The aims of our mathematics teaching at Brecknock align with the aims of the National Curriculum: to encourage children to make connections across mathematical procedures and concepts to ensure fluency, mathematical reasoning and competence in solving problems in maths lessons and in other areas of the curriculum.
Growth Mindset: Children are encouraged to believe they are all capable of learning and doing mathematics, given sufficient time, good teaching, appropriate resources and effort.
- Everyone can learn mathematics to the highest levels if they work hard
- Mistakes are valuable if we learn from them and support others (“Good mistakes”)
- Asking questions is important (especially when unsure)
- Depth of understanding is more important than speed and providing quick answers
- Children are working towards their own goals and personal bests
Certain principles and features of a mastery approach have been adopted:
- Teachers reinforce an expectation that all pupils are capable of achieving high standards in mathematics if they work hard.
- The large majority of pupils will progress through the curriculum content at the same pace. Differentiation is achieved by emphasising deep knowledge and through individualised support and intervention. Tasks are varied to challenge those with secure understanding; there should be no acceleration through new content.
- Learning and memorising key facts and procedures and practicing them regularly is essential – this involves developing a strong sense of number in KS1 and being able to solve problems using mental and written calculation methods with increasing efficiency.
- Teachers are encouraged to spend longer in class on a small number of fundamental maths topics, going into much more detail and depth. Teaching is focused, rigorous and thorough, to ensure that learning is sufficiently embedded and sustainable over time.
- Teaching is underpinned by methodical curriculum design with key concepts revisited and interlinked with one another.
- Lessons follow a gradual step-by-step teaching approach whereby the use of varied visual representations, carefully chosen resources, language structures and use of mathematical vocabulary foster deep conceptual and procedural knowledge.
- Practice and consolidation play a central role. Carefully designed variation within this builds fluency and understanding of underlying mathematical concepts in tandem.
- Teachers use precise questioning in class to test conceptual and procedural knowledge, and assess pupils regularly to identify those requiring intervention so that all pupils keep up.
Teachers should provide a long-term vision with children, explaining the importance of making links and developing relationships when introduced to new concepts. Teachers use the White Rose medium term yearly planner and use the small steps and key questions guidance as a basis for each unit. Teaching focuses on children’s fluency and promotes reasoning and problem solving. There is also a strong emphasis on increasing children’s ‘arithmetical proficiency’ – being able to recall as many facts as possible (tables, number bonds halves and doubles) quickly and accurately, so they can then apply these facts to calculations.
Teachers should also use the relevant DfE Maths guidance documents to support long-term, medium-term and short-term planning. At the long-term planning stage, the guidance can be used to ensure that the most important elements that underpin the curriculum are covered at the right time, and to ensure that there is continuity and consistency for pupils as they progress from one year group to the next. At the medium-term planning stage, teachers can use the guidance to inform decisions on how much teaching time to set aside for the different parts of the curriculum. Teaching time can be 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. At the short-term planning stage, the guidance can be used to inform teaching strategy, and the representations and ‘Language focus’ features can be used to make concepts more accessible to pupils.
Intelligent Practice – all tasks are chosen and sequenced carefully with purpose, offering appropriate variation (procedural and conceptual) in order to reveal the underlying mathematical structure, concept or process to pupils.
- Exploring – revealing new mathematics, multiple representations, building / deconstructing mathematical models/ ideas, explaining new language, identifying misconceptions, making connections, considering emerging generalisations
- Clarifying – clear modelling and SC to help guide children
- Practising – allowing teachers to assess a child’s level of understanding
- Applying – deepening and mastering concepts by: questioning in unfamiliar contexts; through non-routine problems; making the children choose the technique/concept to be used; making links; connecting the unfamiliar with familiar
Basic Lesson Design:
Teachers should use DfE maths guidance to look at each ready-to-progress criterion, including core mathematical representations, language structures and discussion of connections to other criteria.
Difficult points need to be identified and anticipated when lessons are being designed and these need to be an explicit part of the teaching, rather than the teacher just responding to children’s difficulties if they happen to arise in the lesson. Teachers should work together with other teachers, as well as use the “misconceptions in the key objectives” support document, to help them consider various possible misconceptions and plan for them. The teacher should be actively seeking to uncover possible difficulties because if one child has a difficulty it is likely that others will have a similar difficulty. Difficult points also give an opportunity to reinforce that we learn most by working on and through ideas with which we are not fully secure or confident. Discussion about difficult points can be stimulated by asking children to share thoughts about their own examples when these show errors arising from insufficient understanding. Mistakes are ‘good’ if we can learn from them.
Daily ‘Do Now’ Tasks
In KS2, children start all lessons with either times tables practice or arithmetic practice which recaps and consolidates prior learning. This is to ensure children retain key information and become more efficient. Each week there is a differentiated ‘X Factor’ Times Tables quiz and an arithmetic quiz. In KS1, the focus of the ‘Do Now’ tasks is to increase ‘arithmetical proficiency’ – being able to recall as many facts as possible (tables, number bonds and doubles) quickly and accurately, and then apply these facts to calculations.
