The St Mark’s approach to Mathematics
Maths teaching at St Mark’s is centred around building confidence – so much of a child’s success in the subject is dependent on self-belief, so that they feel able and ready to tackle problems which arise, as opposed to feeling intimidated by them. Having long worked in sets, we moved from February 2020 across to whole class teaching of maths across the school. Through this, in combination with our other support measures, we are able to support those requiring it, and stretch each child as far as they are able to be stretched, with all children having access to materials and content based around advanced reasoning and mastery of each subject area. Our intent is that this will help enable our middle achievers particularly to achieve all they are capable of achieving, whilst still supporting our lower ability and challenging our most able pupils by encouraging them to go deeper into each subject through use of open-ended application of skills.
We want all our children to become numerate, economically aware young adults, in a modern Britain where the ability to understand and use numbers, and especially money carefully, has never been more important. We achieve this by focusing on fluency of arithmetic skills, developing a solid foundation in these, upon which we build increasingly sophisticated reasoning and problem-solving abilities, in the pursuit of creating dynamic, flexible mathematicians who demonstrate a deep understanding and are equipped with a range of skills to enable them to continue their maths development into secondary school and beyond.
Wherever possible, we aim to make maths teaching relevant to the children and their lives, now and in the future. Teaching may be linked to areas of interest for them such as hobbies, toys and games, or shopping. If children can see the benefit to them in developing certain skills, we hope it will help give them understanding of their impact in context, and help engage their interest too. In Early Years, children practice and improve their skills in counting, simple addition and subtraction through everyday activities such as calculating how many children are present.
In implementing our vision for maths, we follow several key principles:
1. A structured progression
We are aligning with the White Rose Maths scheme – a nationally recognised model of whole school structured mathematical learning. Each year, learning is split into extended blocks where subjects can be studied in depth, through learning a variety of small steps. These build sequentially to develop secure skills in each block, whilst throughout, exposing the children to reasoning and deeper thinking opportunities to enable them to apply their understanding and make links between areas of maths.
2. Repetition of topics.
Some children are very fortunate and pick up new concepts quickly and easily, but for many, it may take several revisits of an area before they become truly confident working with it. As such, through use of starter and fluency sections of each lesson, we aim to meet different small steps from blocks several times within a year, touching on them ‘little and often’. A key tenet of lessons should be that they should often each contain three or more different aspects of maths to enable this frequent revisiting. This approach is also recognised as being of great benefit to children who may be affected by dyscalculic traits, which given our high levels of SEND is a particularly key consideration for us. A key tool in this is the use of ‘Flashback’ White Rose resources, exploring up to four different areas briefly as a starter activity each day, before moving onto a fluency / arithmetic focus and then a main area. Consequently, lessons are pacey and offer plenty of opportunity to reinforce previous skills and make links. Fluency sessions offer flexibility to revisit previous learning as necessary and to look forward to future small steps. Consolidation time is also built into each half term to enable individual classes and year groups to spend time on identified areas as necessary.
Skills are built upon through repeated challenges and tasks, for instance through an increasingly tricky times-tables challenge from Year 2 onwards. Those who grasp concepts quicker are encouraged to delve deeper, developing a fuller understanding, rather than moving onto new topics, perhaps through open-ended questions, or exploring ‘always, sometimes, never’ conclusions. In Early Years, mathematics is not only encountered through discreet lessons, but also in everyday play activities.
3. Great emphasis on the development of mental maths and arithmetic skills.
Children are constantly encouraged to develop key skills such as number bonds, doubling, halving, fluent addition and subtraction and, of course, times tables. These skills are the bedrock upon which all else is built, and the more confident and proficient children become in these, the easier they will find all the written areas of maths. Given this importance, a portion of every lesson is spent in securing these foundations, especially in use of the four operations (+, -, x ÷ ) and key fraction, decimal and percentage skills, alongside development of a solid appreciation of place value. A child who can develop confidence in all these will be a child who can go on to tackle any other area of maths. Some aspects of place value were identified as requiring further attention following monitoring of end of year assessments in Summer 2019, and teachers were encouraged to revisit these areas further in the 2019/20 academic year. The White Rose scheme places significant emphasis on this area at the start of each academic year, so will be a focus across the whole school each September.
4. Seeing the bigger picture and becoming maths problem-solvers.
It is all too easy to see Maths as a set of unrelated rules to be learnt and followed. Far better, we feel, to wherever possible show children how areas link together, making crossovers between them, and enabling them to make their own useful links when tackling problems and investigations. Additionally, we encourage them to develop a broader understanding of concepts, so they can apply their skills more widely. For example, it is one thing to be able to round 23 to the nearest 10. It is another to know all the possible whole numbers which would round to 20 when rounded to the nearest 10, and be able to explain why. This is a key tenet of our approach to children achieving mastery in mathematics, and all lessons for all abilities contain reasoning opportunities and extension activities for children to demonstrate their more thorough understanding of a concept. Use of the White Rose resources is central to effective resourcing of this, allowing children to move rapidly from conceptual understanding and fluency practice to application and reasoning through the resource sheets they provide for each small learning step in each block in each year. In addition, Maths lessons usually begin with a ‘Flashback’, allowing daily opportunities to apply their knowledge, whilst recapping and revising previous areas, and additional reasoning, problem solving and investigational opportunities are factored into blocks of learning throughout the year to encourage this further.
