Mathematical language carries precise meaning. An unfamiliar term, symbol or command word can prevent a pupil showing what they understand. Pre-teaching should focus on the small number of words essential to the next concept or problem type, not a long vocabulary list detached from the lesson.

Select the essential language

Before a topic, identify the terms pupils must understand to access the explanation, representation and questions. Include:

• the mathematical concept, such as factor, ratio or difference;

• related notation or symbols;

• a command word where its meaning is important, such as estimate, justify or compare;

• a contrasting term that helps define the boundary, such as factor and multiple.

Choose only a few terms at one time. Include words that mean something different outside maths, such as product, volume, mean and table, because pupils may bring the everyday meaning to the question.

Link meaning, representation and use

Use a consistent teaching sequence:

1. Say and display the word.

2. Give a concise, pupil-friendly definition.

3. Connect it to a symbol, diagram, object or worked example.

4. Show a non-example or related term where useful.

5. Ask the pupil to use the word while explaining the mathematics.

For example, teach factor using 18. Show the numbers that divide 18 exactly, connect these with arrays or multiplication pairs, and contrast 5, which is not a factor. At Secondary, put related terms side by side. Show 3x + 2, 3x + 2 = 11 and 2(x + 1) ≡ 2x + 2, and ask which is an expression, which is an equation and which is an identity. Then ask which one can be solved.

Keep the language available

Use a short word bank on the desk, board or knowledge organiser. Include meaning and a useful representation, not just the word. A Frayer model (the word in the middle, with boxes for a definition, key features, examples and non-examples) is a quick format for one key term. Refer to it during worked examples and pupil explanations.

Revisit the terms across several lessons and contexts. Ask pupils to restate a question in their own words before choosing a method. Gradually reduce the prompt once the pupil recognises and uses the language securely.

Avoid keyword shortcuts

Do not teach words as automatic operation signals. More does not always mean add, and difference does not remove the need to understand the relationship in the problem. Read the whole question and connect the language to the mathematical structure.

Further reading

The EEF disciplinary-literacy resource for maths describes the particular demands of mathematical vocabulary, notation and syntax. The EEF mathematics guidance covers representations, reasoning and explicit problem-solving strategies.