At Greenbank, we have adopted an engaging and accessible style of mathematics teaching. Mathematical concepts are explored in a variety of representations and problem-solving contexts to give pupils a richer and deeper learning experience. We strive for our pupils to master mathematics so that they can represent a concept or skill in multiple ways, have the mathematical language to communicate related ideas, and can independently apply the concept to new problems in unfamiliar situations. This fits in very well with our school vision, that ‘We aim to provide a learning environment where all children can achieve their highest potential and to foster a climate where all children, regardless of class, race, gender or disability feel secure and can grow in confidence and self-esteem’.
‘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.‘ (National Curriculum July 2014)
Intent
A child’s ability to calculate; apply knowledge; to communicate fluently; to reason and to solve problems mathematically, forms the backbone of their education for life. Therefore, our intention here at Greenbank is to help children:
· enjoy maths through practical activity, exploration and discussion
· understand the importance of mathematics in everyday life
· become confidence and competent with numbers and the number system
· become fluent in the fundamentals of mathematics
· develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately
· to reason mathematically by following a line of enquiry,
· spot relationships across domains, make generalisations and express an opinion using mathematical language
· solve problems by applying their mathematics to a variety of routine and non-routine problems, including breaking down problems into a series of simpler steps
· keep persevering in seeking solutions and be aware that there are often many or even no solution
· develop an appreciation of the creative aspects of maths; awareness of its aesthetic appeal
· see the historic context and present day relevance of mathematics
Implementation
Maths is a core subject, given significant time on the timetable, with a daily lesson in every class, and Basic Skills sessions placed strategically throughout each week. We implement our approach though quality first teaching and the delivery of appropriately pitched work for all groups of learners supported by the materials from White Rose Maths and NCETM which are both fully aligned to the National Curriculum as well as the RtP criteria.
Visible throughout lessons are the 5 Principles of Mastery. Staff ensure that lessons are coherent; they are broken down into small, connected steps that gradually unfold the concept, providing access for all children and leading to a generalisation of the concept and the ability to apply their knowledge and skills to a range of concepts. Representations are used in lessons to expose the mathematical structure being taught, with the aim that pupils can do the maths without recourse to the representation. Mathematical thinking encourages the pupils to think, reason and discuss ideas and strategies within their classroom environment. Pupils become fluent mathematicians through quick and efficient recall of facts and procedures and the flexibility to move between different contexts and representations of mathematics. Variation is built over a sequence of lessons and representing concepts in more than one way.
The concept of teaching mathematics to mastery is to ensure that topics are well developed. Pupils will spend enough time to fully explore a concept before moving on to a different topic. As ideas are well formed they are reinforced by ample practice. New knowledge is then used on subsequent lessons so that all ideas build on top of each other and pupils have ample opportunity to develop relationships between the topics. Ideas are revisited in a spiral as pupils progress through the years, each time at a higher level. This ensures that the children see maths in a wider context, in different formats and in increasingly complex forms. Links are made with other subjects and the maths used cross-curricular, is of an appropriate standard for the age group.
The subject is well resourced with practical materials, and children are expected to learn when and where to use these resources. Plus, they should over time, identify which calculations need a practical tool for support; which should be completed using a formal method; and which should be done mentally or with jottings. Teachers use and emphasise mathematical vocabulary, and link the teaching to real-life situations, wherever possible.
Pupils in Foundation Stage will access their maths learning through daily lessons and continuous provision. Mathematical concepts are introduced and built upon through a series of direct teaching sessions. Within the provision, children have the freedom to further explore these mathematical concepts through concrete resources and creative opportunities. In addition to this, they are encouraged to follow their own mathematical lines of enquiry, which are supported through effective adult modelling and interactions.
Y1 through to Y6, Maths lessons are planned and delivered using the White Rose Maths programme. It is underpinned by the concrete, pictorial, abstract (CPA) approach. Varied starting points and timely teacher interventions are utilised in response to teachers’ ongoing formative assessments through effective deployment of teaching assistants.
Other key features within our teaching of mathematics that enable pupils to gain a deep understanding of mathematics:-
Mathematical talk and questioning: The way that children speak and write about mathematics has been shown to have an impact on their success. Our maths provision uses a carefully sequenced, structured approach to introduce and reinforce mathematical vocabulary. Every lesson includes time focused on vocabulary, use of stem sentences throughout with the expectation that children respond in full sentences and opportunities for children to explain or justify their mathematical reasoning.
Reasoning and problem solving: Mathematical reasoning and problem solving is at the heart of our approach – it is both how children learn maths, and the reason why they learn maths. By accumulating knowledge of mathematics concepts, children can develop and test their problem solving in every lesson. Pupils are encouraged to make connections across mathematical procedures and concepts to ensure fluency, mathematical reasoning and competence in solving problems.
Our lessons follow a 6-part structure. This structure keeps the lesson pacey, gives flow and allows more opportunities to teach creatively, give feedback and assess learning. The part are: Review and Do, New Learning, Guided Practice, Develop Learning, Independent Task, Plenary. All of this allows for cumulative, scaffolded learning where assessment is crucially feeding in to subsequent segments. Pupils are ‘doing’ straight away and no time is wasted.
Assessment takes place during every lesson, so that children are moved on quickly; at the end of a topic; and formally each term, to ensure that the children have achieved and continue to achieve. Support and intervention (for those who need it) is key in maths lessons, but the children are encouraged to work independently and strategically through their tasks.
Impact
By the end of KS2 we aim for children to be fluent in the fundamentals of mathematics with a conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. They should have the skills to solve problems by applying their mathematics to a variety of situations with increasing sophistication, including in unfamiliar contexts and to model real-life scenarios. Children will be able to reason mathematically by following a line of enquiry and develop and present a justification, argument or proof using mathematical language. Children will also recognise the importance of Mathematics as a facilitating subject to enable them to access other areas of learning and operate successfully is everyday life both now and in the future.
Factual fluency progression
Additive factual fluency
It is expected that pupils will have rapid recall of the following addition and subtraction facts –
Reception – Addition and subtraction facts for each number to 5
Year 1 – Addition and subtraction facts for each number to 10 and to count in 1s, 2s, 5s and 10s.
Year 2 – Addition and subtraction facts for each number to 20 and to count in 3s and 4s.
Year 3 – Sustain and maintain fluency in addition and subtraction facts.
Multiplicative factual fluency
It is expected that pupils will have rapid recall of the following multiplication and division facts –
Year 2 – To recall multiplication & division facts for 1s, 2s, 5s and 10s.
Year 3 – To sustain and maintain fluency in the multiplication and division facts for 1s, 2s, 5s, and 10s as well as learn to recall multiplication & division facts for 4s, 8s.
Year 4 – To sustain and maintain fluency in yr3 multiplication tables as well as the multiplication and division facts for 7’s, 3’s, 6’s, 9’s, 11’s and 12’s.
Year 5 + Year 6 – sustain and maintain fluency in all multiplication tables and corresponding division facts up to 12×12
For more any more information speak to Mrs Plant (Mathematics Lead).
