Mathematics

At Chapel End Junior Academy, our mathematics curriculum  builds on the content and principles of ‘Mastery’ taken from the National Curriculum, which itself reflects on the teaching found in high performing education systems internationally, particularly those of east and south-east Asian countries such as Singapore, Japan, South Korea and China. We have carefully considered the impact of the cultural differences and tailored our curriculum accordingly to meet the specific needs of our children. Following the National Curriculum Programmes of Study for Mathematics, our work with NCETM, White Rose Hub and our own action research, we have developed a curriculum that provides the children with more opportunities to reason and problem-solve thereby fostering a deeper understanding and greater mastery of mathematics. Through our mathematics curriculum, not only do we aim to provide our children with essential skills for life but also to develop their curiosity and enjoyment of the subject.

  Fundamental Great British Values

At Chapel End Junior Academy we understand clearly our responsibility to prepare children for their next stage of education and for the opportunities, responsibilities and experiences of later life, laying the foundations so that they can take their place successfully in modern British society. We promote a respect for and understanding of different faiths, cultures and lifestyles. The spiritual, moral, social and cultural development of each child is central to everything that we do as a school and central to our vision of “Dream Believe Achieve”. This is evidenced through our teaching and learning, our inclusive environment and through the many opportunities provided for our children to understand democracy, law, liberty, mutual respect and tolerance.

The Principles and Features Characterised in Our Curriculum:

  • Teachers reinforce an expectation that all children are capable of achieving high standards in mathematics.
  • Teachers provide children with rich and varied opportunities to reason and problem-solve in mathematics
  • Teachers encourage children to monitor and reflect on their own progress during lessons through timely individualised feedback in the moment
  • Teachers encourage children to actively challenge themselves, to identify areas for development and to conscientiously build on their own learning
  • The large majority of children progress through the curriculum content at the same pace. Differentiation is achieved by emphasising depth of knowledge and through individual support and intervention.
  • Pre-teaching interventions that focus on subject knowledge and growth mindset are used to ensure that children have the confidence and preliminary understanding to access learning in class
  • Conceptual understanding is developed by systematic progression through concrete, pictorial and abstract representations
  • Teaching is underpinned by methodical curriculum design and supported by carefully crafted lessons with varied representations and resources that foster deep conceptual and procedural knowledge.
  • Practice and consolidation play a central role. Carefully designed variation within this builds fluency and understanding of underlying mathematical concepts in tandem.
  • Teachers use precise questioning in class to test conceptual and procedural knowledge, and assess children regularly to identify those requiring intervention so that all children keep up.
  • Children are articulate in explaining, justifying and reasoning about their mathematics orally when discussing their work and when answering questions.
  • Children have regular opportunities to work both collaboratively and independently to reason and problem-solve

The intention of these approaches is to provide all children with full access to the curriculum, enabling them to achieve confidence and competence – ‘mastery’ – in mathematics, to develop the maths skills they need for the future and spark a deeper curiosity and interest in mathematics.

Our Curriculum Objectives

Our curriculum is designed with the goal of developing a love of the subject and an ability to connect areas of learning and solve problems; and know that they can achieve in the mathematics whilst at school and in the future. To achieve this we aim to ensure:

  • All children should become fluent in the fundamentals of mathematics, including through varied and frequent practice, so that children develop conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems.
  • Mathematics is taught in mixed ability groups that focus on the life skills of collaboration, growth mindset, resilience and problem solving as much as discrete mathematical knowledge.
  • Children who grasp concepts rapidly are challenged through rich and sophisticated problems as well as developing their understanding and social skills by supporting others.
  • Children who are not sufficiently fluent with previous concepts are provided with opportunities to consolidate their understanding, including additional pre-lesson and post-lesson practice.

Curriculum Design

  • Chapel End Junior Academy’s carefully considered teaching cycle is employed to ensure that children:
    • review previous learning required for new learning
    • have an opportunity to develop fluency through carefully planned practice activities
    • make connections between other areas of mathematics by applying new and existing knowledge across a range of situations.
  • A detailed, structured curriculum is mapped out across both phases, ensuring continuity and supporting transition.
  • Mathematical topics are taught in block to ensure depth of knowledge and thorough coverage of each topic. Mathematical content is revisited across blocks, thereby developing conceptual connections.
  • Effective mastery curricula in mathematics are designed in relatively small carefully sequenced steps (small steps), which must each be mastered before children move to the next stage. Fundamental skills and knowledge are secured first. This often entails focusing on curriculum content in considerable depth for extended periods of time in each year group.
  • The learning journey for each block is made clear to the children through CEJA’s cover sheets, which show all small steps in child-friendly language. Children can assess themselves against these to gauge progress in each area. These assessments are quality assured by the teacher who uses these to feed into their own teacher assessments.

