Intent: The knowledge and skills that pupils will gain at each stage of the curriculum
As stated in the National Curriculum, ‘A high-quality mathematics education 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’. Therefore, at St Louis Catholic Primary School, we aim to deliver a rich maths curriculum which is challenging, yet accessible to all. We strive to provide all pupils with the knowledge, skills and confidence needed to enable progression. It is our aspiration that our children develop a sense of enjoyment and curiosity towards maths whilst showing bravery when it comes to challenging themselves.
In line with the National Curriculum, we aim for all of our children to become fluent in the fundamentals of mathematics. We base our curriculum content on the following classifications: declarative, procedural and conditional as exemplified in the Ofsted Research Review as set out below.
“Declarative knowledge is static in nature and consists of facts, formulae, concepts, principles and rules.”
“Procedural knowledge is recalled as a sequence of steps. The category includes methods, algorithms and procedures: everything from long division, ways of setting out calculations in workbooks to the familiar step-by-step approaches to solving quadratic equations.”
“Conditional knowledge gives pupils the ability to reason and solve problems. Useful combinations of declarative and procedural knowledge are transformed into strategies when pupils learn to match the problem types that they can be used for.”
We deliver engaging lessons to enhance our students’ understanding and therefore enabling them to make long term connections between their learning across topics and year groups. We are committed to ensuring that our students can see the significance and purpose of the subject and are provided with opportunities to relate their learning to the real world. We intend for our children to understand the link between maths and other subjects – particularly science and technology. By acquiring the skills needed to recall facts, they should be able to transfer and apply these skills to different contexts.
We have high ambitions for all our pupils. For pupils with SEND, we plan inclusive lessons enabling them to access the curriculum. When a new concept is introduced, a concrete, pictorial and abstract approach is used, along with strategies to scaffold learning – as found in the Teacher Handbook: SEND. However, our long term aim is for pupils to move away from scaffolded support as soon as possible, as declarative and procedural knowledge becomes embedded in pupils’ long term memories. .
EYFS: Building Good Habits
Developing a strong grounding in number is essential so that all children develop the necessary building blocks to excel mathematically. At this stage declarative knowledge is developed through teaching mathematical facts, concepts and rules. Children should be able to count confidently, develop a deep understanding of the numbers to 10, the relationships between them and the patterns within those numbers.
Children are encouraged to learn and recall facts fluently.
By providing frequent and varied opportunities to build and apply this understanding - such as using manipulatives, including small pebbles and tens frames for supporting counting and number bonds - children will develop a secure base of knowledge and vocabulary from which mastery of mathematics is built.
In addition, it is important that the curriculum includes rich opportunities for children to develop their spatial reasoning skills across all areas of mathematics including shape, space and measures. It is important that children develop positive attitudes and interests in mathematics, look for patterns and relationships, spot connections, ‘have a go’, talk to adults and peers about what they notice and not be afraid to make mistakes.
KS1: Journey of Discovery
KS1 children will continue to build on their declarative knowledge from EYFS, developing confidence and mental fluency with whole numbers, counting, place value, number bonds and halves and doubles.
They will begin to use procedural knowledge by using the appropriate methods to solve number sentences. They will initially use concrete, pictorial and abstract methods to solve number sentences involving the four operations, developing their knowledge and understanding of efficient methods.
Pupils will continue to build upon their knowledge when recognising, describing, drawing, comparing and sorting shapes. In our ‘measure’ lessons, children will describe and compare different quantities. They begin with non-standard units of measure in Year 1 and move onto standard units of measure by Year 2.
As pupils become confident and fluent with declarative and procedural knowledge, they are introduced to conditional knowledge. This is done by applying their learning to problem solving and reasoning questions.
KS2: Broadening Horizons
Building upon their knowledge from KS1, KS2 children will continue to develop their understanding of the four operations – solving questions both mentally and using a formal written method. As the children move up the school, our intention is that pupils will become fluent applying their knowledge to different concepts and will be confident choosing the most efficient methods to solve questions involving number. They should be fluent with their times tables, able to solve problems and start to apply their learning to other subjects.
Conditional knowledge becomes more of a focus at this point, whereby children are taught the skills to reason and problem solve.
In KS2, children are able to see the relationship between declarative, procedural and conditional knowledge.
Implementation: How the curriculum is taught and assessed
Maths is taught as a distinct subject from Reception onwards through daily lessons with teacher input and activities for pupils to practice or apply their knowledge. Manipulatives are available to scaffold learning, however teachers regularly assess their use and when to withdraw them to avoid an over-reliance.
As a school, we use the scheme ‘Collins: Busy Ant’ as a basis for our maths planning – supplemented by White Rose, NCETM and Ready to Progress. This ensures that every aspect of the curriculum is covered whilst following our school learning cycle. We believe that adapting this scheme enables us to tailor the sequence of lessons to best suit our pupils and ensure that they have secured the skills needed, before moving the learning forward.
