At St John Fisher Catholic Voluntary Academy, we follow a Mastery approach to Mathematics. We view Mathematics as a tool for everyday life; a network of concepts and relationships which provide a way of viewing and making sense of the world, central importance for everyday life. At our school we equip children to be curious about mathematics, making connections between concepts and reasoning mathematically. We foster analytical minds, confident communicators of information and ideas to tackle a range of practical tasks and real-life problems, so that our children have the cultural capital to succeed in life. We, therefore, believe it is important to ensure all children have the best possible mathematics opportunities through cross-curricular learning.
We have a commitment to high achievement in mathematics by children regardless of gender, race, class or ability. We believe that all children have the potential to achieve, no matter what their starting point.
We uphold and nurture the following underlying principles for the teaching and learning of mathematics in our school, aiming to ensure that all pupils (including those who are disadvantaged, vulnerable or classed as SEND):
- Become fluent in the fundamentals of mathematics, through varied and frequent practice, which increases in complexity over time, so that pupils develop conceptual (why?) and procedural (how?) understanding and the ability to recall and apply ‘sticky’ knowledge rapidly and accurately.
- Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language, e.g. “Convince me that…” or “I know that…so…”
- Can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
- Are taught through the Concrete→ Pictorial → Abstract sequence at our school, to ensure that they gain a thorough understanding of the mathematical concepts/skills they are learning.
- See themselves as mathematicians and are given the opportunity to explore the lives of significant individuals within mathematics and the wider STEM world.
- Should be given the opportunity, in every relevant subject, to develop their mathematical fluency and mathematical skills, so that they have the knowledge and cultural capital they need to succeed in life.
The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich mastery and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier procedural skills should consolidate their understanding, including through additional practice, before moving on, whist still being exposed to problem solving and reasoning style questioning at their level.
Through our ambitious mathematical curriculum, we aim to develop:
- A positive attitude towards mathematics and an awareness of the fascination of mathematics.
- A competence and confidence in mathematical knowledge, concepts and skills
- A mathematical readiness at each stage of learning (EYFS through to KS3) so that children leave in Year 6 fully able to access mathematical learning in Year 7 and beyond.
- An ability to solve problems, to reason, to think logically and to work systematically and accurately.
- An initiative and an ability to work both independently and in cooperation with others
- An ability to communicate mathematics and mathematically, developing a broad mathematical vocabulary.
- An ability to use and apply mathematics across the curriculum and in real life
- An understanding of mathematics through a process of enquiry and experiment
At St John Fisher CVA, we believe that it is important to ensure that all children in EYFS develop firm mathematical foundations in a way that is engaging, and appropriate for their age. In EYFS, children learn about Maths through play and their daily experiences – the more meaningful to them and hands on it is, the better! Throughout EYFS, the children have the opportunity to start developing their early Maths learning which will underpin everything they will encounter as they progress in their Maths learning in Primary school: Cardinality and Counting; Comparison; Composition; Pattern; Shape and Space; Measures. Teachers use a variety of materials, including resources from the White Rose Scheme of Learning to support teaching in these areas. The CBBC Numberblocks programmes are also used to support the teachers in confidently helping children bring numbers and ideas to life in the real world around them. The resources support the teachers in drawing out and building on the Maths that is embedded through the use of stories.
Teachers in EYFS base their teaching and learning on objectives within the Framework for Foundation Stage; this ensures that they are working towards the ‘Early Learning Goals For Mathematical Development’. Towards the end of the year, teachers aim to draw the elements of a daily mathematics lesson together so that by the time children move into KS1 they are familiar with a more formal maths lesson.
KS1 and KS2 Curriculum
In KS1 and KS2, we use the White Rose Scheme of Learning (3.0) to help us plan and sequence our curriculum. The key composites have been thoroughly thought about in conjunction with the National Curriculum (DfE, 2014), Ready-to-Progress Mathematics Guidance (DfE, 2020) and the knowledge of our children and context.
In most cases, our school follows the White Rose blocks in sequence, allowing children to become proficient in their procedural and conceptional understanding of Place Value and Four Operations, before applying their knowledge to Fractions and the wider maths curriculum. This is linked to the principles of ‘Cognitive Load Theory’ (Sweller, 1988), allowing children to commit ‘sticky knowledge’ to their long-term memory.
Each White Rose block is split into ‘small steps’ and these form the components which help to inform teacher planning and aid the building of disciplinary knowledge. The Ready-to-progress documentation is used to help teachers prioritise the teaching of key areas of the curriculum so that they know who long to spend on each component. This means that key areas of learning can be built upon step by step, sequence by sequence and year on year so that the children have several opportunities to embed their leaning.
Although largely based on the White Rose, our scheme of learning is a working document, which is adapted specifically to the needs of the individual cohorts. In some cases, blocks are split or taught in a slightly different order (especially in Year 2 and 6) to ensure that a breadth of content in covered before the SATs and that the needs of the individual cohort are met.
