Maths
‘We Are Mathematicians’ at Powers Hall Academy
At Powers Hall Academy, we believe that the teaching of mathematics should equip children with unique, powerful tools to help them understand and make sense of the world around them. These tools include logical reasoning, problem solving skills and the ability to think in abstract ways.
Mathematics is a whole network of concepts and relationships which children can use to analyse and communicate information and ideas and to tackle a range of practical tasks and real-life problems. Mathematics is important in everyday life. It is integral to all aspects of life and we will endeavour to ensure that children develop a healthy and enthusiastic attitude towards mathematics that will stay with them and make them happy, confident lifelong learners.
The National Curriculum for mathematics aims to ensure 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 routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions. Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas.
Maths lessons are planned and delivered using the NCETM materials which draws together the DfE guidance on curriculum prioritisation and classroom resources provided by the NCETM Primary Mastery PD materials. It is underpinned by the concrete, pictorial, abstract (CPA) approach. Classrooms have a range of mathematical resources made available for children. These include, but are not limited to, Base 10, place value counters, Bead string, number lines, digit cards and a hundred squares.
Teachers use the NCETM sequencing to inform decisions on how much teaching time to set aside for the different parts of the curriculum. Teaching time is weighted towards the ready-to-progress criteria. The ready-to-progress tables at the start of each year group and the ‘Making connections’ features support medium-term planning by demonstrating how to make connections between mathematical ideas and develop understanding based on logical progression.
The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly , acceleration into new content is avoided. Instead, these students are challenged by deeper analysis of the lesson content and by applying the content in new and unfamiliar problem-solving situations to achieve greater depth. If pupils complete an activity before the rest of the class is ready to move on, we encourage pupils to deepen their learning through ‘Dive Deeper’ tasks (‘Draw it’, ‘Explain it’, ‘Make a mistake’, ‘Tell a Maths story’, ‘Prove it’).
- ‘Can you demonstrate your solution another way?’
- ‘Can you model your answers using concrete materials?
- Can you explain your solution to a partner?’
- ‘Is there another way of working out the answer? And another way?’
- ‘Have you found all the solutions?’
- ‘Is that always true?’
- ‘What’s different between this question and that question? And what’s the same?’
INTENT
High Expectations | All children are expected to succeed and make progress from their starting points. Children learn the same concept in small, cumulative steps, each finding and mastering challenge at their own level. |
Mastery Modelling | Teachers teach the skills needed to succeed in mathematics providing examples of good practice through high quality modelling and having high expectations of all pupils. We do this by using the “I do, we do, you do” approach. |
A Vocabulary Rich Environment | We intend to create a vocabulary rich environment, where talk for maths is a key learning tool for all pupils. Pre-teaching key vocabulary is a driver for pupil understanding and develops the confidence of pupils to explain mathematically. |
Making Connections | All children will have opportunities to identify patterns or connections in their maths; they can use this to predict and reason and to also develop their own patterns or links in maths and other subjects. |
Implementation
Pupils are taught through an evidence-based “I do, We do, You do” approach using worked examples (Example-Problem-Pairs) and are given the opportunity to practice using their Power Maths Practice Books. These questions are progressive and include a mix of fluency, reasoning and problem-solving so that children have opportunities to make explicit connections throughout their independent practice. Differentiation, for the most part, is outcome-based and not question-based.
Assessment questions from the year below are used at the start of a unit to check that pupils have the pre-requisite knowledge and skills. These assessment questions, based on questions in the DfE guidance, are used formatively or in low-stakes testing throughout the year.
IMPLEMENTATION
Lesson Structure | Maths lessons are designed with a concrete, pictorial and abstract (CPA) approach, providing our pupils with the scaffolding required to access the learning at all levels.
Every lesson begins with a year group specific times table activity to activate learning and reiterate the importance of fluently learning times tables and an active review session to check/build upon previous learning. This is usually the previous lesson’s reflect question.
We then move on to explicitly teach vocabulary that is relevant to the lesson, and that vocabulary is modelled consistently throughout. Stem sentences encourage children to use full sentences when reasoning, explaining or discussing maths. Pupils are then introduced to a practical (where applicable real-life) problem to investigate and arouse curiosity. Teachers use the “I do, we do, you do” approach to show mathematical thinking, display a high-quality worked example and use precise mathematical vocabulary. The repetitive nature of the model allows pupils the opportunity to practice and embed skills.
Teachers use an AFL or hinge tasks to assess which children are ready for independent practice, and scaffold where necessary. Open ended questioning is used to check for understanding and misconceptions are planned for, uncovered and addressed rather than side-stepped or ignored through modelling and timely feedback. |
Power Maths Practice | To demonstrate their mathematical understanding, children are given progressively challenging questions in their Power Maths Practice Books at age-related expectations (ARE), including varied fluency embed in reasoning questions. Our intention is that differentiation is made through outcome. |
Daily Arithmetic Practice | Daily ‘Fluent in Five’ arithmetic lessons take place in all classes. Children are given time to practice and develop a quick and efficient recall of facts and procedures including giving pupils the opportunity to make appropriate decisions when estimating, calculating and evaluating the effectiveness of their chosen methods. |
Times Tables
As the ability to recall multiplication tables is imperative to becoming a fluent, competent and confident mathematician, we strongly encourage and support children to learn their tables. At Powers Hall Academy, we believe that children should be able to go further than merely recall multiplication facts. Learning times tables begins in the classroom, where children learn about the fundamentals of multiplication and division in Maths lessons. It is vital that children have a secure conceptual understanding of the meaning of a multiplicative calculation, as opposed to just learning by rote. Once a child has demonstrated they know their multiplication tables (and any corresponding division facts), they are awarded certificates.
At Powers Hall Academy, we use Times Table RockStars as an online learning resource for children to practise their fluency and mental recall. It is an educational learning platform which is specifically designed to support children in learning and becoming more fluent in their times tables.
Exploration and practice
The broad shape of our approach used:
- Component 1: In each class, a whole half term is devoted to a new times table.
- Component 2: Within that half term, three whole lessons are devoted to exploring each new times table – developing connections, exploring the patterns and creating a deeper understanding of multiplicative reasoning
- Component 3: Three or more times a week in every class there’s a five- to ten-minute ‘retrieval practice’ session, including one or more of the following: games, counting-stick work, step counting using manipulatives, chanting and technology-based, quick-reaction exercises. Pupils will then be asked to complete a 60 mixed practice question test.
Impact
Pupil Voice | Through discussion and feedback, children talk enthusiastically about their maths lessons and speak about how they love learning about maths. They can articulate the context in which maths is being taught and relate this to real life purposes. Children show confidence and believe they can learn about a new maths area and apply the knowledge and skills they already have. |
Evidence in Knowledge | Pupils know how and why maths is used in the outside world and in the workplace. Mathematical concepts or skills are mastered when a child can use an appropriate representation and mathematical language to explain their ideas, and can independently apply the concept to new problems in unfamiliar situations. Children demonstrate a quick recall of facts and procedures. This includes the recollection of the times tables. |
Evidence in Skill | Pupil’s use acquired vocabulary in maths lessons. They have the skills to use methods independently and show resilience when tackling problems. The flexibility and fluidity to move between different contexts and representations of maths. They will use arithmetic and timetables fluently and make connections in order to solve real life problems. Children show a high level of pride in the presentation and understanding of the work. |
Outcomes | Children will make good progress in Mathematics from their last point of statutory assessment. Children who have gaps in their knowledge receive appropriate support and intervention. |