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Mathematics
“Mathematics is a creative and highly inter-connected 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.”
National Curriculum 2014
At Barnes, we aim for our maths teaching and learning to resonate with this statement. We fully appreciate the contribution of mathematics to everyday life and society. Equally, we value the contribution of mathematics in other areas of the curriculum and in promoting children’s curiosity, enjoyment of learning and intellectual development.
We aim for children to:
- enjoy the maths they are taught;
- notice and appreciate maths in the world around them;
- have a positive attitude towards learning maths and expect to be successful;
- acquire a strong fluency in basic number facts and procedures;
- calculate using a range of strategies, choosing the most efficient methods;
- talk and reason about their understanding, using precise mathematical language;
- identify underlying structures, patterns and relationships;
- approach problems with resilience and creativity;
- have a deep conceptual understanding, representing key ideas in diverse ways and appreciating connections between different areas of the curriculum;
- develop both decision making and logical thinking;
- apply and develop their mathematical understanding and knowledge in all other areas of the curriculum;
- work both collaboratively and independently.
“You don’t have to be fast at maths, you just have to be curious!”
Inspired by Marcus du Sautoy.
“Sometimes the questions are complicated, and the answers are simple.”
Dr. Seuss.
Our approach
Here is a summary of the school’s approach towards mathematics and outlines how our vision is implemented. A teaching for mastery approach is used throughout the school, based on the National Centre for Excellence in the Teaching of Mathematics’ (NCETM) “Five Big Ideas”, first published in 2017. Further information about the Five Big Ideas (coherence, variation, fluency, mathematical thinking and representation and structure) can be found on the NCETM’s website https://www.ncetm.org.uk
Planning
Planning in mathematics is in line with the National Curriculum Programmes of Study for mathematics. These set out what should be taught in each year group from Year 1 to Year 6. Each year group maps out how many weeks will be spent on each different aspect of mathematics; within each of these units of learning, a clear sequence of learning objectives is established. Each learning objective may be the learning focus for one or several sessions. Each daily session is planned directly into ActivInspire flipcharts and incorporates a coherent journey with small progressive steps in order for all children to secure the learning.
Teachers draw on a number of high quality resources to support with planning. These include: the National Centre for Excellence in the Teaching of Mathematics (NCETM) spines; White Rose premium resources; Power Maths; nrich; Gareth Metcalfe reasoning and problem solving.
Resources
One of the key aspects of effective mathematical pedagogy is the use of both physical resources (manipulatives) and pictorial representations alongside abstract mathematical recording. Concrete and pictorial representations are chosen carefully to reveal the underlying structures, patterns and relationships of the mathematics. It is important that links between the three stages (concrete – pictorial – abstract) are explicitly made during teaching and that all children, regardless of attainment or age, are exposed to a variety of different representations as a result of planned conceptual variation. Manipulatives are removed at an appropriate stage when conceptual understanding is secure so they are not used procedurally during calculations.
Lesson structure
The structure of a lesson will vary based on the topic covered and the needs of the pupils. Steps throughout a lesson are small to ensure that all pupils understand the key concepts before they are exposed to new ones.
During a lesson, children will typically be given the opportunity to review previous learning, link previous learning to new learning, practise new skills, apply these skills in different ways and reason and explain about the concept. Lessons will include a mix of direct teaching, paired tasks and independent practice.
Support and extension
The majority of children in a class move through the programme of study at broadly the same pace and are exposed to the same learning opportunities. Children in all classes sit in mixed attainment pairs to promote collaborative learning, exposure to different ideas and opportunities for discussion. Learners are supported by the clear structure of the lesson, their peers and additional adults as well as scaffolds provided by teachers. Children are extended through: higher order questioning; the expectation to use precise mathematical vocabulary in both oral and written explanations; the exposure to rich extension tasks. It is expected that all pupils will experience challenge in a lesson.
Marking
All adults in the classroom mark during the lesson giving children immediate feedback and support. Towards the end of a lesson, children have an opportunity to check their understanding and self-assess. Teachers review work following a lesson to ensure all children have secured the learning objective. Yellow highlighting indicates accurate work and strong understanding; green highlighting indicates errors to review. If appropriate, teachers will suggest next steps to be able to meet the learning objective or might pose a question to support the pupil to close the gap. If there is a common misconception, the whole class will be exposed to it within the next lesson. At the beginning of the following session, pupils are given an opportunity to review marking, correct errors and respond to teacher feedback.
The following documents set out how the four operations of addition, subtraction, multiplication, and division are taught from Year 1 to Year 6.
Essential principles
With thanks to Professor Jo Boaler, Professor of Mathematics Education at the Stanford Graduate School of Education for her guiding words of wisdom.
Encourage children to play maths puzzles and games. Puzzles and games will help children enjoy maths, and develop number sense, which is critically important.
Always be encouraging and avoid telling children they are wrong when they are working on maths problems. Instead find the logic in their thinking; there is always some logic to what they say.
Never associate maths with speed. It is not important to work quickly, and we now know that forcing children to work quickly on maths can cause maths anxiety for children. Instead of speed drills use visual, fun activities.
Be positive about maths even if your feelings about your own maths education is not!
Encourage number sense. What separates high and low achievers is number sense – having an idea of the size of numbers and being able to separate and combine numbers flexibly. For example, when working out 29 + 56, if you take one from the 56 and make it 30 + 55, it is much easier to work out. The flexibility to work with numbers in this way is what is called number sense and it is very important.
Encourage a “growth mindset” let your children know that they have unlimited maths potential and that being good at maths is all about working hard. When children have a growth mindset, they do well with challenges and do better in school overall. When children have a fixed mindset and they encounter difficult work, they often conclude that they are not “a maths person”. One way in which parents can encourage a fixed mindset is by telling their children they are “clever” when they do something well. Instead, use growth praise such as “It is great that you have learned that!”, “I really like you’re thinking about that!”. When they tell you something is hard for them, or they have made a mistake, tell them: “That’s wonderful, your brain is growing!”
Point out the maths in everyday life and in notice patterns in the natural world. Include your child in activities involving numbers and measuring, such as shopping, cooking, travelling and telling the time.
https://www.nationalnumeracy.org.uk/helping-children-maths/family-maths-toolkit
The National Numeracy Family Maths Toolkit is full of ideas and free activities to help families enjoy maths together.
https://www.youtube.com/user/MathsOnToastChannel
Maths on Toast’s mission is to make maths a creative, enjoyable, hands-on, social activity for families and communities. There is a wealth of creative, stimulating ideas for fun with maths at home, all supporting the national curriculum and your child’s development in number, shape and pattern.
https://thirdspacelearning.com/blog/how-help-child-with-maths-at-home/
This is a very helpful year-by-year guide to the different aspects of maths your child will encounter and where there might be difficulties. It will help you to understand how maths is taught and the language used.
