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.
Children at Christ Church follow the White Rose schemes of learning in Maths. This follows the mastery curriculum which ensures that our children develop a deep and secure knowledge and understanding of mathematics at each stage of their learning.
Our Maths teaching aims to:
promote a positive attitude towards mathematics in all pupils
ensure all pupils are engaged in and are enjoying exploring Mathematics
enable all pupils to find links between mathematics and other areas of the curriculum, including Science
ensure all pupils progress in mathematics and are challenged appropriately through an in depth understanding
use a wide range of concrete, pictorial and abstract representations to develop all pupils’ relational understanding of mathematics
ensure all pupils are confident using mathematical vocabulary when reasoning about mathematics
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.
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. White Rose follows the 'concrete, pictorial, abstract' approach to teaching Maths and we encourage the use of practical apparatus for the introduction and reinforcement of concepts as well as mathematical language.
In line with National Curriculum’s expectation that the ‘majority of pupils will move through the programmes of study at broadly the same pace’, all children will have access to the same content. To meet the differing learning needs of the children, teachers may adjust the pace of the lesson, provide further reinforcement or greater depth, reasoning and problem solving learning opportunities.
Times Tables Rock Stars
In Year 4, all children nationally will be taking an online Times Table Check on all multiplication facts up to and including 12x12 (you can find the Parent Information Guide attached below). To support this, children in Years 1-6 have access to Times Tables Rock Stars through their own username and password. Children have the opportunity to practice and build upon their times tables skills in a motivating and engaging way.
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 see below for our calculation policy
Pupils learn in an environment where maths is promoted as being an exciting and enjoyable subject in which they can investigate and ask questions. As a result, pupils have a positive view of maths. Positive relationships between staff and pupils mean that children feel safe to make mistakes and know that it is OK to be ‘wrong’ because the journey to finding an answer is most important. Children are confident to ‘have a go’ and can use manipulatives, along with learnt strategies to solve problems.
Our children have a good understanding of their strengths and targets for development in maths and what they need to do to improve. Our maths books evidence work of a high standard of which children clearly take pride; the activities demonstrate good coverage of fluency, reasoning and problem solving.
Our feedback and interventions support children to strive to be the best mathematicians they can be, ensuring a high proportion of children are on track or above.
Our school standards are high, we moderate our books both internally and as part of the wider Kaleidoscope MAT and children are achieving well.