By Jo Cayley – January 2023
I have recently made the move from a mainstream primary to a special school after teaching in mainstream for 25 years. As a Teaching for Mastery specialist, my first question was ‘How can Teaching for Mastery be adapted for a special needs setting?’ Having used and applied the NCETM five big ideas over the course of my Teaching for Mastery journey, a key question we must ask when working in special education is: “how do the five big ideas of teaching for mastery apply to children with high levels of special needs?”. Many children in special school settings are learning mathematics at levels which are earlier than National Curriculum descriptors, some are even pre-numeric and non-verbal, and the five big ideas as they currently stand might not serve our purpose. Nevertheless, the mathematical world is part of their practical and social lives, and we should therefore aim to help them develop the fundamental roots of mathematical learning that is essential to their lives. Within our special settings there are a wide range of children with very different needs. Working in a special school can allow teachers to focus on each student as an individual with needs that need addressing. While mainstream teaching can allow us to make a positive impact on many children, within special schools we can have a deep impact on individual learners.
A key aim of Teaching for Mastery is to be inclusive for all pupils. In whole class teaching, the use of one curriculum that works for all is encouraged, with everybody studying the same topic and being provided with support and challenge as needed. High expectations can still be applied within special education and children within the same class may be able to access the same curriculum to a certain extent, but the use of individual differentiation may be needed, and children are more likely to learn at different rates, with some needing more support and repetition than others. Within our school, we wonder if we need one curriculum for all, one curriculum for each class or one curriculum for each learner. In reality, it is often the latter but working together with others on the same mathematical task is an important part of mathematical learning that we try to enable whenever possible. In some classes, groups of children can be taught together, in others it is more individualised. The Ofsted framework says ‘teachers present subject matter clearly…they respond and adapt their teaching as necessary, without unnecessarily elaborate or differentiated approaches’ but also ‘the provider has the same academic, technical or vocational ambitions for almost all learners. Where this is not practical – for example, for some learners with high levels of SEND – its curriculum is designed to be ambitious and to meet their needs.’ (2022) The mastery principle suggests that pupils should broadly move through the curriculum at the same pace. As far as possible, pupils should stay together on the same topic with necessary differentiation such as removing barriers and providing targeted support, but without the need for many different levels for each step. ‘Low floor, high ceiling tasks’ support this approach to differentiation together with reasoning and problem-solving questions that will challenge all pupils and allow all children to access the maths at their own level. This approach works well within special schools, with children being able to work together on the same task at different levels, and we have found many useful activities from websites such as Nrich, I see maths and Youcubed as well as engaging children with creative activities and maths games.
Many of the teaching strategies we advocate for all pupils are particularly useful for pupils with SEND. For example, using concrete and pictorial representations. The use of concrete and pictorial representations to develop strategies to deepen and embed understanding is important for all learners, particularly those with special educational needs. For many pupils, the CPA approach is a ‘way in’ to a topic whilst also it can be challenge for pupils to find an alternative representation to the ones they already have. It is essential for teachers to model the use of manipulatives and make it clear that the resources are accessible for all to use. Children with special educational needs may rely on the representations and may need support to make the links between the concrete and abstract. Sometimes, the use of too many representations may be confusing for children and it may be that one representation is more useful than another. In my class, Unifix cubes have been particularly useful in teaching the numbers to 20 as they are easy to handle and manipulate. Groups of 5s or 10s helps the children to use these benchmark numbers and relate to the fingers on their hands. The rekenrek has also been useful and we have been successfully following the Mastering Number programme in many of our primary and secondary classes.
Teaching for Mastery promotes multiple opportunities to look at topics again in new contexts. This enables teachers to support students who have struggled with a topic to spend more time reconsidering and developing their understanding. Retrieval tasks are ideal to assess what has been learnt and what might need further work or intervention. Children with special educational needs may need more opportunities for revisiting and retrieval to embed the learning.
Planning for misconceptions by pre-empting examples of where pupils could go wrong, and challenging the pupils to spot, explain and rectify errors is an essential part of Teaching for Mastery. Pupils’ responses to these prompts helps teachers to identify and tackle misunderstandings early on rather than let these incorrect ideas become established in pupils’ minds. Thinking about what pupils need to have covered before in order to access a step and assessing these are important. Incorporating revisiting these before a topic is taught, helps support learning throughout the unit and ensuring connections are made. Children with SEND will often need support to see these links and have them made explicit to them.
When teaching, we need to consider the key aim or aims of a lesson and be aware of cognitive overload. Fluency is an important part of maths, but some children struggle to recall facts, so support such as a prompt sheet may help children to access the mathematics and not get bogged down with the calculations. For example, if the focus of a lesson is understanding that the area of a rectangle is found by multiplying the length by the width, then providing pupils with times-tables grids or calculators will help them to focus on area rather than struggling with the mechanics of the calculations if these are an obstacle.
Pre-teaching; going through some key ideas with pupils in short, targeted sessions before the topic is taught, enables them to have a head start and be prepared for what’s coming up, often hugely increasing confidence and participation at the start of a topic. Providing additional individualised support after lessons through targeted interventions can help to close gaps and/or deepen understanding. It may be necessary to look back at previous steps to support this.
