Mathematics

Intent

At Ashmead school, we want our mathematicians to develop confidence, and a sense of enjoyment and curiosity about mathematics. Our high-quality mathematics curriculum aims to develop the knowledge and skills necessary to provide a foundation for understanding the world. Mathematics is essential to everyday life and therefore forms part of our wider curriculum where we continue to contextualize learning through real life examples, encourage pupils to transfer skills and develop a healthy and enthusiastic attitude towards mathematics. We place emphasis on concrete resources and pictorial representations to enable pupils to fully understand concepts and principles, when presented with abstract calculations and questions. We believe encouraging pupils to make rich connections across mathematical ideas secures mathematical fluency, key skills, and understanding of mathematical concepts as an essential, and a pre-requisite, to be able to reason and solve problems with confidence.

Implementation

At Ashmead school mathematics is taught daily. We have developed a mathematics curriculum, which reflects The Early Years Statutory Framework and the National Curriculum programmes of study. Our progress document has been developed using resources from the NCETM (National Centre for Excellence in the Teaching of Mathematics) and the categories indicated below have been further divided to illustrate progression in key areas:

• Number and Place Value
• Addition and Subtraction
• Multiplication and Division
• Fractions (including decimals and percentages)
• Ratio and Proportion
• Measurement
• Geometry – properties of shape
• Geometry – position and direction
• Statistics
• Algebra

While not all categories are taught explicitly within all age phases or year groups, Early Learning Goals and National Curriculum objectives have been identified to ensure that connected prior learning supports new learning, e.g. Algebra.

AGE PHASE OVERVIEWS

Early Years

In Early Years, mathematics is one of the specific areas of learning. Pupils develop a strong grounding in number and are able to count confidently, develop deep understanding, and identify relationships and patterns to 10 through varied opportunities which are both adult and child led. Pupils will also develop their spatial reasoning skills across all areas of mathematics including space, shape and measure. Pupils are provided with opportunities to develop their knowledge, skills and vocabulary through a talk and language rich environment from which mastery of mathematics is built in.

Key Stage 1

Within Key Stage One, year 1 use Numicon resources to complement teaching and learning, and support the transition from EYFS to KS1. In Year 1, the curriculum overview provides a spiral curriculum approach enabling pupils to build on securing number fluency from 10 to 100 in preparation for year 2. Across Key Stage One, the focus of mathematics is to ensure pupils develop confidence and mental fluency with whole numbers, counting and place value. This involves working with numerals, words and the four operations (+ - x ÷) including practical resources. They will develop their ability to recognise, describe, draw, compare and sort different shapes and use 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 will be precise in using and understanding place value and know number bonds to 20.

Lower Key Stage 2 (Years 3 and 4)

In Years 3 and 4, pupils will become increasingly fluent with whole numbers and the four operations (including number facts and place value). Pupils begin to develop efficient written and mental calculations with increasingly large whole numbers. They begin to develop their ability to solve a range of problems, including simple fractions and decimal place value. Pupils develop mathematical reasoning to help them analyse shapes and their properties and confidently describe their relationships. By the end of Year 4, pupils will have memorised their multiplication tables up to and including the 12 times table and be able to show precision and fluency in their work.

Upper Key Stage 2 (Years 5 and 6)

In Years 5 and 6, pupils will extend their understanding of the number system and place value to include larger integers. They should be able to make connections between multiplication and division with fractions, decimals, percentages and ratio. Pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems that demand the use of efficient written and mental methods of calculation. They are introduced to algebra as a means for solving a variety of problems. Pupil’s understanding and knowledge in geometry and measures consolidates and extends the knowledge they have developed in number; pupils should be able to classify shapes with increasingly complex geometric properties, using the vocabulary they need to describe them with accuracy and confidence.

We have adopted ‘Band Statements’ based on our use of Target Tracker for summative assessment of the core subjects against the National curriculum. These outline the objectives and expected outcomes for each year group (as per our Mathematics progression document) and ensure mastery of each concept. Teachers formulate objectives to target each statement, breaking these down into ‘smaller steps’ where appropriate.

We have developed a calculation document for the four operations: addition, subtraction, division and multiplication, which identifies examples of intended outcomes for each year group, alongside varied concrete, pictorial and abstract strategies for teaching through a mastery approach.

Within mathematics, pupils are encouraged, where appropriate, to select the level of challenge, strategies, processes and approaches when reasoning and solving problems. Mathematical investigations, enquiries and journaling are weaved into the mathematics curriculum to enable pupils to draw upon their prior knowledge and utilise a wide range of concepts and skills. These are open-ended allowing pupils to set their own ceiling while developing conceptual understanding. This also provides opportunities for speaking and listening, as it fosters communication, discussion and debate ensuring pupils think and talk like a mathematician. Skills such as collecting, analysing, deducing and concluding, for example, are also developed, which support pupils’ wider life skills. There is a growing balance between opportunities to learn new skills and application of these.

