Mathematics

'The essence of mathematics is not to make simple things complicated, but to make complicated things simple.'

Stan Gudder

Mathematics at Our Lady and All Saints

The aim of mathematics at our school is to build confidence and fluency in mathematical knowledge, concepts and skills and support our children in using and applying mathematical knowledge across the curriculum and in real life contexts. We seek to foster an enjoyment and enthusiasm for mathematics and promote curiosity and fascination in seeking solutions to problems. We utilise mathematics lessons along with regular 'morning maths' sessions and weekly 'Big Maths (Key Skills) sessions to secure the fundamentals of mathematics and develop fluency so that our children are then able to reason and problem solve, and apply skills to a variety of routine and non-routine problems. Logical thinking and working systematically are also key elements of our mathematics curriculum, fostering initiative and an ability to work both independently and in co-operation with others.

From the beginning of their learning journey in our early years (Nursery and Reception), we ensure children develop a strong grounding in number which is essential so that all children develop the necessary building blocks to excel mathematically. They learn to count confidently, develop a deep understanding of the numbers to 10, the relationships between them and the patterns within those numbers. We provide frequent and varied opportunities to build and apply this understanding so that our children develop a secure base of knowledge and vocabulary from which mastery of mathematics is built. In our early years, we provide rich opportunities for children to develop their spatial reasoning skills across all areas of mathematics including shape, space and measures. We help our children to develop positive attitudes and interests in mathematics, look for patterns and relationships, spot connections, ‘have a go’, talk to adults and peers about what they notice and not be afraid to make mistakes.

As our children move in to Class Two (Key Stage One), our principal focus is to ensure that children develop confidence and mental fluency with whole numbers, counting and place value. They develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Our children also learn to use a range of measures to describe and compare different quantities. By the end of year 2, our children should know the number bonds to 20 and be precise in using and understanding place value. 

When children move to Class Three (Lower Key Stage Two), our principal focus is to ensure that children become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. They develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers. In Class Three, they also develop their ability to solve a range of problems, including with simple fractions and decimal place value. Our children learn to draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. By the end of year 4, our children should have memorised their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work.

In Class Four (Upper Key Stage Two), the principal focus is to ensure that our children extend their understanding of the number system and place value to include larger integers. They learn to make connections between multiplication and division with fractions, decimals, percentages and ratio. Our children develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. Our children are introduced to the language of algebra as a means for solving a variety of problems. In geometry and measures, our children consolidate and extend knowledge developed in number. They learn to classify shapes with increasingly complex geometric properties. By the end of year 6, our children should be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages.

Meeting the needs of our pupils in Mathematics

Across all year groups, there is a focus within mathematics of securing the foundations in fluency. Through daily maths recall and a determined drive to secure knowledge in the fundamentals of mathematics, pupils develop perseverance and are able to complete basic number calculations with ease, providing more cognitive space for the more challenging elements of the curriculum.

Lesson design focusses on fluency, reasoning and problem solving, taking children on a journey through the concrete, into the pictorial and then to the abstract representations. This rich diet enables students to grow in confidence as they make connections in their learning and understand concepts at a deeper level.

Programme of Study of The National Curriculum

The national curriculum for mathematics aims to ensure that all pupils:

• 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.

Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.

The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

Spoken language

The national curriculum for mathematics reflects the importance of spoken language in pupils’ development across the whole curriculum – cognitively, socially and linguistically. The quality and variety of language that pupils hear and speak are key factors in developing their mathematical vocabulary and presenting a mathematical justification, argument or proof. They must be assisted in making their thinking clear to themselves as well as others and teachers should ensure that pupils build secure foundations by using discussion to probe and remedy their misconceptions.

School curriculum

The programmes of study for mathematics are set out year-by-year for key stages 1 and 2. Schools are, however, only required to teach the relevant programme of study by the end of the key stage. Within each key stage, schools therefore have the flexibility to introduce content earlier or later than set out in the programme of study. In addition, schools can introduce key stage content during an earlier key stage, if appropriate. All schools are also required to set out their school curriculum for mathematics on a year-by-year basis and make this information available online.