Our vision for Mathematics: Curriculum implementation
Mathematics is at the core of our curriculum and it is through our teaching in this subject that pupils learn crucial life skills, including resilience and problem solving. They also have opportunities to lead, teach, support and mentor each other. Our curriculum is designed to enable children to gain an in-depth understanding of maths by teaching fluency, reasoning and problem solving on the children's journey to mastery of the curriculum.
Early maths skills are reinforced through practical activities, often outside, and using a wide range of physical resources, often linked to role-play and developed through enhanced provision. Challenges are posed to encourage problem solving and application of their learning with Forest School sessions continuing the active learning.
In all sessions, variation is paramount and provided through different starting points, range of challenge and the support of practical resources and groupings. Children may work with a teacher for guided maths, independently to access activities of an appropriate level of challenge, in groups to support each other or as part of a whole class to draw their learning together.
In maths we use a range of strategies to capture the children's learning journey, from teacher observations, photos and video clips to exercise books and White Rose workbooks.
Our long term plan follows the White Rose small steps, although this is supplemented with a wide range of additional resources. Each topic is mapped out for the children on class learning walls (see right), which act as a glossary of strategies and knowledge as these are taught. As the children become more independent in their learning, Maths Glossaries are used to support autonomous learning by reflecting the key learning and to act as a reminder when a topic is revisited.
Fluency, Reasoning and Problem Solving
The first aim of the National Curriculum in England (DfE 2014) is that all children will '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'. As this suggests, fluency is the ability to know different mathematical strategies and to understand how to use them at an appropriate time.
The second aim of the National Curriculum is that all children can 'reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language'. Reasoning is a child's ability to explain their understanding of a mathematical concept. In being able to articulate their knowledge, a child is building a secure understanding of a concept, rather than a superficial one which may later lead to misconceptions.
The third aim of the National Curriculum is that all children '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'. This is where children are applying their knowledge in different contexts, which enables a greater depth of learning.
The concrete-pictorial-abstract approach
In order to help the children develop a deep conceptual understanding, we try to build solid foundations using the concrete-pictorial-abstract approach.
Concrete: In this stage, the children are first introduced to an idea or skill by acting it out with real objects. For example, in division this might be done by separating balls into colour groups.
Pictorial: When a child has sufficiently understood the hands-on experiences, they can progress to relating them to different representations, such as a bar model, part whole diagram or picture of the objects. With our division example, this could be done by the action of circling groups of objects.
Abstract: This is the symbolic stage, where the children are able to represent problems using mathematical notations e.g. 10÷5=2. The children will only progress to the abstract stage when they have enough context to understand what they mean, as this is the 'final' and most challenging of the three stages.
To further help, we have uploaded our progression of skills document as a guide to how mental and written methods are developed at Langrish from the Early Years, through the Infants and beyond. Please use this as a manual when helping your child with their home learning. We have also added two documents with links - one a page of useful websites to further the children's learning, the other with a list of videos to show you how we introduce different skills using the concrete-pictorial-abstract approach. These are listed by objective and are age-appropriate.
Here are some useful websites to help support your child's maths learning at home.