Mathematics

Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history's most intriguing problems. It is essential to every day life, critical to science, technology and engineering, and most forms of employment.  A high quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the power of mathematics and a sense of enjoyment and curiosity about the subject.

 

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 have 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 then by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems in to a series of simpler steps and persevering in seeking solutions.

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.

EYFS

The first few years of a child’s life are especially important for mathematics development, as they begin to make sense of the situations they find themselves in and find solutions to problems the are faced with. These are key skills they they will use throughout their learning of maths. The focus in our foundation stage is to ensure that all children develop firm mathematical foundations in a way that is engaging, and appropriate for their age through experiences with concrete resources and practical activities. Throughout their time in reception our children will be assessed against the new statutory framework which sets out what skills the children need to achieve the 'Early Learning Goals'.  The 'Early Learning Goals' for maths are outlined below.

ELG: Number
Children at the expected level of development will:
- Have a deep understanding of number to 10, including the composition of each number;14
- Subitise (recognise quantities without counting) up to 5;
- Automatically recall (without reference to rhymes, counting or other aids) number bonds up to 5 (including subtraction facts) and some number bonds to 10, including double facts.
ELG: Numerical Patterns
Children at the expected level of development will:
- Verbally count beyond 20, recognising the pattern of the counting system;
- Compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or the same as the other quantity;
- Explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally.

By the time they are ready to enter year one children should be able to

  • Count confidently and have developed a deep understanding of the numbers to 10,
  • Understand the relationships between these numbers and the patterns within them
  • Children should also have developed their spatial reasoning skills across all areas of mathematics including shape, space and measures.
  • Children should have developed  a positive attitude and interests in mathematics, be able to 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. 

Key stage One

The principle focus of mathematics teaching in Key Stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value.  This should involve working with numerals, words and the four operations.

At this stage, pupils should develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary.  Teaching should also involve using a range of measures to describe and compare different quantities such as length, mass, capacity / volume, time and money.

By the end of Year 2, pupils should know the number bonds to 20 and be precise in using and understanding place value.  An emphasis on practice at this early stage will aid fluency. 

Pupils should read and spell mathematical vocabulary, at a level consistent with their increasing word reading and spelling knowledge at Key Stage 1.

 

Lower Key Stage Two 

The principle focus of mathematics teaching in lower Key Stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value.  This should ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers.

At this stage, pupils should develop their ability to solve a range of problems, including the simple fractions and decimal place value.  Teaching should also ensure that pupils draw with increasing accuracy ad develop mathematical reasoning so that they can analyse shapes and their properties and confidently describe the relationships between them.  It should ensure that they can use measuring instruments with accuracy and make connections between measure and number.

By the end of Year 4, pupils should have memorised their multiplication tables up to and including the 12 x table and show precision and fluency in their work. 

Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word reading knowledge and their knowledge of spelling.

 

 Upper Key Stage Two

The principle focus of mathematics teaching in upper Key Stage 2 is to ensure that pupils extend their understanding of the number system and place value to include large integers.  This should develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio.

At this stage, pupils should develop their ability to solve a wide range of problems, including increasingly complex properties of number and arithmetic, and problems demanding efficient written and mental methods of calculation.  With this foundation in arithmetic, pupils are introduced to the language of algebra as a means for solving a variety of problems.  Teaching in geometry and measures should consolidate and extend knowledge developed in number.  Teaching should also ensure that pupils classify shapes with increasingly complex geometric properties and that they learn the vocabulary they need to describe them.

By the end of Year 6, pupil should be fluent in written methods for all 4 operations, including long multiplication and division and in working with fractions, decimals and percentages.

Pupils should read, spell and pronounce mathematical vocabulary correctly.

 

 

 

At Christ Church we use The Chris Quigley Essentials Curriculum to complement the objectives of the National Curriculum. It sets out essential coverage, learning objectives and standards which are required for subjects. It provides progress measures and emphasises the importance of developing the depth of childrens learning. 

 

Essential characteristics of mathematicians

  • An understanding of the important concepts and an ability to make connections within mathematics.
  • A broad range of skills in using and applying mathematics.
  • Fluent knowledge and recall of number facts and the number system.
  • The ability to show initiative in solving problems in a wide range of contexts, including the new or unusual.
  • The ability to think independently and to persevere when faced with challenges, showing a confidence of success.
  • The ability to embrace the value of learning from mistakes and false starts.
  • The ability to reason, generalise and make sense of solutions.
  • Fluency in performing written and mental calculations and mathematical techniques.
  • A wide range of mathematical vocabulary.