Curriculum Leader - Ms Jessica Crisp
At St. Mary's C of E Primary Academy we want all our children in mathematics to:
- Learn as much as possible, so all children are fluent in the fundamentals of mathematics. We want our children to be able to reason mathematically and to be able to recall and apply their knowledge effectively to solve problems.
- Ignite Curiosity by using practical equipment to solve problems.
- Become confident speakers and communicators as they reason and explain their mathematical thinking.
The National Curriculum for Mathematics aims to ensure that all pupils:
At St Marys C of E Primary Academy we are developing the mastery approach to mathematics. To ensure children learn as much as possible and become competent in mathematics, pupils need to develop the three forms of knowledge:
- Fluency (Factual) I know that … NC 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.
- Problem-Solving (Procedural) I know how … NC 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
- Reasoning (Conceptual) I know why … NC reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
Our Mathematics curriculum is driven by the White Rose materials. During 2021-2022 we will use the NCETM Curriculum Prioritisation materials to lead the curriculum. Teachers follow the Long Term Plans from White Rose/NCETM however these are adopted flexibly to meet the needs of the class. Teachers plan units of work which vary in length depending on the topic and year group.
Planning a Teaching Sequence
Staff follow Long Term Plans provided by the Maths Leader which are based on the White Rose materials for Mathematics. The Long Term plans reflect individual units of work to be taught across the year, ensuring full coverage of the National Curriculum. The class teacher will ensure these are used flexibly to meet the needs of their class.
Learning Aims and Success Criteria
The daily learning objective(s) will be taken directly from the National Curriculum. This may be the whole National Curriculum objective, or part of a National Curriculum objective if it needs breaking down across the week. Every lesson should have a clear set of success criteria.
It is essential that the learning pathway over the course of a lesson is clear and can be evidenced in children’s books. Small developmental steps should be clear, and each lesson should build on the last. The learning pathway should be clear across a week.
The mastery approach aims for all children to be working at a similar level. However, the work given to children must match their level of ability.
All children will be involved in and participate in mathematics lessons. The opportunity for children to communicate, listen to the reasoning of others and use the concrete, pictorial, abstract model (CPA) can really benefit children working below age related expectations.
Children who are working significantly below age related expectations will still be included in the main teaching of the lesson. They will have Learning Support Plans written to support their specific mathematical learning needs.
Teachers will use lesson observations, class work and the assessment tracker to identify children for targeted intervention and daily guided group support.
Pre Topic Assessments
Before beginning each unit of work identified on the Long Term Plan the teacher will gain an understanding of prior learning and the children’s current level of ability through a pre-topic assessment. This will be a short sequence of questions related to National Curriculum objectives. The results of this assessment will then be analysed and used to inform planning. Teachers can use the Third Space Learning resources (which can be found on the school network) or the Ready to Progress materials for their pre-topic assessment.
Fluent in 15
Children from Year 2 upwards have daily ‘Fluent in Fifteen’ sessions. This consists of 15 questions which they have 15 minutes to answer. The questions will be differentiated by their order, therefore all children will access the same daily sheet. Teachers will use their professional judgement about any children with SEND who may not access the same questions. In Year 2 the teacher will mark the children’s work. In Key Stage Two children will mark their own fluency while the teacher goes through the questions at the end of the 15 minutes. The teacher will pick out one or two questions that they have identified the children having most difficulty with and model the correct working out for these. Year 1 children will be introduced to ‘Fluent in Fifteen’ during the year. Children in Years 3 and 4 should use one of their Fluent in Fifteen sessions each week to practice their times tables electronically.
Resources to Support Teaching and Learning
Teachers will create their own resources tailored to the children in their class and the learning sequence.
- The White Rose Hub provides planning guidance which can be used to support short term planning.
- The NCETM website has teacher guides and representations for many aspects of mathematics.
These are the preferred resources for teaching mathematics.
- The Numberblocks support materials available through the NCETM website will support Early Years and Key Stage 1.
- ‘I See Reasoning’ will be used to provide children with suitable questions.