The Ofsted maths review (2021) says a great deal about pupils with SEND, and it seems worth quoting this in depth:
Pupils with SEND benefit hugely from explicit, systematic instruction and systematic rehearsal of declarative and procedural knowledge. The benefits of these approaches extend beyond enhanced academic attainment and proficiency. The relationship between cognitive ability and academic attainment, including in numeracy, is in fact bidirectional. Therefore, educational outcomes for pupils with SEND are likely to improve if teachers use systematic instruction and rehearsal to help pupils learn planned content. This approach is particularly useful for pupils with moderate learning difficulties who have slower cognitive processing speed. Systematic approaches increase the amount of content considered per unit of time. Systematic curricular approaches give pupils with SEND and disadvantaged pupils a better chance of success, of keeping up and therefore of feeling included.
Playing to pupils’ strengths: the powerful declarative memory systems of pupils with autism
Many pupils with autism have ‘normal to above average algorithmic thinking ability’ but can struggle with reasoning and problem-solving because of:
language processing deficits
difficulties in classifying problems by type
lack of knowledge of strategies
the use of ‘inefficient and overly complex procedures’ for calculation
Teachers can fill these gaps in knowledge with systematic curriculums, teaching approaches and rehearsal. For example, teaching efficient algorithms to pupils with autism speeds up their calculations. They then have more time to learn strategies for solving classes of problem. However, research also shows that the unique organisation and powerful declarative memory systems of many people with autism help them study, and develop proficiency in, the subject. Potentially, a powerful declarative memory system can take on a compensatory role; thus many pupils with autism might benefit from a deliberate focus on memorisation of core facts and methods.
Leaders should therefore consider ways to give autistic pupils more time to study core content so that they can close gaps in learning through deliberate memorisation. Leaders should also make sure pupils’ lesson time is used efficiently and effectively.
Based on the above, high-quality maths education may have the following features:
New content draws on and makes links with the content that pupils have previously acquired.
Curriculum progression is by intelligent design rather than by choice or chance.
Rehearsal sequences align with curriculum sequences.
Pupils who are more likely to struggle or who are at risk of falling behind are given more time to complete tasks, rather than different tasks or curriculums, so that they can commit core facts and methods to long-term memory.
The ATM / Mathematical Association response to the Ofsted Review has some useful practical ideas to support these statements. Adapting Teaching for Mastery for SEND has been a challenge, but the more I have thought about and understood the five big ideas, the more I have been able to apply these to the individual children I work with. Here is the current version of our school’s Maths Curriculum (it is still work in progress):
Curriculum Aims: The Intent - The Why
We strive to make maths link to real life and be relevant, engaging and fun. Maths can be found in every part of day-to-day life and is a fundamental skill that we need to support our pupils to develop in preparation for adult life.
Curriculum Content: The What
We teach the fundamental skills needed for future life. Our delivery is based on the maths mastery approach and closely mirrors the National Curriculum expectations. There is a strong emphasis on developing number skills as well as a focus on :
- Measurement — weight, capacity, length and height
- Time
- Money
- Shape
- Pattern
- Statistics
- Maths skills are generalised and extended within all curriculum activities.
Curriculum Delivery: The Implementation – The How
In primary and secondary semi-formal classes, maths skills are taught though the context of familiar stories, where abstract maths ideas are introduced in a fun and ‘imagined’ way so that children are encouraged to think freely and learn creatively. Interventions have a maths mastery approach though play. Maths is delivered in context and follows three stages.
Firstly, ‘Concrete’ using tactile (physical) objects that build on a child’s existing understanding of maths and makes ‘unfamiliar’ or abstract concepts such as ‘fractions’ to life by allowing children to interact, solve problems by experiencing and handling concrete objects. For example, using real fruit for the story ‘Handa’s Surprise’
The ‘Pictorial’ stage is using visual representations of concrete objects used to model problems. Children are encouraged to make connections between the concrete objects and abstract concepts of math e.g. ‘fractions’ and by ‘seeing’ the pictorial image, helps children to visualise the abstract problem and makes it more accessible and understandable.
The final stage is ‘Symbolic’ stage. This is where children use abstract symbols such as ‘+.-,=.x,÷’ to solve problems. This stage requires adult modelling of mathematical symbols and concepts using numbers, names and notations. It is the final stage of maths mastery where fluency and reasoning of maths skills are related from stories and applied to different contexts and everyday life.
Teaching and learning maths in stories combine all three of these stages. The following interventions craft a powerful mental connection children make between, concrete, pictorial and the abstract stages, whilst being attuned to the child’s own learning style. In secondary formal classes maths is taught through half termly units there is strong focus on practical application and problem solving. In sixth form maths is delivered through a series of projects that link to real life events. Maths is delivered through taught sessions, across the curriculum and in the community. There is a strong focus on money and time for example budgeting and shopping within cooking sessions. The school shop offers an opportunity for pupils to consolidate, generalise and extend their maths skills.
Special Events: The Celebration
In the Autumn term we have a half termly focus on maths this includes special events such as the shopping street, maths week and a celebration of learning maths in the outdoor area. The Christmas Bazaar is organised and run by the students.
Pupil Attainment and Progress: The Impact
We have developed our own assessment system based on National Curriculum expectations. These are called the Rainbow and Gemstone levels. Progress is tracked within an app called Evidence for Learning.
Pupils in KS4 and above follow accredited courses linked to Equals moving on, OCR life and living skills, Entry Level and functional skills.
I am at the start of my journey of using Teaching for Mastery within a special school context, but it is already proving to be interesting!
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