Learning & Teaching Mathematics at Greenleas
The content and principles underpinning the 2014 mathematics curriculum reflect those found in high performing education systems internationally, particularly those of east and south-east Asian countries such as Singapore, Japan, South Korea and China. Although there are many differences between the education systems of England and those of east and south-east Asia, we can learn from the ‘mastery’ approach to teaching commonly followed in these countries. Greenleas has established the principles and features which characterise this methodology to address the three aims of the National Curriculum – Fluency – Reasoning – Problem Solving.
Following a successful trial of textbooks five years ago, Maths No Problem resources and textbooks are used across the school in years one to four to support our Teaching for Mastery approach.
- Whole class together – we teach mathematics to whole classes and all children are encouraged to believe that by working hard they can succeed in maths. Lessons are planned based on formative assessment of what is already known and we include all children in learning mathematical concepts. At the planning stage, teachers consider what scaffolding may be required for children who may struggle to grasp concepts in the lesson and suitable challenge questions for those who may grasp the concepts rapidly. Decisions are not made about who these children may be prior to the lesson.
- Longer and deeper – in order to address the aims of the National Curriculum, our planning has been adjusted to allow longer time to be spent on topics. Each lesson focuses on one key conceptual idea and connections are made across mathematical topics. It may appear that the pace of the lesson is slower, but progress and understanding is enhanced. Our assessment procedures recognise that the aims of the curriculum are addressed through depth within a topic.
- Key learning points are identified during planning (collaboratively in year groups) and a clear journey through the maths is shown in lessons and also reflected on working walls. Carefully planned questions will probe pupil understanding throughout. Teachers model the key learning points in full sentences and responses are expected back in full sentences, using precise mathematical vocabulary. Stem Sentences are used to scaffold and enable the teacher to provide a sentence starter for children to communicate their ideas with more mathematical precision and clarity. These stem sentences express the key learning points and help build understanding and embed knowledge.
- Difficult points and potential misconceptions are identified during the planning process and used as opportunities for learning. Children are then supported through these.
- Fluency – We recognise that ‘fluency’ is not just about remembering facts and aim to develop all aspects of fluency through lessons. As a school we focus on instant recall of key facts, such as number bonds, addition, subtraction and multiplication table facts. Increasing fluency in basic facts allows children to free up working memory to solve more complex problems.
- Split lesson – Maths lessons are split into two 30 minute sessions. Dividing the maths in this way affords the optimum time to sustain children's concentration and allows for concepts and methods to be recalled and applied after a short break so building them into long term memory.
- Exploration - instead of ‘Let me teach you…’ as a starting point, children are encouraged to explore a problem themselves to see what they already know. At the beginning of each lesson this exploration is begun with an ‘anchor task’. Lesson objectives are not always shared with children at the beginning of the lesson because we wish the children to reason for themselves. At some point from the middle or even at the end of the lesson, the children may be asked to reflect on what they have been learning that day.
- Develop reasoning and deep understanding – problems are usually set in real life contexts with carefully chosen representations (manipulatives and images) used by all to explore concepts. The use of practical resources, pictorial representations and recording takes place in every lesson following the Concrete Pictorial Abstract approach (CPA).
- Structuring - the teacher will organise the findings of the exploration, comparing and contrasting strategies to guide towards the most efficient strategy (or the one being learned that day).
- Step by step approach – ensures a carefully considered journey through the mathematics is developed. At the beginning of a lesson or when introducing a new concept these steps are small to build coherence. Through careful representation and variation links and jumps can be made and an extra challenge introduced.
- Questions – teachers use carefully planned questioning throughout every lesson to check understanding and to challenge thinking. A variety of questions are used to foster different levels of thinking e.g. How do you know? Can you prove it? Are you sure? Is that right? What’s the same/different about…? Can you explain that? What does your partner think? Can you imagine? Questions are also used to explore in greater depth for children who have grasped the concept.
- Discussion and feedback – children have opportunities to talk to their partners and explain or clarify their thinking throughout the lesson. They are expected to listen to each other’s responses and may be asked to explain someone else’s ideas in their own words, or share their own reasoning, including whether they agree or disagree.
- Practising - not drill and practice, but intelligent practice characterised by carefully considered variation. Children use the Maths No Problem workbooks which they are expected to complete independently to apply and practise what they have learned at the beginning of the lesson.
- Journal – the use of journals gives children opportunities to reflect on their learning. Answers to maths problems are recorded along with strategies used and thinking.
- Rapid intervention (same day catch up) – in mathematics lessons new learning is built upon previous understanding. In order for learning to progress and to keep the class together, areas of difficulty are dealt with as and when they occur. These are addressed through same day intervention.
- Marking – the marking policy follows the NCETM guidance published in April 2016. Children’s work is highlighted with green or orange, and a comment will only be made if this is necessary to move learning forward. The most valuable feedback will be given verbally and immediately, during lessons.
At Greenleas we aim to nurture a Growth Mindset ethos. We have high expectations of all children and believe that everyone can achieve in mathematics if they work hard and are given opportunities to practise. Challenge is provided through problem solving to achieve a greater depth of understanding. We also recognise that some children may need longer to grasp concepts and require careful scaffolding or extra time and support.