Very low calculation and applying-mathematics scores indicate a broad difficulty that needs separating into its component parts. A pupil may struggle with facts, procedures, mathematical language, representing a problem, choosing a strategy or several of these at once.

The assessment should show what to teach next. It should not simply confirm that attainment is low.

Assess calculation separately

Use age-appropriate tasks across relevant operations. Ask the pupil to show and explain their method. Examine:

• recall and derivation of number facts;

• place-value understanding;

• choice and execution of mental and written methods;

• accuracy and self-correction;

• estimation and checking;

• whether learning is retained and transferred.

Record the nature of errors and the conditions in which performance improves. For example, a pupil who writes 38 + 25 = 513 has added each column without regrouping, so the gap is place value in a written method. A pupil who cannot answer 7 × 8 at once but reaches it by counting in eights knows the relationship and needs retrieval practice.

Assess problem-solving separately

Use problems with varied structures and contexts. Check whether the pupil can:

• explain the question;

• identify relevant information;

• represent the mathematical structure;

• select a suitable operation or strategy;

• carry out the necessary calculation;

• judge and communicate whether the answer is reasonable.

Reduce reading demand where necessary so the assessment does not confuse literacy difficulty with mathematical reasoning. Also test the required calculation outside the word problem.

If a pupil answers “I gave away 7 stickers and now have 12. How many did I start with?” with 12 − 7, ask them to draw it. Choosing subtraction because of “gave away” shows they are matching words to an operation without picturing the problem.

Decide the intervention route

Add the pupil's view of which maths feels hardest and what helps, and ask home how maths homework goes. Then summarise the strongest evidence for the primary barrier:

• insecure number foundations;

• weak fact or procedural fluency;

• difficulty understanding mathematical language;

• difficulty representing and planning solutions;

• a mixed profile requiring a staged plan.

Set the first teaching priorities and decide whether one intervention should precede another. Establish a baseline, review progress frequently and check application in ordinary lessons.

If the pupil makes limited progress despite precise, well-delivered teaching, consider a broader specialist assessment, for example by a specialist maths teacher or an educational psychologist. A low screening score does not by itself establish a diagnosis.

Useful guidance and tools

• EEF: Improving Mathematics in Key Stages 2 and 3

• DfE mathematics guidance for primary schools

• SASC list of suitable tests

Check the current age range, norms, qualification requirements and intended purpose of any formal test before use. Combine standardised results with informal tasks, classroom evidence and response to teaching.