Exploring mathematical skills and knowledge in depth helps them to gain a secure understanding of each topic. By having a spiral curriculum, we can ensure that key skills are revisited regularly allowing repetition to embed the learning into pupils’ long term memories. The whole school maths overview outlines the topics taught by each year group and when.
In the EYFS, in addition to teacher led sessions, there are opportunities for children to consolidate learning through activities in the continuous provision both indoors and outside. Adults are aware who needs to access these activities in order to ensure all children meet the milestones as set out in the long term plan for maths.
At the beginning of every maths lesson from Year 1 onwards, our pupils have the opportunity to practise the four operations. They are provided with four questions which they answer using the methods appropriate for their year group. At St Louis, we have our own calculation policy for each operation. This policy ensures consistency and progression throughout the school. Process maps are available for students who may require additional support in this area so they are able to tackle the questions independently.
In order to practice and consolidate learning, St Louis children are encouraged to ‘strive for five’. This means once they have correctly answered five questions, they move onto the next challenge. During the lesson, pit stops are used for students to mark their own work to check they are on track. This information may be used to form new targeted groups or to highlight to pupils that they are ready to move on to a more challenging activity.
Problem solving and reasoning opportunities are built into each unit so that children can apply their skills. Problem solving is taught explicitly with worked examples to help ensure pupils understand what is being asked of them; to use what they already know; and to select the most efficient methods of solving the problem. These lessons take place on a Friday. Pupils in KS2 are expected to use abstract methods to solve these problems, rather than manipulatives and pictorial approaches, particularly in the older year groups. Problem solving and reasoning questions may come from a range of sources such as White Rose, NRich and Test Base.
Pupils will be introduced to a range of problem types: word problems, visual problems, finding all possibilities, logic problems and rules and patterns.
The school uses the RUCSAC approach to problem solving: Read the question, Understand what the problem is and the best approach to solving it, Decide which Calculation/s is needed, Answer the problem using an appropriate/ most efficient method, Check their answer, including if it seems sensible.
Although problem solving and reasoning is taught explicitly during a lesson on a Friday, other opportunities for pupils to apply their skills can be offered in other lessons throughout the week if deemed appropriate by the teacher, but pupils should have previous experience of similar problems.
Maths is assessed through targeted questioning within lessons and the marking of books – both in the moment and at the end of a lesson. Low stake but timed quizzes are also used. This enables staff to identify the knowledge that has been embedded into the long term memory and where support may be needed for future lessons.
In line with our scheme, maths topics are revisited throughout the year. This enables teachers to formatively assess who knows more, can remember more and do more by building on knowledge gained earlier in the year as well as in previous years. In addition to this, summative assessments take place twice a year, using GL Assessment papers from Year 1 onwards. Previous years’ SATs papers are used in Year 2 from Lent (Spring) term onwards and throughout the year in Year 6.
Aside from daily maths lessons, the pupils are provided with another opportunity to consolidate their learning from the topics covered through ‘Maths in 2’ during the afternoon. This is an opportunity to recap and consolidate learning in areas other than the four operations eg time, shape. This is introduced in Year 1 onwards once children have the appropriate declarative and procedural knowledge in number.
At St Louis, from Year 2 onwards, the children have ‘Times Tables Rock Stars’ accounts which they can access at home to practise multiplication and division. Similarly, they have ‘MyMaths’ accounts which are used at home. The students are set one piece of homework per week based on the learning that has been taught during that week.
Pupils are taught in mixed ability classes, with support for those who need it including those with SEN provided for within the classroom wherever possible.
Impact: The outcomes pupils achieve
Lesson visits show the learning that is taking place. Pupils will be able to answer questions based on their knowledge they have gained and they will be able to talk about their prior learning. As the pupils progress through the school, they will become increasingly confident in talking about how they have developed their skills and will be able to apply both old (in previous units and year groups) and new skills (developed in their current unit) to their maths.
Children will be able to recall age appropriate maths facts (declarative knowledge) through discussion and quizzes. They will be able to demonstrate the correct and most efficient method of calculation through work in books. The pupils will be able to talk confidently to an adult about what they have learnt in their maths lessons. They will begin to use maths specific vocabulary where appropriate and will be able to talk about the skills that they have developed and used in their lessons, particularly when problems solving and reasoning.
The work in the children’s books should reflect their journey throughout a unit, with sufficient demonstration of consolidation and challenge. The books will show the development of the knowledge and skills of the children throughout the unit, the year, and from year group to year group, demonstrating progress, a deepening knowledge and a development of skills over time.
Summative assessments should show an increase in accuracy at the end of the academic year compared to the beginning, as the pupils will be able to use their knowledge and skills that they have built up to help them to answer the questions.