Our Vision:
“We are here to bring learning to life for every member of our school community, just as water brings life to the world. We are here to prepare children for their journey through life as responsible respectful citizens of the future who are ambitious, courageous and kind. We are a school that is proud to be creative, caring, nurturing and challenging in equal measure. We aim to develop life-long learners who thrive in our care and bring life to the future of our world.”
And so, our vision for Maths is to for children to see themselves as mathematicians. We promote a ‘can do’ attitude to maths without a fear of making mistakes to produce individuals who are numerate, creative, independent, inquisitive, enquiring and confident. We aim to develop happy and confident mathematicians, throughout their learning and into their adult life.
Early Maths
In Early Maths, we aim for all children to develop a firm mathematical foundation. There is a focus on developing mathematical language to reason and discuss, developing mathematical thinking and fluency through making connections and using manipulatives and representations to develop understanding. There is a dedicated time for children to learn mathematics and opportunities for children to apply/practise mathematical skills within the continuous provision. Early maths teaching builds on what children already know and is based on the six NCETM key concepts-cardinality and counting, comparison, composition, pattern, shape and space, measures. Our daily maths sessions are based on the national Mastering Number programme, which focuses on developing a strong number sense. This programme purposefully focuses on small numbers so that children are confident number experts and develop a deep understanding of number. Sessions includes lots of opportunities for the children to use maths talk, reason, explain their thinking, visualise number patterns, count, subitise, explore composition and comparison. There are also planned activities for the children to explore other aspects of early maths including shape, space, pattern and measures.
The Teaching of Maths
5 main ideas underpin the teaching of maths at St. George’s.
Using these 5 main ideas, we follow the White Rose block units and small steps for learning. There is a focus on fluency with each lesson beginning with a short ‘Toolbox’ session. This enables children to practise and apply number facts and timetables knowledge in a range of contexts and/or mixed concepts.
Concrete, Pictoral & Abstract
Lessons are taught using the Concrete, Pictoral & Abstract (CPA) approach.
Concrete representation
The children are first introduced to an idea or a skill by acting it out with real objects. In division, for example, this might be done by separating apples into groups of red ones and green ones or by sharing 12 biscuits amongst 6 children. This is a ‘hands on’ approach using real objects and it is the basis for conceptual understanding.
Pictorial representation
This is used when a child has sufficiently understood the hands-on experiences performed and can now relate them to representations, such as a diagram or picture of the problem. In the case of a division exercise this could be the action of circling objects.
Abstract representation
The symbolic stage – a child is now capable of representing problems by using mathematical notation, for example: 12 ÷ 6 = 2. As understanding develops, children move on to use some form of abstract representation. This could be giving values to rectangular bars (bar model) to identify what is known and what is unknown, using a symbol to stand for a number or something else.
CPA are not stages gone through once, but a continuum. There will be occasions when a child will use concrete, pictorial and abstract representations all in one session. A child who uses abstract representations in one area may need concrete representations in another. On a different occasion, a child may need to revisit a concrete representation before moving on to a pictorial or abstract one. Therefore, it is important that a variety of representations are available for children to use at all times. Our calculation policy demonstrates the progression of objectives through CPA representations.
The maths learning environment Each classroom has a maths area which is equipped with accessible resources for the children to use. Prompts support and show progression in the current learning and scaffolded sentence starters are displayed. These are modelled by staff and support children when talking about maths, giving pupils the confidence to communicate their mathematical thinking and ideas.
Reasoning Sentence Starters 
Fluency, reasoning and problem solving underpins the deepening of understanding.
Strategies to develop pupils’ reasoning skills:
- Spot the mistake / Which is correct?
- True or false?
- What comes next?
- Do, then explain
- Make up an example / Write more statements / Create a question / Another and another
- Possible answers / Other possibilities
- What do you notice?
- Continue the pattern
- Missing numbers / Missing symbols / Missing information/Connected calculations
- Working backwards / Use the inverse / Undoing / Unpicking
- Hard and easy questions
- What else do you know? / Use a fact
- Fact families
- Convince me / Prove it / Generalising / Explain thinking
- Make an estimate / Size of an answer
- Always, sometimes, never
- Making links / Application
- Can you find?
- What’s the same, what’s different?
- Odd one out
- Complete the pattern / Continue the pattern
- Another and another
- Ordering
- Testing conditions
- The answer is…
- Visualising
Assessment
Teachers’ assess maths against the NCETM progression charts and Development Matters for EYFS, the Early Learning Goals at the end of Reception and the National Curriculum Objectives. Year 1 – 6 take part in termly PUMA or SATs assessments. To assess progress within a number or calculation unit, there are cold and hot tasks. The cold task is at the beginning of the block and focuses on assessing key objectives from the previous year group. This supports identifying key gaps in learning and also to ensure there will be appropriate challenge within a unit. The hot task is towards the end of the block and assesses taught objectives. There is time after the hot task to address any misconceptions or extend children’s learning before moving to the next unit. Both tasks focus on fluency, problem solving and reasoning. Pre teaching or specific targeted interventions are used to support children who are not on track to meet expected levels of attainment or to reach their own specific progress measures such as greater depth. These can be in the form of a precision 1:1 maths intervention such as “Power of Two” or through booster maths sessions using the NCETM ready to progress materials.
More information about how we teach Maths at St. George’s.
