Intent- Maths at Parkfield Primary School

 “Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.” ― Archimedes

We strive to deliver a stimulating and enjoyable maths curriculum, whilst ensuring that through appropriate support and challenge, learning is tailored to each and every child. We recognise that fluency, problem solving and application of maths in context are fundamental qualities of our children as mathematicians and this approach reflects the aims of the National Curriculum (2014).  

The National Curriculum (2014) aims that all children:

• 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.
• Can 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.

Recent research used to inform practice: In the recent Coordinating mathematical success: the mathematics subject report (2023) it states, in the last few years, a resounding, positive shift in mathematics education has taken place in primary schools. Curriculum is now at the heart of leaders’ decisions and actions. Generic approaches, such as the expectation that all teaching should always be differentiated, have dissipated. We now see high quality curriculums, collaborative support for teachers and a focus on mathematics teaching. Leaders intend that pupils ‘keep up, not catch up’. These approaches set out a better path to proficiency for pupils. In the EEF Improving Mathematics in EYFS and Key Stage 1 overview it states, manipulatives and representations can be powerful tools for supporting young children to engage with mathematical ideas. As well as using a variety of methods to assess children’s mathematical understanding. Moreover, the KS2 EEF overview suggests using tasks to build conceptual knowledge in tandem with procedural knowledge and when problem solving and reasoning children should use worked examples to enable them to analyse the use of different strategies. That said, in the recent mathematics report it reports that true proficiency in maths is superseded by ‘age related expectations’ which roughly equates to 50% accuracy in end of key stage 2 tests. As a result, many pupils aren’t as prepared for the rigours of secondary education as they could be.

Implementation

EYFS

Our maths programme of study begins in EYFS. The EYFS framework is structured very differently to the National Curriculum. There are seven areas of learning and development that must shape educational programmes in early years settings. All areas of learning and development are important and inter-connected.

These are the prime areas:

• communication and language

• physical development

• personal, social and emotional development

Within the four specific areas are:

• literacy

• mathematics

• understanding the world

• expressive arts and design

The most relevant Early Years outcomes for maths are taken from Communication and Language and Mathematics- which are the prerequisite skills for maths within the National Curriculum.

There is a strong focus on the characteristics of effective learning which includes Playing and Exploring, Active Learning and Creating and Thinking Critically. When children have reached their Early Learning Goals, they can: Have a deep understanding of number to 10, including the composition of each number; 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 to10, including double facts; 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 and explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally.

Maths in Reception is a very ‘hands-on’ and collaborative subject.  Children use a wide range of concrete apparatus to ensure they build secure foundations in their understanding of number, shape and pattern. By the end of the year, the children will have been taught all the skills they need to meet the requirements of the EYFS profile and achieve the Early Learning Goals for maths.

At Parkfield, we use stimulating visual resources with our key spine for umber being Number Sense. In addition, we use ‘Master, and materials from the National Centre of Excellence for the Teaching of Mathematics (NCETM), to introduce the maths concepts to the children. We then build on this by providing a variety of practical experiences to reinforce and deepen their understanding.  Alongside this, we add the non-number units such as geometry and measure.

Children learn maths everyday through a variety of approaches: daily teacher-led maths learning and ongoing provision of child-initiated maths learning and learning through play.  They have a stimulating classroom and outdoor environment, which provide access to a variety of quality maths resources. Relevant maths vocabulary, symbols and recording is introduced and modelled by the teaching staff at appropriate times throughout all maths learning opportunities.

During teacher-led maths learning, concepts are introduced to the class by the teacher, usually using the ‘Number Sense’ animations as a stimulus.  The children then build on this learning by practising the skill in mixed-ability groups, completing a range of practical activities. Adults support and extend the children’s learning during these activities, as appropriate. For example, the children may be introduced to the concept of ‘1 more’ using a ‘Number Sense’ animation, which is followed by teacher modelling and questioning to reinforce the key learning points. The children then move into groups to work on a series of carefully planned, engaging activities where the children explore and practise finding ‘1 more’ using a variety of different concrete resources and representations. This could be counting 1 more on a number line, using objects to add 1 more to a group, or rolling a dice and counting 1 more than the number shown.  Using a variety of representations to apply their learning, ensures concepts are embedded and it gives teaching staff the opportunity to use skilful questioning to assess learning and then support or deepen the children’s understanding as appropriate.

Key Stage 1 and 2

Our maths curriculum in Key Stage 1 and 2 fundamentally covers the statutory learning objectives outlined in the Primary National Curriculum, which is progressive in nature.  However, this varies slightly due to sequencing of the NCETM’s curriculum prioritisations materials.  This resource provides coherent sequencing for the primary maths curriculum and draws together the DfE guidance on curriculum prioritisation, with quality classroom resources provided by the NCETM.

We recognise that knowledge and skills are linked, where each year group’s learning objectives and vocabulary build upon the previous year group’s coverage; our main aim being to ensure the building blocks of knowledge and skills are in place to underpin further learning.  

Our vision for the children of Parkfield School is to underpin mathematical learning by developing an even balance between conceptual understanding and procedural fluency. Children are taught to understand how and why mathematical procedures are used, in order to develop their arithmetic proficiency and their ability to 'unpick' and solve real-life mathematical challenges. To support this development, we use concrete apparatus and pictorial representations in whole class and small group activities throughout the school. As appropriate, we provide 1:1 and small group interventions for pupils across the school to ensure that children reach their full potential and make good progress in developing as life-long learners.

