Pedagogical Strategies⁽ⁱ⁾

Inclusion in Mathematics

This resource is licenced under an Open Government Licence (OGL).

This resource is adapted from the 2008 National Strategies: Secondary 'Framework for secondary maths'. The resource is available in format, and editable (File:Inclusive Teaching in maths.doc) format. It can also be downloaded from the National Archives [[1]].

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Inclusive teaching in mathematics

Introduction

Your vision for planning and teaching will apply to all classes and groups of pupils, and to each individual pupil. Only occasionally are the needs of individual pupils or groups of pupils so distinct that entirely different approaches are needed in order to help them learn mathematics and engage fully in lessons. In these instances, specialist guidance more detailed than that given in this short introduction will be needed.

In the main, you will adapt existing planning and teaching principles in order to include all pupils. This section responds to two considerations about planning and teaching mathematics:

• What is the best way to support the mathematical progress of pupils who have particular needs? For example, pupils learning English as an additional language or those with special educational needs, learning difficulties or disabilities.

• What are the most effective actions to take if any individual pupil or groups of pupils are not making expected progress?

In most cases the suggestions on the following pages involve adjusting existing practice rather than doing something new. For example:

• If you believe that pupils need to work together and to talk about their mathematics, the task is now to facilitate this collaboration more strategically for a pupil with emotional difficulties or a pupil who is not yet fluent in English.
• If you are working to develop a more open questioning style which allows pupils time to think, the task is now to choose questions so that pupils with misconceptions have them revealed and addressed.

The guidance that follows is based on strategies which have been tried and tested in the classroom. Each section includes references to further Strategy resources which will provide more background detail and more practical support.

You will notice that all entries in this section recommend keeping expectations high. Where expectations are high and teaching reflects this, most pupils, whatever their starting point, can aim for two levels of progress during Key Stage 3. For example

• design lessons so that all pupils are included in ways that enhance their progress (see below)
• aim to keep an accurate picture of pupils’ progress towards their targets (see ‘Assessment and target-setting’)
• when underperformance is identified, make a swift and strategic response (see Intervention in mathematics).

A fair ‘rule of thumb’ is to

• know the pupils well
• What can they already do mathematically?
• What helps them learn effectively?
• know the mathematics well
• What is needed to tackle the tasks?
• What connections can be made?
• What is this leading to?
• respond to the learning
• How effective is the learning in these lessons?
• Is the pace appropriate?

Pupils with English as an additional language (EAL)

EAL pupils may need support to develop language and to access the mathematics curriculum. It is easy to underestimate what pupils can do mathematically simply because they are new learners of English. Planning, teaching and learning for pupils learning EAL should be underpinned by the following key principles

• Bilingualism is an asset and the first language has a continuing and significant role in identity, learning and the acquisition of additional languages.
• Cognitive challenge can and should be kept appropriately high through the provision of linguistic and contextual support.
• Language acquisition goes hand-in-hand with cognitive and academic development, with an inclusive curriculum as the context.

Planning for EAL learners is most effective when

• it is part of the planning process of the whole department and is embedded in the usual planning format
• it takes account of the prior learning of the pupils, whether in the UK or abroad
• the role of additional adults with EAL expertise and/or bilingual or multilingual skills is clearly indicated and they are either involved in the planning process or have plans shared with them at the earliest opportunity
• contexts for learning are relevant, motivating and culturally inclusive
• it takes account of the language demands of the curriculum, including the use of subject- specific vocabulary where words have specific meanings in mathematics that are different from their ordinary use (e.g. mean, power, root) and grammatical complexities such as comparatives, conditionals and connectives
• it provides opportunities for speaking and listening, collaborative work and other strategies for language development
• consideration is given to the language of the task, how the pupils are grouped, and use of first language for learning.

Aim for EAL learners to hear good models of language from peers and adults as a regular feature of mathematics lessons. They are more likely to make progress in their learning when working alongside peers with simlar cognitive ability and greater linguistic proficiency. Use cooperative small group work so that EAL pupils work collaboratively with more expert speakers of English as well as pupils who share their first language.

Language learning styles vary and some pupils will not want to speak until they feel confident that they can produce an accurate and complete utterance. A silent period, where pupils are learning receptively by listening, is a natural stage that many early-stage learners of EAL go through.

Adapt your questioning so that EAL learners feel included and are encouraged to contribute orally when they are ready to do so.

