'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 Dropmore Infant School
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 Dropmore 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.
We started our journey to improve the teaching and learning of mathematics for every child in September 2017. There are several elements which have influenced improvements in attainment and progress in mathematics for our children.
Mathematics is led by Miss Beeks who was part of a Maths Mastery Teacher research group last year. This page sets out our approach and the reasons why maths at Dropmore Infant School may look a little different to other schools, or the way lessons/books looked a few years ago.
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.
Examples of some on the concrete equipment we use is found below
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 =
- 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 visitors it may appear that the pace of the lesson is slower, but progress and understanding is enhanced.
- Key learning points are identified during planning and key 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 and stem sentences.
- Fluency – there is a school focus on developing an instant recall of key facts, such as number bonds, times tables, division facts, addition and subtraction facts. This will be seen in maths lessons and during Maths Fluency sessions .
- DISCOVER – 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. 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 often used during this part of the lesson to enhance the learning experience, providing a high quality resource for children and teachers.
- SHARE and THINK TOGETHER - 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 KS1. In childrens' books you will see a range of activities, including those requiring written explanations of the children’s understanding.
- PRACTISE – not drill and practice but practice characterised by variation – 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 independent 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.
- 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. The EYFS team will be using the new White Rose Maths Scheme to support their Mastery Maths planning and teaching in Early Years. They will also be taking part in a mastery EYFS work group to support us in adopting a mastery approach in Mathematics in Reception.
Key Instant Recall Facts ( KIRFS)
KIRFs (Key Instant Recall Facts) are designed to support the development of the mental skills that underpin much of the mathematics work in school. They are particularly useful when calculating, be it adding, subtracting, multiplying or dividing.
Each year group is allocated up to six facts to focus on throughout the year, in line with age related expectations. Time is to be dedicated at least 3 times each week, possibly in smaller daily bursts to ensure that the KIRF is practiced and learnt so that children grow in confidence to recall their facts instantly.
The links below has useful ideas for how to support your child to learn their KIRFs at home.