'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'. (National curriculum 2014)
Mathematics at Rosehill
We believe that:
- Every child has the right to achieve their maximum potential without a pre-conceived limit being put on their ability and attainment.
- The ability to succeed is not fixed and this is clear in both lesson design and class teaching.
- Learning in maths should focus on depth of understanding before breadth.
- Pupils should ‘keep up’ over ‘catch up’- all children should be given the opportunity to access the lesson regardless of previous attainment.
- High expectations should be made clear to all learners.
- Emphasising the high value of mathematics education to all staff, pupils, parents and carers is key to our children becoming successful Mathematicians.
- All staff should actively attempt to improve their pedagogical understanding of maths mastery wherever possible, and feel supported by school leadership to this aim.
At Rosehill Infant School we aim to equip all pupils with the skills and confidence to solve a range of problems through fluency with numbers and mathematical reasoning. Children are encouraged to see the mathematics that surround them every day and enjoy developing vital life skills in this subject.
We started our journey to improve the teaching and learning of mathematics for every child in September 2016. There are several elements which have influenced improvements in attainment and progress in mathematics for our children. Mathematics is led by Miss Asia who is undertaking the Mastery Specialist Teacher this year. This document sets out our approach and the reasons why maths at Rosehill Infant School may look a little different to other schools, or the way lessons/books looked a few years ago.
The three aims of the NC should be addressed every day (not just in the maths lesson):
Fluency – Reasoning – Problem Solving.
- Whole class together – we teach mathematics to whole classes and do not label children. Lessons are planned based on formative assessment of what students already know and we include all children in learning mathematical concepts. At the planning stage, teachers consider the scaffolding that may be required for children struggling to grasp concepts in the lesson and suitable challenge questions for those who may grasp the concepts rapidly. In line with NCETM advice, one form of depth frequently used, during the first part of the lesson, is variation theory (conceptual and procedural). Variation is one of the five ‘big ideas’ at the heart of Teaching for Mastery. For example, a child who can produce a quick correct answer may be asked to solve the question using more than one other procedure, to represent the question in more than one way (such as the bar model or part whole).
- Longer but deeper – in order to ensure children have a secure and deep understanding of the content taught, our plans have been adjusted to allow longer on topics and we move more slowly through the curriculum. We use the Power Maths planning in line with White Rose Maths and ideas from Maths no problem textbooks to support progression and variation. Teachers adapt each lesson to meet the needs of their children and add extra questioning / tasks which will allow children to learn the content more deeply. The learning will focus on one key conceptual idea and connections are made across mathematical topics. To outsiders it may appear that the pace of the lesson is slower, but progress and understanding is enhanced.
- Key learning points are identified during planning (collaboratively in year teams and where possible supported by Miss Asia) and a clear journey through the maths should be shown on flipcharts (also reflected on working walls). Learning points may appear to be very small but this is deliberate. For example, a whole lesson may be spent on adding the ones to a 2 digit number. The expectation is that every child will master the concept and some children will work more deeply on the same concept using variation theory and challenge tasks.
- Questions will probe pupil understanding throughout, taking some children’s learning deeper. Responses are expected in full sentences, using precise mathematical vocabulary.
- Fluency – there is a whole school focus on developing an instant recall of key facts, such as number bonds, times tables, division facts, addition and subtraction facts.
- Exploration – instead of ‘Let me teach you…’ or giving a learning objective as a starting point, children are encouraged to explore a problem themselves to see what they already know. At the beginning of each lesson or unit this exploration is referred to as the ‘Let’s discover’. During this time, the teacher and teaching assistant will spend time observing and questioning the children. The understanding of children who provide a quick correct answer will be probed further using questions based around variation theory. Power Maths is used during this part of the lesson to enhance the learning experience, providing a high quality resource for children and teachers.
- Develop reasoning and deep understanding (contexts and representations of mathematics) – problems are often set in real life contexts – carefully chosen practical resources and pictorial representations are used to explore concepts. These pictorial representations will appear in books as children show their understanding, rather than answers to a series of calculations. The use of practical resources, pictorial representations and recording takes place in every lesson (the CPA approach).
- Structuring – the teacher will organise the findings of the exploration, compare/contrast strategies and guide toward the most efficient strategy (or the one being learnt that day).
- Step by step approach – journey through the mathematics (these steps may appear small, especially at the beginning of a lesson, there are points when suddenly a jump appears to have been made, or an extra challenge appears – this is normal).
- Questions to challenge thinking – teachers use questioning throughout every lesson to check understanding – a variety of questions are used, but you will hear the same ones being repeated: How do you know? Can you prove it? Are you sure? Can you represent it another way? What’s the value? What’s the same/different about? Can you explain that? What does your partner think? Can you imagine? Listen out for more common questions you hear.
NB: Due to the style of the lessons with frequent questioning, lessons may appear to move slower than in the past. There will be more talking and less recording in books. We do not want children to attempt independent recording until we believe they are secure with the concept. We do not want them to practise errors.
