Maths

HETTON PRIMARY SCHOOL

Mathematics Policy

We aim to make maths exciting, enjoyable and stimulating. We provide high quality maths teaching, which is engaging, interactive and builds upon children’s prior learning. As a school we have invested in the White Rose Maths Scheme. Every resource has been carefully designed to ensure it addresses the three key aims of fluency, reasoning and problem solving and follows the principles of teaching for mastery. It is designed to support pupils to be able to perform simpler tasks so they can then move on to perform more complex tasks. For example, we cannot expect pupils to add two numbers together before they understand what each individual number represents. This provides pupils with a deep understanding of the subject through a concrete, pictorial and abstract approach. This ensures pupils fully understand what they are learning. We have always put tremendous effort and resources into getting children to have instant recall of their multiplication table facts. Being fluent in calculation and knowing multiplication tables by heart are a maths essential. Knowing the multiplication tables (and their associated division facts) supports mathematical learning and understanding. Those children who have a strong grasp of them tend to be more self-assured when learning new concepts.

Purpose                                                                                    Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. In the area we live, being a competent mathematician is vital in the world of work with companies such as Nissan and Newcastle airport needing skilled mathematicians. A high-quality mathematics education is therefore critical in providing a foundation for understanding the how maths links to local technologies, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.

Aims                                                                                                                       The National Curriculum for mathematics aims to ensure that all pupils:

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

Our vision for Mathematics

• To promote a positive attitude towards mathematics in all pupils
• To ensure all pupils are engaged in and are enjoying exploring Mathematics
• To enable all pupils to find links between mathematics and other areas of the curriculum, including Science
• To ensure all pupils progress in mathematics and are challenged appropriately through an in depth understanding
• To use a wide range of concrete, pictorial and abstract representations to develop all pupils’ relational understanding of mathematics
• To ensure all pupils are confident using mathematical vocabulary when reasoning about mathematics
• To promote a growth mindset in all pupils, particularly when Problem Solving

School Curriculum

Each class teacher is responsible for the Mathematics in their class in consultation with, and with guidance from, the Mathematics subject leader.

Mathematics is taught for at least one hour per day (or five hours per week). However, when required, teachers may choose to include additional mathematics lessons in their weekly timetable. In addition to this one hour, Rec-Y3 complete 10 minutes of Flash Back 4 maths to recover maths concepts from the previous year group to help us with our ‘know more, remember more’ mantra. In addition to this, 10 minutes of mastering number is also taught. From Y4-6 Flash Back 4 is taught followed by Number Sense Times Tables program during the first 20 minutes of the afternoon sessions (3/4 times per week)

We are currently using the White Rose Maths schemes of learning which provide teachers with exemplification for mathematics objectives and are broken down into fluency, reasoning and problem solving; key aims of the National Curriculum 2014. They support a Mastery approach to teaching and learning and have numbers at their heart.  They ensure teachers stay in the required key stage and support the ideal of depth before breadth. They support pupils working together as a whole group and provide plenty of time to build reasoning and problem solving elements into the curriculum. White Rose Maths follows the Concrete-Pictorial-Abstract (CPA) approach and is set into blocks throughout the year in which children build on prior knowledge.

Teachers in the Early Years Foundation Stage (EYFS) base their teaching on ‘Development Matters’ and the White Rose Hub EYFS scheme of learning to ensure that the children are working towards the ‘Early Learning Goals for Mathematical Development’.

The Foundation Stage teachers delivers whole class teaching and adult focus led Maths activities together with the teaching assistant each day. The children also access a range of Maths activities within continuous provision. Towards the end of the Reception Year, teachers aim to draw together the elements of a daily Mathematics lesson. The readiness of the cohort is taken into consideration when preparing for transition into Year 1.

‘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.’ (National Curriculum)

Teaching and Learning - A ‘Mastery’ Approach

What is Fluency?

Fluency comes from deep knowledge and practice. This is the first stage of pupils’ understanding.

Fluency includes:

Accuracy – Pupils carefully completing calculations with no or few careless errors.

Pace – Pupils are able to quickly recall the appropriate strategy to solve the calculation and progress through a number of questions at an age appropriate pace.

Retention – Pupils will be able to retain their knowledge and understanding on a separate occasion to when the concept was first introduced.

What is Reasoning?

Verbal reasoning demonstrates that pupils understand the mathematics. Talk is an integral part of mastery as it encourages students to reason, justify and explain their thinking.

What is Problem Solving?

Mathematical problem solving is at the heart of the Mastery Approach. Pupils are encouraged to identify, understand and apply relevant mathematical principles and make connections between different ideas. This builds the skills needed to tackle new problems, rather than simply repeating routines without a secure understanding.

Mathematical concepts are explored in a variety of representations and problem-solving contexts to give pupils a richer and deeper learning experience. Pupils combine different concepts to solve complex problems, and apply knowledge to real-life situations. Through problem solving, pupils are required to select their mathematical knowledge and apply this to a new concept.