Teaching resources

  • A coherent programme of high quality curriculum materials is used to support classroom teaching. Concrete, pictorial and abstract representations of mathematics are carefully selected to build procedural and conceptual knowledge together. Exercises are structured with great care to build deep conceptual knowledge alongside developing procedural fluency.
  • The focus is on the development of deep structural knowledge and the ability to make connections through reasoning and problem-solving. Making connections in mathematics deepens knowledge of concepts and procedures, ensures what is learnt is sustained over time, and cuts down the time required to assimilate and master later concepts and techniques.
  • The NCETM and White Rose materials facilitate appropriate coverage. Teachers are skilled in developing these ideas using a wide range of high quality resources to ensure every learning intention is taught in a way that maximises learning.

Lesson design

  • Lessons are crafted with similar care and are often perfected over time with input from other teachers and teaching assistants in daily feedforward / feedback meetings, drawing on evidence from observations of children in class. Lesson designs set out in detail well-tested methods to teach a given mathematical topic. They include a variety of representations needed to introduce and explore a concept effectively and also set out related teacher explanations and questions for children.
  • Self- and peer-assessment are integral to all lessons
  • Learning intentions and steps to success breakdown learning into key steps enabling children to self-monitor during activities and self- and peer-assess at the end, thereby fostering a greater sense of responsibility for and ownership of their own learning.

Teaching methods

  • Teachers are clear that their role is to teach in a precise way which makes it possible for all children to engage successfully with tasks at the expected level of challenge. Children work on the same tasks and engage in common discussions. Concepts are often explored together to make mathematical relationships explicit and strengthen children’ understanding of mathematical connectivity.
  • Precise questioning during lessons ensures that children develop fluent technical proficiency and think deeply about the underpinning mathematical concepts. There is no prioritisation between technical proficiency and conceptual understanding; in successful classrooms these two key aspects of mathematical learning are developed in parallel.

Pupil support and differentiation

  • Differentiation occurs in the content, support and intervention provided to different children. Differentiation occurs through questioning and scaffolding that the individual children receive in class as they work through problems, with higher attainers challenged through more demanding problems which deepen their knowledge of the content. Children’ difficulties and misconceptions are identified through immediate formative assessment and addressed with rapid intervention – commonly through individual or small group support.

Productivity and practice

  • Fluency comes from deep knowledge and practice. Children work hard and are productive. At early stages, explicit learning of number bonds and multiplication tables and inverse operations and commutative laws is important in the journey towards fluency and contributes to quick and efficient mental calculation.
  • Deliberate practice leads to other number facts becoming second nature. The ability to recall facts from long term memory and manipulate them to work out other facts is also important. Communicating the importance of this learning to our children so they take ownership of their learning is key part of our approach.
  • All tasks are chosen and sequenced carefully, offering appropriate variation in order to reveal the underlying mathematical structure to children. Both class work and homework provide this ‘intelligent practice’, which helps to develop deep and sustainable knowledge. Homework is carefully designed to reinforce the children’s previous learning in class rather than requiring new learning.

Assessment

We assess children half-termly using PUMA assessment tools. The results of these tests are recorded and analysed to produce an age standardised score, which teachers use to track progress from term to term and year to year. Using the Hodder Scale, we can also track each child’s progress in relation to age-related expectations. Teachers assess children using the maths assessment grid and the small steps grids on the cover sheets. We also assess children at the beginning and end of each block using cold and hot tasks. The cold task gives an indication of a child’s prior knowledge at the beginning of a topic highlighting any common gaps or misconceptions, which are fed forward into planning. Progress is then reassessed at the end of the topic when children complete the hot task. Children directly compare their performance on the hot task to their cold task performance and self-assess accordingly using the cover sheets, which are then quality assured by the teacher. In addition to these assessments, children are assessed half-termly on their times tables.

Targets for 2018-19

  • To improve reasoning and problem-solving skills in all year groups
  • To raise the profile of self- and peer-assessment in maths in line with Visible Learning principles
  • To continue to improve fluency in times tables and mental arithmetic through regular teaching, practise and assessment