“There is no such thing as a maths gene. With the exception of children with specific neurological conditions, everyone can be a successful mathematician. If you share this belief, then greater depth for all should be your goal.” (Andrew Jeffrey; 2019; 13)
At St. Peter’s, we believe every child has the capacity to become an able mathematician. Our primary aim is to create a sense of curiosity in mathematics, where our pupils acquire a genuine fascination. We aspire to create ‘real mathematicians’ – children who don’t just receive lots of ticks in their maths books or score well during their formal assessments, but individuals who are passionate for maths, become deeper mathematical thinkers and have a sense of wonder and curiosity for this subject.
We recognise the importance of offering activities where correct methods are modelled by teachers and then students practise the concept taught to build confidence in their methods, but we also value opportunities for our pupils to develop their conceptual understanding so we encourage them to question and to think, to make conjectures and to create mathematical generalisations in order to establish links with their learning. Whilst modeling is important, our lessons are not dominated by teacher talk (Hattie; 2012; 80), but through carefully constructed lessons, the teacher guides the pupils through a series of steps that: offer examples and non-examples to examine; identify and tackle potential misconceptions; and encourage mathematical exploration. We skill our pupils in the art of ‘exploratory talk’ (Monaghan; 2010) so when the children respond to the whole class or speak to one another, they are able to carry out effective discussions with their peers. We value the importance of learners having the time and opportunity to talk about their thinking processes in order to make them more explicit (O’Sullivan et al; 2005; 18), and hold the belief that external expression is a contribution which thinking mathematically can make to the general social development of our learners (Mason et al; 2010; 234).
Collaborative discussion is real in our classrooms as we believe the process of communicating mathematics to be integral to our pupils’ learning of mathematics (Harrison & Howard (2009;7). To this end, staff are mindful, of deliberate planning as we genuinely consider what problems to be worthwhile, what groupings will sustain collaborative discussion, how the social rules will be established and what reporting strategies will focus the group (Ryan & Williams; 2011).
Using well established talk rules (created at the start of each year by each class) and by confidently using a range of metacognitive strategies (learning muscles), our pupils are increasingly resilient in responding positively to open questions posed; are increasingly encouraged to persevere when thinking deeply about a range of mathematical concepts; and are given opportunity to use one’s own and others’ thinking to engage in high quality collaboration. These approaches increase the chances of our pupils making mathematical connections and ‘fixing’ knowledge and skills to their long term memory, so they acquire a strong sense of confidence when climbing into the learning pit, providing them with a greater chance of reaching a high level of attainment throughout a variety of mathematical concepts. With the support of high quality teacher questioning – our students are given the opportunity to develop building blocks in their learning, which leads to their own individual deeper thinking. We work hard to ensure that pupils’ emerging ideas are shared in a positive classroom environment and making mistakes is viewed by all as a natural ingredient to deeper success. Age appropriate vocabulary is shared at the start of specific topics (see progression of vocabulary) and is visited and revisited throughout lessons. It is displayed in the classroom and pupils are encouraged to use correct language whilst collaborating with others - vocabulary is key.
