How to Achieve Mastery in Maths at KS2
“The pupils that are receiving the programme have shown an excellent improvement in their confidence as well as competency in key areas. The progress reports clearly show how a pupil’s understanding is developing over time.”
What is mastery in maths and why is it important?
Mastery maths teaching focuses on ensuring children develop deep, long-lasting retention and appreciation of mathematical concepts and procedures. It should mean that children are better able to recognise numbers and shapes and perform key operations, allowing them to become adept problem solvers too.
How to develop mastery at KS2
Mastery teaching can be achieved by applying the NCETM’s ‘Five Big Ideas in Teaching for Mastery’:
- Coherence: This is where lessons are broken down into smaller, connected steps, helping pupils to access a concept initially then build upon their understanding. This enables them to then generalise the concept so that they can apply it to a range of different contexts.
- Representation and Structure: In Mastery teaching it’s important that we use representations (concrete or pictorial) to help explain and reinforce the concept being taught. This is with the aim of ultimately being able to remove the representations and for pupils still being able to do the maths in question.
- Mathematical Thinking: When pupils learn new ideas passively (i.e. when they’re not encouraged to think about and work with what they’re learning) it is less likely they will come to confidently understand them. For this reason, in mastery teaching we expect pupils to think about, apply, discuss and reason with the concepts that they’re learning.
- Fluency: Fluency is a core part of a mastery approach, to help pupils become confident, flexible and resilient problem solvers. We need to help them develop their ability to quickly and efficiently recall number facts and procedures so that they can move between different contexts.
- Variation: To develop a deep and holistic understanding of mathematical concepts, variation is key. This means both representing concepts in different ways when they’re being taught (such as switching between concrete and pictorial representations) and varying the type of questions you’re asking pupils to answer and explore (e.g. gradually adjusting the type of challenge in subtraction questions by looking at crossing different boundaries). In this way pupils have to pay attention to what is the same and what changes, helping to build up their understanding of the connections that can be made within and between mathematical concepts.
How Third Space Learning supports all KS2 pupils towards achieving mathematical mastery
We help schools provide mastery maths teaching through our programmes of 1-to-1 interventions and high-quality resources.
Schools choose which of their pupils require additional 1-to-1 support and then each week they receive 45 minutes of online teaching from their own dedicated tutor.
Unlike other online maths programmes, as pupils are communicating over a headset and interactive screen with their tutor, the live conversation provides many more opportunities to develop mastery. Tutors work closely with pupils to help secure their understanding of the concept in question then apply it to a problem. Pupils are encouraged to verbalise the steps they take for every question, improving their mathematical thinking and fluency.
Alongside this, Third Space Learning schools get access to hundreds of resources which enhance whole-class teaching and support pupils to achieve mastery in maths.
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Four of the best ways to develop mastery in maths at KS2
- Whole-class teaching to support all pupils
A mastery approach starts initially by focusing on high quality whole-class teaching. All pupils should be given the opportunity to access the lessons being taught and guided to master new concepts before moving on to the next area within a scheme of learning. The aim is that no pupils should be left behind.
As part of our year-round intervention and resource programmes Third Space Learning provides access to collections of ready-to-go lesson slides. From September these will be available for all years from Year 1 to 6. These save teacher time and provide a range of mastery activities, allowing all pupils to access the same lesson content at the same time, as is the case in Singapore, Shanghai and other areas where mathematics has been taught with a mastery approach.
2. Responsive and timely interventions
Even with high quality whole-class teaching, there will often be pupils who need further support. When following a mastery approach, it’s important to identify those pupils who are taking longer to master a certain topic or procedure and provide intervention as soon as possible.
Third Space Learning’s online intervention programmes allow schools to provide timely intervention for those who need it, with weekly online lessons which are personalised to each pupils’ gaps and misconceptions through online diagnostic assessment. Pupils sit an initial assessment to identify areas where they most need support and tutors then adapt each lesson to suit their individual needs.
3. Lesson design
Well-designed lessons pinpoint the new concept that is being taught and the key steps in grasping that concept. Following a mastery approach, it helps to break them down into smaller steps which pupils can connect together to develop their understanding. This structure helps to identify possible misconceptions that could arrive and offers pupils a carefully sequenced journey through their learning.
Both the online 1-to-1 lessons in our intervention programmes and our downloadable ready-to-go lesson slides have been designed with all these considerations in mind, allowing back and forth interaction between pupil and teacher, with in-built quality questioning, modelling, short tasks, explanation, reasoning and mathematical discussion.
4. Key facts, procedural fluency and intelligent practice
It’s essential that key facts are mastered early on, allowing children to become procedurally fluent. When a child can recall their number bonds and times tables with automaticity, it avoids cognitive overload in the working memory allowing them to proceed through calculation more efficiently. This helps them to master new concepts quickly.
Opportunities should therefore be provided for regular, intelligent practice, to further children’s procedural fluency and allow for them to deepen their conceptual understanding of mathematics too.
Third Space Learning’s intervention curriculum has been designed to ensure that procedural fluency and conceptual understanding develop concurrently, with pupils being guided through intelligently designed mathematical tasks by their own dedicated specialist maths tutor. All 1-to-1 lessons provide warm-up activities with the chance for procedural practice and pupils have the opportunity to answer additional online practice questions in the time between their weekly sessions.