A high-quality mathematics education provides our pupils with the foundations for understanding much about the exciting world they live in, through the varied topics within the subject curriculum. Maths has helped to shape lives in the modern world and has generationally improved people’s prosperity. Therefore, all pupils at St. Paul’s are taught essential aspects of maths, contextualised and applied directly in the subject itself, and within the wider curriculum. Maths learning at St. Paul’s serves to drive curiosity in the theories and models, develop the pupils as mathematical explorers and create independently engaged learners. Gaining an understanding of the subject this way, fosters an appreciation of the ‘power’ of maths, provide financial literacy and helps to broaden their opportunities and make them life-long learners who love Maths! Therefore, Maths must and does take a central position within St. Paul’s, ensuring we are mathematicians together who inspire each other.
Through building up a body of key knowledge, pupils recognise the influence of maths in their everyday lives and the importance of thinking mathematically. They develop knowledge of the fundamental mathematical concepts and language, become fluent in vital calculation methods, whilst reasoning logically and applying what they know to solve problems. As they mature as learners, they gain a holistic view of maths and recognise the connective nature of all of its elements – developing their mathematical awareness further, as they move forward in their lives.
How Mathematics is taught at St. Paul’s.
The national curriculum for mathematics sets a number of key learning goals:
- 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 routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions
At St. Paul’s, we recognise that the study of maths is a highly interconnected practice, which requires a multi-disciplinary approach to both teaching and learning – as such we have adopted models that support this. Furthermore, as a family of learners, we continually evaluate the way we deliver maths to meet the changing needs of our community and the latest research in learning.
All learning requires an initial input of knowledge and as such this represents the ‘new learning’ phase. Core blocks of study are planned and delivered to introduce pupils to or develop their knowledge of, the fundamental concepts at each stage or phase of their learning. These are programmed and mapped to fit with our whole curriculum – they provide teachers and learners with a ‘base’ for development.
Through the programme, pupils will learn fluency in key mathematical operations, related to each concept, ensuring that at the same time they gain an understanding of the specialist language associated with all areas of the field of study.
Please click here to view a copy of our calculation policy.
Central to the learning journey, is also the need for pupils to reason and problem solve – learning to select the correct strategy for each problem encountered. As such at St. Paul’s, every maths lesson incorporates an element of reasoning, so that this skill is well practised. Every attempt is also made to provide pupils with real life references and experiences where they can apply their mathematical knowledge.
Please click here to view a copy of our Long Term Plan for Maths
Please click here to view a copy of our Maths Subject Pathway
Our Learning approaches:
Here at St. Paul’s we also recognise that varied, planned and adaptable approaches to the learning process enhance outcomes for pupils and enable teachers to support individual learning needs. Specifically, we identify with four key strategic methods, when teaching maths at St. Paul’s. (See diagram below)
- Blocked delivery of new learning, to introduce concepts and or stages of mathematics.
- Spaced learning delivery, to promote recall, retention and application within varied contexts – allowing pupils to re-visit, develop and consolidate knowledge and skills gained during initial blocked phases, minimising risks of regression between associated blocks.
- Interleaved learning, incorporating varied mathematical concepts during one period of time - requiring the pupil to draw upon and select the correct strategy to solve problems or complete calculations, which have been deliberately mixed. This requires a greater degree of mathematical thinking.
- Continuous Provision – pupils are provided with and directed to independent exploration and development opportunities around mathematical concepts, where a need has been identified or teachers have identified an opportunity to facilitate further practice.
Throughout the school, implementation of maths learning is supported by dedicated time for the subject, including core lessons, basic skill sessions and targeted interventions. Maths learning is derived from either the curriculum map, outcomes of varied formative and summative assessments, or from the provision of planned cross-curricular learning activities.
Within Phase 1 and Phase 2, maths learning is also drawn from and supported by the ‘Mathematics Mastery’ programme. Click here for more information about Mathematics Mastery.
Encouraging Mathematical Thinking
Mathematical thinking plays a key role in the successful understanding of maths and is something that must be taught. Many pupils overlook their ability to think mathematically, favouring a focus on procedural elements of maths – seeking what might be perceived as the ‘correct’ answer, as this is automatically intrinsically rewarding. With the latter approach, little thought is given as to why something is done in a particular way, or even whether it could have been achieved with an alternative method or approach. This misconceived technique can lead to mechanical and robotic thinking and an inability to succeed in novel situations, because they think that they have ‘not done this before.’
Mathematical thinking is more than just arithmetic or solving a problem with a recognised method- it’s about breaking something down into its parts and analysing the underlying patterns. Maths is all about patterns! The ability to see these patterns in maths can then also aid the student in identifying patterns within nature and wider society, once again enhancing a student’s appreciation for and curiosity of maths. It is the quality of the questions pupils ask and are asked during maths, that leads to great mathematical thinking, not just the process of completing set calculations.
On identifying mathematical tasks, it is important that pupils explore the situation, with sufficient time and on a regular basis – this is how we encourage mathematical thinking at St. Paul’s: through spaced, interleaved and continuous provision opportunities. Furthermore, pupils are encouraged to consider mathematical tasks in stages or steps:
- Split tasks into smaller parts and or steps
- Make connections with similar or previous tasks that they may have done
- Carefully select appropriate knowledge and skills
- Consider assumptions that might be made (correct or incorrect)
- Select an appropriate strategy
- Consider possible alternative approaches – ‘rule them out’
- Look for patterns and connections
- Create further examples to help prove the technique works.
At St. Paul’s, it is the journey that matters more – we must be able to consider alternative routes to our destination (answer), if we are to travel through the world of maths and become mathematicians of the future.
Helping your child with Mathematics.
Parents are an integral part of a child’s ‘learning journey’ and more so than you might imagine for the learning of mathematics. There are many activities you can either encourage your child to do, support then with, or join them with and so learn together. Here are a few suggestions:
- Encourage them to regularly practice timetables and number facts – a great place to do this is online at either their individual Times Tables Rock Stars account (click here) or at the ‘Hit The Button’ website (click here).
- Play maths games with them: from Sudoku to Monopoly.
- Involve your child in real world maths conversations: discussing the cost of shopping and associated money facts; measuring length as part of a DIY project; calculating distances on a journey; counting items and sharing them out. The opportunities are endless and apply to real-world maths.
- Supporting them with maths homework – exploring the methods and reasoning, not just looking for the answer.
- Take the opportunity to learn something new with them – recap your own understanding.
- Speak to your child’s teacher or the Maths Lead (Kirsty Morrison) at St. Paul’s, if they are unclear about their maths learning.