MATHEMATICS

Teaching for Mastery in Maths

Over the last three years at Tyntesfield Primary School, we have been developing a Teaching for Mastery approach to maths. Working with Mastery Specialists within the school and in collaboration with the Turing Maths Hub, we have been able to observe lessons delivered by specialist teachers, as well as developing our subject knowledge, which has led to a deep and sustainable understanding of maths, which has then been passed on to pupils. It has been an exciting journey, which included a Shanghai exchange and enabled pupils to be taught by Shanghai teachers in showcase lessons, shared with other local schools. Below is some further information on the principles of Teaching for Mastery.

What does it mean to master mathematics?


A mathematical concept or skill has been mastered when a pupil can represent it in multiple ways, has the mathematical language to communicate related ideas, and can independently apply the concept to new problems in unfamiliar situations.


Mastery is a journey and long-term goal, achieved through exploration, clarification, practice and application over time. At each stage of learning, pupils should be able to demonstrate a deep, conceptual understanding of the topic and be able to build on this over time.


This is not about just being able to memorise key facts and procedures, which tends to lead to superficial understanding that can easily be forgotten. Pupils should be able to select which mathematical approach is most effective in different scenarios.


All pupils can achieve in mathematics


It is not the case that some pupils can do mathematics and others cannot. The focus is keeping up over catching up. By making high expectations clear and emphasising the value of mathematics education, pupils are encouraged to build confidence and resilience. Abilities are neither fixed nor innate, but can be developed through practice, support, dedication and hard work. Natural talent is just a starting point and does not determine who has more or less potential to achieve.


Deepen understanding before accelerating content coverage


All pupils benefit from deepening their conceptual understanding of mathematics, regardless of whether they've previously struggled or excelled. Pupils must be given time to fully understand, explore and apply ideas, rather than accelerate through new topics. This approach enables pupils to truly grasp a concept, and the challenge comes from investigating it in new, alternative and more complex ways.

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Concrete, Pictorial, Abstract


Objects, pictures, words, numbers and symbols are everywhere. The mastery approach incorporates all of these to help pupils explore and demonstrate mathematical ideas, enrich their learning experience and deepen understanding. Together, these elements help cement knowledge so pupils truly understand what they’ve learnt.


All pupils, when introduced to a key new concept, should have the opportunity to build competency in this topic by taking this approach. All pupils are encouraged to physically represent mathematical concepts. Objects and pictures are used to demonstrate and visualise abstract ideas, alongside numbers and symbols.


Concrete – Students should have the opportunity to use concrete objects and manipulatives to help them understand and explain what they are doing.


Pictorial – Students should then build on this concrete approach by using pictorial representations. These representations can then be used to reason and solve problems.


Abstract – With the foundations firmly laid, students should be able to move to an abstract approach using numbers and key concepts with confidence.


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Teaching supports the aims of the National Curriculum

Problem solving

Mathematical problem solving is at the heart of our approach. Pupils are encouraged to identify, understand and apply relevant mathematical principles and make connections between different ideas. This builds the skills needed to tackle new problems, rather than simply repeating routines without a secure understanding.


Mathematical concepts are explored in a variety of representations and problem-solving contexts to give pupils a richer and deeper learning experience. Pupils combine different concepts to solve complex problems, and apply knowledge to real-life situations.


Reasoning

The way pupils speak and write about mathematics transforms their learning. Mastery approaches use a carefully sequenced, structured approach to introduce and reinforce mathematical vocabulary. Pupils explain the mathematics in full sentences. They should be able to say not just what the answer is, but how they know it’s right. This is key to building mathematical language and reasoning skills.


Fluency

Pupils should be able to recall and apply mathematical knowledge both rapidly and accurately. However, it is important to stress that fluency often gets confused for just memorisation – it is far more than this. As well as fluency of facts and procedures, pupils should be able to move confidently between contexts and representations, recognise relationships and make connections in mathematics. This should help pupils develop a deep conceptual understanding of the subject.


Secure the fundamentals

A large proportion of time is spent reinforcing number to build competency and fluency. Number is usually at the heart of any primary mastery scheme of learning, with more time devoted to this than other areas of mathematics. It is important that pupils secure these key foundations of maths before being introduced to more difficult concepts.


This increased focus on number will allow pupils to explore the concepts in more detail and secure a deeper understanding. Key number skills are fed through the rest of the scheme so that students become increasingly fluent.


Adapted from https://www.tes.com/teaching-resources/teaching-fo...

September 2019

Thumbnail Title File Size File Type Download
Year 1 AgeRelatedExpectations.pdf 162.87 KB PDF
Year 2 AgeRelatedExpectations.pdf 163.40 KB PDF
Year 3 AgeRelatedExpectations.pdf 163.75 KB PDF
Year 4 AgeRelatedExpectations.pdf 164.20 KB PDF
Year 5 AgeRelatedExpectations.pdf 164.91 KB PDF
Year 6 AgeRelatedExpectations.pdf 163.53 KB PDF

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