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“A high quality maths education 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.”
Primary National Curriculum 2014
The mathematics curriculum at St Robert Bellarmine Primary School embraces this principal and aims to ensure that all of our children, from EYFS to year 6 are fluent in the fundamentals of maths, are able to reason mathematically and become confident problem solvers.
Fluency means becoming fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems.
In our school we ensure that children become confident in the two types of fluency.
e.g. exploring five strands of place value, what an equivalent fraction is and identifying features of different representations of data.
e.g. +- x ÷ calculation methods linked to whole numbers, fractions and decimals and exploring step by step methods.
Children at St Robert Bellarmine will be given regular opportunities to recall known facts, develop number sense, know why they are doing what they are doing and know when it is appropriate and efficient to choose different methods and will apply skills to multiple contexts e.g. x by 10 to convert units of measurements.
To ensure that children have accurate recall of facts and methods we give high priority to practise and consolidation. We keep this fluency ‘bubbling’ through regular practice to ensure children do not forget e.g. 4-a-day sessions and number of the week. We do this through the children selecting and choosing an appropriate method/strategy e.g mentally, jot or annotate or choosing an expanded or compact written method.
We Are Confident Reasoning Mathematicians at St Robert Bellarmine
Reasoning mathematically means following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.
In our school we ensure that children become confident in mathematical reasoning through providing opportunities for them to:
Conjecture relationships and generalisations e.g. if I add an odd and an odd number it will always result in an even number or all quadrilaterals have 4 right angles – true or false?
Developing an argument, justification or proof using mathematical language e.g. prove it, justify, convince me, how can you work it and how did you work it out?
Reasoning twists – this is explored through challenges such as: alike and different, odd one out, true or false, spot the mistake and sometimes, always or never true. These reasoning challenges can be adopted or adapted for any strand of mathematics: number, measurement and geometry.
The children champion Captain Conjecture as their mascot for mathematical reasoning.
To ensure that our children are confident in mathematical reasoning we model and encourage children to consider what sort of answer or working out is required linked to different reasoning questions e.g. verbally explaining, using words or numerals and symbols, pictorial representations such as ten frames, place value charts or tables and use of concrete equipment such as Numicon, base 10, bead strings
We Are Confident at Problem Solving at St Robert Bellarmine
Problem solving means applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
Problem solving requires the children to be secure in and build upon conceptual understanding (fluency) and mathematical thinking and language (reasoning) to help solve sophisticated problems in unfamiliar contexts.
We explore the five types of problem solving in different strands of mathematics –
The White Rose Maths Hub materials form the basis of the teaching sequences from EYFS to Year 6 at St Robert Bellarmine. This underpins our maths philosophy and ensures that fluency, reasoning and problem solving are taught through a concrete, pictorial and symbolic methodology.
Haylock’s Cognitive Connections, which is based upon Bruner’s Theory of Learning, underpins our mathematical rationale to the effective teaching and learning of mathematics. Bruner’s theory of learning is based upon the principle that new concepts (regardless of the age of the learner) are taught enactively (concrete), iconically (pictorial) and symbolically as ways of capturing experiences in the form of knowledge and understanding in the working and long-term memory.
Becoming a mathematician is a process that requires active involvement. We aim to provide opportunities for our children to become actively engaged in the learning process, to inspire children by giving them a lively sense of interest and enjoyment in mathematics, with an understanding of its practical and creative use in everyday life.
We believe that mathematics is best learned through activities that allow students, no matter what age or ability, to explore and understand the mathematical concepts with concrete apparatus. Using equipment helps to deepen understanding and creates visual and concrete images from abstract concepts. All classes from nursery through to year six use equipment in lessons. Children will be provided with opportunities to explore varied representations of the same concept using a variety of different equipment to support connections in their learning.
We aim to develop mathematicians who are confident to choose to use the most appropriate concrete, pictorial or symbolic resources for all aspects of fluency, reasoning or problem solving. A wide variety of resources are available in each classroom.
Real life Context
We encourage all our children to see that maths is an essential part of their everyday life. We try at all times to show them how maths is used in real life situations. To promote meaningful connections in learning, children are given real-life contexts to understand and to use and apply their mathematical knowledge. It should be presented through a real life context, which is meaningful and stimulating for all children at their own level. e.g. When teaching rounding and estimating in year 4, questions could be linked to the context of numbers of people in an audience or crowd. This begins in EYFS with the use of Maths Eyes and encouraging children to make sense of the world around them.
Quality questioning underpins our philosophy for teaching mathematics. At the start of every teaching sequence questioning enables teachers to assess where the children are in their learning and provides assessment allowing us to plan effectively for the future needs of the children. Questions are open ended and used as a basis for further questioning, to unpick misconceptions and deepen the children’s knowledge and understanding. The questions enable teachers to adapt their teaching to the needs of the children offering them the opportunities to exceed expectations and add depth to their understanding.
Mathematical language and definitions is explicitly taught, modelled and explored with children during fluency, reasoning and problem solving. A range of strategies and approaches are used to raise the profile of correct mathematical terminology and definitions e.g. whole school agreed glossary, mathematical dictionaries, displayed vocabulary and steps to success. Children are encouraged as mathematicians to be precise and accurate in their use of mathematical language when explaining, justifying or improving their reasoning.
Teaching for Mastery
Mastering maths means pupils acquiring a deep, long-term, secure and adaptable understanding of the subject. The phrase ‘teaching for mastery’ describes the elements of classroom practice and school organisation that combine to give pupils the best chances of mastering maths. Achieving mastery means acquiring a solid enough understanding of the maths that’s been taught to enable pupils to move on to more advanced material. (NCETM)