Our philosophy for the teaching of mathematics
"A person who never made a mistake never tried anything new! Pure mathematics is, in its way, the poetry of logical ideas."
At Avenue Primary Academy we believe that mathematics is fundamental to the overall development of the child and their ability to problem solve, reason and develop resilience. We aim to provide children with a broad, varied and engaging range of activities to stimulate their mathematical thinking. We strive for the highest standards in teaching and learning so that each child can develop a love of mathematics and lasting confidence to fulfil their mathematical potential that can support them in their future. 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.
We aim to deliver high quality teaching in mathematics to enable children to become confident and successful in all areas of the subject through our mastery approach. We follow the new National Curriculum, alongside other guidance, including our medium-term plans that have been informed by documents from the White Rose.
The principle focus of mathematics teaching is to ensure that pupils are able to 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.
A comprehensive and detailed medium-term plan has been developed for each year-group from Reception to Y6 which is in line with the expectations set out in the Mathematics Programmes of Study. Objectives within the plans are broken down into small sequences of learning to ensure that each mathematical concept is linked thoroughly from one year to the next providing tight progression of knowledge and skills through opportunities for pupils to revisit prior learning, learn new content and consolidate this through plenty of practice.
Individual lessons are carefully structured with fluency, reasoning and problem-solving opportunities and tasks. Lessons are designed to ensure that all children can fully access the learning and challenge is provided through carefully thought-out teacher questioning, and Greater Depth challenge tasks throughout the lesson as well as part of the independent work.
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 by the use of 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.
Fluency and arithmetic practice:
To ensure that children develop the necessary fluency in order to become competent problem solvers, regular fluency and arithmetic practice has been built into the mathematics curriculum in all year-groups. This involves focused teaching of a specific fluency and arithmetic skill that is practiced and tested throughout the week. The impact of these are measured through ongoing assessment and recording of results. Morning work is then used to address any misconceptions.
Mathematics is taught through a quality curriculum, with effective and engaging teaching, and we endeavor 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 are able to 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.
Use the links below to access the calculation policies. These will provide and overview of the learning taking place in each year group.
Use the links below to view the Mathematics Road Maps:
Below are links to videos that demonstrate the methods we teach children in their maths lessons. These can be used to support any home learning that is taking place.
1. What is Teaching for Mastery?
2. What is Subitising?
3. Structures of Addition
4. Context concrete pictorial abstract
5. Column addition using Dienes
6. Intro into bar modelling
7. Structures of subtraction
8. Mental method of subtraction
9. Column subtraction using Dienes and PV counters
11. Short and long multiplication
13. Short and long division