All newly arrived pupils who have attended school in their home country will have studied mathematics. These pupils enter the English education system with a very diverse range of mathematical skills.

Planning for inclusion

The national curriculum and the Framework for teaching mathematics: years 7, 8 and 9 are the starting point for planning a school curriculum that meets the specific needs of newly arrived secondary school pupils. The national curriculum inclusion statement outlines how teachers can modify, as necessary, the national curriculum programmes of study to provide all pupils with relevant and appropriately challenging work at each key stage. It sets out three principles that are essential to developing a more inclusive curriculum:

• setting suitable learning challenges
• responding to diverse learning needs
• overcoming potential barriers to learning and assessment for individuals and groups of children.

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Setting suitable learning challenges

Schools should aim to give every pupil the opportunity to experience success in learning and to achieve as high a standard as possible. The national curriculum programmes of study set out what most pupils should be taught at each key stage but teachers should teach the knowledge, skills and understanding in ways that suit their pupils' abilities. For some groups of newly arrived pupils this may mean choosing knowledge, skills and understanding from earlier or later key stages and from different yearly teaching programmes or termly planning grids in the framework so that individual pupils can make progress and show what they can achieve.

A similarly flexible approach will be needed to take account of any gaps in pupils' learning resulting from missed or interrupted schooling. A small number of pupils arriving in the UK may not have received any previous schooling or their education may have been interrupted because of war. These pupils will have fewer mathematical skills than their peers. The 'Children with little or no prior education' area of this site gives further guidance on this.

Mathematics teaching in some countries may place greater emphasis on basic calculation and less on other aspects of mathematical knowledge, skills and understanding, for example understanding of the number system, repertoire of computational skills, inclination and ability to solve problems in a range of contexts, and practical understanding of the ways in which information is gathered by counting and measuring and is presented in graphs, diagrams, charts and tables. Handling data is a very common gap in the prior experience of newly arrived children.

The marginal notes in the national curriculum document for each key stage are the guide for teachers on the main emphases in that key stage's programme of study. The mathematics programme of study can be seen on the National curriculum online website. For an example of the marginal notes look up 'Key stage 3: using and applying number and algebra'.

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Responding to pupils' diverse learning needs

When planning, staff should have high expectations and provide opportunities for all pupils to achieve. Teachers will be aware that pupils bring to school different experiences, interests and strengths which will influence the way in which they learn. The experiences of pupils who have lived overseas can be an asset to the mathematics class. However, it is important to understand that some pupils may wish to put their experiences behind them and might feel uncomfortable if required to draw on recent traumatic events as part of their learning in school. Drawing on pupils' past personal experience requires appropriate professional judgement and sensitivity. Even work in mathematics that does not appear to be directly related to the experiences of the pupil may raise difficult issues.

Teachers are expected to plan their approaches to teaching and learning so that all pupils can take part in lessons. This will include the planning of work that is accessible for pupils with English as an additional language (EAL), as well as work that extends their language skills.

Teachers will need to plan appropriately challenging work for those whose ability and understanding of mathematical concepts are in advance of their language skills. This may mean pupils using their first language in mathematics lessons. Engagement and access to mathematics can be impeded if a pupil's first language is not appropriately supported. The 'English as an additional language' area of this website gives further guidance on this.

The Ofsted report Managing the Ethnic Minority Achievement Grant: good practice in primary schools (2004) gives a number of examples of good classroom practice and case studies and stresses:  

Once pupils learning EAL have gained a good working knowledge of everyday English they should be expected to progress at the same rate as other pupils in their class. The success of pupils learning EAL should be perceived as a central part of the school's improvement agenda and integrated into the departmental development plan. Whether a class has one or a significant number of pupils learning EAL, their progress depends upon close monitoring against their academic and personal targets.
(Unlocking potential: raising ethnic minority achievement at key stage 3, Ofsted, 2002)

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Overcoming potential barriers to learning and assessment for individuals and groups of pupils

A minority of pupils will have particular learning and assessment requirements which, if not addressed, could create barriers to learning. For newly arrived pupils these are most often linked to progress in learning English as an additional language. It is important to assess the data collected during the initial assessment of the pupil to identify learning needs. The 'Initial assessment' area of this site gives further guidance on this.

