Mathematics

‘The only way to learn mathematics is to do mathematics.’

Paul Halmos

We believe that mathematics is an important part of everyday life. Therefore, we aim that through our teaching of mathematics our children become fluent, confident and independent mathematicians, who can positively use and understand mathematical knowledge and language in everyday life.

We provide a language rich mathematics curriculum where, through carefully considered adult questioning and modelling, we aim that children become confident in their talk as mathematicians and that they explain their understanding using the correct mathematical language.

We place high importance on the number aspects of mathematics to ensure that our young learners grasp a secure understanding of the key calculations of addition, subtraction, division and multiplication. We want our learners to have a deep understanding of number to enable them to make connections and to develop fluency, which will then allow them to develop their reasoning and problem-solving skills.

Our children are taught mathematical knowledge by moving through the concrete, into the pictorial and then into the abstract. Children are provided with a range of practical resources to support understanding by helping them to visualise, handle and to make sense of, such as numicon, dienes and counting objects. When they have developed a secure understanding at this stage the pictorial representation will then be shown to further support understanding. The abstract concept (using numbers and symbols and written methods) will be introduced when children are ready to progress. Mathematical reasoning, problem solving and an understanding of how to interpret written questions is important at this stage.

Mathematics in the Early Years Foundation Stage

Mathematics in the Early Years Foundation Stage (EYFS) is based around the youngest learners grasping a deep and secure understanding of the number system to 10 (starting first to 5). Within the numbers 0-10 they will begin to understand place value, number bonds and simple addition and subtraction. Time is spent finding out about a number in depth. For example, when looking at the number 5 they will understand the counting order, learn to subitise, find different combinations to make 5 (e.g. 5 + 0, 4 +1, 3+2), know 5 as an array and as a tally, find 5 o’clock, recognise 5 pence and also 5 as a measure. This aims to provide them with a solid foundation for Key Stage One to then be built upon.

Children move through the concrete, pictorial and abstract stages. Lots of opportunities for children to handle concrete resources are provided in Nursery and Reception.

Maths is taught daily in the EYFS through teacher led directed activity as well as carefully planned opportunities through high quality provision areas both indoors and outdoors and also through the daily experiences and routines within the school day, such as the register, snack time and tidy up time.

The EYFS curriculum and framework, White Rose Maths and the NCTEM materials are used to support the planning and resourcing of the teaching of maths across the EYFS.

How is maths taught?

Maths in Key Stage One is taught daily through discrete lessons. We use the expectations set out in the National Curriculum for mathematics and planning is supported by the White Rose Maths Hub schemes of learning and the NCTEM materials to support teacher subject knowledge and understanding. Additional short fluency sessions also take place outside of the maths taught lessons to ensure that children remember and revisit key knowledge regularly such as place value and number bonds. It is important that children are given time and practise to develop basic concepts and are not moved on too quickly. Everyday opportunities and routines are also utilised to encourage children to use maths to solve every day mathematical problems. These opportunities are particularly important to cover mathematical concepts such as measure and time in real life contexts.

Taught maths lessons include the following:

• Recap and review of prior learning– Each lesson will start by revisiting prior knowledge so that children can make meaningful links and can check understanding. Teachers will see at this stage if children have remembered what has been taught and also mathematical vocabulary will be reinforced at this stage.
• Modelling– New learning and revisited learning will be clearly modelled using small steps to show the knowledge, understanding, skill and vocabulary which is needed. The ‘I do, you do, we do’ modelling approach will make sure that enough time is given for the children to fully understand what has been taught to them. Modelling is a crucial part in supporting a child’s understanding so teachers will provide more than one model and in a variety of ways, which could be through variation in the way questions and activities are presented. At this stage the teacher will be talking out loud as a mathematician using the correct vocabulary and language.
• Scaffolding– Children will be provided with a scaffold to their learning to ensure that they are supported. The teacher will remove a scaffold when they feel the child is ready for this.
• Guided practice– Children are supported as they practice and are given clear feedback and are questioned to check their understanding. Children are encouraged to use the mathematical vocabulary and talk as a mathematician to fully explain their thinking and understanding.
• Independent practice and challenge– Children will independently practise the new learning and all children are challenged at the stage they are working at. Challenge will be given through questioning and the tasks that are set.

Questioning by the adults is crucial through all elements of the teaching. Misconceptions will be addressed and overcome at each stage and next steps will be carefully planned for. Teachers will ensure that children have grasped the knowledge before moving them on too quickly. Interventions such as the same day intervention and pre-teach will be delivered to children where this is needed.

In mathematics, pupils will have the opportunity to:

• become fluent in the fundamentals of mathematics through daily practice
• develop their understanding of number and the number system in a deep way to allow them to make important links and connections which will be crucial for later maths learning
• recall and apply their mathematical knowledge rapidly and accurately
• reason mathematically by following a line of enquiry, connecting relationships and developing an argument, justification or proof using mathematical language
• 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 when seeking solutions.