For each block, children complete a pre-learning task style assessment, which helps to identify which of the small steps (components) need to be covered; this means that any individual children who present gaps in their knowledge can be quickly identified and supported; this is especially important following the disruption to learning as a result of the COVID-19 pandemic. Similarly, children who show a secure knowledge of the small steps (components) at the beginning of the week can be given further opportunities to explore the concepts at a greater depth.
KS1 and KS2 Maths Lesson Structure
To support knowledge retention, maths lessons begin with a 20 minute ‘Daily Practice’ session, which is used to recall and revisit key arithmetic knowledge. These sessions are linked to ‘Rosenshine’s Principles’ and are designed to ensure that knowledge is constantly revisited so that it moves quickly from the pupil’s short-term memory to their long-term memory; thus reducing the cognitive load when applying their knowledge. These sessions also give children the opportunity to apply their arithmetic knowledge in a problem solving and reasoning context, scaffolded by teacher modelling. Constant AfL throughout lessons and information from summative assessments, ensures that focus of these sessions is based on the needs of the individual cohort.
At St John fisher CVA, children are taught as a whole class. Our lessons are structures to support our Mastery Approach; promoting both Fluency and Problems Solving & Reasoning opportunities, which all children are able to access at an age-expected level. Staff use the White Rose Premium resources, which includes videos, teaching slides and worksheets, to support them in implementing the mastery approach to learning mathematics.
An example progression of tasks would appear as follows:
Task 1: Basic fluency/Skills
Task 2: Varied fluency
Task 3: PS&R – Focus on Problem Solving
Challenge: PS&R – Focus on Reasoning
Each of these tasks should be modelled by the teacher, and scaffolded for all learners through the use of the CPA approach, ‘Teacher talk’ and sentences stems to model correct mathematical vocabulary. Children are then given time to work individually, in pairs or in group to answer similar questions and then feedback their understanding, using sentence stems. This means that the children’s knowledge is continually assessed through AfL; ensuring that they begin at the appropriate starting point, any misconceptions are addressed instantly and that the pace of learning is adjusted. It is our aim that, at the end of each lesson, every child is given the opportunity to apply their learning to a Problem Solving and Reasoning ‘Challenge’, differentiated by the amount of scaffolding used.
Where there is a need to support pupils to keep up, this is provided through same day catch up or teaching. This is flexible and tailored to the children’s needs. There will be times when a start to the lesson can be used to provide a whole class pre-teaching opportunity, to cue pupils back into prior learning, reactivating and rehearsing this before building on this in the main focus. There will also be times when a carefully selected group of pupils require some tailored pre-teaching or same day catch up. For example, supporting pupils to access the language that will be needed. Where individual pupils or a small group are unable to secure the learning after teaching time, the aim is for this to happen as close to the learning as possible. It may require re-explanation of the learning and rehearsal of the concept, or tracking back to a piece of previous learning which has been found to be insecure.
Working walls are used to support learners with the current topic and used during lessons to model essential procedures and highlight key language. Children are also provided with a year group specific knowledge organiser, at the front of their book and a more specific knowledge organiser for each topic. This contains the WR small steps (components) that the children are going to complete in the block of learning as well as key vocabulary and models that the children might need to refer to during the lessons – this is stuck over their pre-learning task.
Each class is also equipped with ‘Maths Tool kits’, for each table group. These contain year-group appropriate concrete manipulatives (as set out in the school Calculation Policy), which are used to support the mathematical understanding of all pupils.
At St John Fisher CVA, formative assessment is used to help pupils find their strengths, but also highlights any area for development which can be furthered through clear, direct feedback. The SRSCMAT Assessment Framework allows continual assessment to ensure that children know and remember more and are ready for their next phase of their education.
Summative assessment is used 3 times per year in the form of NFER/SATs papers to check retention and the transfer to long term memory.
Teaching and Professional Development
Teachers have good subject knowledge of the primary maths curriculum including starting points and end points of the primary phase. The monitoring schedule allows time to complete learning walks, book looks and pupil voice interview. When gaps in a teacher’s subject knowledge or paedology are identified, they are supported by the subject leader and SLT. Maths staff meetings are held every term and are seen as profession development for all staff. The school is currently part of the NCETM Maths Mastery Readiness Programme, which supports the subject leader and staff in their delivery of a mastery curriculum.
Maths in the real-world
Throughout lessons, teachers constantly refer to how the maths being learnt is linked to the real-world and, where relevant, make links to the work of significant mathematicians. The children’s cultural capital in maths is further developed through a lunchtime ‘Maths Club’, regular TTRS/Numbots competitions and the use of dedicated maths days (e.g. NSPCC Number Day). These days are used to highlight the importance of maths in the real world and where relevant, high quality maths related picture books are used to engage the children.