- Other publications and websites may be used on an ad hoc basis to support teaching and learning. They should be used with caution and should not form the structure of a lesson.
Effective Classroom Practice
Thinking and Talking Mathematically
During mathematics lessons, teachers will allow opportunities for children to discuss their work with a partner. These opportunities provide valuable time for the children to communicate their mathematical ideas with precision and clarity. One way that staff will do this is to use STEM sentences. The ‘I say, you say, you say, you say, we all say’ strategy is an effective strategy. For example the teacher will provide the STEM sentence eg. ‘two add two equals four’ and then choose 3 individual children to repeat it before asking the whole class to say it together. Children will also be asked to fill in missing parts of a sentence, varying the parts but keeping the same STEM sentence. For example ‘There are 12 stars, 12 is the whole, part of the whole is one half, 6 stars is equal to one half of 12’. Children will be encouraged to answer mathematical questions in full sentences to develop their skills to speak and be clearly understood. It is essential that our mathematics lessons are language rich with lots of opportunities for children to ‘think out loud’.
Mixed Ability Groupings
At St Mary’s C of E Primary Academy School, our approach to Mathematics teaching and learning is based on the principles of mixed ability teaching and child led learning. All children, of all abilities are involved within Maths lessons in the classroom in order to experience the rich vocabulary and conversation that takes place. Children will take part in paired and group work activities throughout the week and these may be ability based, or mixed ability based, depending on the task. Guided groups will be organised daily (with the teacher or teaching assistant) in order to target children with similar ‘gaps in learning’ or needs. These guided groups will not always be made up of the same children. All children will be encouraged to reflect on their own ability, to challenge themselves appropriately in order to make progress and to be the leader of their learning journey. This is child led learning.
Manipulatives are physical objects that are used as teaching tools to engage children in the hands-on learning of mathematics. They are designed so that children can perceive a mathematical concept through manipulation. They can be used in all areas of maths and are vital in the concrete, pictorial, abstract (CPA) model, particularly in the concrete stage.
The mastery approach dictates that all pupils (regardless of their age or ability) must always have access to apparatus to support calculating and reasoning. Children should use apparatus as part of their reasoning. The term apparatus refers to Numicon, tens frames, base 10, Cuisenaire rods, concrete resources etc… not to worksheets or textbooks.
Concrete, Pictorial, Abstract Model
The CPA approach builds on children’s existing knowledge by introducing abstract concepts in a concrete and tangible way. It involves moving from concrete materials, to pictorial representations, to abstract symbols and problems. Good practice involves always introducing a new concept through concrete materials. Moving towards the abstract stage too quickly will create gaps on the children’s knowledge and understanding.
Concrete is the “doing” stage. During this stage, children use concrete objects to model problems. The CPA approach brings concepts to life by allowing children to experience and handle physical (concrete) objects. With the CPA framework, every abstract concept is first introduced using physical, interactive concrete materials.
Pictorial is the “seeing” stage. Here, visual representations of concrete objects are used to model problems. This stage encourages children to make a mental connection between the physical object they just handled and the abstract pictures, diagrams or models that represent the objects from the problem.
Abstract is the “symbolic” stage, where children use abstract symbols to model problems. Students will not progress to this stage until they have demonstrated that they have a solid understanding of the concrete and pictorial stage. The abstract stage involves the teacher introducing abstract concepts (for example, mathematical symbols). Children are introduced to the concept at a symbolic level, using only numbers, notation, and mathematical symbols (for example, +, –, x, ÷ ) to indicate addition, multiplication or division.
The Use of Whiteboards
Individual whiteboards can be used for children to practise their skills. If the work on the whiteboards forms part of the sequence of learning then it will be photographed or photocopied and stuck into the child’s book. If the work forms part of the guided practice and the children will then move on to recording in their book, then no record of the whiteboard work is required. Children may also use a ‘jotter’ book to replace the need to use whiteboards.