At St. Peter’s, we use the sequencing structure of White Rose Maths to ensure progression is clear and consistent across all mathematical topics. White Rose Maths’ mantra that ‘Everyone Can Do Maths’ rings true at St. Peter’s as does their belief that: “We’re building a whole new culture of deep understanding, confidence and competence in maths – a culture that produces strong, secure learning and real progress… we’re shaping assured, happy and resilient mathematicians who relish the challenge of maths. They [Our pupils] become independent, reflective thinkers, whose skills not only liberate them in maths but also support them across the curriculum.” White Rose Maths shows how children can move their understanding from concrete to pictorial to abstract thinking for each step. The small steps approach builds on prior learning from the previous steps as well as the previous year. Topics are revisited each year except for year-specific topics. Each year group begins with the essential mathematical building blocks of place value, addition and subtraction, and multiplication and division. Using St. Peter’s written calculations policy, rather than focusing exclusively on the approaches in White Rose, the strategies for +, -, x & ÷ focus on embedding the children’s understanding of place value through written methods, sometimes with the use of visual (images) and physical (apparatus) representations. Eventually the children (when ready) will be taught more efficient strategies that help them to complete written methods at speed but not at the expense of their understanding. Research suggests that once students have memorised and practised a method that they do not understand, they have less motivation to understand the meaning or the reasoning behind them. Also, children who engage in a lot of practice without understanding what they are doing often forget, or remember incorrectly, those procedures. At St. Peter’s, we recognise that it is important to provide children with a variety of strategies to give them the ownership over what procedures they use. This, in turn, allows them to make critical judgments about which strategies are appropriate for use in particular situations; however, it is essential that these strategies are not at the expense of their understanding of why. Children need to be both procedurally and conceptually fluent – they need to know both how to do something and why they are doing it.
Whilst the content of the White Rose lesson plans offers a heavily weighted support for St. Peter’s staff, teachers are also given license to use their expertise in varying the structure of lessons to keep the learning fresh, to provide appropriate choice and to ensure there are lots of opportunities to explore different representations and models when learning something new or revisiting prior content. Whilst we recognise the importance of practising a concept in order to become procedurally fluent, challenge for all is at the forefront when planning lessons, and rich and open questioning (such as What do you notice? Always, Sometimes, Never? Have you found all the possibilities to…and how do you know?) is key to encouraging our pupils to take their learning deeper to establish genuine interest and curiosity. Asking our pupils to ‘prove it’ is common practice in our classrooms as it acts as a mechanism for our pupils to think and learn at a deeper level.
Akin to the mastery model, pupils are taught together to master their own year group’s objectives and deepen rather than rushing onto the next year’s content. The rationale behind this policy is that in order for children to grow as mathematicians, they need to gain a deep understanding of the concepts underpinning mathematics in order to flourish in the three aims of fluency, reasoning and problem solving.
A variety of question types that promote fluency, reasoning and problems solving are ever present in lessons; these deliberately crafted questions – led by the teacher at the beginning of lessons – are conjectured before pupils move onto independent or collaborative activities. Tasks that allow deliberate practice to take place in order to become procedurally fluent occur at this stage of a lesson but the opportunity to develop proficiency in a range of problems are also actively encouraged; often, pupils choose where to pitch their own independent/collaborative learning, with some choosing activities that secure a concept whilst others engage in a task with increasing complexity, unfamiliar scenarios or opportunities to connect knowledge across Maths. Whilst teachers use their own professional judgment in offering this as a form of self-differentiation, ownership promotes a greater sense of motivation and, closely monitored by the teaching staff, enables the individual to challenge themselves appropriately. With a top down planning approach, the needs of all pupils are met and additional challenges help to ensure more of our pupils become deeper thinkers. Where additional support is needed, aside from quality first teaching, interventions take place outside of the classroom and include small group learning with a TA, or in some cases 1:1 with the child’s teacher during AfA time.
We recognise a lack of knowledge of multiplication tables to be a significant impediment to fluency with multiplication and division (and other associated concepts) and so times tables are a crucial component of our daily maths lessons; short, regular practice is noted in most lessons so pupils can rapidly recall those facts. We also value revisiting prior learning; this occurs daily (sometimes outside of the maths lesson, such as during registration), sometimes as a whole class discussion but usually in the form of our pupils responding to discrete questions which are then debated afterwards. This helps to embed knowledge and skills into our pupils’ longer term memory. Each set of questions target learning from last year, last unit of learning, last week and the previous day.
Parental involvement is an integral part of our pupils’ learning. Aside from parents’ evenings, we offer annual workshops to share our pedagogical approaches as well as to explain strategies within each of our year group’s written calculation’s policies; the latter ensures parents, during their children’s home learning exercises, are confident to teach the same methods as are used in school and are not tempted to move to more formal methods before their child is ready.