National Curriculum Purpose of Study:
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, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.
We follow the National Curriculum programmes of study.
At Hagbourne CE Primary, the aims of the National Curriculum (fluency, reasoning and problem solving) are at the core of our Maths teaching. Children are given regular opportunities to solve problems, therefore fluently applying their knowledge and conceptual understanding, then reasoning about what, how and why. We use the mastery approach to support children in their ability to think clearly and logically so as to develop an understanding of mathematics that is formed on secure concepts. We believe mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas and encouraged to make connections between ideas. This enables them to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. We also provide opportunities to apply their mathematical knowledge to science and other subjects.
We plan our maths teaching using the ‘Teaching for Mastery’ approach in accordance with the requirements of the National Curriculum and using the White Rose Guidance (and supported by the NCETM and DfE). We believe that the mastery approach is for ALL children and can be applied to ALL objectives across the maths curriculum. The mastery approach involves: deep and sustainable learning; the ability to build on something that has already been learnt, the ability to reason about a concept and make connections and having conceptual and procedural fluency. It provides a rich mathematical experience through which children can view and make sense of the world, analyse and communicate information and ideas whilst tackling a range of practical tasks and real life problems. In line with this, an objective of our teaching is to create a deeper understanding of mathematical knowledge that is appropriate to age (and to support children in achieving the expectation of recalling it rapidly and applying it fluently and accurately) rather than to accelerate pupils into new content.
Our Teaching for Mastery approach involves whole class, mixed ability teaching whereby children take small steps through the curriculum moving broadly at the same pace. Decisions about when to progress are always based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly are challenged through being offered rich and sophisticated problems to deepen their understanding before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, and timely intervention to address misconceptions (keep up not catch up) before moving on.
The ‘Teaching for Mastery’ approach has 5 big ideas that are evident in lessons:
Through the mastery approach, you will see teachers fostering mathematical understanding of new concepts and methods through their explanations, choice of models, images and resources and the way they require pupils to think and reason mathematically for themselves. Children are actively encouraged and provided with opportunities to broaden and deepen their understanding of concepts and activities. Much of this is taught in the daily Maths lesson, but additional opportunities for developing investigational strategies are also provided in both the timetabled fluency sessions (to support rapid recall of number facts and application) and through making purposeful links across the curriculum.
In lessons, we ensure that children’s conceptual understanding is sound. Children are encouraged to actively question and ask why things are true. Lessons are planned using Slides to carefully step the children through the learning using rich activities, deep questions and well structured lessons. Lessons typically follow the whole class teaching model (a key feature of teaching for mastery) and focus on depth of learning. We take small steps through the curriculum ensuring that children are secure in their knowledge before moving on. The impact of this in our teaching is that the ‘next steps’ will be the next lesson.
We plan lessons using the White Rose Small steps and progression documents which are designed to ensure clear progression in mathematical concepts. Teaching is blocked to allow pupils to gain a deeper understanding and make connections between mathematical ideas. Lessons are planned using concrete, pictorial and abstract approaches as appropriate to support and underpin concepts being taught. There is a strong focus in lessons on precise mathematical language, vocabulary and reasoning. Teachers provide immediate feedback to children during the lesson. In lesson feedback and marking of books inform the next step of planning, teaching and learning.
Differentiation, Support/Intervention and Challenge
We aim to keep the whole class together and move through the curriculum at broadly the same pace. Whilst doing this, differentiation will take many forms but may include giving pupils differing amounts of time, using concrete resources to help them grasp concepts, and giving ‘rapid-graspers’ more challenging questions and problems to work on, and reason about. Teachers act swiftly to help those having difficulty to make sure they keep up, and to stretch and deepen the learning of the ‘rapid-graspers’. Rapid graspers will have a ‘star challenge’ available to complete during the lesson (a rich and sophisticated problem rather than an acceleration), will be expected to prove and explain their answers and are provided with activities designed to deepen (rather than accelerate) their understanding. To further develop their understanding, we encourage children to not just show the answer but to prove and explain their work in different ways.
Teachers will use flexible groups as needed within lessons to support those they identify as needing support and will use ‘keep up not catch up’ intervention before the next lesson to further support any children who have struggled so they are ready to continue with the rest of the class in the next lesson. Children having difficulty may be given different resources/models/images to use, further adult support or explanation in a different way, extra time on an objective or an immediate intervention. They will be supported in consolidating their understanding before moving on.
Most feedback is given verbally, immediately in lessons as teachers work with a group or circulate to support children as needed. Children can act on this feedback straight away either adapting their approach, going deeper or using their purple pen to edit their work. Where needed, written feedback will be provided and may give children something additional to do to address misconceptions, support or extend their learning. Children respond to this feedback regularly (verbally or written) so as to move their learning on. It is normal that responses to this feedback will form the next lesson, whereby the whole class can respond together. Children are encouraged to self-assess and reflect on their own learning and progress using their purple pens so as to form part of the assessment process. As a result of this, you will see children who are starting to fluently and accurately speak the language of maths, children who are not afraid to make mistakes but know how to respond to them and move on and who have a positive, confident attitude towards mathematics.
Tracking Attainment and Progress
We have termly Pupil Progress meetings with the Headteacher and Maths Subject Leader to track attainment and progress in maths and to highlight children who need further support due to progress concerns or whose accelerated progress means we need to further challenge. These meetings are based on teachers’ knowledge and evidence/assessment from Insight tracking, hot and cold tasks, formal assessments, informal observations and evidence in books and White Rose assessments to focus on the most important things ready for the next stage/year/term and highlight target children. These meetings, along with observations, book scrutiny and learning walks, provide the Headteacher and Maths Subject Leader with the opportunity to tackle inconsistencies in the teaching and provision of maths across the school.