retrieval, procedure and mathematical language. A correct rehearsed calculation can hide difficulty choosing the method in an unfamiliar problem.

Connect representations

Move between objects, diagrams, spoken explanations and symbols while keeping the mathematical relationship clear. Model one decision at a time. Reduce copying or memory demands when those are incidental to the objective. Teach essential vocabulary explicitly, including words that have a different everyday meaning.

A classroom example

A pupil calculates 24 divided by 6 but cannot solve a sharing problem. Represent 24 counters shared into six groups, then connect each part of the written question to the representation. Change the objects and wording in a later question to check that the pupil recognises the relationship rather than the surface story.

Review understanding and independence

Use a small set of fresh questions, ask for an explanation and record the support needed. Separate faster recall from better reasoning. Persistent difficulty should be considered alongside teaching history, language, attention and the pupil’s experience of maths.

Further reading

EEF: Special Educational Needs in Mainstream Schools · SEND Code of Practice

General guidance for school staff. Apply professional judgement, current school policies and advice based on the individual pupil’s circumstances.

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