Maths at St. Monica's 

Intent 

As stated in the National Curriculum 2014, we intend to ensure that all pupils: 

1. Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately

2. Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language

3. 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.

Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. This fulfils OFSTED guidance that, for high quality maths education, educators plan to give pupils opportunities to consolidate learning that go beyond immediately answering questions correctly (OFSTED 2021). They should also apply their mathematical knowledge to science and other subjects. 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 and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

We aim to teach maths using the mastery approach. Maths is a journey and long-term goal, achieved through exploration, clarification, practice and application over time. At each stage of learning, children should be able to demonstrate a deep, conceptual understanding of the topic and be able to build on this over time. Learning should be secure in all areas, where knowledge and understanding can be recalled, used, transferred and applied in different contexts. As recommended by OFSTED, teachers remember that it is not possible for pupils to develop proficiency by emulating expertise, but by emulating the journey to expertise (OFSTED 2021).

Implementation

• Staff are clear on the design and intent of our maths mastery curriculum and why. They have a secure knowledge of the stages of learning, understanding the progression in each area and using this to support their teaching. As a school, we follow the White Rose schemes of work from Reception, with Master The Curriculum being used in Nursery. Twinkl, Headtstart and Master the Curriculum and Power Maths are used to supplement the White Rose scheme, where appropriate. No scheme is followed prescriptively and lessons are adapted to suit the needs of individual classes/pupils. We feel that the White Rose schemes meet OFSTED high quality maths education advice as:
• The planned curriculum details the core facts, concepts, methods and strategies that give pupils the best chance of developing proficiency in the subject.
• The teaching of linked facts and methods is sequenced to take advantage of the way that knowing facts helps pupils to learn methods and vice versa
• Sequences of learning allow pupils to access their familiarity with the facts and methods
• New content draws on and makes links with the content that pupils have previously acquired.
• Curriculum progression is by intelligent design rather than by choice or chance.
• Rehearsal sequences align with curriculum sequences. OFSTED 2021

Mastering Number is used daily in KS1 to develop firm foundations in the development of good number sense.

Also, teachers are able to emphasise the connections between different aspects of mathematics, and do this consistently. They also plan lessons that utilise pupils quickly and consistently retrieving and using their previous learning of arithmetic facts, all of which, the EEF state as exemplary practise (Improving Mathematics review).

For each of the four operations, our Stages of Progression document clearly identifies each stage the children should work through (and the expected year groups) to fully be able to access to expected calculations. This fulfils OFSTED guidance of having school-wide approaches to calculation and presentation in pupils’ books and ensures children are confident in using linked facts and methods that are the building blocks of strategies, before strategies are taught. Teachers teach a range of mental, and pencil-and-paper methods, and encourage pupils to consider when different methods are appropriate and efficient (EEF state as exemplary practise in their Improving Mathematics review).

Staff recognise and understand of a Concrete, Pictorial, Abstract* (CPA) approach to maths teaching and learning. Objects, pictures, words, numbers and symbols are vital. The mastery approach incorporates all of these to help children explore and demonstrate mathematical ideas, enrich their learning experience and deepen understanding. Together, these elements help cement knowledge so pupils truly understand what they’ve learnt. As noted by OFSTED, they avoid creating a reliance on outsourced memory aids or physical resources, moving children on as soon as they are secure (OFSTED 2021). Teachers enable pupils to understand the links between the manipulatives and the mathematical ideas they represent. Teachers use manipulatives to develop pupils’ independent understanding of the mathematics (EEF state as exemplary practise in their Improving Mathematics review).

All pupils, when introduced to a key new concept, should have the opportunity to build competency in this topic by taking this approach. Pupils are encouraged to physically represent mathematical concepts. Objects and pictures are used to demonstrate and visualise abstract ideas, alongside numbers and symbols. For all children, activities involve overlearning to ensure full understanding (Highlighted by OFSTED as a feature of high quality maths education, OFSTED 2021).

Discussions are a vital part of our lessons, both for teachers to model skills of reasoning, justifying and conjecturing and for children to be able to consolidate their learning through explanations. They are also then able to hear key vocabulary being used effectively by adults and peers. Discussions can also highlight misconceptions as well as being essential for building confidence in our children. Teachers are able to orchestrate productive classroom discussions. Pupils actively take part in discussions (EEF states this as exemplary practise in their Improving Mathematics review). Discussions also support the development of children’s mathematical vocabulary. Teachers use precise mathematical language themselves. Teachers support pupils to recognise mathematical structure, for example by rephrasing pupils’ responses that use vague, non-mathematical language with appropriate mathematical language (EEF state as exemplary practise in their Improving Mathematics review).

When staff have identified misconceptions, they intervene as swiftly as possible to help pupils having difficulties to keep up. Teaching Assistants work within lessons to support targeted groups of children to support pupils’ learning. Teachers have a good knowledge of the common misconceptions in maths and why they arise. These misconceptions are identified in planning and teaching staff use this knowledge to inform their assessment (EEF state as exemplary practise in their Improving Mathematics review). As OFSTED recommend, pupils who are more likely to struggle or who are at risk of falling behind are given more time and support to complete tasks, rather than different tasks or curriculums, so that they can commit core facts and methods to long-term memory (OFSTED 2021).

Assessment is used both formally and informally to review progress. 

- Children complete a baseline assessment at the start of the year and then, at the end of each term, children complete formal assessments. These results are tracked to inform future planning. Children who are judged not to be making their expected progress are then targeted for additional support.

- Teaching staff are constantly assessing through observations, discussions and written work completed. Lessons are adapted in response to these assessments to ensure the children are being taught at the appropriate level and pace. Informal assessments, as stated by OFSTED as high quality maths education, are also used as

- Teachers plan frequent, low-stakes testing to help pupils to remember content.

- Lessons incorporate timed testing to help pupils learn maths facts to automaticity. When a pupil is identified as struggling teachers quickly identify the specific reason(s) why. Teachers use this information to intervene and address the aspect of maths that the pupils is struggling with (EEF state as exemplary practise in their Improving Mathematics review).

There is an annual “St. Monica’s Maths Day” where Maths is celebrated. Strong links are made with parents to enable them to support their children’s learning. Parents’ Courses are undertaken to show parents how we complete calculations using the CPA approach. This ensures parents know what is expected of their children and understand how they can help them outside school.

Impact

In response to our teaching and their learning, our children will have:

• A quick and secure recall of facts and procedures
• The flexibility and fluidity to move between different contexts and representations of mathematics.
• The ability to recognise relationships and make connections in mathematics.

A mathematical concept or skill has been mastered when a child can show it in multiple ways, using the mathematical language to explain their ideas, and can independently apply the concept to new problems in unfamiliar situations. Our children will, as far as possible, master our curriculum.

We will have a school of confident, enthusiastic, resilient mathematicians who are equipped not only for future learning but for future life.

The education inspection framework (EIF) makes it clear that schools are expected to ensure that the mathematics curriculum ‘helps pupils to gain enjoyment through a growing self-confidence in their ability’. OFSTED May 2019.

*Concrete – children have the opportunity to use concrete objects and manipulatives to help them understand and explain what they are doing.

Pictorial – children then build on this concrete approach by using pictorial representations, which can then be used to reason and solve problems.

Abstract – With the foundations firmly laid, children can move to an abstract approach using numbers and key concepts with confidence.

References:

1. OFSTED Research review series: mathematics Published 25 May 2021

2. School Inspection Handbook OFSTED May 2019

3. EEF IMPROVING MATHEMATICS IN KEY STAGES TWO AND THREE A self-assessment guide - exemplary