The Assessment in mathematics toolkit (EAL support) (see downloads) is a resource to help teachers gauge whether pupils in the early stages of learning English will be able to access the mathematics in the planned teaching programme for the year group concerned. This document is directed at teachers of pupils working in key stage 3. It provides a useful starting point which will enable teachers to:

• identify strengths and gaps in pupils' mathematics learning
• provide appropriate mathematics teaching to secure progress.

The Assessment in mathematics toolkit, which is available on a CD-ROM, suggests assessment activities against key objectives from each strand of the Framework for teaching mathematics: years 7, 8 and 9. An extensive range of resources to use for these activities is provided. The assessment activities are designed to be visual and not reliant on understanding the English language.

The way in which schools will use the toolkit will depend on their pupils' circumstances. The aim is to assess the pupil’s attainment in as comfortable a way as possible. Assessment can be in English or in a language with which the pupil is familiar.

It is recommended that teachers:

• use an appropriate task to assess the pupil at the beginning of a unit of work
• begin with the task that is appropriate for the pupil's year or close to it
• demonstrate and model what the pupil is to do using the resources
• observe the confidence with which the pupil approaches the task.

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The key criterion for decisions about setting and streaming is ability rather than what a pupil has previously studied or their fluency in English. The 'Initial assessment' area of this site gives further guidance on this.

QCA's Using assessment to raise achievement in mathematics gives examples of effective questions and the use of questions to find out pupils' specific misconceptions in section 2, 'Using effective questioning techniques'. Teachers may wish to adapt these for their own purposes.

Some EAL pupils may not respond to verbal questioning. Pupils whose language skills are weak may use a non-verbal framework for thinking. These pupils may be able to demonstrate understanding when a calculation is shown to them using objects, a computer screen calculation or pictures. It is important that teachers recognise pupils' achievement and analyse assessment data to highlight the relative performance of particular groups.

If you are trying to make comparisons between one group and another, it is helpful to think first about how to record your pupils at the top of the analysis sheet. For example, you could group EAL pupils first, then boys, then girls, then pupils who received early, additional or further literacy support. The overall picture will then become clearer.

It is important when doing a test breakdown to identify not only the questions pupils got right and wrong but also the questions they did not attempt. This could indicate that topics were not taught sufficiently in terms of coverage, or that an EAL pupil is unfamiliar with the formal language of test questions.

It is helpful to compare the performance of your class or cohort with other schools and the national picture. Work with a colleague from a neighbouring school to identify similarities and differences. Use the QCA 'Implications for teaching and learning' posters to see the national picture. The Autumn Package on the Standards site provides detailed but useful performance data. Teachers may wish to match this information with the evidence they have of the performance of their new arrivals to identify where more information or more support is needed.

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Recognising the mathematical ability of pupils learning EAL

It is easy to underestimate what pupils can do mathematically simply because they are new learners of the English language. In assessing pupils' mathematical understanding it is important to give pupils the opportunity to demonstrate their understanding and skills in their first language if their English is limited.

In taking account of the accessibility of the planned content for pupils who are learning English as an additional language it is important to ensure that the content is sufficiently challenging and that attempts to simplify the language involved in the mathematical activity do not unintentionally result in simplifying the mathematics.

Developing spoken and written language for mathematics: vocabulary and register

Pupils learning EAL may acquire mathematical terminology quickly. However, the mathematical register used in lessons may be more challenging. Words such as 'expand', 'simplify', 'mean' and 'mode' have a specific meaning in mathematics but a broader meaning in everyday language. Pupils need the opportunity to practise both the mathematical and general meaning of such words. Grammatical words such as comparatives ('less than'), conditional ('if…then') or connectives ('unless') are also difficult and need practice.

You should emphasise the importance of pupils learning to understand, speak, read and write mathematics. Pupils should learn to say, read and write numbers and other signs and symbols such as percentage (%), pi  and root. Pupils may well be familiar with the meanings of such words in their home language.

Context-embedded problem solving also requires considerable fluency and understanding of English. Pupils need to understand sentence structures used in word problems. Many newly arrived pupils report that they find word-based problems very difficult. Some may have difficulty holding a question or problem in their head.

