Hextable Primary School

Happy, Positive, Successful Life-Long Learners

Mathematics

 Aims of the new national curriculum

 The national curriculum for mathematics aims to ensure that all pupils:

  • become fluent in the fundamentals of mathematics through varied and frequent practice with complexity increasing over time. 
  • develop conceptual understanding and ability to recall and apply knowledge rapidly and accurately.

  •  Reason mathematically; follow a line of enquiry, conjecture relationships and generalisations

  • develop an argument, justification and proof by using mathematical language. Problem solve by applying knowledge to a variety of routine and non-routine problems, breaking down problems into simpler steps and persevering in answering

Maths At Hextable Primary School

Our aim at Hextable Primary is for all children to enjoy mathematics and have a secure and deep understanding of fundamental mathematical concepts and procedures when they leave us to go to secondary school. We want children to see the mathematics that surrounds them every day and enjoy developing vital life skills in this subject.

 

Aims for our pupils

  • To develop a growth mindset and positive attitude towards mathematics.
  • To become confident and proficient with number, including fluency with mental calculation and look for connections between numbers.
  • To become problem solvers, who can reason, think logically, work systematically and apply their knowledge of mathematics.
  • To develop their use of mathematical language.
  • To become independent learners and to work co-operatively with others.
  • To appreciate real life contexts to learning in mathematics.

 We aim to provide a stimulating and exciting learning environment that takes account of different learning styles and uses appropriate resources to maximise teaching and learning.

 

Teaching for Mastery Approach

In September 2019, Hextable Primary School began transitioning towards a mastery approach to the teaching and learning of mathematics. We understood that this would be a gradual process and take several years to embed. The rationale behind changing our approach to teaching mathematics lay within the NCETM Maths Hub Programme as well as the 2014 National Curriculum, which states:

  •  The expectation is that most pupils will move through the programmes of study at broadly the same pace.
  • Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content.
  • Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on 

Mastering maths means pupils of all ages acquiring a deep, long-term, secure and adaptable understanding of the subject. The phrase ‘teaching for mastery’ describes the elements of classroom practice and school organisation that combine to give pupils the best chances of mastering maths. Achieving mastery means acquiring a solid enough understanding of the maths that’s been taught to enable pupils to move on to more advanced material.

 

The 5 Big Ideas of Mastery

 

Coherence

Lessons are broken down into small connected steps that gradually unfold the concept, providing access for all children and leading to a generalisation of the concept and the ability to apply the concept to a range of contexts.

Representation and Structure

Representations used in lessons expose the mathematical structure being taught, the aim being that students can do the maths without recourse to the representation.

Mathematical Thinking

If taught ideas are to be understood deeply, they must not merely be passively received but must be worked on by the student: thought about, reasoned with and discussed with others.

Fluency

Quick and efficient recall of facts and procedures and the flexibility to move between different contexts and representations of mathematics.

Variation

Variation is twofold. It is firstly about how the teacher represents the concept being taught, often in more than one way, to draw attention to critical aspects, and to develop deep and holistic understanding. It is also about the sequencing of the episodes, activities and exercises used within a lesson and follow up practice, paying attention to what is kept the same and what changes, to connect the mathematics and draw attention to mathematical relationships and structure.

  

Teaching for Mastery Principles

 Underpinning our Teaching for Mastery approach are the following key principles:

  • It is achievable for all – we have high expectations and encourage a positive ‘can do’ mindset towards mathematics in all pupils, creating learning experiences which develop children’s resilience in the face of a challenge and carefully scaffolding learning so everyone can make progress.
  • Deep and sustainable learning – lessons are designed with careful small steps, questions and tasks in place to ensure the learning is not superficial.
  • The ability to build on something that has already been sufficiently mastered – pupils’ learning of concepts is seen a continuum across the school.
  • The ability to reason about a concept and make connections – pupils are encouraged to make connections and spot patterns between different concepts (E.g. the link between ratio, division and fractions) and use precise mathematical language, which frees up working memory and deepens conceptual understanding.
  • Conceptual and procedural fluency – teachers move mathematics from one context to another (using objects, pictorial representations, equations and word problems). There are high expectations for pupils to learn times tables, key number facts (so they are automatic) and have a true sense of number. Pupils are also encouraged to think whether their method for tackling a given calculation or problem is Appropriate, Reliable and Efficient (A.R.E).
  • Problem solving is central – this develops pupils’ understanding of why something works so that they truly have an appreciation of what they are doing rather than just learning to repeat routines without grasping what is happening.
  • Challenge through greater depth - rather than accelerated content, (moving onto next year’s concepts) teachers set tasks to deepen knowledge and improve reasoning skills within the objectives of their year group.

 

Curriculum Design and Planning

Staff use White Rose Maths Schemes of Learning as a starting point in order to develop a coherent and comprehensive conceptual pathway through the mathematics, alongside the NCETM Learning Spines for introducing key concepts in small steps. The focus is on the whole class progressing together. Collaborative planning with year group colleagues is encouraged to ensure consistency.

Learning is broken down into small, connected steps, building from what pupils already know. The lesson journey should be detailed and evident on lesson slides as there is no requirement for teachers to produce detailed paper plans.

Difficult points and potential misconceptions are identified in advance and strategies to address them planned. Key questions are planned, to challenge thinking and develop learning for all pupils. Contexts and representations are carefully chosen to develop reasoning skills and to help pupils link concrete ideas to abstract mathematical concepts

The use of high-quality materials and tasks to support learning and provide access to the mathematics, is integrated into lessons. These may include White Rose Maths Schemes of Learning and Assessment Materials, NCETM Mastery Assessment materials, NRICH, visual images and concrete resources.

All classes have a daily mathematics lesson where possible.  In Key Stage 1 lessons are 45-60 minutes and in Key Stage 2 at least 60 minutes. These lessons are taught in the morning section of the school day.

Teachers of the EYFS ensure the pupils learn through a mixture of adult led activities and pupil-initiated activities both inside and outside of the classroom.  Mathematics is taught through an integrated approach.

 

 Flashback 4/Magic 10

Magic 10 is a whole school fluency initiative, whereby at some stage every day, every class makes time to have ten minutes focusing on factual fluency. It might be first thing in the morning, or after break, or as a starter for the maths lesson.

What is involved:

  • Children singing, chanting or rehearsing a set of number facts, then representing those facts (maybe using the part/part/whole model)
  • Reciting these facts and then most importantly looking at how they can apply those facts, so they can derive other facts from that.

If I know that 12 x 4 = 48 then I also know that 12 x 40 = 480 and 120 x 40= 4800. What else do I know from this original calculation? 

 

 In Key Stage 1 , it is predominantly used for number bonds, across all numbers, so not just within ten. Then moving on to times table facts and also deriving division facts as well as multiplication facts.

In Key Stage 2 we are using it to improve and consolidate children’s time table knowledge. It has also been used for learning prime numbers to 100. Our aim is that it will improve children’s recall of any number facts they may need quickly.

Flashback 4 is another whole school approach which focuses on the consolidation of prior learning, ensuring children have secure knowledge, and to address misconceptions in learning. At a point in the day (maths lesson starter, early learning etc.) Children will answer 4 quickfire questions, which could take the form of a diagnostic style, related to learning from the previous lesson, previous week, previous term and previous year. 

 

Links

Please click here for the Maths Calculation Policy

Please click here to access our Whole School Progression of Skills. 

Please click here to access our Maths: Teaching for Mastery Policy

Please click here to access our Key Mathematical Vocabulary List