Mathematics

Intent:

Our goal is to cultivate an environment where every child has a clear opportunity to succeed and takes pleasure from the learning of maths, whose relevance to the wider world is emphasized as children recognize the value of skills beyond the pages of their maths books. Achievement is celebrated in all its forms.

The school has a whole-school approach to calculation which has continuity and progression throughout KS2, enabling all pupils to develop a thorough understanding of number and achieve their potential.

The aim of teaching and learning of calculations throughout school is always towards procedural fluency (using efficient and reliable methods for calculations) while ensuring children have conceptual understanding (being able to grasp and explain what they are doing on a practical level).

To help ALL children understand what is really an abstract concept, all teaching starts with - and then builds on – concrete methods. This involves using a range of manipulatives (physical resources, number lines, arrays, 100 squares etc…) in class and making connections between them. This enables children to see the links between different representations and so increase conceptual understanding.


Progress towards more efficient written methods is then started as the child is ready for that stage of development, and always done by making links with what has already been learned. In every lesson, teachers ask the questions, ‘what is the same?’ and ‘what is different?’ to help the children build on their existing understanding. Teaching aims to move through the transitions between stages of development, sometimes using temporary representations (such as arrays and grids) with the end goal in mind, without leaving anyone ‘stranded on a stepping stone’


Maths is a subject where children continually make links between their different areas understanding, building on their existing knowledge to further the limits of what they can do. As they approach a range of problems, children are encouraged to explore, experimenting with different approaches to come up with their own conclusions. Children select (reason) from their skills toolkits to use the most suitable methods for the job, evaluating their success as they do so and thinking about how they could adapt their practice in future.

The end goal is always for children to become fluent with the standard methods of each operation, with complete conceptual understanding and be able to apply these to different real-life situations.



I

Implementation:

Our teaching of maths involves facilitating rich discussion and debate, where children compare and refine approaches. A risk-taking environment is encouraged where children become articulate at explaining their methods and where the process is more important than the ‘answer’. Indeed, children are encouraged to explore (by means of comparison, experimentation, analysis and discussion), all in the process of forming their own conclusions and building links in their own minds. Instead of ‘telling’ children the knowledge and skills, the teacher is the ‘facilitator’ who, through expert questioning, guides the children to uncover their own learning-discoveries.

In all of this, children increase their mathematical fluency by increasing efficiency with procedures (such as multiplying) while being able to explain what they are doing.

Fluency work consists of short activities which may be separate to the Main Topic of the lesson. These include ongoing development of progressing fundamental skills. Informed by the medium term plan, this ensures appropriate progression of fluency skills across the key stage. This is interactive work to develop fluency and efficiency of key skills (x tables, operations, number bonds, use of inverses etc…).

Main whole class teaching is linked to the learning intention and context of the lesson. Topic work is an ongoing learning journey and so starts with what the children already know and, through exploration, discussion and practice, enables children to make their own connections, building on their understanding. The vast majority of activity is performed by the class with the teacher directing.

There is a balance of content aimed at achieving fluency for the main foci in the ages taught. These are:

- Number and the four operations (including number facts and the concept of place value).

- Fractions / decimals (y4 onwards) / percentages (y5 onwards)

- Measures

- Properties of shape

- Position and direction (y4 onwards)

- Statistics

- Ratio and proportion (y6)

- Algebra (y6)

Teachers aim to provide as many different representations of a concept as possible; i.e. not just 3 x 4 = 12 but also:

4 x 3 = 12; 12 = 4 x 3; 12 = 3 x 4; 12 ÷ 3 = 4; 12 ÷ 4 = 3; (2+2) x 3 = 12 etc…

…not to mention all the related place value permutations and rich variety of word questions that could be posed and compared!

Manipulatives are made available in every class, right up to year 6, in order to support the learning of all children (particularly the visual / kinaesthetic learners). In many cases children choose their own resources, thereby becoming more independent and making their own links to that with which they themselves are already familiar.

It is important that children finding a concept difficult are allowed time to consolidate and fully grasp an idea before moving on. Each lesson includes at least 3 levels of challenge, to which children are given the freedom to select, encouraging a growth-mindset, self evaluation and greater ownership. If a child - by their own or an adult’s judgement – needs more work then this is given during the lesson and/or at a later time.

Problem solving is a regular part of our lesson structure. Those not requiring further consolidation are given a rich variety of appropriately challenging problems (which we call 3 chilli challenges) to allow them to ‘go deeper’ with their learning.

Calculations are taught in the context of word problems from the start to develop understanding. The emphasis is on problem solving where children can explain their reasoning throughout.

All lessons include an opportunity to discuss or explain strategies, vocabulary etc. ‘Talking partners’ are planned for to allow pupils to work out a solution together or explain a procedure etc. All lessons follow the structure ‘review, teach, practice, use and apply and assess’. They cater for visual, auditory and kinaesthetic learners and include demonstrating and modelling. Ensuring the learning is put into context is particularly important to ensure pupils use and apply their knowledge and skills.


Impact:

It is important that subjects are not taught and then quickly forgotten. To this end, lessons regularly include quick revision activities to practise a wide range of skills as well as those which have been recently taught.

Children become secure with the fundamentals of maths, building-on and making connections between these, extending the limits of their own understanding.

Children are not allowed to fall behind as interventions happen daily and, through expert teacher formative assessment, gaps in learning are identified and addressed in a timely manner. As a result, teachers, working with the subject lead, are able to map each child’s flight-path through school enabling them to become the best mathematician they themselves can be.

All teachers know where their children are through the use of concise assessment, prior learning and maths talk. They also understand where their children need to be through a secure understanding of the year group expectations and/or pre-key stage expectations

Children’s progress is assessed using the White Rose Hub unit and termly assessments, which allow teaching and learning to be planned according to need. Additional assessments are also carried out for baseline and end of year data, which will also take into account teacher assessments. The impact of teaching and learning in maths is assessed in many different ways:


- Discussions with children (pupil voice)

- Book scrutinies

- Formal observations

- Drop-ins