In Early Years, as in all others, the Greater Depth judgement for mathematics will always be aimed for if a child shows evidence of achieving at all the Expected descriptors. Throughout the school, whether it be little notes to support mental maths, missing numbers entered onto the sides of graphs or notes to keep track of lengths or numbers of lines on complex shapes, annotations and workings are promoted as an absolutely essential tool for children to use (and adults to model) when tackling mathematical problems. They are also a key foundation for coping with more complex mathematics in secondary school and beyond.
5. VAK, giving children tips and tricks to support themselves, and giving them choice.
Just as in spelling, where little rhymes and mnemonics may help children remember the order of letters, so in Maths we encourage the children to develop systems to support their own memory of methods and approaches. For example, this could be in the form of useful visual strategies to lay out techniques to help them perform key arithmetic operations. Additionally, we expose children to various different methods of tackling problems or completing calculations – whilst basing progression on our whole school calculation policy – and encourage children to work with the one that is best for them. Maths is not one-size-fits-all! This will mean, for instance, children are shown how to use different methods for subtracting two digit numbers- mentally, using base ten resources, using a number line and the gradual introduction of the column method. Discussions then follow as to which the most efficient strategies might be to solve a particular calculation – a key component of our approach to mini-plenaries, which may appear in any part of the lesson, as appropriate. Throughout the school, as the needs of each class and child dictate, this includes building up a secure visual and kinaesthetic understanding of number and number operations, such as through using physical resources like Numicon, Dienes and Place Value Counters, and developing visual ways to approach calculations when developing pencil and paper methods. Central to the White Rose approach is exposure to a wide range of visual and practical models, and learning often takes a concrete-pictorial starting point. In Early Years, children are encouraged to find ways to solve problems, make predictions and test their ideas.
6. Breakaway teaching, intervention and challenge
Children develop an understanding of mathematical concepts at different rates, and require differing levels of support to do so. Each block of learning begins and ends with an assessment to gauge a starting point knowledge base (to inform focus areas for planning and to anticipate misconceptions) and to assess understanding at the end (to inform ongoing assessment of key objectives and continuing intervention programmes). In addition, common features of our lessons are initial assessment activities to ascertain when children can be moved on rapidly to more challenging tasks and thus towards developing a mastery of the area. Alongside this, breakaway teaching will also be seen, whereby following an input, those children requiring some additional support can immediately receive it by the teacher or a Teaching Assistant, often utilising alternate ways and resources to illustrate the process or approach most useful to the child. Where further additional support is needed, flexible, targeted and responsive intervention groups run outside of the maths lesson where small groups of children can receive specific extra guidance to enable them to progress appropriately. A full range of auditory, visual and kinaesthetic approaches, including Numicon, are employed as appropriate. Ongoing formative assessment is very much at the heart of teaching across the school, including in effective Early Years practice; here, learning through play is given the centre stage and children are encouraged to have a ‘can do’ attitude, which is then built on and developed throughout the rest of the school. ‘Wrong’ answers are learning opportunities and are treated as such to remove fear of them.
Whilst mastery activities are built into each of White Rose small steps sheets, an additional bank of activities is also used in each year group for teachers to incorporate extension activities to stretch the most able learners further, enabling them to go deeper into each topic.
Effective use of breakaway teaching, initial assessments, moving on quickly, extensions and use of mini plenaries will be foci for monitoring of planning and learning walks in mathematics over the 2020/21 academic year.
7. Home-learning and parental involvement
Homework is set each week to enable children to reinforce learning. Guidance is given to enable parents to see methods in use at school, to enable them to better support approaches being taught. Parents evenings and written reports identify specific focus areas for children to work on at home. In addition, children have full access to IXL and Times Tables Rock Stars and are encouraged to make use of these at home to enhance their learning, each being promoted in school by year groups. Maths events are held on occasions to help raise the profile of maths in the school, for example 100 Day. Periodic parental maths information events have been run to enable current approaches to maths to be modelled and for parents to have questions answered. We are looking to run our next set of these during the 2020/21 academic year, as ongoing circumstances allow.
Children should leave St Mark’s with a solid foundation in the key skills which will enable them to go on to be mathematically literate, valuable members of society. Whilst delivering the whole curriculum, we have identified key objectives within each year that we consider to be fundamental to children achieving this. We track these objectives throughout the year, reporting on them in parents evening and reports, and delivering intervention and support to children identified as having difficulties throughout the year. Use is made of White Rose start and end of block assessments in collation of evidence of these, as is regular use of Testbase materials. We are developing our use of all of these throughout the 2020/21 academic year. On a regular basis, teachers monitor children’s success with taking on different concepts, making use of 1:1 help, breakaway teaching and small group intervention.
Summative evidence is collected across the school twice a year from NFER assessments, all of which are fully question level analysed, leading to additional, targeted intervention support as necessary, delivered by staff in year groups. Any trends arising from assessment evidence across the school are also monitored and identified, with action taken to address them through staff training and professional development, alongside acquisition of additional resources as appropriate. Similar analysis takes place following end of Key Stage assessments, to enable lessons to be learnt across the school. All data from February 2020 assessments was analysed and disseminated to staff in a staff meeting, which fed directly into curriculum planning for the coming half term, so that identified needs and areas for further development could be addressed. This has also led to the move across to a full implementation of the White Rose Framework from September 2020 onwards, and the 2020/21 year will be a year of fully embedding this approach across the school, monitoring its implementation and impact as we go.
Monitoring of planning, teaching, assessment and folders of work is carried out by the Senior Leadership Team and Maths Subject Leads as appropriate. Additional internal moderation of maths assessment work takes place in phase meetings, with a staff meeting each year allocated to whole school moderation of Year 2 assessments before they are submitted.