Problem solving is more than just word problems but the RUCSAC approach can be applied to this style of question:

1) Read / look at the problem

2) Understand the problem by underlining or discussing: What is the problem about?

3) Choose – Choose the operation required, the number facts or the approach.

4) Solve – Solve the problem by completing jottings on the page

5) Answer – complete the answer to the problem

6) Check – have I correctly answered the given problem or is there another step?

The teaching and learning of mathematics at Hetton Primary School should include aspects of the following Mastery approach strategies in every lesson and/or over a series of lessons:

                   ‘Concrete, pictorial, abstract (CPA) is a highly effective approach to teaching that develops a deep and sustainable understanding of maths.’ (Maths - no problem!)

Concrete                                                                                                                                                                                   Concrete is the ‘doing’ stage, using concrete objects to model problems. Instead of the traditional method of mathematics teaching, where a teacher demonstrates how to solve a problem, the CPA approach brings concepts to life by allowing pupils to experience and handle physical objects themselves. Every new abstract concept is learned first with a ‘concrete’ or physical experience.

For example, if a problem is about adding up four baskets of fruit, the pupils might first handle actual fruit before progressing to handling counters or cubes which are used to represent the fruit.

Pictorial                                                                                                                                Pictorial is the ‘seeing’ stage, using representations of the objects to model problems. This stage encourages pupils 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.

Building or drawing a model makes it easier for pupils to grasp concepts they traditionally find more difficult, such as fractions, as it helps them visualise the problem and make it more accessible.

Abstract                                                                                                                                          Abstract is the ‘symbolic’ stage, where pupils are able to use abstract symbols to model problems (Hauser).

Only once a child has demonstrated that they have a solid understanding of the ‘concrete’ and ‘pictorial’ representations of the problem, can the teacher introduce the more ‘abstract’ concept, such as mathematical symbols. Pupils are introduced to the concept at a symbolic level, using only numbers, notation, and mathematical symbols, for example +, –, x, ÷ to indicate addition, subtraction, multiplication, or division.

The White Rose Maths yearly overview provides a Long Term Plan and is arranged into ‘Blocks’.

For each term, the Learning Objectives are listed and are time related to ensure coverage and pace.

Mathematical Talk

A mastery classroom should never be a quiet classroom. The way pupils speak and write about

mathematics transforms their learning. Mastery approaches use a carefully sequenced, structured approach to introduce and reinforce mathematical vocabulary.

To encourage talk in mathematics, teachers may introduce concepts by including sentence structures (stem sentences). Pupils should be able to say not just what the answer is, but how they know it’s right. This is key to building mathematical language and reasoning skills. This gives pupils the confidence to communicate their ideas clearly, before writing them down.

Example Stem Sentences:

The denominator is 5 because the whole has been divided into 5 equal parts.

The numerator is 3 because 3 equal parts have been shaded/circled.

Teachers then maintain a high expectation upon pupils to repeat and use the correct mathematical vocabulary to explain their understanding verbally and in their reflection comments. By also displaying the vocabulary during the lesson, pupils will be able to use this independently.

When questioning and encouraging mathematical talk, teachers should provide regular, purposeful opportunities. For example:

- Show me how to complete the calculation                                                                                      - Teach your friend how to complete the calculation                                                                                          - How do you know which operation to use?                                                                                                    - Why have you chosen this method?                                                                                                                   - How else can you represent this number?                                                                                                             - What have you learnt today?                                                                                                                                   - True or False                                                                                                                                          - Prove it!                                                                                                                                                 - Odd one out                                                                                                                                     - Sometimes, Always, Never

Differentiation                                                                                             Children are placed in groups of similar ability for mathematics lessons. There is flexibility within these groups so that a child may be altered to another group if their performance suggests that it would be beneficial for them.

In the majority of mathematics lessons in KS1 and KS2 children taught the same concepts and differentiation will be seen through the amount of adult support, the questions pupils are guided to answer (e.g. LA may only be required to focus on between 1 and 3 questions and HA/GD pupils may be required to focus on the RPS problems rather than completing the fluency in certain lessons. Practical resources are available for all abilities to enhance the learning and deepen discussion.

Some lessons provide open ended tasks where differentiation will be by outcome. Some lessons may be planned to allow children to work in mixed ability groups thus allowing higher ability children to consolidate their learning by discussing with and teaching children of lower abilities.

Resources                                                                                                             We have a range of practical resources to support learning including Numicon, Base10 and counters which are stored in individual classrooms where they are easily accessible to all children. These are used on a regular basis to ensure a solid understanding of the fundamentals of Mathematics. Additional resources are stored centrally in the Mathematics resources cupboards.

Each classroom has an interactive maths ‘working wall’ featuring examples of the topic currently being covered and with an interchangeable display of mathematical symbols, numbers, times tables and vocabulary appropriate to the age range. Working walls are used throughout school to reinforce and consolidate children’s knowledge and understanding of mathematical concepts.