- Discussion and feedback – pupils have opportunities to talk to their partners and explain/clarify their thinking.
- Recording the learning – not just pages of similar calculations – ideas taken from Power Maths practise books are used across the school. In childrens' books you will see a range of activities including those requiring written explanations of the children’s understanding.
- Practising – not drill and practice but practice characterised by variation – EYFS and Key Stage One use Power Maths planning and Maths No Problem textbooks to provide children with carefully chosen questions and are essential in assessing how the children have understood the concept taught. You will also see another level of differentiation within childrens' maths books as some children rapidly grasp the concepts and therefore complete the indepedent task and quickly and move onto questions or activities where their understanding can be developed to a greater depth. Some children will work very hard in the lesson to complete the work independently, some children will need additional support to complete the work and some children will sometimes be provided with different tasks and questions appropriate to their understanding of a concept.
- Rapid intervention – in mathematics new learning is built upon previous understanding, so in order for learning to progress and to keep the class together pupils need to be supported to keep up and areas of difficulty must be dealt with as and when they occur. Ideally this would happen on the same day but this is not always possible so it may be the following morning but will be before new learning is introduced.
- Gap tasks - Gap tasks or challenges may appear for individual children in their books, but usually gaps are addressed through same day or early morning catch up and therefore will not always be recorded in books. The most valuable feedback is given during a lesson. Very often the children’s next steps are addressed in the subsequent lessons and therefore will not appear as questions for some children to answer after a lesson has taken place.
- SEND pupils – may be supported by additional adults, different resources, differentiated activities. They will also complete additional activities outside of the mathematics lesson.
- Children in EYFS explore mathematical concepts through active exploration and their everyday play based learning. Children are taught key concepts and application of number using a hands on practical approach. EYFS practitioners provide opportunities for children to manipulate a variety of objects which supports their understanding of quantity and number. The CPA approach is used when teaching children key mathematical skills. Practitioners allow children time for exploration and the use of concrete objects helps to support children's mathematical understanding. Maths in the early years provides children with a solid foundation that will enable them to develop skills as they progress through their schooling and ensures children are ready for the Nation Curriculum.
NB: We do not label our children. We have high expectations of all children and strongly believe that all children are equally able in mathematics. Some may take longer to grasp concepts and may need careful scaffolding or extra time/support (guided groups, same day catch-up, additional homework, pre-teaching, intervention group, specific parental support).
Mastery with greater depth
Is characterised by children who can:
- solve problems of greater complexity (i.e. where the approach is not immediately obvious), demonstrating creativity and imagination
- independently explore and investigate mathematical contexts and structures
- communicate results clearly and systematically
- explain and generalise the mathematics
How Mathematical skills are taught
Mathematical skills are taught using concrete, pictorial and abstract methods.
Children first learn skills using concrete objects to demonstrate their understanding. This is done through using a range of concrete resources represented in different ways linked to the learning objective.
After learning skills using concrete objects, children learn pictorial methods of representing their work to show their thinking processes. Pictorial is the “seeing” stage, using representations of the objects to model problems. This stage encourages children to make a mental connection between the physical object and abstract levels of understanding by drawing or looking at pictures, circles, diagrams or models which represent the objects in the problem.
Only once a child has demonstrated that they have a solid understanding of the “concrete” and “pictorial” representations of the problem, the children are introduced to the more “abstract” concept, such as mathematical symbols. Children are introduced to the concept at a symbolic level, using only numbers, notation, and mathematical symbols, for example +, –, x, / to indicate addition, multiplication, or division.
e.g. 6 + 1 =
9 - 5 =
20 x 2 =
Our intended outcomes
By the end of the EYFS pupils should count reliably with numbers from one to twenty, place them in order and say which number is one more and one less than a given number. Using quantities and objects, they add and subtract two single digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing.
Mathematics: Shape space and measure
By the end of EYFS pupils should use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems. They recognise, create and describe patterns. They explore characteristics of everyday objects and shapes and use mathematical language to describe them.
Key stage 1
Our pupils will learn to:
- Develop the appropriate mathematical language associated with number, shape and position
- Use and apply mathematics in practical tasks and in real life problems
- Understand and use the four operations of number in relevant contexts
- Understand relationships between umbers and learn basic number facts
- Understand place value in our counting system
- Use their mathematical skills in simple problem solving
- Collect, interpret and represent data
- Develop mental methods of calculation
- Recognise, describe and represent shapes and patterns in terms of their properties
- Measure quantities including length, area, volume/capacity and angle
What the children say about Maths at Rosehill Infant School
"I like maths because it's fun and you learn about lots of things"
Child in Year 1
" I love maths because we get to use objects and we can do lots of fun stuff " (Mominah in Year 2 )
" Me and Asim are mastery partners and we work together. If I'm not sure then Asim helps me and if he's not sure then I help him"
Child in Year 2
" I know i need to check my work if there is an orange mark near my answer "
Child in Year 1
" I am good at maths because I can explain things and tell my friends how to make groups when we are learning about sharing "
Child in Year 1
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