Teaching Mathematics for Mastery at Bozeat Community Primary
“A commitment to producing individuals who are numerate, creative, independent, inquisitive, enquiring and confident who make secure and sustained progress over time.”
At Bozeat Community Primary School we teach mathematics for mastery, an engaging and accessible style of mathematical teaching, inspired by Singapore and Shanghai. Our approach develops mathematical understanding, confidence and achievement for all children.
Children are encouraged to physically represent mathematical concepts. Concrete Objects and pictures are used to demonstrate and visualise abstract ideas, alongside number and symbols.
Mathematical concepts are explored in a variety of representations and problem-solving contexts to give pupils a richer and deeper learning journey.
Bozeat Community Primary has participated in the National Collaborative Project funded by the Maths Hub Programme and trialled the use of Maths No Problem textbooks. Following the success of this initiative, textbooks were introduced into Years 1-4 to support teaching for mastery. Years 5 and 6 follow the same lesson structure but produce their own resources to match the needs of their children.
What is teaching for mastery?
Inspired by teaching approaches developed in Singapore and Shanghai, mastery is a method of teaching that is founded in the understanding that all pupils can achieve in maths. A concept is considered mastered when learners can represent it in multiple ways, can verbally communicate solutions and reasoning, using mathematical language and can independently apply the concept to new problems. During a pupil’s mathematical journey through school, achieving mastery means acquiring a secure enough understanding of the maths that’s been taught to enable him/her to move on to more advanced material however, we embrace a growth mindset and ensure all children are challenged at their level and able to progress at their own rate.
Our approach is based on key principles:
Mathematics equips pupils with the uniquely powerful set of tools to understand and change the world. These tools include logical reasoning, problem solving skills and the ability to think in abstract ways. As a result, mathematical problem-solving is central to our approach. Children are encouraged to identify, comprehend and apply relevant mathematical concepts and make connections between different ideas. This develops the skills needed to approach new problems, rather than simply repeating routines without grasping the principles.
It is vital that a positive attitude towards Mathematics is encouraged amongst all of our pupils in order to foster confidence and achievement in a set of skills that are essential to our society. We are committed to ensuring that all pupils achieve this in the key concepts of Mathematics, appropriate for their age group, in order that they make genuine progress and avoid gaps in their understanding, which provide barriers to learning as they move through education. We believe no child should be left behind and we do this by making high expectations clear – and emphasising the high value of mathematics.
Concrete, pictorial, abstract
Objects, pictures, words, numbers and symbols are all around us. Our teaching approach integrates all of these to help children explore and demonstrate mathematical ideas, enhance their learning experience and deepen understanding. Together, these elements help strengthen knowledge so pupils truly understand what they’ve learnt in a maths lesson.
Depth before breadth
All learners benefit from deepening their conceptual understanding of mathematics, regardless of previous academic attainment. We believe children must be given time to fully understand, explore and apply ideas - rather than accelerate through learning. This approach enables learners to truly comprehend a concept, and the greater challenge comes from investigating it in new, multi-layered and more complex ways.
The way children utilise language and write about mathematics transforms their learning. We use a structured approach to introduce and strengthen the use of mathematical vocabulary. We always ask pupils to explain the mathematics in full sentences (not just what the answer is, but how they know it’s the right answer). This is key to building mathematical language and reasoning skills.
What will I see in mathematics lessons at Bozeat Community Primary School?
Whole class together – we teach mathematics to whole classes. We do not believe in labelling children, so we do not set, but encourage mixed ability collaboration. Lessons are planned based on formative assessment of what pupils already know and we include all children in learning mathematical concepts. At the planning stage, teachers consider the necessary scaffolding that may be essential for children struggling to grasp concepts in the lesson and suitable challenge questions for those who may grasp the concepts rapidly.
Longer and but deeper – Lessons are based on Maths No Problem text book progression and supplemented with other resources such as White Rose Maths and ‘I See Maths’ for reasoning and problem solving. Teachers adapt each lesson to meet the needs of their children and add extra questioning /tasks which will allow children to learn the content more deeply.
Questions- will probe pupil understanding throughout and responses are expected in full sentences, using precise mathematical vocabulary.
Fluency – There is a whole school focus on developing an instant recall of key facts, such as number bonds, times tables and unit + unit addition facts. Teachers supplement children’s learning of fluency through the use of ‘Fluent in Five’ and ‘Maths Meetings’.
Following the Singapore approach to the teaching of mathematics we structure our lesson into the following sections:
This is an independent problem for children solve in pairs or by themselves. – problems are often set-in real-life contexts and chosen practical resources and pictorial representations are used to explore concepts. These pictorial representations will appear in books as children show their understanding, rather than answers to a series of calculations. The use of practical resources, pictorial representations and recording takes place in every lesson (the CPA approach). If children finish quickly they have pre planned questions to deepen their understanding and are encouraged to comment on their journey and how they were able to answer the problem.
The adult teaching will organise the findings of the exploration, compare/contrast strategies and guide toward the most efficient strategy (or the one being learnt that day). They will also channel the journey of the mathematics through small carefully crafted steps to support deep understanding. Children who found the ‘In focus’ challenging have the opportunity to learn not only from their teacher but also their peers.
This is where, through assessment for learning, the teacher will support the children completing activities from the guided practise. Pupils will have opportunities to talk to their partners and explain/clarify their thinking. There will be more talking and less recording in books until children are secure in their understanding. At the discretion of the teacher, some children may record their workings in their maths books.
This is practicing a specific mathematical skill or method. This practice should not be by drill and but “intelligent practice” characterised by variation. Throughout, to challenge thinking and to ensure understanding, teachers use questioning such as: How do you know? Can you prove it? What’s the same/different about? Can you explain that? Teachers should ensure that children are identifying variation and drawing children’s attention to this to ensure that the richness of the concept is at the forefront of children’s thinking.
How to extend?
In line with the Singapore approach children should be moving at the same pace through the curriculum. Those that have mastered a concept are given opportunities to deepen their understanding. These need to be a more obscure problem or a problem where they have to explain their understanding of a concept in greater detail. Examples of these can be found in the NCETM assessment materials.
At the end of each lesson children need to be given an opportunity to reflect on their learning. In Key Stage One, reflections may be modelled to support children develop metacognition skills. Sentence stems are provided in Key Stage Two to help with the use of language in children’s evaluations of their learning. These are displayed in the classroom.