# Mathematics

## Albert Einstein

Mathematics teaches children how to make sense of the world around them through developing their ability to calculate, reason and solve problems. Mathematics is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment.

During their time at Mossgate, we want children to be confident in making connections across mathematical ideas as a result of developing fluency, mathematical reasoning and competence in solving increasingly sophisticated and contextual problems. Our children will have the ability to reason mathematically, apply their mathematical knowledge across the curriculum and have a sense of enjoyment and curiosity about the subject.

As Mossgate Mathematicians, we want children to:

• Be confident and have a positive attitude towards the learning and use of Mathematics, making every experience enjoyable.
• Understand the importance of Mathematics in everyday life, especially in relation to essential skills, such completing calculations, telling the time, using money and understanding tables and charts.
• Have the flexibility and fluidity to move between different contexts and representations of mathematics.
• Clearly explain their reasoning and justify their thought processes.
• Take risks and recognise that mistakes and errors mean we are being challenged and learning something new.
• Be resilient and persevere when reasoning across the curriculum.
• Choose efficient strategies, both mental and written, when calculating.
• Quickly recall number facts.
• Solve problems through connecting ideas, decision-making and applying their mathematical skills in a range of contexts, both practical and investigative.
• Recognise relationships and make connections in mathematics.
• Reason by following a line of enquiry, developing an argument and making justifications using mathematical language.
• Display a sound practical understanding of the ways in which information is gathered, presented and used.
• Be confident with complex numbers and the number system.

Our Approach

Mossgate’s ‘Great Teaching’ approach has five key principles, drawn from research evidence.

1. Coherence: Lessons are broken down into small connected steps that gradually unfold the concept, providing access for all children and leading to a generalisation of the concept and the ability to apply the concept to a range of contexts.

1. Variation: An important aspect of our approach is the use of ‘variation’ (the sequence and the way the maths is represented) when we carefully plan and design the children’s learning.  We believe that it is important that the children experience maths in a broad range of contexts and representations to help them to develop a deeper understanding and to make connections in their learning.  This supports the children to become flexible thinkers and more confidently apply their skills and knowledge to solve problems.

1. Mathematical Thinking: Another core principle of our curriculum is to ask children to reason about maths.  This is an opportunity for the children to talk or write about the maths they are using, patterns they observe or general rules they have learnt and applied.  This again helps the children to develop a deeper understanding of mathematical ideas and to more confidently explain their thinking.

1. Fluency: As part of our curriculum, we also support the children to develop their mathematical fluency.  This encompasses a number of different ideas including the quick and efficient recall of number facts (such as number bonds or times tables) to having the ability to choose efficient methods and strategies when solving a problem. All lessons begin with a short starter activity for retrieval practice and develop long-term memory.

Lesson structure

A typical Maths lesson will encompass a mix of exploration, teacher led practice and independent thinking. Each lesson may include the following:

• Warm Up– this is a starter activity to help the children to focus and practise important skills.
• An Initial problem – this is an opportunity for the children to explore a mathematical idea in a real-world context or problem, often supported with concrete or pictorial resources.  In this stage, the children share ideas and discuss the maths they observe, making connections to previous learning.
• Teaching and Guided Learning – the children have the opportunity to apply new strategies and skills in a guided context, exploring different representations of the maths they are learning and discussing misconceptions.
• Independent Practice – the children continue their learning journey answering questions which have been designed and sequenced to develop and challenge the children’s thinking.
• Deepening Learning - challenges provide an opportunity for the children to apply their new learning to a problem which is presented in a different way or context.  The children apply their knowledge, making connections to their learning within the lesson.  This helps to further develop the children’s reasoning and their use of mathematical vocabulary.
• Reflection – this takes place throughout the lesson through questioning and discussion.

Children are taught through clear modelling and have the opportunity to develop their knowledge and understanding of mathematical concepts. Our approach incorporates using concrete objects, pictures, words and numbers to help children explore and demonstrate mathematical ideas, enrich their learning experience and deepen understanding at all levels.

Within this lesson structure, there is flexibility for the class teacher to tailor their teaching to the needs of the children in their class.  For example, during the guided and independent learning, some children may be supported in different ways while others may be challenged through differentiated activities.

We place mathematical vocabulary and oracy at the heart of our learning through shared work and class discussions. Use of appropriate vocabulary is modelled throughout lessons by both staff and children, allowing everyone to ‘talk like a mathematician’. Once a child can articulate their understanding of a concept, they can truly begin to make connections within their learning and when reasoning.

Resources and representation

When learning, we recognise how important it is that the children use practical resources and pictorial representations, before proceeding to more abstract ideas.

• Concrete– children have the opportunity to use concrete objects and manipulatives to help them understand and explain what they are doing.
• Pictorial– children then build on this concrete approach by using pictorial representations, which can then be used to reason and solve problems.
• Abstract– With the foundations firmly laid, children can move to an abstract approach using numbers and key concepts with confidence.

In each classroom, we have a range of resources available, from which the children can choose from, to help with their learning.

Maths Fluency

In addition to our daily Maths lesson, we have a Maths Fluency lesson which is taught daily from Years 1 to 6 focussing on the four operations, both mental and written calculations and other arithmetic skills. This aims to keep calculation skills fresh by providing regular practice of skills. Each lesson lasts no more than 15 minutes with the children answering 3-10 questions independently, followed by opportunities to peer mark with a focus on discussing efficient methods.

Calculations

The mental and written calculation policies are used within school to ensure a consistent approach to teaching the four operations over time – both written and mental.

Mrs H Taylor - Mathematics Subject Leader

Updated 30.11.22