Burwash School Mathematical Pedagogy 2022-23
Our Vision for Mathematics
Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, and in children’s ability to understand the world.
The Burwash curriculum for mathematics aims to ensure that all pupils:
become fluent in the fundamentals of mathematics,
experience varied and frequent practice of mathematics with increasingly complex problems over time,
develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately,
can reason mathematically so that they can solve problems by applying their mathematics to a variety of problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
Principles of Implementation
At Burwash School we use many principles of mastery and adapt others to meet the needs of our pupils.
Whole class moves through content at the same pace
Mastery - When teaching maths for mastery, the whole class moves through topics at broadly the same pace. Each topic is studied in depth and the teacher does not move to the next stage until all children demonstrate that they have a secure understanding of mathematical concepts.
Burwash - Children move through the topics at roughly two to four week intervals. Each topic is covered two to three times a year. There needs to be a balance between curriculum coverage and depth. Depth, fluency and retention are enhanced by coming back to topics regularly. Burwash School does not believe it is right that the whole class have to demonstrate they have a secure understanding before moving on: an individual will receive intervention support to consolidate their learning.
Time to think deeply about the maths Mastery - Students are given time to think deeply about the maths and really understand concepts at a relational level rather than as a set of rules or procedures. This slower pace leads to greater progress because it ensures that students are secure in their understanding and teachers don’t need to revisit topics once they’ve been covered in depth. Burwash - Deep thinking is helped by paired discussion, skilled teacher questioning and activities to promote reasoning and problem solving. Pace may need to vary according to the needs of the children. Topics will need to be revisited to reinforce learning, develop depth and avoid memory loss. Builds self-confidence in learners
Mastery - In a traditional primary school maths lesson, children are put in different groups and given different content based on their anticipated ability. This means that from an early age children are classed as those who can and can’t “do maths”. Teaching maths for mastery is different because it offers all pupils access to the full maths curriculum. This inclusive approach, and its emphasis on promoting multiple methods of solving a problem, builds self-confidence and resilience in pupils.
Burwash - We abolished ability groups for maths, for the whole school, over fifteen years ago for mastery reasons and for teaching efficiency. Every teacher is skilled in delivering to the whole class with children accessing personalised learning where appropriate. In addition we use principles of Growth Mindset in class to help build a positive and confident learning environment, develop resilience and independence in learning.
Differentiates through depth rather than acceleration
Mastery - Though the whole class goes through the same content at the same pace, there is still plenty of opportunity for differentiation. Unlike the old model, where advanced learners are accelerated through new content, those pupils who grasp concepts quickly are challenged with rich and sophisticated problems within the topic. Those children who are not sufficiently fluent are provided additional support to consolidate their understanding before moving on.
Burwash -For all pupils: there is curriculum and question adaptation within each topic giving children a personalised experience within a whole class topic .High quality maths teaching has always included offering rich extension activities as well as extra contextual difficulty.
Children requiring support: we offer differentiated questions, peer support, TA support, teacher support and booster sessions for children needing consolidation.
High attainers: we follow the National Curriculum 2014 approach, “Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content.” We believe that high attaining children can and should be challenged, not held back and that new concepts that build on the learning in their year group can benefit able children.
Further elements of the mastery approach used in Burwash School
The 5 big ideas as published by the National Centre for Excellence in Teaching Mathematics (NCETM) in 2017:
Coherence: Maths is broken into small steps which build on each other.
Representation and Structure: How you show mathematical concepts (pictures, annotations, concrete materials).
Mathematical Thinking: Using logic to link different areas of maths together to solve a problem.
Fluency: How well you know your number facts and methodology (quick recall multiplication tables).
Variation: Using multiple methods and approaches to solve a problem.
Innovative annotation for example: bar modelling; factor bugs; part, part whole.
Moving from concrete to pictorial through to abstract methods derived from mathematical thinking and fluency. A move towards abstract as the children become more confident and have concepts embedded.
Details of how we are continuing to develop our practice are found in the SDP and Maths SEF and Action Plan.
Burwash School has not bought a maths scheme for the following reasons:
We believe that lessons best fit the needs of children if they are planned and delivered by a teacher who is familiar with the needs of the pupils in the class. Schemes are written for a generic group of children.
Schemes are written using the current approach at that point in time. As ideas and needs progress the scheme maintains the methods and approaches of the date of its commission;
Schemes are not as flexible as considered lessons, curriculum adaptation is needed for national events such as the pandemic and recovery afterward and the need for moderation at key assessment points relevant to the school and its setting..
Over reliance on schemes can deskill teachers.
Without a scheme, teachers are free to create their own, or choose, the best available resources for the needs of the children in their class.