Mathematics at Kingston Community School.
We use the Mathematics Mastery approach to teach Maths across the year groups. The following information is taken from the Mathematics Mastery website to explain the approach in more detail.
The ‘mastery approach’ to teaching maths is the underlying principle of Mathematics Mastery. Instead of learning mathematical procedures by rote, we want pupils to build a deep conceptual understanding of concepts which will enable them to apply their learning in different situations
The Mathematics Mastery curriculum is cumulative – each school year begins with a focus on the concepts and skills that have the most connections, which are then applied and connected throughout the school year to consolidate learning. This gives pupils the opportunity to ‘master maths’; by using previous learning throughout the school year, they are able to develop mathematical fluency and conceptual understanding
So how do we avoid teaching procedures and instead get pupils to develop a deep understanding in mathematics?
1 We use our Dimensions of Depth to deepen pupils’ understanding.
These are: Conceptual understanding; Language and communication; Mathematical thinking; Problem solving is at the heart of the mastery approach, so we make sure to dedicate sufficient time to each new concept so every pupil can gain the reasoning they need to solve new problems in unfamiliar contexts.
In Mathematics Mastery, our pupils are expected to all solve the same investigations by the end of the lesson, meaning the key concepts and objectives are met by all pupils. Instead of accelerating higher attainers onto new content, we differentiate through depth, to develop pupils’ conceptual understanding.
Conceptual Understanding: A crucial part of a ‘deep understanding’ in maths is being able to represent ideas in many different ways. Using objects and pictures to represent abstract concepts is essential to achieving mastery.
At Mathematics Mastery, we have taken on this approach by developing Concrete-Pictorial-Abstract (CPA) representations. Reinforcement of learning is achieved by going back and forth between these representations, building pupils’ conceptual understanding instead of an ‘instrumental understanding’.
- Concrete – the doing: A pupil is introduced to an idea or a skill by acting it out with real objects. This is a ‘hands on’ component using real objects and it is the foundation for conceptual understanding. ‘Concrete’ refers to objects such as Dienes apparatus, fraction tiles, counters, or other objects that can be physically manipulated.
- Pictorial – the seeing: A pupil may also begin to relate their understanding to pictorial representations, such as a diagram or picture of the problem.
- Abstract – the symbolic: A pupil is now capable of representing problems by using mathematical notation, for example: 12 ÷ 2 = 6. This is the most formal and efficient stage of mathematical understanding. Abstract representations can simply be an efficient way of recording the maths, without being the actual maths.
We believe the meaning of symbols must be firmly rooted in experiences alongside real objects and pictorial representations, otherwise this becomes rote repetition of meaningless memorised procedures. Concrete and pictorial representations support with the development of a deep conceptual understanding.
We believe it is essential for pupils to develop mathematical thinking in and out of the classroom in order to fully master mathematical concepts. We want children to think like mathematicians, not just DO the maths.
- We believe that pupils should:Explore, wonder, question and conjecture,
- Compare, classify, sort,
- Experiment, play with possibilities, vary an aspect and see what happens,
- Make theories and predictions and act purposefully to see what happens, generalise.
It is important that we support all pupils in developing their mathematical thinking, both in order to improve the way in which they learn, as well as the learning itself. Good questioning can be used to develop pupils’ ability to compare, modify and generalise, all building a deeper understanding of mathematics.
Language and communication
We believe that pupils should be encouraged to use mathematical language and full sentences throughout their maths learning to deepen their understanding of concepts. Every Mathematics Mastery lesson provides opportunities for pupils to communicate and develop mathematical language through:
- Sharing the key vocabulary at the beginning of every lesson in the Do Now section, and insisting on its use throughout;
- Modelling clear sentence structures and expecting pupils to respond using a full sentence;
- Talk Task activities, allowing pupils to discuss their thinking and reasoning of the concepts being presented;
- Plenaries which give a further opportunity to assess understanding through pupil explanations.
Pupils should revisit mathematical language from previous years and explore the concepts in greater depth. There should be opportunities for pupils to clarify vocabulary and explore activities that develop an understanding of the different concepts.
We believe that a problem-solving approach is the key to mathematical success, and should be used continually throughout lessons to build on depth of understanding.
At Mathematics Mastery, problem solving is at the heart of our curriculum as the essence of everything we do as mathematicians. Problem solving should not be an add-on at the end of a maths lesson or a weekly investigation lesson.
Pupils must be given every opportunity to explore, recognise patterns, hypothesise and be empowered to let problem solving take them on new and unfamiliar journeys. Even the most straightforward tasks can be an opportunity for pupils to investigate, seek solutions, make new discoveries and reason about their findings.