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.
Singapore Maths and CPA approach
What is Singapore Maths?
At a glance
- Singapore consistently top the international benchmarking
- studies for maths teaching
- A highly effective approach to teaching maths based on research and evidence
- Builds students’ mathematical fluency without the need for rote learning
- Introduces new concepts using Bruner’s Concrete Pictorial Abstract (CPA) approach
- Pupils learn to think mathematically as opposed to reciting formulas they don’t understand
- Teaches mental strategies to solve problems such as drawing a bar model
Our school uses Maths- No Problem from year one to four. We are embedding the Singapore style of learning throughout the whole school using investigation based lessons on the CPA approach.
Maths- No Problem is a scheme of learning based on the National Curriculum which allows children to deepen their understanding of mathematics and aids their learning through visual representations. It is based on research and theories by notable experts such as Jerome Bruner, Richard Skemp, Jean Piaget, Lev Vygotsky, and Zoltan Deines.
What is the CPA approach?
At a glance
- An essential technique of maths mastery that builds on a child’s existing understanding
- A highly effective framework for progressing pupils to abstract concepts like fractions
- Involves concrete materials and pictorial/representational diagrams
- Based on research by psychologist Jerome Bruner
- Along with bar modelling and number bonds, it is an essential maths mastery strategy
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.
Key Stage 1 - Years 1 & 2
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 2 - Years 3 & 4
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 2 - Years 5 & 6
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.
The Chris Quigley Maths Essentials Curriculum sets out essential coverage, learning objectives and standards which are required for the subject. 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.
- A commitment to and passion for the subject.
Learning objectives in line with the National Curriculum for
Key Stage 1 and 2
|To know and use numbers||To use fractions||To use measure|
|To add and subtract||To understand the properties of shape||To use statistics|
|To multiply and divide||To describe position, direction and movement||To use algebra|
Please click on the link below to see a full overview of the Maths objectives by year group: