Our mathematics curriculum is the product of careful selection, sequencing and linking of declarative, procedural and conditional knowledge.
Declarative knowledge is static in nature and consists of facts, formulae, concepts, principles and rules. All content in this category can be prefaced with the sentence stem ‘I know that’. Here, pupils learn facts and formulae and the relationship between facts (conceptual understanding).
Procedural knowledge is recalled as a sequence of steps. The category includes methods, algorithms and procedures: everything from long division, ways of setting out calculations in workbooks to the familiar step-by-step approaches to solving quadratic equations. All content in this category can be prefaced by the sentence stem ‘I know how’. Here, pupils learn methods and the relationship between facts, procedures and missing facts (principles/mechanisms).
Conditional knowledge gives pupils the ability to reason and solve problems. Useful combinations of declarative and procedural knowledge are transformed into strategies when pupils learn to match the problem types that they can be used for. All content in this category can be prefaced by the sentence stem ‘I know when’. Here, pupils learn strategies and the relationship between information, strategies and missing information (reasoning).
Mathematics is essential for everyday life and understanding our world. It enables the development of pupils’ natural ability to think logically and solve puzzles and real-life problems. Pupils learn to think creatively and make links between mathematical concepts through exploring patterns in the number system, shape, measures, and statistics. They make and discuss propositions, explaining their reasoning and justifying their answers. They develop the skills, knowledge, and efficient methods of calculation necessary to support their economic future and problem-solving in life.
We teach maths at Abbott in a way that enables all the children to think clearly about how to tackle a problem, have better reasoning knowledge and skills that they can utilise as they progress through their education and life, and work fluently and efficiently. Rather than having one method to solve five questions, we want our children to learn five methods to solve one question. This mantra has helped shape our approach to teaching maths. Maths lessons are structured in a variety of different ways to ensure that the children in our school make the best possible progress and have a secure understanding and knowledge of different concepts.
Power Maths ensures children have the chance to fully understand a concept and utilises the Concrete to Pictorial to Abstract approach. It incorporates reasoning and problem solving into all lessons so that the children apply their maths knowledge and skills. Sometimes, lessons are taken outside of the classroom so that the children can practice what they have been learning in the ‘real world’. An example of this is when our EYFS children work in our Forest School and use non-standardised measurements such as sticks they have collected to compare different lengths.
When teaching times tables, the inverse facts are also taught so that the children understand what times tables mean and how to use them effectively when they have to apply their knowledge. Additionally, we teach arithmetic daily and explicitly to ensure that the children are well-equipped to become fluent mathematicians.
National Curriculum Aims
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 nonroutine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
Maths in Key Stage 1
The principal 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 4 operations, including with practical resources [for example, concrete objects and measuring tools].
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.
Maths in Lower Key Stage 2 - Years 3 and 4
The principal focus of mathematics teaching in lower key stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the 4 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 with simple fractions and decimal place value. Teaching should also ensure that pupils draw with increasing accuracy and develop mathematical reasoning so 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 multiplication 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.
Maths in Upper Key Stage 2 - Years 5 and 6
The principal 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 larger 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 wider range of problems, including increasingly complex properties of numbers 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, pupils 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.