Learn how to teach mixed ability maths (mastery) in your primary school class and how to differentiate Maths lessons for top set, bottom set and all ability levels.

In a typical class of Year 6 children there is likely to be a seven year gap between achievers in Maths.

A number of measures are used to manage these gaps and children may be divided into different, and apparently homogeneous ability groups or sets. However as more schools embrace mastery and the principles of Asian Maths, whole class teaching in Maths is making a return, with the greater likelihood that your teachers will be supporting or teaching children of very different abilities in your Maths lessons.

Why not just stick to setting by ability?

When children of different abilities are separated from each other then ‘top’ and ‘bottom’ can label themselves in self-fulfilling ways and pupils are not exposed to the stimulus of discussions with others at different levels of knowledge and understanding. Teaching in sets can also mean that individual strengths and weaknesses can easily be missed.

Many teachers have a real problem with the label ‘bottom set’. It’s a powerfully derogatory and divisive term that injects failure and unambitious expectations into the minds of young learners. Low ability is also a no no. It is well documented that learners’ perception of their own ability is a commanding influencer on their attitude to learning. Pupils in ‘the bottom set’ seldom find it very difficult to develop a Growth Mindset and that’s just wrong.

For the arguments for and against ability grouping read this post: Mixed ability vs ability grouping in the primary school classroom: Where do you stand

Grouping by ability doesn’t reflect reality

We obsess with our language for learning but not enough when it comes to setting and grouping. All mathematicians are developing mathematicians and to clump a group of learners together as the ‘bottom’ bunch is not helpful. Mathematicians of all ages will find that they are better at some parts of the Maths curriculum than others. There are only a few that are good at everything. There is no wrong thinking in Maths – concepts are in embryo and stages of conceptual development are not always quick to develop. It could take you years to learn how to multiply – it also might never come. The idea that you have a group of bottom, middle or top learners is flawed because there will be learning gains and natural fluid movement. All children can learn Maths but not all teachers can teach it. All children deserve access to a demanding Maths curriculum.

What the research says about mixed ability Maths

Research has shown that mixed ability teaching has always been more effective than setting when it comes to Maths. A study called ‘Effective classroom organisation in primary schools’ found that there was no evidence that children learn more effectively in sets for Mathematics at any level. Critics argue that mixed ability classes can be a curse to able children as teachers spend a disproportionate amount of time helping so-called ‘weaker’ pupils. Perhaps, but the riposte is still the same: if the Maths teaching is good then all abilities will excel.

Whole-class mastery: access all areas

Teaching children Maths in mixed ability groups can make some teachers anxious, especially if they’ve only ever taught one ability set. With the whole class teaching model presented by the mastery approach to Maths differentiation is critical when teaching the same topic to a class with different levels of attainment.

According to the NCETM’s Developing Mastery in Mathematics, characteristics of teaching for mastery means:

  • An expectation that all pupils can and will achieve.
  • The large majority of pupils progress through the curriculum content at the same pace. Differentiation emphasises deep knowledge and individual support/intervention.
  • Teaching is underpinned by methodical curriculum design, with units of work that focus in depth on key topics. Lessons and resources are crafted carefully to foster deep conceptual and procedural knowledge.
  • Practice and consolidation play a central role. Well-designed variation builds proficiency and understanding of underlying Mathematical concepts in tandem.
  • Teachers use precise questioning to check conceptual and procedural knowledge. They assess in lessons to identify who requires intervention so that all pupils keep up.

Differentiation strategies to try in Maths

Differentiation in teaching for mastery is about how pupils can be helped to understand new concepts and techniques. Once upon a time this meant preparing different activities or worksheets for different groups of pupils and that is still okay. Catering for the different needs of the children in your class inevitably means using various strategies and there can be advantages and disadvantages to each.

  • Task/activity – different sort of tasks: visual, hands-on, auditory can all play a part in helping a learner to access the topic
  • Outcome – what their end product will be, e.g. a model, a picture, written explanation
  • Amount and rate of work
  • Questioning
  • Expectation – how far you expect children to go in an exploration/investigation and what you expect them to learn/conclude
  • Resource – e.g. some may use number lines, other may use mental images
  • Adult support
  • Peer support –Maths partners
  • Role – offering children specific roles within group work, e.g. calculator, spokesperson, decision maker, recorder, tabulator, statistician, treasurer, banker

Differentiation strategies work in some situations but not in others. It is not always possible or appropriate to differentiate by changing e.g. the range of numbers used in an activity but sometimes this is the appropriate step to take.

For a bunch of engaging and varied activities designed for use in a mixed ability classroom, download this resource

Classroom resources free

Mastering Mixed Ability Maths Resource

8 different Low Threshold, High Ceiling activities for upper & lower KS2 Maths that feed into the national curriculum's broader Primary aims for effective learning

22 mastery techniques to try with your mixed ability class

When it comes to catering for the needs of children in a mixed ability class, there are lots of features to maximise learning. Including all of these features would be unrealistic and inappropriate but including some of them will help you design a plan for catering for different needs. The key issue is the intent behind each one and not just the act itself.

  1. Have high expectations of everyone
  2. Build on the knowledge learners already have
  3. Encourage reasoning rather than answer getting
  4. Use a rich mixture of practical apparatus, images and representations (like the Singaporean model of concrete-pictorial-abstract)
  5. Consider how much time pupils are given using concrete resources
  6. Use a variety of skilful questions and prompts tailored to understanding
  7. Milk the Maths – everyone can be given the same ‘sum’ but this can be deepened in a variety of ways
  8. Focus on misconceptions
  9. Initiate Maths talk, rich discussions and learning conversations
  10. Emphasise that there is ‘always more than one way to bake a cake’ and so it is with Maths
  11. Listen to what children are saying and teach them to actively listen
  12. Encourage children to explain their thinking without loss of pace
  13. Insist on the precise use of Mathematical terms and vocabulary
  14. Create connections between topics
  15. Make teaching as interactive as possible
  16. Demonstrate or model Mathematical ideas
  17. Use children’s methods and working as teaching points
  18. Ensure that TAs are fully briefed and know how to help
  19. Share ideas and strategies
  20. Evaluate and correct children’s responses
  21. Reflect on what has been learnt
  22. Use concept cartoons

For more detailed activities, see this Maths activities to use with mixed ability groupings blog post.

How to adjust lessons for children who struggle

According to Steve Chinn in his book The Trouble with Maths adjusting lessons to help pupils who are having difficulties in learning Maths should be based on 4 principles:

  1. Empathetic classroom management – an active awareness and adjustment to the learning strengths and difficulties of pupils
  2. Responsive flexibility – ensuring teachers have a repertoire of resources and strategies which respond to the individual and their changing needs
  3. Developmental methods – methods that address the remedial need whilst developing Maths skills and concepts
  4. Effective communication – an awareness of thinking and learning style and an awareness of limitations such as language skills, poor short-term memory or slower speeds of working

Chinn argues that the application of these principles should affect all levels of work from the construction of the syllabus and lesson plans to the setting and marking of work.

Master your mastery based Maths curriculum

The bottom line is this: pupils are individuals and we need to teach to the individual in the group. Some pupils will respond to certain strategies better than others but the key to helping all our children is to understand them on their own personal Maths turf and not on our own soil. There is no intervention that will work for everyone as interventions have to be engineered on a personal level.

If you enjoyed this, you’ll love our Beginner’s Guide to Becoming a Maths Mastery Expert – the blog with everything you need to get to grips with Mastery in primary schools.

John Dabell , Teacher , Former School Inspector

A former school inspector with a background in teaching and education, John frequently writes for the Third Space blog on a variety of topics.