"So teach us to number our days that we may get a heart of wisdom"
Statement of Intent
Our aim is to equip all students with the skills and confidence to solve a range of problems through fluency with numbers and mathematical reasoning. Students are encouraged to see the mathematics that surrounds them every day and enjoy developing vital life skills in this subject.
As a school, we believe that students from all backgrounds can succeed in mathematics and that mathematics is a key that opens the door to other aspects of life and underpins other areas of the curriculum. We aim for every child to develop a complete understanding of maths, equipping them with the skills of calculation, reasoning and problem solving that they need in life beyond school.
We want all learners to appreciate
- Mathematics is a universal language, it allows us to communicate with others and to understand, affect and develop the world around us.
- Mathematics is a subject of beauty and this can be seen in many things from the plants and people we see around us to the machines and technology we design and use in our daily lives.
- Mathematics fosters reasoning and problem solving leading to mastery and logical thinking which builds well rounded and aspirational citizens of the future.
We aim to ensure that all students:
· become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that they have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems
· 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.
The principle focus in EYFS is that children leave this stage with a strong sense of number. They have developed fluidity and flexibility with numbers and have an understanding of what numbers mean, and can begin to perform simple mental mathematics. They can count reliably with numbers from 1 to 20, as well as (when using quantities and objects) add and subtract and solve problems that involve doubling, halving and sharing.
Key Stage 1
The principle focus of mathematics teaching in Key Stage 1 is to ensure that students develop confidence and mental fluency with whole numbers, counting and place value. This involves working with numerals, words and the four operations.
Lower Key Stage 2 – Years 3-4
The principle focus of mathematics teaching in lower Key Stage 2 is to ensure that students become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. This should ensure that students develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers.
At this stage, students develop their ability to solve a range of problems, including with simple fractions and decimal place value.
Due to the Times Table Check at the end of Year 4, all pupils in Lower Key Stage 2 have time each day on our school laptops, using the program Times Table Rockstars. The aim of the program is for the children to develop rapid and consistent recall of their multiplication facts. Doing this ensures that they are ready for the next steps on their maths journey in Upper Key Stage 2.
Upper Key Stage 2 – Years 5-6
The principle focus of mathematics teaching in upper Key Stage 2 is to ensure that students extend their understanding of the number system and place value to include larger integers. This should develop the connections that students make between multiplication and division with fractions, decimals, percentages and ratio.
At this stage, students develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. With this foundation in arithmetic, students are introduced to the language of algebra as a means for solving a variety of problems.
By the end of Year 6, the aim is for all students to be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages.
Planning and Teaching
Whole class together
Mathematics is taught to the whole class over five 60-minute lessons per week in KS1 and 2, and with five 20-30 minute lessons per week in EYFS. Lessons are planned based on formative assessment of what students already know and all students are included in learning mathematical concepts. At the planning stage, teachers consider what scaffolding may be required for students who may struggle to grasp concepts in the lesson and suitable challenge questions for those who may grasp the concepts rapidly, altering and adapting White Rose plans where necessary.
Potential misconceptions are identified during the planning process and key questions are constructed to allow students the opportunity to address these misconceptions. These possible misconceptions are always planned for and students will be supported when addressing these.
Questions are used to challenge thinking as well as to probe student understanding. Responses from students are expected in full sentences, using precise mathematical vocabulary.
Key questions are planned for and often repeated in order to provide many reasoning opportunities for the students: How do you know? Can you prove it? What would happen if…? What’s the same/different …? Can you explain…?
Questions are also used to challenge students who have grasped the concept. Students are expected to listen to each other’s responses and may be asked to explain someone else’s ideas in their own words, or if they agree/disagree etc.
Achieving depth of understanding
As we aim to embed a deep understanding of maths, we employ the concrete, pictorial, abstract approach (CPA) across all phases– using concrete materials (e.g. objects) and pictorial representations (e.g. pictures, diagrams) alongside the use of numbers and symbols. This supports students to develop a deeper conceptual understanding of the underlying mathematical structure as opposed to solely learning routines, procedures and algorithms without developing a deep understanding of mathematics.
We recognise that ‘fluency’ is not just about remembering facts and develop all aspects of fluency through lessons. Fluency encompasses skill and dexterity when using number, being able to use number creatively and with skill. This is based on a fluency with basic facts - there is a whole school focus on developing an instant recall of key facts, such as number bonds, times tables and root addition facts.
In mathematics new learning is built upon previous understanding, so in order for learning to progress and to keep the class together, students need to be supported to keep up and areas of difficulty must be dealt with as and when they occur. We do this through same day feedback, targeted to students in lessons as teachers ‘helicopter mark’ around the classroom. In addition, we still run intervention sessions outside of the maths lesson for some targeted students, based on the marking and feedback from formal assessments.
- have high expectations of themselves and all students
- are precise in their written mathematics and also in their spoken mathematics. We expect all learners to display and communicate using correct terminology to help solidify the meaning of keywords
- are expected to impart knowledge accurately and with enthusiasm which generates high levels of commitment from students
- support students to make rapid and sustained progress in lessons
- support students to develop independence
- systematically check understanding, intervening in a timely manner when needed
- Provide students with adequate challenge in order to deepen their understanding of concepts
- regularly provide constructive feedback to students
Teachers use formative assessment to help decide on what they should do next with students and the progress they are making. This allows them to understand how to support and extend their students appropriately.
Staff recognise the difference between performance and learning and understand that student performance in the lesson today does not necessarily translate into the type of learning that will be evident tomorrow. As a result, the use of low stakes tests - such as on Times Table Rockstars, or in pop-quiz style lessons in EYFS - will enable staff to regularly assess what learning has been retained by students over longer periods of time. This also provides students with the regular opportunity of retrieving information from memory, which consequently facilitates learning.
Formative assessment opportunities:
· assessment for learning
· student voice
· challenge tasks
· quizzing, multiple choice and end of unit questions
· standards of learning in books
· spaced retrieval practice