We at Westminster Cathedral Primary School teach maths for mastery. It is a transformational approach to maths teaching which stems from high performing Asian nations such as Singapore. Teachers have access to extensive online- daily planning, online resources, textbooks, workbooks and concrete mathematical manipulative as well as termly curriculum objective overviews.
The method used to help our pupils with calculations has been devised to meet requirements of the National Curriculum for the teaching and learning of mathematics. It is also designed to give pupils a consistent and smooth progression of learning in calculations across the school.
Teaching maths for mastery: The whole class works through the programme of study at the same pace with ample time on each topic before moving on. Ideas are revisited at higher levels as the curriculum spirals through the years.
Differentiated activities : Tasks and activities are designed to be easy for pupils to enter while still containing challenging components. For advanced learners, the textbooks also contain non-routine questions for pupils to develop their higher-order thinking skills.
Problem solving: Lessons and activities are designed to be taught using problem-solving approaches to encourage pupils’ higher-level thinking. The focus is on working with pupils’ core competencies, building on what they know to develop their relational understanding, based on Richard Skemp’s work.
Variation: The questions and examples are carefully varied by expert authors to encourage pupils to think about the maths. Rather than provide mechanical repetition, the examples are designed to deepen pupils’ understanding and reveal misconceptions.
International research: By incorporating established learning research into a highly effective approach, Singapore has become a “laboratory of maths teaching”. The Primary Maths Series is founded on the international research of Piaget, Dienes, Bruner, Skemp and Vygotsky and has been tested and refined over the last 30 years in Singapore.
UK evidence: The MNP Primary Series was assessed by the DfE’s expert panel, which judged that it met the core criteria for a high-quality textbook to support teaching for mastery. As a result, the Maths – No Problem! Primary Series are recommended textbooks for schools on the mastery programme.
The Primary Series is one of the few textbooks that complies with the UK’s high-quality textbook guidance published by the National Centre for Excellence in Teaching Mathematics (NCETM).
Concrete, Pictorial, Abstract (CPA) approach: Based on Jerome Bruner’s work, pupils learn new concepts initially using concrete examples, such as counters, then progress to drawing pictorial representations before finally using more abstract symbols, such as the equals sign.
Pupils can be first introduced to an idea or skill by acting it out with real objects (a hands-on approach).
Pupils then are moved onto the visual stage, where pupils are encouraged to relate the concrete understanding to pictorial representations. The final abstract stage is a change for pupils to represent problems by using mathematical notion.
Pupils are taught strategies to develop and strengthen their mental agility on a daily basis. They also need to be able to apply written calculation skills in order to:
• represent work that has been done practically
• support, record and explain mental calculation
• keep track of steps in a longer task
• work out calculations that are too difficult to do mentally
Children become confident in choosing and using a strategy that they know will get them to the correct answer as efficiently as possible; pupils are free to choose their preferred method to solve calculations. Although we’ve discussed CPA as three distinct stages, a skilled teacher will go back and forth between each stage to reinforce concepts.
Alongside the scheme it is agreed that teachers are given the freedom to deviate slightly if they deem necessary as a result of using their professional judgement and formative assessment skills. This means some calculations may be concise or some may be referred to at a later stage.
It is also noted that some SATs-style revision may not always follow the regimented MNP scheme for every set of lessons. However, it is important to add that MNP strategies and principles will incorporate their overall Year 6 learning experience.