Acquisition of academic language will usually take considerably longer to develop than social language. Try not to compromise on the cognitive challenge in the mathematics and use bilingual approaches strategically; for example, pupils’ understanding can be supported by exposing and discussing common misconceptions using the first language.

You will need to think carefully about how to build on the knowledge EAL pupils bring to a sequence of lessons. Encourage other pupils and teaching assistants to provide a listening focus by using additional props and prompts as they explain and discuss during lessons. Try to model this in your whole class work by using images and models, making appropriate use of ICT where possible. Offer further support by providing note-taking frameworks and pre-teach specific vocabulary.

When pupils arrive in school, their prior knowledge of mathematics must be assessed across a range of strands of mathematics and a range of levels. Assessments can use either English or a language with which the pupil is familiar. It is helpful if someone from the mathematics

department is involved in the assessment. Bear in mind that some pupils will find questions set in context more difficult to interpret, so provide a range of question types. Assessment activities should be as practical as possible and be modelled for the pupil. The ease and confidence with which they approach or carry out the task from the cues given will be crucial elements affecting the judgment you reach. This is not a ‘test’; it is Assessment for learning and should result in both teacher and pupil having a sense of what needs to happen next to support learning.

A culturally diverse cohort provides an opportunity for mathematics teaching and learning. The National Curriculum emphasises the importance of the history of mathematics and the mathematics of different cultures. Much of algebra and trigonometry owe their origins to Arab mathematicians. Pascal’s triangle appears in Chinese mathematics some 300 years before Pascal was born. There are many games and puzzles from Africa, China and India which can be used to explore mathematical reasoning. Pupils will also bring a range of cultural perspectives and experiences to the classroom, which can be reflected in the curriculum and used to further the pupils' understanding of the importance of the issues of diversity. This also enables pupils’ cultures to be valued.

‘The nature and severity of the cognition and learning needs of pupils learning English as an additional language are easily underestimated or overestimated. The identification and assessment of the special educational needs of children whose first language is not English requires particular care. It is necessary to consider the child within the context of their home, culture and community.’ SEN Code of Practice 2001 5.15

Pupils with special educational needs (SEN)

Special educational needs/learning difficulties and disabilities

(SEN/LDD)

Approximately 20 per cent of the school population is defined as having special educational needs (SEN) and/or learning difficulties or disabilities (LDD).

Some of these pupils will also have learning difficulties linked to social deprivation and some pupils with special educational needs will also have disabilities. The learning difficulties encountered are often, but not always, associated with literacy and numeracy development and are sometimes aggravated by missed or interrupted schooling, perhaps due to long-term medical conditions.

In many cases, pupils’ needs will be met through appropriate intervention (see ‘Intervention in mathematics’), including the differentiation of tasks and materials. Rich tasks can be particularly useful in enabling access at different points for different pupils. You can ensure that pupils with SEN/LDD make good progress by

• entitling all pupils to equal access to a full learning entitlement, whatever their starting point
• ensuring that there is high quality, differentiated assessment of individual need
• managing and liaising with additional adults
• planning lessons effectively to ensure appropriate progress, and differentiation using the ‘Waves model’ for intervention and making use of the National Strategy progression maps to identify suitable curricular targets at class, group or individual levels (see ‘Intervention in mathematics’)
• ensuring that unit and lesson plans include a suitable range of objectives
• using a variety of teaching and learning styles
• using data effective assessment to check pupil’s understanding against learning objectives, in class and over timeto track pupils’ progress against curricular targets (see ‘Assessment and target setting’)
• using a mix of whole class, small group, paired and individual work to allow the support and development of individuals’ needs
• presenting information in a variety of forms – diagrams, models, verbal explanations and written explanations – to ensure accessibility
• providing structure for longer tasks; for example, through the use of speaking or recording frames.

A smaller number of pupils may need access to specialist equipment and approaches, or to alternative or adapted activities. There may be pupils in a class who need support in order to take part in whole-class work.

This support may take the form of

• specific help with the recall of mathematical facts, to compensate for difficulties with long- or short-term memory
• help with the interpretation of data represented in graphs, tables or charts, to compensate for difficulties with visual discrimination
• access to tactile and other specialist equipment for work on shape, space and measures, to overcome difficulties with sight or in managing visual information
• help with interpreting or responding to oral directions, to compensate for difficulties with hearing or in auditory discrimination
• tasks designed to have smaller steps, which hold pupils into the content and pace of the lesson.

