When pupils show very low scores in both arithmetic fluency and applying mathematics, further investigation is justified. Every assessment and referral decision must remain individual.

The purpose is to determine where each pupil's mathematical process breaks down and how that should change teaching. The result does not establish a diagnosis.

Start with an individual evidence review

Bring together:

• the pupil's full assessment profile;

• examples from maths lessons;

• previous attainment and attendance;

• intervention history and response;

• the pupil's explanation of what they find difficult;

• relevant information from home.

Define the question that remains unclear. For example: are insecure number foundations causing calculation errors, or does the pupil understand calculations but struggle to represent and plan solutions?

Assess calculation separately

Use age-appropriate oral and written tasks. Ask the pupil to show and explain methods. Examine:

• number-fact retrieval and derivation;

• place-value understanding;

• mental and written procedures;

• accuracy and self-correction;

• estimation and checking;

• retention and transfer.

For older pupils, include relevant whole-number, fraction, decimal and percentage calculations.

Assess mathematical problem-solving separately

Use familiar and unfamiliar problems. Check whether the pupil can:

• explain the question;

• identify relevant information;

• represent the mathematical structure;

• choose an operation or method;

• carry out the calculation;

• check and communicate the answer.

Reduce reading demand where necessary and test the required calculation outside the problem. This distinguishes a mathematical-application difficulty from literacy or fluency.

Use error analysis

Record the strategy, misconception and point of breakdown. A total score cannot show whether the next step should be number foundations, fact fluency, a written method, mathematical vocabulary or problem representation.

Summarise:

1. secure knowledge;

2. earliest insecure component;

3. supports that improve performance;

4. first intervention target;

5. likely intensity and review period.

Pupils can be grouped only when this evidence identifies a sufficiently similar starting point.

Assessment, guidance and next steps

• DfE mathematics guidance for primary schools provides free concept progressions and examples. Teachers can use these to find gaps, but they are not a standardised assessment.

• EEF: Improving Mathematics in Key Stages 2 and 3 explains evidence-informed assessment and teaching principles.

• The SASC assessment-materials list can help suitably qualified professionals identify current formal tests. Check the edition, UK norms, age range, construct, qualification requirements and purpose before use.

Use findings to continue or change intervention, seek specialist discussion or consider referral. Screening and assessment through teaching inform these decisions but do not establish a diagnosis.