To ensure fluency, multiplication and division facts need to be regularly taught, revisited and explored through a range of strategies – concrete, visual and abstract. Our ‘Multiplication and Division facts document’ identifies the knowledge and skills required for pupils to access and tackle more complex problems within multiplication and division. Key strands from the National Curriculum have been identified and mapped to ensure that pupils are given the opportunity to learn their multiplication and division facts to 12x12 by the end of year 4. Pupils in Year 4 are required to take a ‘Multiplication Tables Check’ (MTC) in June. Where pupils are secure with their times tables, further challenge and extension is provided to ensure they are masters. Where pupils are not meeting age-related expectations, further interventions are put in place. We also use TT Rockstars and Purple Mash to support the curriculum.

Our vocabulary progression document ensures that pupils have the tools to ‘talk like a mathematician’ and are able to reason and problem solve within mathematics to deepen their understanding of key knowledge and skills.

While all mathematical concepts have been sequenced to build knowledge progressively, within each year group, we expect teachers to identify where rich connections can be made, learning adapted, revisited or introduced to support pupil progress. All teachers ensure learning is consolidated before moving onto teaching new concepts.

In Early Years, pupils complete both adult-led and child-initiated mathematics activities. In Year 1, pupils remain in mixed ability classes to support their transition from Early Years. Lessons are structured to provide a wealth of adult-led and independent activities to support the learning objective. From year 2 onwards, pupils are set for mathematics. Based on historical school data, this approach has been successful for maintaining outcomes by ensuring that class content is well targeted to pupil needs. Sets are initially identified based on the end of year outcomes, but are not fixed and therefore reviewed regularly using a range of evidence and data so all pupils are suitably supported and challenged.

Through lesson planning we value multiplicity – all the different ways pupils think. We want to provide pupils with the skills and knowledge to be able to say: ‘I know that’, ‘I know how’ and ‘I know when’. Rosenshein’s principles of instruction underpin our approach to mathematics teaching and learning. These fundamentals are categorised to ensure retrieval, explicit teaching and practice.

Daily, weekly and ongoing review, questions and checking for understanding, ensure pupils have the opportunity to review prior learning, strengthen knowledge and skills to support new learning, and reduce cognitive load. We use RAP time as a strategy for addressing misconceptions and enabling pupils to respond to feedback, supporting, consolidating or challenging their learning. Explicit instruction provides, models and scaffolds when presenting new learning in small and progressive steps. Questioning, activities or tasks, and focused discussions, are facilitated for pupils to practice new learning and make connections, enabling pupils to move from guided to independent practice.

Pupils with additional needs are supported through identified objectives, strategies and interventions within their EHCPs or support plans. These ensure pupils make progress towards, and within, the expected National Curriculum outcomes. In addition to Quality First Teaching, interventions also take place which focus on those pupils who need targeted support.

Assessment

A wide range of formative and summative assessment strategies are used within mathematics to ensure that teaching and learning is adaptive to the needs of the pupils. Progress and attainment are monitored against the National Curriculum to ensure high expectations. 

Live feedback and marking enable same day intervention ensuring misconceptions are identified and addressed quickly. Purple pens are used to review, edit and correct responses to support pupils with the process of self-reflection and independence.

At the end of each unit, mini assessments are created to capture pupil’s learning and support teaching to address any further intervention prior to introducing a new unit of work. Summative assessments are also used to support teacher assessment and inform adaptive teaching and learning. This also includes ensuring pupils are familiar with assessment techniques and requirements so that formal testing does not demotivate or cause anxiety for our pupils. These questions are based on National Curriculum expectations and involve both arithmetic and reasoning questions.

Target Tracker is used to monitor pupils progress and attainment through band statements. It is also used to identify areas of strength and areas for development alongside other forms of monitoring at a classroom, cohort, phase and whole school level.

Further detail regarding assessment is outlined in a Feedback for Learning policy.

Statutory assessments

Pupils are prepared for any external assessments through our curriculum model for mathematics.

Impact

Our mathematicians will be confident and resilient when approaching their learning. Mathematics will be seen as a positive and integral part of promoting independence in their day-to-day lives. Pupils take pride in their work, speak positively of the subject and thrive on challenge. We achieve high outcomes in mathematics at the end of Key Stage Two and our pupils make strong progress during their time with us. Monitoring through a wide range of strategies, at regular intervals, such as: learning explorations, CPD, observations and data analysis, ensure increase conceptual understanding and high expectations. Equipped with essential knowledge and skills, we give our pupils the tools so they are prepared for the next stage of their education and ready for life in the wider world.