There will be occasions when it is also appropriate to seek advice and further support from the leadership team, other professionals, outreach from special schools and external specialists., as described in the SEN Code of Practice or, in exceptional circumstances, through a statement of special educational need.

Pupils with disabilities

All schools are required to make ‘reasonable adjustments’ to enable pupils with physical difficulties to access the statutory curriculum. Support for most pupils with physical or sensory disabilities will generally take place in mainstream lessons as they work on the same mathematics programme as their peer group. Modifications to materials, equipment and furniture can help to meet the pupils’ particular needs so that they can work alongside their peers. For example, some pupils may need to use ICT to assist them in reading or recording their work. Pupils with hearing or visual impairments may need to be appropriately positioned in a class or helped to take part in an activity through signing or support by another adult.

Other adaptations which may be necessary include preparation for oral and mental work and the pace at which it is conducted, the use of signing, Braille and symbols, and the provision of materials that can be physically manipulated, including specific ICT aids and adapted measuring equipment.

Although pupils with disabilities often need time to become proficient with aids, expectations for them should remain high, with the focus on giving them maximum access and independence.

Pupils with emotional and behavioural difficulties

Many pupils with emotional and behavioural difficulties have poor literacy and numeracy skills as a result of their inability to maintain concentration and persevere with tasks. They can be supported by

• ensuring that expectations are high, to prevent them becoming bored (e.g. not oversimplifying tasks)
• structuring lessons to maintain pace, giving opportunities for independent working and using a variety of activities
• using additional adults to help pupils begin tasks and to help them maintain concentration
• using praise to reward good learning behaviours (e.g. working effectively in groups)
• making mathematics relevant by relating it to the real world.

All pupils have an entitlement to the opportunity to develop emotional and social literacy but pupils with emotional and behavioural difficulties have an urgent need in this area.

Pupils with communication difficulties

Pupils with communication difficulties face particular challenges in mathematics. They need clear, effective teaching, which steadily builds their confidence and participation. Try to use a structured approach to the mathematical language required and frame its use by pupils. Some pupils with speech and language impairments have no other developmental difficulties and their mathematics lessons provide the opportunity to work alongside peers, practising and discovering strategies to overcome their difficulties.

Pupils who have autistic spectrum disorders, however, require well-structured lessons with clear routines and predictable parts. They respond best when the language used is concise, teaching is explicit, and challenges are direct and well focused. Try to ensure that your expectations are made crystal clear. Be explicit about what you expect the pupil to learn and exactly what you expect them to do. Explain this clearly for the lesson overall and then re-clarify for each separate part of the lesson or activity.

Pupils who are working well below national expectations for their age group

Where schools have significant numbers of pupils starting Key Stage 3 at level 3 or below in mathematics, it will be necessary to adapt the yearly teaching programmes more significantly. In general this can be achieved by using those from the preceding year, adding adjustments as necessary to reflect areas of particular difficulty or relative strength.

Pupils who are very able at mathematics

The Schemes of Work tend to provide yearly teaching programmes in this Framework are targets for the majority of pupils in the year group. Able pupils deal with abstract mathematics more readily than do other pupils. They will progress more quickly through these programmes and will need extension and enrichment activities to develop the breadth of their mathematics and the depth of their thinking. They can be stretched by being given extra challenges and harder problems to do when other pupils are consolidating, by offering occasional differentiated group work, and by drawing work from the teaching programmes for older pupils. Homework also provides opportunities to set suitably challenging tasks.

Where numbers permit, able pupils frequently benefit from being able to work collaboratively with pupils of similar ability on challenging tasks. Where this is not possible, very able or gifted pupils who are markedly ahead of the rest of their class can follow individualised programmes at appropriate times, with far fewer practice examples and many more challenging problems to tackle, including work that draws on other subjects. Of course, they still need some teaching to ensure that they understand what they have read and know how to present their work.

Some capable pupils working ahead of age-related expectations can benefit from programmes which lead to early entry for GCSE, say in Year 10. But research indicates two important criteria for these to be successful in helping good mathematicians reach their potential. Firstly, the teaching and learning need to be appropriately stimulating and engaging to foster and maintain an enthusiasm for the subject. Secondly, there need to be clear and accessible routes beyond GCSE (e.g. through Year 11) which will ensure continued engagement with and progression in mathematics.

Inclusion in Science

This resource is licenced under an Open Government Licence (OGL).