Effective oral and written questioning is essential in Mathematics lessons and will be planned carefully by the teacher to ensure that the questions used are purposeful. Questions will be used to …
- assess children’s understanding
- give opportunities for children to reason and explain
- deepen children’s knowledge
- move children’s learning on in small steps, but with appropriate pace
The following question types will be used regularly
- How do you know?
- Can you tell me more?
- Why do you think that?
- Can you prove it?
- How did you get that answer?
- How do you know you are right?
- What would happen if…?
- What could you do to make it correct?
- Do you agree? Why?
Written questions will allow children to see pattern and to use the pattern to develop their thinking, this is called procedural variation. The questions will increase in difficulty slowly, but without losing pace.
Reasoning opportunities will be built into daily lessons. The reasoning could be one specific question at an identified part of the lesson, but equally it could be a whole lesson devoted to reasoning on the current topic being taught. The evidence in books will be explanations from the children in their own words. There will also be evidence of pupil voice.
Each fortnight there will be one maths lesson devoted to reasoning. There will be a whole school focus for these lessons linked to specific reasoning skills and questions eg. ‘Odd one one’ or ‘Always, Sometimes, Never’. In these lessons the children will be taught how to answer the reasoning question and then they will be provided with questions to practise the skill with a variety of contexts.
All maths work in books should be dated. Children will use pencil to record in their mathematics book. The majority of the work in a child’s book will be their own recording, with limited use of worksheets. Children’s jottings, calculations and reasoning will be evidenced and will be presented with care.
Expectations will always be high. Pupils work will always be presented to a high standard and addressed promptly if not. Teachers set the standard and their presentation will always be of a high standard. Rulers will always be used to draw lines – this is by both adults and children. The only exception is when the child is using jottings.
As children present their work neatly, they will be required to place one digit in each square of their book (from Year 2 onwards).
Each classroom will have a Mathematics Working Wall. The wall will sequence the learning that is taking place and show where it fits into the bigger picture. The working wall will contain sentence stems for the children to use when reasoning and relevant questions to extend their thinking. Ultimately the working wall is for the children and should be used by the children.
In Mathematics lessons all pupils are encouraged to ask questions, take risks, and explore alternative solutions safely. We will promote the concept that it is ok to be wrong and that we can learn and grow mathematically through making mistakes, talking to a partner and trying again. This will develop resilience.
Marking and Feedback
Teachers will mark in green pen. A small neat tick will be used to evidence where a child has got the correct response. If a child has made an error then it will be highlighted pink. Ideally, the exact part of the response which is incorrect will be highlighted pink and not the whole answer.
Teachers will give verbal feedback where possible and written feedback if needed. Children will write neatly in purple pen, there should be no scribbling out. If they are not able to write neatly then they will not use a purple pen. A next step will always move a child’s learning on. Next steps will be mostly personal to the individual child. They do not need a pink marker, but should have a neatly drawn ‘next steps’ symbol. A next step will not to be used just to signal the next part of a lesson. They will be used when a child has made an error and they need guidance on how to move forward.
End of Year Expectations
In Key Stages 1 and 2 we expect the children to be working at age related expectations or above by the end of the year and to be secure in the objectives for reading and writing that are set out in the National Curriculum. At the end of the Foundation Stage (Reception Year) we expect the children to have achieved the Early Learning Goals for Literacy and to have secured a Good Level of Development.
Teacher will assess daily and weekly, and update the primary tracking document on a weekly basis. Gaps in learning can be picked up in future lessons, intervention, home learning and fluency 15 activities
Summative assessment will take place through
- end of Key Stage SATs in Year 2 and Year 6
- White Rose termly assessments in Years 2 to 5 (TBC)
- Year 4 Multiplication Check
The Maths Leader will work alongside the other members of SLT to monitor and evaluate teaching and learning in Maths. This will take the form of learning walks, book and planning scrutiny, gathering pupil voice, discussions with staff and lesson observations and will cover all aspects of Maths. The SLT will monitor pupil progress in maths each term by analysing pupil data.
Teaching and learning in mathematics will be monitored through:
- learning walks
- book and planning scrutiny
- formative and summative assessment
- staff meetings
- pupil progress meetings
- performance management meetings