Planning is structured around the concrete – pictorial –abstract approach, providing opportunities throughout for using mathematical vocabulary, developing mathematical thinking and using multiple representations. This is reflected in the school’s calculation policy. Children learn through active, practical enquiry and experiment using concrete materials, represent their mathematical ideas through pictures and images and follow a clear progression toward recording abstractly.
Notes for Calculation Methods
- Regular number practice is essential in creating ‘automaticity’ and ‘arithmetical proficiency’ – being able to recall as many facts as possible quickly and accurately. This is crucial as it frees up the working memory to concentrate more on the underlying concepts being taught.
- Children who make persistent mistakes should return to the method that they can use accurately until they ready to move on.
- Teachers will discuss errors and diagnose problems then work through questions that caused difficulties step-by-step – not by simply re-teaching the method.
- Children should be encouraged to consider if a mental calculation would be appropriate before using written methods.
- All new written methods should be presented alongside the previous method and children should be encouraged to explain ‘what’s the same’ and ‘what is different’.
- Teachers will use meta-language to talk through new written methods e.g. ‘if you know this, then you know this…’
- Children should be encouraged to use the correct language and explain how they have answered a question (e.g. refer to the actual value of digits).
Marking and Feedback: ‘meaningful, manageable and motivating’
During and after every lesson, teachers should assess children’s levels of understanding and mathematical fluency, deciding on their readiness to progress to the next stage of their learning.
Teachers are encouraged to teach ‘with a pen in hand’ as it allows them to identify mistakes in real time and provide immediate feedback. When appropriate, for example with closed tasks or exercises where the answer is either right or wrong, children may mark their own work as it allows them to identify their mistakes. Teachers should use daily assessment, including looking in books, to inform the design and content of the next lesson, considering: the key discussion points (misconceptions), the best ways to model effective, efficient strategies, and the activities and tasks chosen to either move children forward in their learning or re-visit and consolidate key concepts. There is no expectation of a written comment but it should be clear in a child’s book that a teacher is regularly assessing their level of understanding and adapting their practice accordingly.
When teachers look at children’s books, they are expected to distinguish between errors that reflect a misunderstanding, and mistakes that are simple slips. Slips are either dotted or highlighted in green and children should be given adequate time to self-correct. Green boxes indicate where a child should attempt to self-correct. Conceptual misunderstandings will need to be addressed individually, in small groups or during whole class discussion (when a misconception is evident in a large number of books) as close as possible to the teaching moment. Teachers may provide hints or questions in written marking which lead pupils to underlying principles but will, most likely, need to provide extra guidance, modelling and scaffolded support in the next lesson.
The most important activity for teachers is the teaching itself. Thus, marking and evidence-recording strategies should be efficient, so that they do not steal time that would be better spent on lesson planning and preparation. There is no expectation for written feedback if it is clear in a child’s book that a misconception has been addressed in the next lesson. If the teacher wishes to celebrate a child’s success, they may tick in blue or highlight in yellow that section of work. Written praise should be genuine, sparing and related to ‘personal bests’, encouraging a growth mind-set.
‘Challenge’ and ‘Consolidation’ tasks
Children should be given a challenge or consolidation task at least once a week. Following support, children should be given time to practice and ‘consolidate’ their understanding. They must demonstrate they are secure with what they have learnt before moving on. If a child has demonstrated sufficient understanding of a task, they should be moved on quickly. This may include providing a ‘challenge’ task, which should vary slightly to the task set during the lesson (conceptually or procedurally). There should be no acceleration through new content. See the Feedback and Marking Prompts document for examples of both.
Assessment is an ongoing process in the classroom which forms the basis of future action. Every lesson should include a form of formative assessment, based upon practical, written and oral work completed by the children. Teachers must make sure they know how much the child has understood during a lesson so they can plan and adapt the next lesson. A child’s book should provide evidence of how they have progressed, demonstrating aims outlined in medium term planning.
A form of summative assessment should take place at the end of every unit and be used to compare attainment with the teacher’s assessment. Teachers should use the government example assessment questions in the relevant year group guidance document. This can be supplemented with White Rose end of unit tests, a ‘Test It’ end of unit quiz or in upper KS2 a Corbettmaths assessment. Test Base standardised tests are completed at the end of each term and are analysed in order to support ongoing teacher judgement about a child’s overall attainment in mathematics. When possible, each child should be involved in the review of his/her progress and be able to contribute to discussions about different aspects of his/her work.
At Brecknock, we assess whether pupil has a deep understanding of a mathematical concept, idea or technique if he or she can:
- make decisions on what to do and how to do it, choosing the most efficient option for them
- describe it in his or her own words
- represent it in a variety of ways (e.g. using concrete materials, pictures and symbols – the CPA approach)
- explain it to someone else or write an explanation for them clearly and systematically
- make up his or her own examples (and non-examples) of it
- see connections between it and other facts or ideas
- recognise it in new situations and contexts (varied tasks and problem solving tasks)
- challenges him/herself, looking for further opportunities to develop understanding
- does not just accept what others say, they question and test it.
Appropriate homework activities are set for each year group. Teachers will set homework tasks, which may be games to play, facts to learn, or paper based questions to answer and return. There are additional homework activities available on the school website, such as MyMaths. They key facts for each year group are also listed on the school website.