Use headings, a short model and a language frame; allow paired rehearsal before an independent response. Adapt the scaffold to what the learner can already do.
Six ways to make subject language visible
Language skills for EAL learners.
reading · skills
Read the problem before choosing an operation
Teach learners to identify quantities, relationships and the question. A keyword alone is not a reliable instruction to add or subtract.
Try this: A box has 12 pencils. This is 3 fewer than another box. How many pencils are in the other box?
Worked example
The first box has 12. The other has 3 more, so it has 15. The word fewer describes the relationship; it does not tell us to subtract from 12.
Language frame Known: __. Relationship: __. We need to find __.
Teaching sequence
Restate the question without calculating.
Draw or label the relationship.
Choose an operation and check it against the story.
What to look for: The learner can explain the operation using the relationship.
writing · skills
Explain why a step is valid
Model short mathematical explanations alongside symbols. Keep the reason connected to the specific operation.
Try this: Solve 3x + 4 = 19 and explain each transformation.
Worked example
Subtract 4 from both sides to keep the equality: 3x = 15. Divide both sides by 3: x = 5. Substituting gives 3(5) + 4 = 19.
Language frame I __ both sides because __. I checked by __.
Teaching sequence
Annotate one worked example.
Explain a missing step.
Solve a fresh example with a reason and check.
What to look for: The explanation justifies a transformation, rather than describes movement of symbols.
vocabulary · skills
Connect words, symbols and examples
Teach terms in connected sets: ratio and proportion, expression and equation, mean and median. Include everyday meanings that may mislead.
Try this: Distinguish expression from equation.
Worked example
3x + 4 is an expression. 3x + 4 = 19 is an equation because it states that two expressions have equal value.
Language frame This is __ because __. The symbol __ tells us __.
Teaching sequence
Sort examples and non-examples.
Say the notation aloud in context.
Use the term to explain a new item.
What to look for: Learners can classify and explain using the defining feature.
speaking · skills
Compare methods without ranking speed alone
Give pairs a shared problem and different valid methods. Ask them to compare clarity, efficiency and generality.
Try this: Calculate 25 × 16 using partitioning and a quarter-of-100 approach.
Worked example
25 × (8 + 8) = 200 + 200 = 400. Also, 25 is one quarter of 100, so 25 × 16 = 100 × 4 = 400.
Language frame Both methods __. This method is useful when __ because __.
Teaching sequence
Solve or inspect both methods.
Explain one method to a partner.
Compare when each method may be useful.
What to look for: Students justify a choice rather than simply announce the answer.
listening · skills
Listen for the reason behind a worked example
Give learners a specific listening focus during explanation: the decision, the mathematical reason and the check.
Try this: Watch a teacher solve an equation and pause before a transformation.
Worked example
The teacher subtracts the same amount from both sides to preserve equality, then checks the solution by substitution.
Language frame Step taken | Reason | How it was checked
Teaching sequence
First listen for the overall method.
Replay or pause for one decision and its reason.
Reconstruct the solution from short notes.
What to look for: The learner explains why the step is allowed.
Explicitly teach more than, less than, at least, at most, each, per and times as many. Use diagrams and contrasting sentences.
Try this: Compare three times as many with three more than.
Worked example
If B has 4 counters, three times as many is 12, while three more than is 7.
Language frame __ has __ times as many as __. This means __.
Teaching sequence
Represent two contrasting statements.
Match each sentence to a diagram or equation.
Create a new example and explain the difference.
What to look for: Language accurately expresses the quantitative relationship.
Routines that make support part of everyday teaching
Classroom systems for EAL support.
Build language support into planning, modelling, assessment, feedback and multilingual participation. Use these routines consistently, then reduce support as learners become more independent.
planning · systems
Plan the representation and the language demand
Decide how learners will move between concrete or visual representations, notation and explanation.
Try this: For an equation lesson, align the balance model, written equation and spoken explanation.
Worked example
Content: preserve equality. Language: justify doing the same operation to both sides.
Teaching sequence
Choose a representation that reveals the relationship.
Model the words alongside the notation.
Check transfer to a new equation.
What to look for: The scaffold reveals the mathematics without doing the thinking for the learner.
routines · systems
Use a consistent problem-solving routine
Make the routine a way to understand relationships, rather than a checklist of keywords.
Try this: Use read → represent → solve → explain → check across different problem types.
Worked example
A bar model clarifies which quantity is unknown before an operation is chosen.
Teaching sequence
Ask learners to identify the unknown.
Require a representation and a reason.
Check whether the result makes sense in context.
What to look for: A learner can explain and validate the solution.
assessment · systems
Distinguish language difficulty from mathematical misconception
Ask for a diagram, manipulation or short oral explanation as well as written working when diagnosing a difficulty.
Try this: A learner misreads fewer than but can solve the same relationship shown in a diagram.
Worked example
The follow-up task targets relational language; the learner still receives appropriately challenging mathematics.
Teaching sequence
Compare two representations of the same concept.
Identify whether the error is conceptual, procedural or linguistic.
Use the formal assessment rules for the final assessed task.
What to look for: The next teaching step responds to the actual difficulty.
feedback · systems
Make an error something to explain
Use an incorrect example to prompt reasoning. Avoid feedback that only replaces one number with another.
Try this: A learner writes 3x + 4 = 19, then 3x = 23.
Worked example
Subtracting 4 from both sides gives 15. Explain which operation preserves equality and why.
Teaching sequence
Locate the first point where the reasoning changes.
Ask the learner to explain and correct that step.
Test the correction on a fresh equation.
What to look for: The revision shows the principle, not just the corrected answer.
multilingual · systems
Compare terms while keeping notation stable
Invite learners to explain a concept in a language they know, then connect it to English notation and the required explanation.
Try this: Compare how learners describe ratio or a fraction, without assuming direct word-for-word equivalents.
Worked example
A learner sketches the relationship, names it in English and explains it with an example.
Teaching sequence
Keep the diagram and notation visible.
Clarify the English term in context.
Ask for an independent explanation using the shared representation.
What to look for: Students move between languages and representations with mathematical meaning intact.
Course and school systems
Fit the support to your curriculum.
These teaching routines can be adapted to different courses. Use the current subject guide, examination year and school assessment policy to determine the formal requirements.
Context
What to align
Teacher action
KS3 / lower secondary
Subject concepts, progression and the language of explanations.
Connect a modelled response to the next independent subject task.
IGCSE / GCSE
The exact syllabus, command words, paper format and assessment conditions.
Practise the relevant subject response, then fade the scaffold before independent practice.
IB MYP / Diploma
The current subject objectives, criteria and task requirements.
Use the subject’s criteria to judge the response; diagnose language needs alongside conceptual understanding.
HSC / senior secondary
The selected course outcomes, required response forms and current assessment rules.
Use a relevant model and feedback routine without replacing the subject’s criteria.
Use subject-specific reading, writing and talk to make the reasoning visible. Start with an authentic task, identify its language demands and review learner independence.
reading · skills
writing · skills
vocabulary · skills
speaking · skills
grammar · skills
planning · systems