Effective teaching of vocabulary includes:

• using every opportunity to draw attention to new words or symbols with the whole class, in a group or when talking to individual pupils
• explaining the meaning of new words and rehearsing them several times. Encourage pupils to use words in context in oral sessions by using focused questions
• ensuring that, as well as learning new vocabulary, pupils consolidate familiar terms
• being aware of the language demands of particular tasks and how words are used in a mathematics lesson.

Joining in when the whole class speaks aloud provides an opportunity for pupils learning EAL to rehearse the mathematical language. In oral and mental starters, for example, all pupils might speak in unison as they:

• extend a number sequence
• count along a decimal number line
• chant a multiplication table
• read an equation or inequality aloud.

If possible you should allow the class to go through things twice so that pupils with EAL get a chance to listen and repeat. As soon as English-language beginners are reasonably confident at saying something with others, you might ask them to say it again on their own. You should give them plenty of time and check their understanding regularly.

Resources to support the teaching and learning of mathematical language

Mathematics vocabulary flashcards can be downloaded from the Key stage 3 strategy website. The flashcards have all the words from the vocabulary checklist in the Framework for teaching mathematics: years 7, 8 and 9. The vocabulary words are grouped by year and are in six sections:

• applying mathematics and solving problems
• numbers and the number system
• calculations
• algebra
• shape, space and measures
• handling data.

Included in the useful weblinks below are key stage 2 resources that teachers may find useful if pupils have gaps in their knowledge of have missed schooling.

The National numeracy strategy: mathematical vocabulary booklet identifies the words and phrases that pupils need to understand and use if they are to make good progress in mathematics. This will be of particular use to any member of staff supporting EAL pupils who may need to cover mathematics from key stage 2. Vocabulary that is appropriate to the lesson could be displayed the pupils could build their own dual-language dictionary of key words with definitions as a reference to consolidate understanding.

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Approaches to number and algebra

The new emphasis on mental calculation and refining mental calculation methods into informal written methods (before proceeding to standard written methods) might be a source of difficulty for pupils who have been taught a single correct written method of addition.

Early understanding of number and number operations is developed through using base 10 materials, number lines, hundred squares and so on, which encourage mental imagery. Some newly arrived pupils may not have prior experience of this approach and may need to use practical resources.

Teachers might consider working with EAL staff to develop induction materials. Such materials could introduce pupils to the areas where the initial assessment identified gaps in their learning. Some children, however, may need little mathematical induction. Instead, their induction may need to focus on the mathematical register and terminology. The 'Admission and induction' area of this site offers further guidance on this. The 'English as an additional language' area of this site outlines some of the teaching strategies to consider.

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Planning access to mathematical activities

When considering how newly arrived pupils will access mathematical activities successfully teachers are encouraged to:

• model mathematics and mathematical language using appropriate resources and visual displays
• prepare resources that can help pupils make sense of an activity, for example personal whiteboards and counters that also allow pupils to show their answers rather than say them if appropriate
• help pupils solve problems by providing a writing frame so that they can use it to record their questions and strategies
• give time or support before responses are required, for example personal thinking time, partner talk in the home language, more scaffolding until the pupil can answer correctly
• model for the pupils how to represent problems using diagrams, number lines, number sentences and so on
• carefully plan pupil grouping, for example pairing more fluent speakers of English with less fluent speakers.

Where a teacher has in-class support:

• plan jointly with EMA staff and/or other support staff
• plan the use of adult and pupil models of spoken English
• prepare questions so there is a balance of open and closed questions
• plan which pupils will be targeted with which questions
• identify the vocabulary related to the activities highlighting the new words
• plan for pre-tutoring to review the necessary mathematical skills. This may mean consolidating the prior knowledge, skills and understanding needed for the newly arrived pupil to take part fully in the lesson, and/or assessing the support that may be needed in specific parts of the lesson 
• encourage the pupils to practise their responses using their home language with a partner who shares the first language or with an adult
• use ICT resources to develop mathematical understanding (see useful weblinks)
• gather feedback/data from the adult working with targeted pupils to inform future planning.

In lessons without additional support, the EAL support teacher might help prepare visual materials for the activities.

Teachers can offer extra support to pupils by announcing early in the lesson the questions that they will ask at the end of the lesson or during the plenary. Pupils will have had some warning about what is coming and a chance to think about it and translate their ideas.

