Mathematics

Rationale

At Wallington Primary Academy, we aspire to make every child a mathematician and provide them with the opportunities to develop their overall characters through using their abilities to reason, problem-solve and be resilient. We provide high quality teaching and learning, ensuring lessons are engaging and practical to develop their mathematical understanding. To ensure all children make continued progress, we use a Mastery approach to teaching Maths which gives pupils a deep, long-term, secure and adaptable understanding of mathematics. Our academy medium-term plans follow the guidance from the National Curriculum and is enhanced using White Rose documentation.

Maths is taught five times a week across all year groups and follows the same structure in each lesson: flick back 4 (to recap previous learning), input and introduction to new concept (using I do, we do, you do), followed by an independent task. We use Times Tables Rockstars to enhance our teaching of the times tables, allowing children to access this learning at school and at home. The structure of our lessons allows children to engage with and use prior knowledge and it supports children to embed these skills from their working memory to the long-term memory, consequently enabling them to apply this when necessary.

Intent – what do we hope to do

"A person who never made a mistake never tried anything new!  Pure mathematics is, in its way, the poetry of logical ideas."

Albert Einstein

At Wallington Primary Academy, we aspire to create confident and resilient mathematicians through our micro-step progression of skills and concepts taught. We plan a wide range of activities to engage their mathematical thinking and allow them to use concepts taught in previous year groups and develop their conceptual understanding of the skills taught. We believe that all children can gain a deep understanding of mathematical concepts and therefore we aim to encourage them all to develop a growth mind-set by taking risks, asking questions and rising to challenges.

Implementation – what are we doing?

The principle focus of mathematics teaching is to ensure that pupils can reason mathematically and become sound problem solvers as they develop confidence and mental fluency appropriate to their age group. The ‘Teaching for Mastery’ approach is used to achieve this, employing a ‘Context - Concrete - Pictorial - Abstract’ method of teaching: each new concept is introduced through a meaningful context, which is then represented with the use of concrete objects (manipulatives), pictorial representations and then the more abstract written methods.

Our planning is underpinned by our medium-term plans, created by our academy, for Reception to Year 6. These plans use micro-steps of progression to allow children to access new concepts, revise prior learning and have opportunities to use mathematical language when reasoning and problem-solving. Maths is taught five times a week across all year groups and follows the same structure in each lesson: flick back 4 (to recap previous learning), input and introduction to new concept (using I do, we do, you do), followed by an independent task. Teachers devise worksheets that are layered and allow children to practise fluency, reasoning and problem-solving. To ensure that those who need further practise are given that opportunity, a pre-layer is created to allow them to have further fluency practise with more scaffolding provided. The structure of the lessons as well as the independent tasks provided, allows children to have a predictable routine and ensures that they can access the learning and achieve within the lessons. It also ensures that challenge is provided to all and the opportunities to use mathematical language are developed.

Teachers employ a range of planning and teaching strategies, which include:

• Micro-progression in weekly and daily planning: Lessons are planned to build upon prior knowledge from the lesson before but also within the lesson. The small steps that were learnt in the previous lesson are reviewed at the beginning of the next lesson. Tiny steps are made within each lesson to develop a secure understanding of the concept taught.
• Single learning point: Each lesson planned, has a single learning point for all. The lesson focuses on the teaching of a concept, not a procedure.
• Carefully planned questions: Specific questions are planned into every lesson. A range of open and closed questions are asked to encourage all pupils to discuss and share their mathematical understanding and extend children working at greater depth.
• CCPA: Lessons are planned and delivered with the use of context, concrete and pictorial representations that helps pupils make links with mathematical abstraction.
• Misconceptions (True/False questions): These are planned as part of the main lesson to anticipate typical misconceptions and address them within the lesson. Spotting mistakes, enables children to think about the concept at a deeper level.
• Conceptual and procedural variation / Intelligent practice: Numbers, examples and questions are purposefully chosen to reveal the key mathematical structure and aid conceptual understanding.
• Opportunities for greater depth: Greater depth is planned into the whole lesson through different representations and carefully planned questions. This can be accessed by all attainment groups.
• Carefully designed layered tasks: Independent tasks are carefully planned to deepen children’s understanding as they move through them. They are all based on the same concept that gradually deepen a child’s understanding as the questions become more complex. Children are challenged through depth rather than moving onto the next concept or working on higher numbers. Greater Depth challenges are accessible by any child that is secure with the concept being taught and not restrictive to any particular group of children.
• Ping Pong: Ideas, activities and exploratory independent work regularly move back and forth between pupils and the teacher. Mini plenaries facilitate drawing conclusions through whole class discussion where children are encouraged to share their ideas through reasoning and speaking in full sentences.
• Stem sentences: All children are expected to understand and use the correct and relevant mathematical vocabulary when explaining their mathematical thinking. They are expected to speak in full sentences when sharing an answer. This is facilitated and supported using stem sentences and sentence stems, which help with the correct phrasing of a mathematical concept and develops children’s ability to generalise, reason and draw conclusions of their mathematical learning.

Developing mathematical fluency and conceptual understanding of different strands within our maths curriculum is vital to the progress of children within maths. To ensure that we are providing them with the opportunities to develop their confidence within new concepts, children are given Early Morning Work tasks linked to their learning that week, provided with homework that allows practise of concepts taught, conferencing to address misconceptions and use of assessment for learning with lessons to address misconceptions as well as formative assessments carried out every term. By ensuring this understanding is secure, the children can then develop and become competent problem-solvers and allows them to use this understanding to reason and explain their answers.

Impact – what do the children get?

Mathematics is taught through a quality curriculum, with effective and engaging teaching, and we endeavour for our pupils to be confident learners, ready for the next stage of learning. Children become more fluent in the fundamentals of mathematics, through varied and frequent practice with increasingly complex problems over time. Pupils will build on their increasingly well-developed fluency skills, which is committed to their long-term memory. They will be able to retrieve these rapidly and accurately to become more independent in applying this knowledge and skills to more complex concepts and procedures. Children can reason mathematically by following a line of enquiry, making links between mathematical relationships; they can justify their reasons using accurate mathematical vocabulary and terminology to then make generalisations. Pupils become more sophisticated problem solvers by applying their mathematics to a variety of routine and non-routine problems, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

National Curriculum

The National Curriculum identifies three main aims to ensure pupils develop mathematical thinking:

• 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

Assessment

Children are assessed throughout all lessons so that misconceptions can be addressed. We provide children with true/false and spot the mistake questions during the input to pre-empt misconceptions and guide children to alter their thinking. We also assess during ping pong activities by looking at children’s whiteboard word, through targeted questioning, faster feedback and how they use prior knowledge to make connections with new learning. Some classes use marking stations to mark work throughout the lesson, others mark as a class at the end. All teachers check books daily to address any misconceptions before moving on the next day.

Pupils are assessed at the end of half terms as well, and teachers track children against their end of year target to ensure they are making good progress. They also provide children with questions that require them to use prior knowledge and make connections to apply their learning. Through these teachers can assess the children’s understanding of concepts.