The NCETM curriculum prioritisation primary scheme of learning (2020) is a key resource which maps out our curriculum to ensure appropriate progression from Year 1- Year 6. This scheme is used alongside other quality resources to ensure children are exposed to a range of fluency, reasoning and problem-solving activities that foster our ‘mastery approach’. 

The ‘mastery approach’ is about teaching for understanding – ensuring the children know why they are doing certain mathematical processes, how they work and how to apply them in a range of situations. It opposes teaching ‘tricks’ or procedures without understanding, which results in superficial learning.  Key aspects of the mastery approach:

• Children learn a maths topic in-depth, before moving onto the next maths topic, this is supported by the NCETM prioritisation curriculum.
• Maths topics are progressive E.g. ensuring place value is secure before working on calculations
• For each National Curriculum objective, children solve questions, problems and work on tasks that are presented in a variety of ways
• Concrete apparatus, pictorial representations and abstract representations are used
• Correct use of mathematical vocabulary
• Collaborative working
• Teachers address misconceptions and address these promptly whilst also using professionalism and experience to pre-empt sticking points in children’s learning.
• Explaining, modelling and justifying mathematical ideas

Children have a daily maths lesson and also additional ‘Number fluency’ sessions throughout the week. In KS1 this follows the ‘Number Sense’ programme which is built upon research from Willingham (2019) and Hasselbring, Going and Bransford (1987) who state that “As children meet mathematical problems in life and school, they need to focus on how to break them down into steps in order to solve them. An essential component of automaticity is that the answer come by means of direct retrieval rather than following a procedure. Although correct answers can be obtained using procedural knowledge, these procedures are effortful and slow, and they interfere with learning and understanding higher-order concepts. Calculating simple arithmetic facts requires working memory (i.e., the mental “space” in which thought occurs). With enough practice, however, the answers can be pulled from memory (rather than calculated) thereby incurring virtually no cost to working memory. Students who automatically retrieve answers to simple problems keep their working memory free to focus on the bigger problem”. In KS2, the children follow our school fluency programme which is designed so the children regularly practise and consolidate number facts, counting, and mental and written calculations.  This regular practice keeps these key skills sharp, and thus reducing cognitive load when problem solving resulting in allowing children the capacity to compute more complex mathematical concepts.

Enrichment

As part of our ongoing commitment to provide enrichment opportunities we regularly take part in competitions and challenges outside of the curriculum, these include: Wellington Maths Challenges.  Maths forms an integral part of our annual STEM week, where visitors inspire children through maths activities.

How is it assessed?

EYFS

The Reception Baseline Assessment (RBA) is a short assessment, taken in the first six weeks in which a child starts reception.

In the final term of the year in which the child reaches age five, and no later than 30 June in that term, the EYFS Profile must be completed for each child.

The Profile provides parents and carers, practitioners and teachers with a well-rounded picture of a child’s knowledge, understanding and abilities, their attainment against expected levels, and their readiness for year 1. The Profile must reflect practitioners’ own knowledge and professional judgement of a child to inform discussions with parents and carers, and any other adults whom the teacher, parent or carer judges can offer a useful contribution.

Each child’s level of development must be assessed against the early learning goals.

Practitioners must indicate whether children are:

• Meeting expected levels of development
• Not yet reaching expected levels (‘emerging’)

In particular, practitioners note the learning that a child demonstrates spontaneously, independently and consistently in a range of contexts. On-going assessment is an integral part of the learning and development process. It involves teachers observing children to understand their level of attainment, interests and learning styles, and to then shape learning experiences for each child reflecting those observations.

In Key Stage One and Two

Throughout the school, all children will complete assessment tasks. Children will complete assessment tasks when they have completed ‘blocks’ of learning and will have termly arithmetic and reasoning tests to support teachers to plan effectively and address misconceptions. 

In the summer term of Year 2, the children will complete the optional ‘End of Key Stage 1’ assessments.  For maths, this consists of an arithmetic test and a reasoning test.  These tests are then marked by the teachers and the results are used by the teachers to help them make a secure judgement for their final assessment of each child at the end of Key Stage 1. The teachers’ assessments will state whether or not each child is ‘working towards the expected standard’, ‘working at the expected standard’ or ‘working at greater depth within the expected standard’.

In the summer term of Year 4, the children will complete the national statutory Multiplication Tables Check (MTC) online assessment.  This consists of a short online assessment where the children are tested on their recall of all times tables up to 12 x 12. Knowing these facts before they move into Year 5 is very important to support them with their future learning.

In the first half of the summer term, the Year 6 children will complete the national statutory End of Key Stage 2 tests.  For maths, this consists of an arithmetic paper and two reasoning papers. These tests are completed on the statutory allocated days, during a week in May.  The tests are marked externally and the raw score is converted to a scaled score.

Impact

By the end of their time at Parkfield, as mathematicians, the children will be: 

• Successful learners who have gained a secure knowledge and understanding of the primary maths curriculum.
• Confident individuals who are able to apply their knowledge to a range of applications as well as being able to ‘talk’ about their mathematics, using appropriate vocabulary, competently.
• Responsible citizens who understand the importance of mathematics in the wider world and have the opportunity to pursue mathematics in their future careers, should they wish.