Portsmouth Ethnic Minority Achievement Service (EMAS) website has a range of guidance, teacher resources and information that will be of use to all teachers. The mathematics area of the site includes downloadable guidance on supporting EAL pupils in mathematics lessons.

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Numerals in different scripts

The form of western numerals differs from those used in many Arabic-speaking Middle Eastern countries, as well as those used in the Indian subcontinent. Older pupils will be familiar with numerals in western and other systems, but younger pupils may not.

Pupils who understand number value and who are able to write numerals in their home language may confuse the two scripts. For example, a Bengali pupil may read 8 as 4 or record 7 with a symbol similar to 9. Compare these examples of scripts. It is easy to see how pupils might confuse some numerals.

Gujarati

sunna 0

ek 1

be 2

tran 3

char 4

panc 5

cha 6

sat 7

at 8

nav 9

das 10

Bengali

(Bengali)
sunna	ek	dui	tin	car	panc	chay	sat	at	nay	das
(Assamese)
	ek	dui	tini	sari	pãs	say	khat	ath	na	dah
0	1	2	3	4	5	6	7	8	9	10

Self-evaluation of approaches to teaching and learning

Pupils have different learning styles. The downloadable self-evaluation grid ('Mathematics self-evaluation') provides a basis for considering the learning needs of individuals or particular groups of pupils and the teaching strategies to support them. You could also use this chart to observe others teaching or for teaching assistants to complete when observing the class teacher as part of their continuing professional development.

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What is the potential in the mathematics curriculum for valuing diversity and challenging racism?

The national curriculum programme of study and the framework provide starting points for valuing diversity and challenging racism in the classroom. On the Respect for all in mathematics website there is guidance on how the programme of study requirements provide opportunities to value diversity and challenge racism. 

Pupils should be taught to view differences in others positively, whether they arise from race, gender, ability, disability, age, religion/belief or sexual orientation. Mathematics teachers can achieve this by using materials that reflect social and cultural diversity, and by providing positive images of race, gender, ability, disability, age, religion/belief and sexual orientation.

Acknowledging the contribution of other cultures

Much of the breadth of study in mathematics has its origins and development in the work of scholars from other cultures. Trigonometry owes its origins to Babylonian mathematicians, while the numerals we use today in the west had their origins in Hindu numbers, developed further by Arabs. This can be acknowledged in lessons, and examples of mathematical problems from other cultures used in class. QCA's Respect for all website provides ideas for this.  

The useful weblinks on this site include sites where you will find information about famous mathematicians in different parts of the world, and resources that may support teachers and pupils in the classroom.

The role of the subject leader

The key stage 3 national strategy booklet Securing improvement: the role of subject leaders is intended to support subject leaders.

The work of subject leaders in schools is vital. With the school's key stage 3 strategy manager, subject leaders are the key contact between the strategy and classroom teachers. They provide the leadership and subject expertise and engender the enthusiasm that teachers need to understand and implement the strategy. This booklet identifies core tasks and areas for development. The booklet has three sections.

Section 1 identifies three core roles: judging standards, evaluating teaching and learning, and leading sustainable improvement. For schools with pupils learning EAL it is equally important to identify, target and sustain improvement in their mathematics.

Section 2 describes what each role entails, and identifies the core tasks for each role.

Section 3 identifies a series of detailed actions for subject leaders using self-evaluation grids, links to key stage 3 materials and some school-based examples.

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Useful weblinks

Please note: QCA is not responsible for the content of external sites

BBC: Schools
Three areas of this website, 'School maths 11 to 16', 'School maths 16+' and 'Bitesize revision: key stage 3', contain revision activities and skills practice for key areas of mathematics. The sites are often recommended to EAL learners who need to catch up on core content, although they are not specifically designed for this.

Becta: ICT advice for teachers
This area of the Becta website offers a range of support and guidance to classroom practitioners. You can search by subject or by EAL to find guidance about how to make the curriculum more accessible to pupils. There are software suggestions and links to other websites.

Birmingham Grid for Learning: Mental gym (community languages version)
A community languages version of the existing Mental Gym activity, now available in Arabic, Bengali, Chinese, English, Somali and Urdu. The activity is designed for key stages 2, 3 and 4.

