Mathematics at Four Lanes Infant School
In September 2017, we began a journey to develop and improve the teaching and learning of mathematics through ‘Teaching for Mastery’. Our school is part of the Primary Mastery Specialist Training programme (Cohort 3) run by the NCETM (National Centre for Excellence in Teaching Mathematics) and we are working with the support of the Surrey Plus and Solent Maths Hubs to develop our expertise in Teaching for Mastery, initially in KS1 but also within the EYFS. This expertise is then being used to support other schools in developing Teaching for Mastery.
Why Teach for Mastery?
At Four Lanes Infant School we are not only passionate that every child achieves to the best of their potential, but further, that children master the mathematics they learn and are confident mathematicians as they progress. We want children to have:
- Deep and sustainable learning
- The ability to build on something that has already been sufficiently mastered
- The ability to reason about a concept and make connections
- Conceptual and procedural fluency
Teaching for Mastery fully supports these aims through:
- The belief that all pupils can achieve
- Keeping the class working together so that all can access and master mathematics
- Development of deep mathematical understanding
- Development of both factual/procedural and conceptual fluency
- Longer time on key topics, providing time to go deeper and embed learning
Features of Planning for Mastery
- Whole class together - we teach mathematics to whole classes whilst being careful not to make assumptions of learns by 'ability' group the. Our philosophy is one of equity rather than equality, recognising that teaching for mastery is not a 'one size fits all' approach. As a result, we promote equal outcomes instead of equal treatment. At the planning stage, teachers consider modifications or adaptations which may be required should learners struggle to grasp concepts and, for those who grasp concepts quickly within a lesson, the teachers tasks of a greater depth to challenge and deepen the learners' understanding further, rather than simply accelerating to new content.
- Longer but deeper – In order to address the aims of the NC, our long/medium term plans have been adjusted to allow longer on topics. We are proud to be using the White Rose materials and some DfE approved textbooks (Maths No Problem) to support this approach to the teaching and learning of mathematics. Each lesson develops the concept from the previous one in logically sequenced small-steps so that progress and understanding is enhanced.
- Key learning points – These are identified during planning and a clear journey through the maths should be shown on flipcharts. Deep questioning will probe learners’ understanding throughout and responses are expected in full sentences, using precise mathematical vocabulary.
- Fluency – We recognise that ‘fluency’ is not just about remembering facts and we develop all aspects of fluency through lessons. This is clear to see when looking at planning and flipcharts. Learners are provided with opportunities to develop their understanding of the relationships between numbers and properties of operations. They are also encouraged to develop and select efficient strategies for fact retrieval through regular practice, although this is an area we are still developing.
Features of Teaching for Mastery
- Lesson structure – lessons are broadly structured into 3 main parts:
- Fluency Focus – A practise or revisit of those all-important facts which children need at their fingertips in order to learn new mathematics without experiencing cognitive overload.
- Guided teaching or Talk Task – This is a period of in-depth instruction by the teacher. It is an opportunity for learners to begin to acquire the new concept and for the teacher to extend their understanding through carefully structured questioning and examples in a ‘Ping-Pong’ style. Learners are very active, practising or exploring the new ideas alongside the adult teaching, repeating Stem Sentences and using precise mathematical vocabulary. Often learners will be exploring a range of concrete resources to support their thinking and expose the key mathematical concepts. Partner or group-work is often employed in this stage encouraging discussion and collaboration. Any learners that need support may have a teaching assistant nearby to assist them in their thinking.
- Independent practice – This is where learners will apply their learning. During this time, adults may be working with a group who have been identified as requiring further support or extension. Tasks are carefully structured to scaffold and progress learners’ understanding, exposing the mathematics and difficult points, to provide intelligent practice, not mechanical repetition. Depth is achieved through sophisticated, rich challenges available to all learners, in order to deepen understanding and develop reasoning and problem-solving skills.
- Multiple models and representations – To help learners make connections and see links, we expose children to a wide variety of representations and mathematical structures (e.g. tens frames, arrays, Numicon, Dienes, part-whole model), employing conceptual variation. We encourage exploration and comparison of different examples as well as non-examples so that learners may better understanding a concept through exploring what it is as well as what it is not. This approach encourages deeper understanding as well as the making of connections between concepts/domains.
- Step-by-step approach – The journey through each lesson is built on carefully structured steps in order to expose the mathematics of the concept being taught with small enough jumps between ideas to try to enable all learners to keep up.
- Resources and pictures – As the Mastery curriculum relies heavily upon the CPA (concrete-pictorial-abstract) model, an investment in resources has been (and continues to be) made. These materials are used to support concept building and reasoning through ‘doing’. They then move to the pictorial stage alongside the concrete, which then encourages the learner to make a mental connection between the physical object and abstract levels of understanding by drawing or looking at pictures, circles, diagrams or models which represent the objects in the problem.
- Questions – To develop deeper understanding and the ability to reason and explain, teachers use effective questioning throughout every lesson to check understanding and prompt thinking. A variety of questions are used but common ones might include: How do you know? Can you prove it? Why? What has changed/stayed the same? What’s the same/different about? Can you explain…? What if…? My friend says…Do you agree? What do you notice? More complex questions are also used to challenge learners who have grasped the concept earlier. Learners are expected to listen to each other’s responses and may be asked to explain someone else’s ideas in their own words, or if they agree/disagree etc.
- Talk – Discussion is a powerful and essential element of each lesson. Learners have frequent opportunities to talk to their partners so that they may explain/clarify their thinking throughout the lesson, as well as opportunities for discussion with the teacher which helps develop their reasoning skills and deeper understanding.
- Mistakes and misconceptions – The importance of the role of making mistakes and using them as opportunities for growth is fully utilised by teachers as part of our ethos of promoting a Growth Mindset. Mistakes are celebrated as important learning opportunities for all, encouraging a positive attitude and resilience.
- Practise – Enough time is given to intelligent practise to enable pupils to grasp concepts fully, but the examples are varied systematically to move learners’ understanding on as they proceed. This is achieved through Conceptual Variation, altering what the concept might look like by using a variety of representations and models, alongside Procedural Variation, for example changing the numbers used in a carefully-structured sequence of problems to expose any difficult points in a scaffolded way, to achieve deeper understanding.
- Reasoning and Problem-solving– We understand that developing strong reasoning skills is an essential process and teaching and capturing this is a developing element of our practice. Each lesson aims to provide the opportunity for all learners to solve problems and reason, encouraging deeper understanding, generalisation and building links to other concepts. Any children who appear to have grasped a concept quite quickly will be challenged to tackle more in-depth problems, which may be inspired by NCETM Mastery or White Rose materials, as well as to explain and justify their answers, through use of precise mathematical language, verbally or written, or using pictures to demonstrate their understanding in a clear, logical way.
- Intervention – For all learners, on-the-spot marking and feedback helps to ensure that most misconceptions and difficulties are picked up within the lesson and addressed there and then. For learners that are struggling with a concept, Same-Day intervention is often employed to reteach or practise the maths, thus trying to ensure all learners are ready to move on together.
- Flexible groupings – We do not group or set learners by ability. Instead, learners sit in mixed attainment groups for the majority of lessons. Our priority is to meet all learners’ needs within the lesson. However, sometimes learners may be reorganised into groups in response to assessment of the outcomes of a lesson where it is clear that they would benefit from further focussed intervention or extension.
- SEND provision – Where appropriate, we involve SEND learners as much as possible in the whole class journey. However, we recognise that this is not always appropriate and, where they require a different or divergent journey and resources, these are fully planned and provided for.