The Teaching of Mathematics at Rivington Primary School
Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject. Where possible our mathematics curriculum will be linked to our school values: Respect, Protect, Give Thanks, Keep Peace.
Our mathematics journey began with the mathematics lead becoming an NCETM accredited professional development lead, which provided an opportunity to consider the pathways presented prior to the launch of the 2014 curriculum. Senior leaders decided to pursue a Singaporean Approach based upon our early experiences of bar modelling which we adopted at the first opportunity. We have proceeded to combine this deep learning exploratory approach with our own school expertise in order to provide the most effective learning programme for our pupils, ensuring that the overarching aims of fluency, reasoning and problem solving are at the heart of our mathematics learning. We see the use of concrete, pictorial and abstract models as key to developing children’s knowledge of mathematical concepts: understanding that this is not a linear process and that careful consideration should be given to which model or combination of models are used depending on the stage of learning in the area being studied.
In classrooms you can expect to see high levels of pupil engagement and involvement. Lessons usually begin with an interesting and engaging problem to solve and the teacher’s role is to make this accessible to all. Concrete and pictorial resources (usually in the form of representations or manipulatives) should be used (in virtually every lesson) to support the children’s thinking as they explore. Pupil talk should be encouraged at every opportunity, enabling peer support, challenge and/or refinement of ideas. Through these, learning should be highly visible. Teachers use pupils’ ideas to create a series of class discussions in which all are encouraged to participate, often attempting to see into the minds of those offering the ideas.
Different ideas are embraced and discussed. The class will spend a significant length of time reflecting on their own and others ideas: they do this through journaling and exploring the thinking of others. Towards the end of each lesson, the children practise what they have learned, usually through a number of examples guided by the teacher and ultimately, independently. The sequence of examples presented is adapted to suit each cohort, while maintaining variation, enabling the children to practise the same kind of problem in a number of different ways. Differentiation is precise and robust. Struggling learners are mainly supported through use of concrete and pictorial resources, peer dialogue and problems that are in real life situations. Gifted learners are challenged from the outset, being asked to prove or justify their ideas, create real-life authentic problems of their own or seek patterns within the problem/concept being explored.
Journals and worksheets are used in most lessons. Journals are used to develop pupils’ communication skills and record children’s thought processes, therefore deepening conceptual understanding. Once children have had the opportunity to refine their thinking, they are expected to record this using diagrams/drawings, writing and abstract mathematical notation. Teachers’ expectations of journals should be high, as should independence levels. Additional expectations of gifted mathematicians should be overt. Worksheets should be used to record children’s independent practice. You may find teachers asking children to annotate their work, explore further, or write similar problems of their own.
Lesson planning is different from lesson design. The Maths No Problem textbook has lessons that have been designed by expert mathematicians, psychologists and researchers. The teachers’ role is to use it as a tool and to bring the lesson to life for the children. As such, mathematics planning should demonstrate that the teacher has understood the lesson, identifying the key learning outcome(s), any particular barriers and opportunities to stretch the gifted mathematicians. In this way, the textbook becomes a supportive tool for teachers and, consequently, helps develop pedagogical subject knowledge.
The impact of a mastery session should be visible – the teachers’ planning should identify what the children’s learning should look like (what you expect to hear and see in the room) hence making it straight-forward to assess the quality of learning. If for some reason the teacher is unable to progress in the lesson (eg because of a misconception), they will take time to consider the most effective next steps. At times this will involve allowing children time to struggle without teacher intervention (to develop resilience and allow for exploration), and at other times it may lead to immediate intervention in the lesson. Feedback ‘in the moment’ should help children to address misconceptions. Feedback in lessons is mainly oral, though you may see teachers marking journals and workbooks whilst the children are writing in them (live marking). Marking after the lesson is in line with the NCETM guidance – if everything is going as it should, a simple acknowledgement will suffice (eg a tick). If something is wrong, the teacher will recognise it and show the pupil the correct way. An intervention may be necessary. If the whole class (or significant part of it) has a misconception the teacher’s planning of tomorrow’s lesson will demonstrate how remediation is to take place and there may be no reference to it in individuals’ books.
Children’s views: In our neighbourhood maths has traditionally had a negative image, with parents and children alike lacking confidence and easily confessing that they are ‘not good at maths’.
Since adopting a deep learning exploratory approach we have seen children’s confidence increase rapidly; they are now eager to talk about their ideas, to challenge and be challenged and consider themselves to be mathematicians.
Teacher confidence has also increased, as in order to ‘go deeper’ we have had to unpick the mathematics to identify key learning points, which in turn has broadened and deepened teachers’ understanding of possible misconceptions.
Equality and SEN Statement
At Rivington Primary School we aim to provide equality of opportunity for all children whatever their age, ability, gender, race, religion or background. We aim to create an environment that values each pupil and enables them to achieve their full potential. We provide a broad and balanced curriculum appropriately differentiated to respond to pupils’ diverse learning needs. The opportunities and experiences we provide enable our pupils to participate fully and give their best across all aspects of school life. We place great value on the quality of relationships within our school community and celebrate the achievements of all pupils.
We appreciate that children may have special educational needs throughout, or at any time during their school career. At Rivington Primary School we aim to facilitate the full inclusion of pupils with special educational needs.
The Progression Maps produced by the National Centre for the Excellence of Teaching in Mathematics show the objectives for each year group within each of the 10 domains.
The yearly overview for each class shows when each topic is taught.