Birmingham Grid for Learning: Collaborative Learning Project
This website contains a range of activities. Some can be ordered but many are available as free downloads.

DCFS: Key stage 3 national strategy
In the 'Publications' area of this website there is a list of all the available publications, including a section on mathematics.

DCFS: Access and engagement in mathematics: teaching pupils for whom English is an additional language
Although this guidance applies the principles of the key stage 3 national strategy to the teaching and learning of mathematics for pupils learning English as an additional language, much of it is equally applicable to teachers of older students. The principles are:

• expectations - establishing high expectations for all pupils and setting challenging targets for them to achieve
• progression - strengthening the transition from key stage 2 to key stage 2 and ensuring progression in teaching and learning across key stage 3
• engagement - promoting approaches to teaching and learning that engage and motivate pupils and demand their active participation
• transformation - strengthening teaching and learning through a programme of professional development and practical support.

The guidance suggests strategies to help teachers provide access for pupils at different points of learning English. It is important to support them to develop both their understanding and use of the English language and to enhance their learning in mathematics lessons.

DCFS: Primary national strategy: Developing the use of first languages in a multi-ethnic, multilingual inner-city primary school
This case study demonstrates how a school has shown significant improvement in achievement as well as attainment of all pupils in English, mathematics and science. The strategies they implemented are described.

Regent's Park Community Primary School is a multi-ethnic multilingual school in an inner-city area of Birmingham. It is in an area of high unemployment and social deprivation. The school is a two-form entry primary school, with a 60-place nursery unit. Ninety-two per cent of its pupils have EAL. Many pupils speak Urdu, Pushtu or Panjabi (Mirpuri) but within the whole-school community there are speakers of over 10 languages. This case study is not specific to mathematics. However, it does offer principles such as paired work in a pupil's first language and whole-group work in more than one language, which is a helpful model.

DCFS: Literacy across the curriculum
The Literacy across the curriculum materials are designed to support schools that have already done considerable work on this aspect as well as those that are just starting. The materials are available from the 'Resources and publications' of the Key stage 3 strategy website.

The training pack contains notes for thirteen possible units of training. Each unit starts with a list of objectives, suggestions for use, resources required and an overview of the session. Associated handouts and OHTs are also supplied. Module 12, ‘All inclusive: supporting EAL learners’ illustrates how EAL learners can be included effectively in planning and teaching and invites participants to review the level of provision for EAL learners and identify where improvements are needed.

DCFS: Unlocking potential: raising ethnic minority attainment at key stage 3
This is a training module aimed at headteachers, school strategy managers, ethnic minority achievement managers and subject leaders in schools. The purpose is for a school to review its current practice in relation to ethnic minority pupils and those learning EAL, and then to identify key actions that will improve the attainment of those pupils. The module includes three school case studies, which can be used individually or as a set across which to track the key themes of managing staff and resources, managing teaching and learning, and monitoring and tracking. The module is available to download from the 'Resources and publications' of the Key stage 3 strategy website.

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DCFS: Primary national strategy: Mathematical vocabulary
The mathematical vocabulary identifies words and phrases that pupils need to understand and use if they are to make good progress in mathematics. It is designed to support the national numeracy strategy alongside the Framework for teaching mathematics. To support the teaching of vocabulary the strategy also produces mathematical vocabulary flashcards (available on the website). These flashcards are word-processor files from which you can print out a set of cards for all the words in the mathematical vocabulary.

DCFS: Primary national strategy: Mathematics and inclusion: materials for providers of initial teacher training
These inclusion materials consist of a file and an accompanying video. They are intended to provide a variety of resources, information and ideas to support tutors in:

• helping trainee teachers to consider the needs of all pupils when planning and assessing mathematics
• enabling trainees to make connections between recent and relevant research related to inclusion and the pupils’ learning experiences
• engaging trainees in debate and evaluation of their own practice with respect to inclusion issues in mathematics.

Much of the material is applicable to teachers and classroom assistants.

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Hounslow Language Service
Here you will find a range of downloadable resources including word lists in different languages, for example Albanian and Somali, strategies for supporting bilingual pupils in mathematics, explanation of mathematical terms in both languages, and dual-text stories in eight different languages.

