At Park we have a passion for high quality teaching and learning of mathematics. We believe that every child can succeed in maths and we aim to instil this belief in the children themselves.
The national curriculum for maths requires that all pupils:
- Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately
- Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
- Can solve problems by applying their mathematics to a variety of routing and non-routing problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions
Mathematics Mastery Curriculum
At Park, we embed the ‘mastery approach’ which relies on deep conceptual understanding. 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.
This is achieved through the Dimensions of Depth:
- Mathematical thinking
- Conceptual understanding
- Language and communication
Mathematical thinking – pupils need to think like mathematicians, rather than DO the maths. At Park, we believe that pupils should: explore, wonder, question, make theories, compare, classify, sort and play with possibilities. This is achieved through carefully prepared maths activities, as well as effective questioning which allows children to compare, modify and generalise, all building a deeper understanding of maths.
Conceptual understanding – refers to the ‘deep understanding’ of maths demonstrated through the ability to represent ideas in many different ways. At Park, we have taken on this approach by embedding a 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.
- 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.
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.
Language and communication
At Park, we believe that pupils should be encouraged to use mathematical language and full sentences throughout their maths learning to deepen their understanding of concepts. This is continuously assessed within each maths lesson through children’s articulation and explanation of a new concept and the careful links made between concepts.
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.
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