Assessment                                                                                                         There is no formal assessment for EYFS within the White Rose Maths schemes of learning.    On-going assessment is formative, based on observations, photographs, video, things that children have made or drawn and information from parents. The Development Matters document is used as a guide to making best-fit judgements about a child’s progress and attainment throughout the year. At the end of EYFS, children are assessed against the Early Learning Goal for Mathematics.

 In Years 1- 6 the children are assessed on a termly basis and at the end of each block in the White Rose Maths scheme. Errors and misconceptions identified in the end of block assessment will be targeted during the opening to maths session in a daily maths meeting.

Assessment results are analysed and children are given an age related expectation from teacher assessment. This information is monitored by the Maths Subject Leader and Senior Leadership Team. Regular arithmetic and times table tests are also carried out and results recorded by individual teachers in Years 3-6 (Year 3 from Spring term onwards) through the Number Sense Times Tables program.

Formative Assessment:

Short term assessment is a feature of each lesson. Observations and careful questioning enable teachers to adjust lessons and brief other adults in the class if necessary.

At the end of each blocked unit of work, the children complete the carefully aligned

White Rose Maths ‘End of Unit Assessment’. The outcome of this is used by the teacher to

ensure that any identified gaps in understanding can be addressed before the next unit is

taught or through targeted DMM sessions.

Summative Assessment:

Teachers administer a termly arithmetic paper and reasoning and problem-solving paper

which specifically links to the coverage for that term. The results of these papers are used to

identify children’s ongoing target areas, which are communicated to the children, as well as

to parents and carers at Parents Evening. They are also used alongside the end of unit

assessments and outcomes of work, to inform the whole school tracking of attainment and

progress of each child. These areas are then targeted during DMM sessions across the next term.

There are no official grade boundaries for the end of term White Rose Assessments. However, in line with the KS1 and KS2 SATs, the following is a guideline:

• KS1 – Year 1 - a consistent score of approximately 60% (15/25) would indicate ‘Expected’ and 85% (21/25) would indicate ‘Greater Depth’.
• Year 2 - a consistent score of approximately 60% (21/35) would indicate ‘Expected’ and 85% (30/35) would indicate ‘Greater Depth’.
• KS2 - a consistent score of approximately 55% (28/50) would indicate ‘Expected’ and 86% (43/50) would indicate ‘Greater Depth’. These tests should be used to inform teacher assessment.

At the end of each term, all teachers attend a Pupil Progress meeting to share data and to discuss pupils who are ‘off target’ on Sims. These pupils should be placed into an Intervention/Booster group with a SMART target.

End of year data is used to measure the extent to which attainment gaps for

individuals and identified groups of learners are being closed. This data is used to inform

whole school and subject development priorities for the next school year.

Special Educational Needs                                                                                   Children with SEN are taught within the daily Mathematics lesson and are encouraged to take part when and where possible (please see the section on differentiation).

Where applicable, children’s IPPs incorporate suitable objectives from the New Curriculum and teachers keep these objectives in mind when planning work.

Within the daily Mathematics lesson teachers not only provide activities to support children who find Mathematics difficult but also activities that provide appropriate challenges for children who are high achievers in Mathematics.

Equal Opportunities                                                                                    We incorporate Mathematics into a wide range of cross-curricular subjects and seek to take advantage of multi-cultural aspects of Mathematics.

In the daily Mathematics lesson we support children with English as an additional language in a variety of ways. eg. repeating instructions, speaking clearly, emphasising key words, using picture cues, playing Mathematical games, encouraging children to join in counting, chanting, finger games and rhymes.

Reporting to parents                                                                                          Parents are given opportunity to discuss their child’s progress on two separate occasions throughout the year. Written reports are distributed at the end of the Summer term.

Teachers use the information gathered from their half-termly assessments to help them comment on the progress of individual children.

Parental involvement                                                                                        Sessions are held occasionally to inform parents about how to enhance their child’s learning in Maths and to inform them of some of the alternative methods of calculation.

Monitoring and Evaluation                                                                                                     The Mathematics Subject Leader follows an annual action plan which has been prepared in line with the whole school development plan.

The Mathematics Subject Leader is released from the classroom in order to monitor standards of teaching and learning and to carry out scrutinies of children’s work. Findings from any monitoring are discussed initially with the Senior Leadership Team and also shared with teaching staff as appropriate.

The Governing Body                                                                                                               A governor responsible for Mathematics is identified from the governing body. Governors are invited to attend any Maths workshops or training days. The Subject Leader reports maths updates to the the governing body.

Thanks to those parents who popped in to chat to me about the Year 4 MTC. If you have any further questions, don't hesitate to get in touch.

Please see below for the presentation - there are web links within it that will take you to online games to practise rapid recall of multiplication facts.