Maths Booster Sea Mission
A series of resources aimed at supporting the development of pupils' mathematical understanding. This is a fun activity aimed at boosting maths development by engaging pupils in a gaming environment: to launch one of the 11 activities the pupil first has to successfully land the submarine. It is now available in community languages including Arabic, Bengali, Chinese, English, Somali and Urdu.

National Association for Language Development in the Curriculum (NALDIC): Publications
NALDIC produces a range of publications, reports and papers that support the work of teachers working with pupils for whom English is an additional language. The paper Defining a role: the EAL teacher in maths describes the language of mathematics with particular reference to pupils learning EAL. Initially discussing how mathematical definitions are presented at lexical level, the author then looks at vocabulary. This includes general vocabulary used in mathematics questions and tasks, technical vocabulary and specialist vocabulary where general words are used that have particular mathematical meanings, for instance 'root' and 'difference'. The paper then considers language at the discourse level with particular emphasis on logical connectives such as 'therefore' or 'unless'. The paper also draws attention to other difficulties for pupils with EAL: syntax, use of symbols and metaphor, and developing competence in reading and writing mathematics. It suggests that pupils need to be made explicitly aware of the features of mathematical language, joining the concepts to the language used to represent them.

National Grid for Learning (NGfL): Inclusion
NGfL provides a catalogue of resources to support individual learning needs for teaching professionals, parents, carers and learners. Resources include publications, software, equipment and online information. Select 'Browse catalogue' on the home page to select an area of interest.

NGfL: Cross-curricular numeracy at key stage 3: number systems and numerical methods
This resource looks at mathematics around the world, focusing on number systems and how the four basic operations are carried out.

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NGfL: Learning from listening: talk in a multilingual mathematics classroom
This paper looks at word problems in the primary mathematics curriculum with particular reference to EAL pupils.

Ofsted: Managing the Ethnic Minority Achievement Grant: good practice in primary schools
This report (2004) includes case studies of schools that manage their Ethnic Minority Achievement Grant (EMAG) funding effectively.

Omniglot
Omniglot is a guide to writing systems and written languages. It includes numerals in different scripts and the appropriate fonts.

QCA: Assessment for learning
General guidance that describes assessment for learning as the process of seeking and interpreting evidence for use by learners and their teachers to decide where the learners are in their learning, where they need to go and how best to get there.

QCA: Assessment for learning: Using assessment to raise achievement in mathematics
Guidance aimed at providing information about involving pupils in assessing their own performance, setting learning goals for pupils and sharing these with them, using effective questioning techniques to assess and further pupils' learning, and using marking and feedback strategies to inform pupils about their progress. Includes four case studies.

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QCA: Inclusion
This area of the QCA website includes references to documents and guidance relating to equal opportunities, and several sets of material on diversity and inclusion.

QCA: Respect for all in mathematics
This guidance encourages teachers to reflect on the values embedded in existing educational approaches and materials. Some of the activities (organised by subject) provide practical help to teachers in dealing with tensions that may arise in the classroom. All the activities aim to foster a greater awareness and understanding of values, cultures and practices.

Portsmouth Ethnic Minority Achievement Service (EMAS)
Portsmouth EMAS produces a range of resources. On this website you will also find exemplar models of good practice with respect to EAL learners and minority ethnic pupils. These demonstrate specific ways in which practitioners' input can directly impact on EAL learners and minority ethnic pupils.

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Further resources

Association of Teachers of Mathematics (ATM): Historical connections 
These are books giving a brief synopsis of famous mathematicians' lives (male and female, ancient and modern and from many cultures) and the mathematics they developed. Includes worksheets illustrating the mathematics. The ATM also produces numeracy posters showing mathematical words and symbols (suitable for key stages 2 and 3), numeracy posters and postcards depicting a variety of methods of computation from different cultures, and activity books that explore designs from American patchwork patterns (suitable for key stage 2).

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Refugee Council
The Refugee Council produces 'Maths words for school use' in the following languages:

• Arabic and English
• Persian and English
• Somali and English
• Tamil and English
• Kurdish and English.

Multiple factors: classroom mathematics for equality and justice, Shan, SJ and Bailey, P, Trentham Books, 1991

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