Maths at St Mary's
Benjamin Franklin: "No employment can be managed without arithmetic, no mechanical invention without geometry."
Carl Friedrich Gauss: "Mathematics is the queen of science, and arithmetic the queen of mathematics."
At St Mary’s we have a mastery approach to the teaching and learning of maths that focuses on the development of mathematical vocabulary, knowledge and understanding. This enables our pupils to make purposeful links between concepts so skills can be applied in a range of different mathematical contexts. We want learners to think about maths beyond what is tested in national examinations and to be equipped with an understanding of mathematics that will be relevant and useful in their future studies and/or in the world of work.
We follow the Mathematics Mastery Program from Early Years through to Year 6 as the program has been designed on principles to provide learners with a deep conceptual understanding of mathematical principles, the ability to confidently communicate in precise mathematical language, while becoming mathematical thinkers.
Principle 1: Conceptual Understanding
Mathematics tasks are about constructing meaning and making sense of relationships. Learners deepen their understanding by representing concepts using objects, pictures, symbols and words. Different representations stress and ignore different aspects of a concept and so moving between representations and making explicit links between them allows learners to construct a comprehensive conceptual framework that can be used as the foundation for future learning. We use the content of the national curriculum as the starting point for our curriculum but this is expanded upon by making explicit the foundational knowledge that learners need to understand in order to access this. Tasks are sequenced to help learners build a narrative through different topics. These topics are then sequenced in a logical progression that allows learners to establish connections and draw comparisons. Multiple representations are carefully selected so that they are extendable within and between different areas of mathematics. Using these rich models encourages learners to develop different perspectives on a concept.
Principle 2: Language and Communication
Mathematical language strengthens conceptual understanding by enabling pupils to explain and reason. This must be carefully introduced and reinforced through frequent discussion to ensure it is meaningfully understood. The more learners use mathematical words the more they feel themselves to be mathematicians. Talk is an essential element of every lesson and time is dedicated to developing confidence with specific vocabulary as well as verbal reasoning. The content of our curriculum carefully progresses in order to induct learners into the mathematical community. A large part of this community is confident use of the language, signs and symbols of mathematics. Verbal and non-verbal communication is part of every sequence of learning in the curriculum. This often starts with more informal language initially, building up to formal and precise mathematical language. Talk tasks are part of every lesson in the curriculum to help with this development.
Principle 3: Mathematical Thinking
By the time they reach school, all pupils have demonstrated a significant range of innate ways of thinking that can be harnessed in the classroom to develop mathematical thinking. We must support pupils to develop mathematical ‘habits of mind’ – to be systematic, generalise and seek out patterns. The creation of a conjecturing environment and considered use of questions and prompts are important elements of encouraging learners to think like mathematicians. Our curriculum is designed to give learners the opportunities to think mathematically. Throughout the curriculum you will see tasks that require learners to specialise and generalise, to work systematically, to generate their own examples, to classify and to make conjectures. This is aided by our prompts for thinking which help make these important parts of mathematics more explicit.
Our maths lessons are delivered with confidence in the knowledge that if a student understands the core principles, they will be able to remember more and do more maths, in whatever context they encounter it.
The six-part lesson
The Mathematics Mastery lesson follows a six-part lesson structure.
1. Do Now
The purpose of the Do Now task is to consolidate previous learning. This could be recapping on what was learnt the day before, a topic from a previous unit that is necessary for the current lesson or a fluency focus.
2. New Learning
The New Learning section introduces the main learning for the lesson, beginning by sharing the lesson’s key vocabulary with the pupils. This segment will require clear explanations and modelling of tasks.
2. Talk Task / Let’s Explore
As language is such an important feature of Mathematics Mastery, Talk Tasks are imperative. This segment allows talking about maths and comprehension to be developed, and provides opportunities to use mathematical language.
4. Develop Learning
The Develop Learning segment is designed to mirror the New Learning earlier in the lesson, but aims to move the pupils’ learning on further and deepen their understanding.
5. Independent Task
This segment gives pupils the opportunity to practise their Develop Learning by working independently and demonstrating what they have understood and learnt. Task will be adapted so they challenge everyone in the class. Whilst the pupils are working independently, teachers will assess progress to pick up on any pupils that are struggling, and to direct how the plenary will be used.
The final part of the lesson is used to reflect on learning, gather evidence for assessments and plan for future learning. It is used to sum up what the children have learnt during the lesson, consolidating all learning, address any common misconceptions, and pose a question for the next lesson.
Daily Maths Meeting, are used to consolidate key areas of mathematics in each year group. Maths Meetings provide an opportunity to teach and revise 'general knowledge maths' which may not explicitly be covered during the maths lesson, and also allows the daily integration of maths into the surrounding environment. This means that pupils are practising concepts and skills on a regular basis, meaning they are continually building on their mastery of these concepts.