This resource is adapted from the 2008 National Strategies: Secondary 'Framework for secondary Science'. The resource is available in format, and editable (File:Inclusive Teaching in Science.doc) format. It can also be downloaded from the National Archives here.

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Inclusion in science

Gifted and talented pupils

The yearly learning objectives in the renewed Framework for secondary science are targets for the majority of pupils in a year group. Able pupils deal with abstract science more readily than other pupils. They will progress more quickly through these learning objectives and will need extension and enrichment activities to develop the breadth of their science and the depth of their thinking.

Previous Government guidance identified seven key features of effective teaching and learning

• conditions for learning
• knowledge of the development of learning
• knowledge of subject and themes
• understanding learners’ needs
• planning
• engagement with learners and learning
• links beyond the classroom.

It is also important that gifted and talented pupils are fully representative of the school or college population. This can mean using multiple criteria and sources of evidence and ensuring that there is shared understanding of the meaning of ‘gifted and talented’.

Supporting English as Additional Language (EAL) learners

Literacy difficulties can slow some pupils’ progress dramatically in science. These issues can apply to a range of groups in school, including EAL learners, who may need support to develop language and to access the science curriculum.

Planning, teaching and learning for pupils learning English as an additional language should be underpinned by the following key principles

• bilingualism is an asset and the first language has a continuing and significant role in identity, learning and the acquisition of additional languages
• cognitive challenge can and should be kept appropriately high through the provision of linguistic and contextual support
• language acquisition goes hand-in-hand with cognitive and academic development, with an inclusive curriculum as the context.

Strategies to support EAL learners in science

It is all too easy to underestimate what pupils can achieve in science simply because they are new learners of the English language. Expectation should be that they progress in their scientific learning at the same rate as other pupils of their age.

Strategies to support learners new to English in science include

• using structured group work to allow intensive, focused teaching input and collaborative work with more expert speakers of English as well as pupils who share a first language
• using structured group work to enable less-confident speakers of English to practise scientific terminology and language in a non-threatening environment so that they can gain confidence in using scientific English appropriately
• using peer-group talk to give pupils time to watch and listen to those fluent in English, and to help them make sense of and apply scientific ideas
• using direct, specific instructions and speaking more slowly, emphasising key words, particularly when describing independent tasks; going through things twice so that pupils get the opportunity to listen and say in their own words what you are asking them to do
• asking individual pupils at the early stages of learning English to present their work orally with support from their peers and only when they are ready
• as soon as English-language beginners are reasonably confident at saying something together with others, asking them to say it again on their own, giving them plenty of time and checking their understanding regularly
• using extra visual clues or gestures, or translation in oral work, and using additional picture cues in written materials
• supporting reading with interactive activities and scaffolds so pupils can access the science learning and ideas
• helping pupils to distinguish words that have different meanings in scientific and everyday contexts
• helping pupils to talk through their ideas before trying to write about them and scaffolding the writing at a level appropriate to the pupils’ skills in writing in English.

Early-stage learners of English

Science lessons are a great place for early-stage learners of English to achieve. Science has the advantage of providing an environment in which learning can occur through using visual and auditory clues. Practical and interactive work provides a great opportunity for early-stage bilingual pupils to learn from seeing and doing, and so start to develop confidence in using English. They can listen to other confident users of English talk about what they are doing in practical work and interactive learning situations.

If the bilingual learner has already been taught science in their first language, then they are likely to know some of the science and start to develop appropriate English to describe the science. If there are other speakers of their first language, they can discuss the science in their first language and then in English, so ensuring that they can learn continue to learn the science and start to develop the English in context.

More advanced learners of English

When a bilingual pupil starts to learn English, they can take up to five years to become fully fluent in all aspects of the language. Initially they will gain confidence in speaking English. This is soon followed by gaining confidence and expertise in aspects of reading. Much later they start to gain skills in writing. Unless EAL pupils are well supported in their reading and writing in science, they often underachieve, particularly in summative assessments and examinations.

In science lessons, pupils need to read and gain meaning from particular types of texts. These texts often include describing

• procedures or experimental investigation
• the form and functions of parts of a system
• processes or mechanisms, such as how a body system or a pulley works. This type of reading requires different skills from reading a novel or newspaper
• article, skills which might be developed in English lessons. Science teachers therefore need to develop the skills of supporting these different types of reading in science for all pupils, but particularly for bilingual pupils.

