Aims and objectives
Mathematics teaches us how to make sense of the world around us. We endeavour to develop each child’s ability to calculate, to reason and to solve problems. Mathematics enables children to understand and appreciate relationships and pattern in both number and space in their everyday lives.
The aims of mathematics are to ensure that all children:
- 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.
White Rose Mathematics
At Galley Common Infant School we closely follow the White Rose Mathematics scheme across the school. White Rose Maths is an organisation that aims to work collaboratively with teachers across the country to improve mathematics teaching. Inspired and informed by robust, world-class research and global maths experts, the scheme aims to transform maths education and change the experience of maths forever. The White Rose approach aims to help all pupils to master mathematics.
What does it mean to master mathematics?
A mathematical concept or skill has been mastered when a pupil can represent it in multiple ways, has the mathematical language to communicate related ideas, and can independently apply the concept to new problems in unfamiliar situations.
Mastery is a journey and long-term goal, achieved through exploration, clarification, practice and application over time. At each stage of learning, pupils should be able to demonstrate a deep, conceptual understanding of the topic and be able to build on this over time.
This is not about just being able to memorise key facts and procedures, which tends to lead to superficial understanding that can easily be forgotten. Pupils should be able to select which mathematical approach is most effective in different scenarios.
All pupils can achieve in mathematics
A positive teacher mindset and strong subject knowledge are key to children's success in mathematics. It is not the case that some pupils can do mathematics and others cannot.
No pupil should be left behind. The focus is keeping up over catching up. By making high expectations clear and emphasising the value of mathematics education, children are encouraged to build confidence and resilience.
Abilities are neither fixed nor innate, but can be developed through practice, support, dedication and hard work. Natural talent is just a starting point and does not determine who has more or less potential to achieve. A positive teacher mindset in maths encourages a love of learning and resilience that enables everyone to achieve.
All children are entitled to learn key concepts and skills
A scheme of work based around the principles of mastery really can be suitable for all. Children should have the opportunity to stay together and work through new content as a whole group. While mastery schemes of work may be challenging for some, the vast majority should be aiming for this standard. In extreme cases, where students have considerable learning difficulties, individual schools may want to put some alternatives in place.
It is important that high-attaining children fully understand key number concepts, rather than simply memorise a process. Teachers can extend high-attaining students through depth, as opposed to acceleration onto new content.
Focus on depth
Deepen understanding before accelerating content coverage
All children benefit from deepening their conceptual understanding of mathematics, regardless of whether they've previously struggled or excelled. Children must be given time to fully understand, explore and apply ideas, rather than accelerate through new topics. This approach enables children to truly grasp a concept, and the challenge comes from investigating it in new, alternative and more complex ways.
Multiple representations for all
Objects, pictures, words, numbers and symbols are everywhere. The mastery approach incorporates all of these to help children explore and demonstrate mathematical ideas, enrich their learning experience and deepen understanding. Together, these elements help cement knowledge so pupils truly understand what they have learnt.
All children, when introduced to a key new concept, should have the opportunity to build competency in this topic by taking this approach. Children are encouraged to physically represent mathematical concepts. Objects and pictures are used to demonstrate and visualise abstract ideas, alongside numbers and symbols.
- Concrete – Children should have the opportunity to use concrete objects and manipulatives to help them understand and explain what they are doing.
- Pictorial – Children should then build on this concrete approach by using pictorial representations. These representations can then be used to reason and solve problems.
- Abstract – With the foundations firmly laid, children should be able to move to an abstract approach using numbers and key concepts with confidence.
Fluency, reasoning and problem solving
Teaching supports the aims of the National Curriculum
Mathematical problem solving is at the heart of our approach. Children are encouraged to identify, understand and apply relevant mathematical principles and make connections between different ideas. This builds the skills needed to tackle new problems, rather than simply repeating routines without a secure understanding.
Mathematical concepts are explored in a variety of representations and problem-solving contexts to give pupils a richer and deeper learning experience. Children combine different concepts to solve complex problems, and apply knowledge to real-life situations.
The way children speak and write about mathematics transforms their learning. Mastery approaches use a carefully sequenced, structured approach to introduce and reinforce mathematical vocabulary. Children explain the mathematics in full sentences. They should be able to say not just what the answer is, but how they know it’s right. This is key to building mathematical language and reasoning skills.
Children should be able to recall and apply mathematical knowledge both rapidly and accurately. However, it is important to stress that fluency often gets confused for just memorisation – it is far more than this. As well as fluency of facts and procedures, pupils should be able to move confidently between contexts and representations, recognise relationships and make connections in mathematics. This should help children develop a deep conceptual understanding of the subject. Frequent, carefully designed, intelligent practice will help them to achieve a high level of fluency.
Number at the heart
A large proportion of time is spent reinforcing number to build competency and fluency. Number is usually at the heart of any primary mastery scheme of learning, with more time devoted to this than other areas of mathematics. It is important that pupils secure these key foundations of maths before being introduced to more difficult concepts.
This increased focus on number will allow children to explore the concepts in more detail and secure a deeper understanding. Key number skills are fed through the rest of the scheme so that children become increasingly fluent.
For more information about White Rose Maths follow the link: