"Mathematical understanding is a journey... not a destination"
- Dr Yeap Ban Haar (Internationally Renowned Maths Expert)
Mathematics underpins our daily lives and is becoming even more important in an increasingly technological world. The Maths Mastery approach of teaching mathematics develops pupils' mathematical ability and confidence and encourages pupils to make connections between concepts, making mathematics more accessible, engaging and fun!
The aim of Maths Mastery is to raise standards of attainment and progress, and ensure every child achieves their full potential as well as promote self-confidence and resilience in Maths. It focuses on the 5 Big Ideas of Mastery - Representation and Structure; Mathematical Thinking; Variation; Fluency; Coherence (see link below for more information) and allows pupils to acquire 'a deep, long-term, secure and adaptable understanding' of Maths (NCETM).
Our 5 Big Ideas
At Lewis Street, we believe that variation is crucial to secure understanding. Variation is twofold. Within each lesson, teachers ensure they represent the mathematical concept being taught in multiple ways and children are encouraged to discuss, compare and record different representations through journaling. Alongside their journals, children may also record their learning in their workbook which poses a further variation of questions designed to challenge their thinking. Teachers use varied questions to further encourage challenge. This carefully designed variation builds pupils fluency and understanding. Maths No Problem planning and textbooks ensure appropriate curriculum coverage and lessons are well sequenced with practice and consolidation of skills playing a central role. New learning is introduced carefully through a series of well crafted, small steps. Pupils explore what stays the same and what changes as they encounter different mathematical ideas. This ensures children are able to build upon their prior knowledge and make connections between different mathematical structures and the relationships between them. In turn, this encourages our pupils to develop deep and sustained knowledge.
Coherence underpins the other 4 principles of our mastery curriculum here at Lewis Street. Teachers strive to make Mathematics lessons accessible to all pupils by breaking the learning down into a sequence of small, progressive steps. In doing so, mathematical concepts are gradually developed and pupils are encouraged to make links in their mathematical thinking, develop flexibility in understanding and apply their learning across a range of contexts. Teacher’s careful planning predicts and prevents misconceptions developing, while every step in learning is carefully thought through to ensure children are noticing key mathematical structures.
Here at Lewis Street, we believe every child can be fluent mathematicians which in return provides confidence when exploring any aspect of the mastery curriculum. If a child is fluent in maths it means they are able to recall facts and procedures quickly and efficiently, moving flexibly between different contexts and representations of mathematics. To help children with this in school we have a fluency recall session at the beginning of each mathematics lesson, practicing these efficient skills in order to help them become faster at recalling facts and methods. We have also invested a lot of time into TimesTable Rockstars, which encourages children to recall their multiplication facts, and practise their number facts.
At Lewis Street, Mathematical Thinking is encouraged through practical investigation, supported through use of our C-P-A approach. First children use concrete materials in order to build a foundation for their mathematical knowledge. They then use onto a pictorial representation when ready, before finally understanding and using an abstract method. This approach is not linear throughout primary school. The CPA approach is used whenever a new idea or concept is introduced. Children are given the opportunity to explore Mathematical problems both collaboratively, independently and through whole class discussions. Pupils are encouraged to make connections between what they already know, and the new areas of learning being taught. They investigate and develop methods to solve problems and these methods are then thought about, reasoned with, and discussed with others. Teachers use precise questioning in class to assess and encourage pupil’s deep knowledge and reasoning skills. Questions asked include: How did you solve this? Can you explain your method? What do you think would happen if? Which method would you use? Why? The objective of the lesson is pulled out from these discussions. Children then record their thinking in their personal journals to be reflected on and built on in future lessons.
Representation and Structure
Representations and structures ‘stand for’ the mathematical object (cf. Duval, 2006; Golding and Shteingold, 2001) and make visible different aspects and characteristics of it.
Mathematics is an abstract subject and representations are a way of helping the children to access and develop their understanding through exposing the mathematical structure. At Lewis Street when introducing and developing a mathematical concept we make sure the children experience multiple representations of that concept. They are encouraged to develop their understanding by thinking about what it is, what it is not and how it connects to other aspects of mathematics. Representations are carefully thought out, in order to draw out the structure of the maths being taught. When planning for the lesson teachers think about what mathematics will be highlighted and how it will be interpreted within the class, making sure that links are made explicit in order for children to notice. By using representations to highlight structure, the aim is that the children will be able to eventually do the maths without relying on the representation.
Transferring Pedagogy into Classroom Practice
Maths Mastery provides pupils with the opportunity to explore and discuss mathematical concepts. Through the use of NCETM materials and White Rose Maths all concepts and skills are taught following the same format. Lessons follow the concrete–pictorial–abstract method. Clear and engaging visuals are used to present concepts, and to model solutions that allow all pupils, regardless of language skills, to focus on the mathematics. The concrete–pictorial–abstract sequence helps students build understanding of mathematical processes and supports them in explaining their thinking using mathematical vocabulary and helps them to identify the most appropriate methods for reasoning and problem solving.