Why Teach 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.
Aims of the New National Curriculum
The national curriculum for mathematics aims to ensure that all pupils:
become fluent in the fundamentals of mathematics, including through varied and frequent practise with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.
can solve problems by 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.
Aims of teaching maths at Christ Church Primary School
To promote a positive attitude towards mathematics in all pupils
To ensure all pupils are engaged in and are enjoying exploring Mathematics
To enable all pupils to find links between mathematics and other areas of the curriculum, including Science
To ensure all pupils progress in mathematics and are challenged appropriately through an in depth understanding
To use a wide range of concrete, pictorial and abstract representations to develop all pupils’ relational understanding of mathematics
To ensure all pupils are confident using mathematical vocabulary when reasoning about mathematics
To promote a growth mind set in all pupils, particularly when Problem Solving
What is Fluency?
Fluency comes from deep knowledge and practice. This is the first stage of pupils’ understanding. Fluency includes: conceptual understanding, accuracy, rapid recall, retention and practice.
Accuracy – Pupils carefully completing calculations with no or few careless errors.
Pace – Pupils are able to quickly recall the appropriate strategy to solve the calculation and progress through a number of questions at an age appropriate pace.
Retention – Pupils will be able to retain their knowledge and understanding on a separate occasion to when the concept was first introduced.
How do we develop fluency at Christ Church?
Christ Church is committed to delivering a curriculum that is built on the latest educational research and evidence. As such, we are currently adopting the 10 Principles of Instruction proposed by Barak Rosenshine. These principles are based on research into how the brain acquires and uses new information; research on the classroom practices of those teachers whose students show the highest gains; findings from studies that taught learning strategies to students.
Principle 1 (Daily Review) states that a 'daily review is an important component of instruction. It helps strengthen the connections of the material learned. Automatic recall frees working memory for problem solving and creativity.' At Christ Church, pupils in years 1-6 begin every maths lesson with 'Flashback 4' - recall questions that require children to recall their knowledge of work that they did yesterday, a week ago, a month ago and a term ago.
Principle 10 (Weekly and Monthly Review) states that 'the effort involved in recalling recently-learned material embeds it in long-term memory. And the more this happens, the easier it is to connect new material to such prior knowledge.' At Christ Church pupils end each week with either an arithmetic test (to improve fluency) or a reasoning test (to improve reasoning). The teacher will then go through the answers with the pupils to enable them to learn from their mistakes and aim to improve their scores next time.
Rosenshine's principles suggest that frequent recall of learned facts will allow pupils to move the learning from their short-term / working memory into their long-term memory. This will enable pupils to become quicker in their recall, free up space in working memory to solve problems and reduce forgetting and thus become 'fluent'. Once fluency has been achieved, pupils are more able to reasoning about their maths journey and solve complex problems.
What is Reasoning?
Verbal reasoning demonstrates that pupils understand the mathematics. Talk is an integral part of mastery as it encourages students to reason, justify and explain their thinking. This is tricky for many teachers who are not used to focusing on verbal reasoning in their mathematics lessons. You might, for example, get young learners to voice their thought processes. Older students could take part in class debates, giving them the space to challenge their peers using logical reasoning.
A mastery classroom should never be a quiet classroom. The way pupils speak and write about mathematics transforms their learning. Mastery approaches use a carefully sequenced, structured approach to introduce and reinforce mathematical vocabulary.
To encourage talk in mathematics, teachers may introduce concepts by including sentence structures (stem sentences). Pupils should be able to say not just what the answer is, but how they know it’s right. This is key to building mathematical language and reasoning skills. This gives pupils the confidence to communicate their ideas clearly, before writing them down.
Example Stem Sentences:
The denominator is 5 because the whole has been divided into 5 equal parts.
The numerator is 3 because 3 equal parts have been shaded/circled.
Teachers then maintain a high expectation upon pupils to repeat and use the correct mathematical vocabulary to explain their understanding verbally and in their reflection comments. By also displaying the vocabulary during the lesson, pupils will be able to use this independently.
When questioning and encouraging mathematical talk, teachers should provide regular, purposeful opportunities.
- Show me how to complete the calculation
- Teach your friend how to complete the calculation
- How do you know which operation to use?
- Why have you chosen this method?
- How else can you represent this number?
- What have you learnt today?
- True or False
- Odd one out
- Sometimes, always, Never
What is Problem Solving?
Mathematical problem solving is at the heart of the Mastery Approach. Pupils are encouraged to identify, understand and apply relevant mathematical principles and make connections between different ideas. This builds the skills needed to tackle new problems, rather than simply repeating routines without a secure understanding.
Mathematical concepts are explored in a variety of representations and problem-solving contexts to give pupils a richer and deeper learning experience. Pupils combine different concepts to solve complex problems, and apply knowledge to real-life situations. Through problem solving, pupils are required to select their mathematical knowledge and apply this to a new concept.
White Rose scheme of work
Christ Church follows the White Rose scheme of work which provides opportunities for children to develop fluency, reasoning and problem-solving in both the teaching part and independent working part of the lesson. Teachers expect that all pupils will access questions in each of these areas, no matter their ability, and will support children where necessary as well as encouraging confident pupils to attempt harder questions.
A key foundation in mathematics is a firm understanding of the four operations (addition, subtraction, multiplication and division). Pupils build on this foundation every year, moving from using concrete resources (Numicon) in key stage 1, to pictorial and abstract representations in key stage 2. For more information on what this looks like at Christ Church please click here to view our calculation policy.