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Maths Mastery

Children’s chances of success are maximised if they develop deep and lasting understanding of mathematical procedures and concepts.


An exchange programme between teachers from England and Shanghai has informed effective pedagogic strategies for achieving mastery of maths. The striking performances of Shanghai and other East Asian countries in maths have become well-established. 


The component thought to be key to the success of the East Asian system is the use of variation theory. Variation theory has several dimensions, including use of multiple representations of what a concept is, and what it is not. It is characterised by a carefully constructed small-step journey through learning. It pays attention to what is kept the same and what changes, in order that pupils might reason. This means that they will make connections and build deep conceptual knowledge. 


Variation is applied to practice questions where attention is paid to the selection and order of the examples. Often just one aspect is changed whilst others are kept the same. The intention is to avoid mechanical repetition but instead to promote thinking to make connections. This is also known as ‘intelligent practice’.


Teaching for mastery is also characterised by a series of beliefs and practices.


Children Succeeding

Mastery is characterised by a belief that, by working hard, all children are capable of succeeding at mathematics. On this basis, children are taught all together as a class and are not split into ‘prior attainment’ groupings. Carefully structured teaching is planned in small steps. This provides both the necessary scaffold for all to achieve, and the necessary detail and rigour of all aspects of the maths to facilitate deep thinking. The small steps are connected and concepts are built. This leads to generalisation of the maths, and the ability to apply it to multiple contexts and solve problems.


Understanding Structures

A focus on exposing the structure of mathematics and developing an understanding of how and why maths works is crucial to mastery. A key skill of the teacher is to be able to represent the maths in ways that provide access and insight for pupils. Concrete materials, contexts, drawings, diagrams and equations all play a role. These are discussed through opportunities for pupil-pupil and pupil-teacher talk, to develop reasoning, flexibility and adaptability in mathematical thinking.


Learning Facts

Memorisation and repetition of key facts (for example, number bonds) are important aspects of learning. Evidence from cognitive science research suggests that learning key facts so they can be recalled automatically ‘frees up’ working memory. It can then focus on more complex problem solving, rather than reaching cognitive overload trying to calculate simple operations. In terms of procedural fluency and conceptual understanding, one should not be prioritised over the other. Learning is most effective when the two are fully integrated.


Mathematical Language

Teaching children precise mathematical language and insisting upon its use supports children's ability to think mathematically. Having the language and using it empowers children’s ability to think about the concept.


Mastery of mathmatics is something that we want for all of our pupils to acquire and to continue acquiring throughout their school lives, and beyond. At Broomgrove Infant School we feel that Mastery is about acquiring a deep, long-term, secure and adaptable understanding of the subject. 


Our Approach

  • Active learning
  • Time for children to think
  • Mastery is achievable for all children


Children working at Mastery:

  • Know how to do it
  • Their knowledge becomes automatic
  • They know that they are really good at it
  • They can show someone else how to do it
  • They have a deep and sustainable learning
  • They have the ability to build on something that has already been sufficiently mastered 
  • They have the ability to reason about a concept and make connections
  • They have conceptual and procedural fluency 


How we enable and develop Mastery:

  • Maths Meetings- children are continually using skills taught, given time to reason and make connections
  • Teachers enable children to make links between their maths learning 
  • Clear 4 rules  guidance to enable all children to master concepts whether at the concrete, pictorial or abstract  stage of learning
  • Time for children to solve problems to apply what they have learnt
  • Encouraging children to think deeper
    • Can they think of an answer
    • Can they think of more than one answer
    • Can they think of all the answers
    • Can they Prove it / explain how they know?

    Parent Sessions

    Teaching and Learning of Maths in EYFS and KS1


    Want to support your child with their maths homework and increase your confidence in maths?


    Please see the attached flier for sessions designed to help parents understand the current methods used in school to support children with their learning in Mathematics. This course is about building parental understanding, knowledge and confidence around all things ‘maths’ so that you feel confident to support your child’s learning journey.




    This is an information based session, where you have the opportunity to explore the apparatus and understand the strategies being used in school to aid your child’s learning. You will not be put on the spot or asked to answer questions. Please do not be fearful of attending these sessions. They are purely a source of information for you as parents.


    Any questions please do speak to Mrs Worth. Alternatively, if you would like to attend the sessions, please complete the link attached in the flier.


    Number Day 2024

    Today we celebrated Number Day alongside the rest of the school. As part of this we dressed as something Mathematical, joined in with a whole NSPCC school assembly, and participted in an HSBC workshop (Day 2). 


    Number Day generated a lot of discussion about what each of us had come to school dressed as:


    "I am Number seven!"


    "I am number 95"


    "I am pi (π)!"

    HSBC Workshops (Day 1)

    Today children at Broomgrove Infant School we welcomed members of the HSBC UK Education Network. Across two days children were involved in activities focused on developing children’s understanding around financial budgeting and in particular money.


    Financial literacy is a critical life skill. HSBC UK runs award-winning financial education programmes for both young people and adults. At the heart of the HSBC UK programme is the opportunity to build the fundamental maths and numeracy skills required by each curriculum across England, Northern Ireland, Scotland and Wales. Important to this aspect of the financial education framework are:

    • Understanding the value of money
    • Performing calculations with money
    • Understanding currencies
    • Appreciating how money works
    • Understanding borrowing and calculating interest


    Across each year group lessons were delivered in person by a member of the HSBC UK Education Network, providing the children with access to these core financial capability skills. Each session lasted up to one hour and follows the HSBC UK learning framework of introduce, discuss and use, allowing for interactive learning and ongoing development of ideas beyond the session itself. The children thoroughly enjoyed this experience to build on from their learning about money.


    For more ideas as to how you can support your child’s learning and development particularly in Mathematics please speak to your child’s class teacher, Mrs Worth (Subject leader and Local Leader in Mathematic Education) or follow the attached link to the Essex Year of Numbers campaign: Essex Year of Numbers 2023-24: Essex Education Task Force



    Maths Club

    Children have loved coming to Maths Club. During these sessions we have played numicon snap, Snakes and Ladders looking at developing our subtising skills, and playing Twister. We have focused on developing our understanding about left and right, understanding specific positional language such as behind, beside and in front of, as well as securing our knowledge of the hungarian frame.

    Concrete, Pictorial and Abstract (CPA)
     We are working using a variety of different approaches to support our learning; Concrete, Pictorial and Abstract (CPA). Through adopting this approach we are able to show our understanding and apply our reasoning and problem solving skills. Where possible we make our lessons personal and link to other areas of the curriculum. The attached pictogram is an example of how we forge links between different areas of learning for example, this terms topic and maths.
    Online Resources

    Action Plan

    Long Term planning