Once EAL pupils have developed the basics of reading English, they still need considerable support to write English using the genres required in science. Just as the types of reading in science are subject-specific, so is the writing. Science teachers need strategies that develop reading and writing skills through science lessons. Teachers can access support from other specialist colleagues in school such as EAL teachers and use literacy in science materials in order to help more advanced bilingual learners to make good progress in science.

Pupils with special educational needs (SEN), learning difficulties and disabilities (LDD)

Approximately 20% of the school population is defined as having SEN and/or LDD. Some of these pupils will also have learning difficulties linked to social deprivation, and some with special educational needs will also have disabilities. The learning difficulties encountered are often, but not always, in association with literacy and numeracy development, and are sometimes aggravated by missed or interrupted schooling, perhaps due to long-term medical conditions.

In many cases, pupils’ needs will be met through differentiation of tasks and materials. A smaller number of pupils may need access to specialist equipment and approaches, or to alternative or adapted activities. For example, there may be pupils in a class who need support in order to take part in whole-class work, such as

• specific help with the recall of scientific facts, to compensate for difficulties with long- or short-term memory
• help with the interpretation of data represented in graphs, tables or charts, to compensate for difficulties with visual discrimination
• access to tactile and other specialist equipment for making observations and measurements during a scientific enquiry, to overcome difficulties in managing visual information
• help in interpreting or responding to oral directions, to compensate for difficulties in hearing or with auditory discrimination.

It is not possible here to give detailed guidance covering every type of special educational need. However, there are four main areas to consider

• communication and interaction
• cognition and learning
• behaviour, emotional and social development
• sensory or physical difficulties.

Communication and interaction

Pupils who have difficulty in communicating or interacting face particular challenges in science. They need clear, effective teaching that steadily builds their confidence and participation. Use a structured approach to develop the scientific language you expect them to use. Some pupils with speech and language impairments have no other developmental difficulties, and science lessons provide the opportunity to work alongside peers, practising and discovering strategies to overcome their difficulties. However, pupils who have autistic spectrum disorders require well-structured lessons with clear routines and predictable parts. They respond best when the language used is concise, teaching is explicit, and challenges are direct and well focused. Your expectations for what these pupils will learn and do, both in the lesson overall and in each separate part or activity, need to be defined very clearly.

Cognition and learning

The attainment of pupils with significant cognition and learning difficulties is likely to be well below age-related expectations. For them, a much greater degree of differentiation will be necessary. You may need to refer to younger pupils’ Schemes of Work, situating them in a context suited to older pupils. Extra ‘small steps’ can be inserted, and contexts for practical work and problem solving adapted. There will then be time for consolidation without sacrificing the breadth of the teaching programmes or the principle of planning from clearly defined objectives.

Behaviour, emotional and social development

Many pupils with emotional and behavioural difficulties have poor literacy and numeracy skills as a result of their inability to maintain concentration and persevere with tasks. They can be supported by

• ensuring that expectations are high to prevent them becoming bored, for example, not oversimplifying tasks
• structuring lessons to maintain pace, giving opportunities for independent working and using a variety of activities
• using additional adults to help pupils begin tasks and to help them maintain concentration
• using praise to reward good learning behaviours, for example, working effectively in groups
• making science relevant by relating it to the real world.

All pupils have an entitlement to the opportunity to develop emotional and social literacy, but pupils with emotional and behavioural difficulties have an urgent need in this area.

Sensory or physical difficulties

Often pupils with sensory or physical difficulties are intellectually able but may need to develop proficiency with particular aids. These pupils will work on the same science programme as their peer group. Expectations for them should remain high, with the focus on giving them maximum access and independence.

Support should enable them to take part safely and as fully as possible in experimental work. Modifications to science materials, equipment and furniture, and the use of specialist science items, will also help to meet their needs.

Where pupils with sensory impairments need signing support, Braille or materials written in signs or symbols, it is likely that provision will be through a Statement of special educational needs. Where necessary, text should be adapted to a larger print size, or translated into Braille or symbols. ICT should be used to help those with visual impairments to gain better access and understanding.

Pupils with hearing impairments will need to be appropriately positioned in a class and should be helped to gain as much access as possible to science activities by using oscilloscopes and sound level meters, the use of visual demonstrations and using the sense of touch to feel vibrations.

Pupils with visual impairments may need extra time to manage visual information, for example, using microscopes or making observations in experimental work. Extra support may be needed in lessons about light; pupils should be encouraged to use their knowledge that many light sources produce heat.