At Dell Primary we use White Rose’s spine materials as a pedagogical approach, as a guide, to the steps children go through to understand mathematical concepts. Our approach involves smaller sequential steps being taught so that our children are able to grasp new concepts and ideas to a reasonable amount of depth. We utilise materials from NCTEM and NRICH.
The materials present mathematical concepts in small, coherent steps, explore the common misconceptions or difficulty points and include research-informed approaches. Due to this and the support of EAT and CPD, our teachers are developing good pedagogical content knowledge.
We follow a mastery approach to teaching, ensuring each idea or concept is understood by the vast majority of each class in every lesson to a reasonable amount of depth. This means that we do not set out a definite number of weeks in which content is taught and understood by pupils. However, we do set out a guide, for each year group the order in which main areas are broached and outline a view to how long each area is likely to take. These timings are flexible and change depending on the needs and understating of key ideas and concepts by our pupils. These decisions are made based on our assessments of the pupils via their procedural understanding and their ability to reason and problem solve. This sequential approach ensures that deep learning is embedded and even though it may take longer, ensures less revisiting is needed.
Our approach of smaller sequential steps in mathematical teaching means that more children are able to access the learning in the lesson and decreases the need for children to catch up or to be not challenged further. Some children will need additional scaffolding for them to understand fully rather than them understanding it procedurally or superficially and a number of children will need to be challenged, not by moving on to another area of mathematics but by being able to reason or problem-solve more deeply. These challenges and scaffolds are planned for and are integrated into every lesson.
Throughout our whole curriculum, there are sufficient opportunities planned to revisit previously learned knowledge, concepts and procedures; this is to ensure that once learned mathematical knowledge becomes deeply embedded in pupils’ memories.
The three aims of the national curriculum are fluency, reasoning and problem-solving.
Fluency is an important mathematical skill and that of which we teach and encourage children to build on in both their procedural (knowing what to do) and conceptual fluency (knowing why to do it) every day and to apply it in familiar and unfamiliar circumstances. Fluency is highly connected to reasoning and problem-solving. These are the ways in which children develop their conceptual and procedural fluency. We know how truly confident children are with their understanding of fluency through their ability to apply it to reasoning and problem-solving.
We understand that children are unable to problem-solve if they cannot reason about the best strategy. We develop children’s understanding of reasoning from describing up to proving.
We define problem-solving as questions for which children do not have ready-made solutions. We ensure that children use and compare different approaches; interrogate and use their knowledge to solve problems; monitor, reflect on and communicate their problem-solving skills.
These three areas are interconnected and as such we at Dell Primary integrate them into every maths lesson. We plan for and identify opportunities when mathematical reasoning and solving problems will allow pupils to make useful connections between identified mathematical ideas or to anticipate contextualised practical problems that they are likely to encounter in adult life and that pupils have sufficient understanding of, and unconscious competence in, prerequisite mathematical knowledge, concepts and procedures that are necessary to succeed in the specific tasks set.
We advocate flexibility within our curriculum planning so that we can address identified gaps in pupils’ mathematical knowledge that hinder their capacity to learn and apply new content.
We teach place value and number at the beginning of the year as we understand that having a secure understanding of place value is incremental and provides the essential number knowledge needed to complete calculations, including addition, subtraction, multiplication, division, and fractions. These concepts then secured translate and into other areas of the mathematics curriculum.
The pedagogy behind our lesson approach over a sequence of lessons includes representation and structure, fluency, variation, coherence and mathematical thinking. We do this by exploring smaller steps of learning in each lesson to ensure mastery and in turn, means: fewer children struggle, children that most children could be challenged to understand the basic idea more deeply and some children might be challenged to reason and problem solve at a greater depth level.
Previously taught content is also revisited in ‘Fluency Sessions' where both the children’s procedural and conceptual fluency is explored looking at the patterns and connections looking not only at the algorithms or arithmetic but at previously taught underlying concepts.
All lessons start with a ‘Do Now’ that gives the children sufficient opportunities that are planned to revisit previously learned knowledge, concepts and procedures. The start of every lesson builds on previous knowledge, concept or idea from the previous lesson or from the content that was taught in the previous year.
All lessons will involve fluency of facts, concept procedures and mathematical language; mathematical reasoning and problem-solving. However, we ensure that children have mastery of fluency of facts, concept procedures and mathematical language before we enable them to apply and deepen their knowledge through reasoning and problem-solving. This means that each lesson may look different or that it may be extended to ensure the learning is secure.
Modelling (MY, YT, OT) ideas are done with manipulatives and representations to ensure the effective teaching of concepts. These scaffolds are only removed when children have developed automaticity of the concepts that are being taught.
Mathematical thinking is integral to children’s understanding and therefore we ensure children talk about their ideas and strategies in every lesson.
Through our maths curriculum children will:
- be engaged and challenged
- be able to use a variety of resources to support learning
- be able to succeed in all maths lessons because learning will be appropriately scaffolded
- make good and better progress from their starting points
- know-how and why maths is used in the outside world and in the workplace
- through discussion and feedback, talk enthusiastically about their maths lessons and speak about how they love learning about maths
Assessment and monitoring in maths:
• Lesson observations, book monitoring and learning walks
• Gathering pupil voice (Junior Leaders)
• Moderating pupil's work in school and in cluster meetings with other schools to ensure accurate assessments are made
• Tracking pupils’ progress each half term
• Check for Understanding is used as a formative assessment tool that informs planning and intervention.
• Pupil progress meetings ensure different groups (including EAL, PP and SEND) and individual progress is monitored, and interventions organised to support good and better progress
• Parents and carers will understand how they can support their children at home and contribute regularly with homework