Ash Grove follows a “teaching for depth” approach to mathematics, which is sometimes termed “mastery”. This approach enables all children to master the mathematics curriculum. It draws heavily upon research conducted by the EEF (Education Endowment Fund) and their recommendations.
What is the intention of our curriculum?
The intention is to ensure depth of conceptual understanding through progressive acquisition of mathematical fluency, problem-solving and reasoning skills. This helps our children to know more, remember more, and do more. The mathematics curriculum is planned and sequenced utilising small step progression through concepts, as well as a concrete -pictoral- abstract approach to the use of models and representations.
All year groups are taught in mixed attainment classes, where scaffolding, timely intervention and directed support are implemented to ensure children are mastering the small steps of progression at roughly the same rate. We ensure challenge for all by giving all children the opportunity to develop their fluency and reasoning skills. Some 'faster graspers' will also have the opportunity to take this reasoning to a deeper level across different contexts. Collaborative learning, including the use of 'hook' questions and dialogic teaching strategies, support the use of rich mathematical talk, giving children the opportunity to explore mathematical concepts, resolve errors and identify misconceptions for themselves.
How is our curriculum designed and implemented?
Our EYFS children access their early maths curriculum through the NCETM Mastering Number programme. This programme aims to secure firm foundations in the development of good number sense for all children in Reception, giving them a confidence and flexibility with number and the building blocks to excel mathematically. They will have gained a deep understanding of numbers to 10, including the composition of each number, and be able to subitise and know number bonds to 5 and 10. They will have looked at patterns within numbers to 10, including evens and odds and double facts, and the pattern of the linear counting system to 20 and beyond. They will also have looked at quantities up to 10 in different contexts and be able to say when one quantity is greater than, less than or the same. They will have been given frequent and varied opportunities to build and apply their understanding through the use of manipulatives, helping them to spot connections, look for patterns and relationships, and develop a ‘have a go’ attitude.
The National Curriculum mathematics programmes of study are the basis for children's learning at Ash Grove Academy. However, we do not follow a particular scheme of work in terms of materials or rate of coverage. The DfE's non-statutory 'Maths Guidance: key stages 1 and 2' document sets out the essential 'ready to progress' criteria for each year group and this, alongside the use of the NCETM's curriculum prioritisation and Primary Mastery Professional Development materials, underpins our pedagogical approach, ensuring teachers can plan and deliver lessons that meet the needs of the children in their class. Small steps for both conceptual and procedural understanding are planned for, giving due consideration to common misconceptions that are likely to occur. Additional quality materials may be used to supplement these. Topics are taught until teachers feel that an appropriate depth of understanding has been achieved by the vast majority of the group. Gaps in learning are identified in a timely manner and addressed through “same day intervention”. Children use concrete, pictorial and abstract models and representations for each topic, as appropriate to the learning context. Research conducted by the EEF underpins our expectation that a variety of manipulatives and representations will be used in all year groups and with children at all levels of attainment. This supports learning before procedural methods are used, and allows children to select from a range of strategies for efficiency and to support success. Procedural methods for calculation are taught alongside mental and structural methods for fluency and variation.
Children will be expected to apply this learning within a range of contexts, rather than completing extended procedural practise. Fluency does not equate to speed but to efficient choice of strategy which may well increase speed, particularly when trying to recall times tables.
A typical series of lessons will usually include:
- An activity linked to prior learning, whether reviewing and consolidation patterns and connections in mathematics, or practising fluency of a particular strategy. Activation of prior knowledge of task, strategy and self may also form part of this activity.
- A “hook” problem or calculation which allows the children to work collaboratively, sharing and explaining their initial ideas and strategies. This problem will then be deconstructed as a whole class and effective strategies shared and discussed.
- A series of "mini task" activities which give the children to further practise and apply the concepts and strategies revealed during the 'hook' problem. These mini tasks will involve a balance of direct instruction, collaboration and dialogue, and independent practise, aimed at consolidating the small idea around which the lesson is based.
- Children will only be asked to complete independent recording tasks when teachers feel they are ready to progress; that is, when they have demonstrated a sound understanding of the concept, both in terms of fluency and reasoning, during a range of mini tasks. These independent recording tasks will also give the children who are 'faster graspers' the opportunity to reason at a deeper level. This approach is intended to provide challenge for all in the context of small-step progression, ensuring all children have the opportunity to apply their understanding of a new concept in both fluency and reasoning questions.
- The independent recording tasks in books will reflect the learning journey of each child across the 'small step' objective. Not all children will have completed all tasks, but will all have had the opportunity to apply their new learning in both fluency and reasoning questions. If the children can successfully and independently complete the fluency and reasoning questions, we can say they are ready to progress. The 'sticking point' for each child should be apparent in their independent work. Teachers will provide focused teaching time with those pupils who may require further support, and pupils are encouraged to actively ask for more help if needed. Some children may move on to problems of greater complexity that may be completed over a series of lessons.
- If children can understand the concept in different ways, in different contexts and with different types of reasoning, the concept has probably been learnt - that is, changed in their long-term memory.
Mistakes are valued and celebrated. Unpicking misconceptions so that children evaluate their thinking is vital in scaffolding children towards greater independent learning.
Marking and feedback is timely and allows children to correct and go deeper with their learning. Children who make no mistakes are not being sufficiently challenged, and we expect all children to respond to marking in a timely manner. The aim of marking and feedback is not simply for children to correct their work, but for them to recall, reflect and self-monitor.
There will be times when the above structure across a series of lessons does not suit the learning taking place, and in these instances the structure will be adapted to best suit the learning process.
On a regular basis, children will be given routine arithmetic questions or problems as a low stakes recall of previous teaching on a range of topics. Depending on the outcome, more or less time in that lesson will be devoted to reviewing and correcting errors, but it does not take the place of quality teaching in that lesson based on the topic planned for. This is an example of well-timed repetition and spaced learning, and leads to greater fluency. Repeated exposure and consideration of key concepts over and over again in different contexts leads to better understanding.
When teachers can, they offer timely, sometimes same day, intervention to ensure gaps and misconceptions are addressed before moving on.
For 2022-2023, Ash Grove Academy will be following the Curriculum Prioritisation Overview as designed by the NCETM. A link to coverage and progression can be found by clicking here.