Approaches to Mathematics
At Crofton Junior School, we recognise that Mathematics is essential to everyday life and that children need to be equipped with the skills necessary so that they become competent and inspired mathematicians during their time here. We aim to provide a high-quality maths education which supports our children in becoming fluent in the fundamentals; being able to reason mathematically and being able to solve a range of increasingly complex problems so that they leave our school with the skills needed to progress to the next stage of their learning.
It is our intention that children:
develop conceptual understanding and the ability to recall and apply knowledge rapidly;
are able to reason and problem solve by applying maths to a variety of problem-solving tasks and challenges;
develop resilience that enables them to reason and problem solve with increased confidence;
have a passion for maths and enjoy the challenges that they are presented with.
This is implemented by following the Primary National Curriculum Programmes of Study for Mathematics, ensuring that there is a progression of skills from Years 3 to 6. Teachers and the maths leader design the year overviews with a large proportion of time spent on number, calculations, fractions, decimals and percentages as these allow children to develop those fundamental maths skills. As the year progresses, children are having more opportunity to apply their knowledge to other areas of maths, as we are beginning to move towards a more ‘spiral’ approach with the maths curriculum.
At the end of the year, teachers RAG (Red, Amber, Green) rate the NC objectives as well as the NCETM Ready-to Progress objectives (using formative and summative assessment data). These documents are passed to the next year group’s teachers for them to be able to identify strengths and areas for development. This supports teachers with their medium term plans, allowing time to revisit objectives as necessary that children are not deemed to be secure in, before beginning the expected learning for that objective/(s).
Because mental arithmetic is vital in supporting children to become competent mathematicians, this has, and continues to be, a focus. In each class, weekly arithmetic sessions take place looking at a variety of strategies that can be used to solve different types of questions. Within lessons, there is a focus on developing efficiency within calculations of the four operations. Even though children are taught how to calculate using formal strategies as stated in the National Curriculum, we encourage children to follow this process by asking themselves (in the order that follows): Do I know the answer? Can I work it out in my head? Do I need a jotting? Do I need a formal calculation? The reasoning is that children become competent mathematicians by being able to build on and develop their mental calculation skills rather than resorting to a formal method when it isn’t most efficient.
It is recognised that children need to demonstrate automaticity in the recall of mental facts to become more fluent and competent mathematicians; the declarative knowledge - 'I know that'. Teachers allow time for regular practice throughout the week, with all of the four operations, with the expectation that they become proficient in the core knowledge which can then be recall with accuracy.
The Calculation Policies have been created to match the National Curriculum year group expectations. They are used to support teachers to develop children's procedural knowledge, 'I know how', when planning and teaching both mental and written strategies. This supports progression and develops children's understanding of the methods. Alongside all methods taught, teachers are encouraged to use resources and the correct language to support the children's conceptual understanding.
Multiplication and division is an area of significant focus from Years 3 to 6. Children need to know and be able to recall with automaticity multiplication and division facts. This is fundamental to most areas of mathematical learning. Therefore, great emphasis is placed on this area.
The National Curriculum states that:
by the end of year 2 (KS1) , children should be able to recall and use multiplication facts for the 2, 5 and 10 multiplication tables;
by the end of year 3, children should be able to recall and use multiplication and division facts for 3, 4 and 8 multiplication tables;
by the end of year 4, children should be able to recall multiplication and division facts for all multiplication tables up to 12 x 12.
This underpins the children’s learning and supports their understanding in Years 5 and 6, with applying their knowledge of the multiplication and division facts into more complex areas, e.g. multiples, factors, prime numbers, formal multiplication and division, a range of different types of problems. Year 4 children take part in the Department for Education, Multiplication Test Check, in June, which focuses on the accuracy of recall for a selection of multiplication facts up to 12 x 12.
TTRockstars is a very popular online learning platform for the children to practise recalling these facts in a fun and exciting way. Children are rewarded with certificates when they achieve Rock Legend or Rock Hero status, as well as monthly certificates for the Most Improved and Fastest Studio Speed. Classroom displays and the school hall display celebrates children’s successes on TTRockstars. Each year, in the autumn term, we hold a whole school Rock Wrangle competition day, where children compete against other children in their year group to be crowned the overall Rock Wrangle champion. This helps to keep the importance of recalling multiplication and division facts high profile for both children and parents.
Rock Wrangle October 2022
The winner and runners up from each year group.
In class, within units of work, there are three stages: Fluency; Reasoning and Problem solving.
Fluency: Fluency focuses on the skills element where the learning and tasks follow a structured approach. Teachers are encouraged to use manipulatives to explore the maths and develop children’s conceptual understanding before progressing to the abstract. How children work through the use of manipulatives and pictorial images is dependent on their understanding of the concept. This can vary depending on a number of factors: children’s previous understanding of the area taught; how quickly children show an understanding of the concept; if it is new learning or the objective is being revisited or children’s confidence and accuracy when using the manipulatives.
Reasoning: Once children have a secure understanding of the skill, they progress to reasoning with tasks which demonstrate a more abstract approach - the conditional knowledge 'I know when' . The children are provided with opportunities to reason through ‘proving’ within a range of different types of tasks. These often include: - What is the same/differ? Do you agree? What error has been made? Use the digits to make the statements correct? Is there a different way to solve it? Which strategy is most/least efficient, and why?
This allows children to apply their knowledge to a greater level of understanding, often including different domains of maths. These are thought of as greater depth tasks and children have to use different skills in order to reach a response. This gives children the opportunity to develop their conditional knowledge by using the declarative and procedural knowledge to solve particular types of problems.
Problem solving for all children is a focus of the School Development Plan. We recognise that all children should be having the opportunity to problem solve and develop skills around resilience and perseverance. Within problem solving lessons, all children are being taught how to approach a problem; how to unpick it; how to record jottings and workings out; how to work systematically adapting as they work; and how to work towards a solution.
Outcomes in Maths books demonstrate high-quality learning through a sequence of carefully planned lessons, where children progress through fluency, reasoning and onto problem solving tasks. Work in books reflect the rich, varied tasks that secure conceptual understanding, whilst also providing challenge to further stretch and promote application of different mathematical concepts.
As children progress through the academic year, and through the key stage, books indicate that they are able to apply more cross-domain learning, which shows that children are beginning to master the content previously taught. This shows that the learning is embedded and children are becoming more competent mathematicians. Topic books also evidence appropriate cross-curricular learning, where children apply learning in different contexts, more notably in Science (data handling) and Geography (measurement and geometry).
Daily, formative assessment allows teachers to evaluate the learning and provide further work as needed, or support a select group of individuals, whilst providing challenge for those children who have developed a secure understanding. The outcomes from Maths lessons inform future planning and teachers revisit areas of learning as needed. This is further supported by the termly summative assessment points using NFER assessments (Arithmetic, Reasoning 1 and Reasoning 2). This provides individual pupil data as well as opportunities to evaluate areas taught and inform future planning on areas which need further consolidation.
The impact of the curriculum is monitored through a combination of discussions with pupils and staff, scrutiny of workbooks and lesson observations, in order to provide a comprehensive understanding of the quality of the curriculum and highlight areas for further development.