Mathematics

Mathematics

'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)

 

INTENT

At Dropmore Infant School we provide a high-quality, balanced and progressive Mathematics curriculum. In line with DfE best practice we have embedded a mastery approach to Maths teaching, focussing on building pupils’ understanding, confidence and independence through the use of concrete and pictorial representations alongside abstract notation. Through our mastery approach we allow for all children to become fluent in the fundamentals of maths, developing their conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. Children will be able to reason mathematically by justifying, making links to known facts, or providing proof using mathematical language. Understanding of concepts will be challenged through solving problems by applying their mathematic knowledge. Links within other subjects will be highlighted allowing children to apply their skills and mathematical knowledge. We will equip children with the foundations of mathematics that are essential to everyday life. 

IMPLEMENTATION

Our teaching for mastery is underpinned by the 5 big ideas of mastery and the teaching for mastery principles:

  •   Opportunities for Mathematical Thinking allow children to make chains of reasoning connected with the other areas of their mathematics.
  •   A focus on Representation and Structure ensures concepts are explored using concrete, pictorial and abstract representations, the children actively look for patterns and generalise whilst problem solving.
  •   Coherence is achieved through the planning of small, connected steps to link every question and lesson within a topic.
  •   Teachers use both procedural and conceptual Variation within their lessons and there remains an emphasis on Fluency with a relentless focus on number and times table facts.

Teaching for Mastery Principles:

o   It is achievable for all we have high expectations and encourage a positive ‘can do’ mindset towards mathematics in all pupils, creating learning experiences which develop children’s resilience in the face of a challenge and carefully scaffolding learning so everyone can make progress.

o   Deep and sustainable learning – lessons are designed with careful small steps, questions and tasks in place to ensure the learning is not superficial.

o   The ability to build on something that has already been sufficiently mastered – pupils’ learning of concepts is seen a continuum across the school.

o   The ability to reason about a concept and make connections – pupils are encouraged to make connections and spot patterns between different concepts (E.g. the link between ratio, division and fractions) and use precise mathematical language, which frees up working memory and deepens conceptual understanding.

o   Conceptual and procedural fluency – teachers move mathematics from one context to another (using objects, pictorial representations, equations and word problems). There are high expectations for pupils to learn times tables, key number facts (so they are automatic) and have a true sense of number. Pupils are also encouraged to think whether their method for tackling a given calculation or problem is Appropriate, Reliable and Efficient (A.R.E).

o   Problem solving is central – this develops pupils’ understanding of why something works so that they truly have an appreciation of what they are doing rather than just learning to repeat routines without grasping what is happening.

o   Challenge through greater depth - rather than accelerated content, (moving onto next year’s concepts) teachers set tasks to deepen knowledge and improve reasoning skills within the objectives of their year group.

The learning is broken down into small steps that build on children’s prior learning. The lesson journey should be detailed in our lesson plans and any relevant learning is reflected onto our class working wall or recorded on flipcharts (Smart notebook or PowerPoint). Difficult points and potential misconceptions are identified in advance and strategies to address them are planned, as well as key questions to challenge thinking and develop learning for all pupils. We also ensure key vocabulary is taught at relevant points in the lesson journey to reinforce mathematical knowledge. Context and representations are carefully chosen to develop reasoning skills and help pupils link concrete ideas to abstract mathematical concepts. All lessons should have elements of the concrete, pictorial, abstract approach (CPA) to mathematical teaching.

The use of high-quality materials and tasks to support learning and provide access to the mathematics are integrated into lessons. These include

  •        White Rose Maths Schemes of Learning and Assessment materials,
  •        Power Maths online materials and textbook activities,
  •        Maths No Problem! textbook,
  •        Number blocks NCETM resources,
  •        NCETM Mastery assessment materials & Spine resources (progress in calculation)
  •        NRICH
  •        visual images and concrete resources.

The children undertake a fluency activity at the start of every mathematics lesson. Where possible we use further opportunities for extra fluency practice (key instant recall of key facts such as number bonds, times tables, division facts), such as morning starters etc.

IMPACT

Children at Dropmore Infant School enjoy Mathematics and understand the important role of Mathematics in everyday life at and age-appropriate level. This is evident through pupil voice and monitoring which takes place every term by the curriculum leader.

Through quality first teaching, a mastery approach, high quality resources and effective feedback, most children achieve age-related expectations by the end of each year group. At the end of KS1, our children leave our school well-prepared for the next step in their mathematical education.

Summative assessment takes place at the end of each term and children’s progress and attainment is discussed with the Headteacher in pupil progress meetings. Formative assessment takes place on a daily basis and teachers adjust planning accordingly to meet the needs of their class.  

EYFS
  • 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 are 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 Stage 1 
How mathematical skills are taught
 

Mathematical skills are taught using concrete, pictorial and abstract methods.

 Concrete

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

 

Pictorial

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. 

 

Abstract

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 =        

How we teach Mathematics at Dropmore Infant School
 
  •         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 lessonis 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 .
Lesson Structure
 
  •        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.

 

Enrichment

Enrichment opportunities are carefully selected to enhance learning opportunities for children by demonstrating real life contextual understanding of mathematics. Dropmore children also take part in a number of activities outside of their Maths lessons including Dropmore shop and silver coin week.

Further Resources/ Useful Links

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.