Oakthorpe’s aims and mathematical philosophy
At Oakthorpe, we believe that all children need to engage with a mathematical curriculum that engages them with real life situations, ensures that they are fluent in the fundamentals of mathematics and can reason mathematically. We feel that children need to develop a desire and curiosity around the subject of maths in order to be confident and competent in the application of their own mathematical understanding. We want the children to see and understand the importance of Mathematics in real life, everyday situations to ensure that they realise its full potential and importance in their lives, in school, and then later on in life. A Maths curriculum which is engaging, promotes finding patterns, problem solving and independence enables our children to think outside the box and apply their learning confidently and in diverse ways.
What does a mastery curriculum look like in practice?
Teachers at Oakthorpe use a variety of resources in order to support children’s fluency, reasoning and problem solving skills. We mainly take our ideas and teaching sequences from the White Rose documents but we have developed these further to ensure that they meet the needs of our children. We have adapted and added to this curriculum to ensure that the small steps of learning are accounted for, thus ensuring that children move through the school with a thorough understanding of key concepts. Children are expected to work at a similar pace through their learning while using a range of models, images, concrete, pictoral and abstract resources.
It is the aim of a Mastery Mathematical curriculum to ensure that all children have the opportunity to be successful and match the ability of their peers. Children are expected to move through the curriculum at roughly the same pace, enabling some children to narrow any gaps within their learning while other children have the opportunity to deepen their understanding in a wide variety of ways. For some children, additional support is required in order for them to fill in any gaps within their learning and to help them progress with their understanding. This is done through interventions which are specifically targeted in key objectives the children are finding a challenge and through consolidation of lessons where they may need a bit more time to become confident. There are also some children for whom this learning develops quicker and they are given additional challenge through tasks which encourage deeper thinking. Children are encouraged to complete tasks which may be open ended, have multiple answers and help to rigorously assess the child’s true understanding through their ability to explain, reason and give alternative methods for what they have done. Variation of key learning themes is a fundamental tool when developing deeper thinking and this is seen by children tackling problems of a similar nature which have a high cognitive demand on the child through the wording, images or lay out of a question.
Number fact fluency
Children’s number fact fluency relate to key facts which children need to develop as they are the solid basis on which all calculations then stem from. When children have a firm understanding of these facts they are able to lessen their cognitive load and focus solely on the method of calculation, not the number facts. Children will develop their understanding of these facts from as soon as they enter school. Some of the key number facts which children need to know are:
- Number bonds to 10
- Number bonds to 20
- Number bonds to 100
- How to use the related facts of number bonds to 10, 20 and 100.
- Times tables facts
- Bridging 10 and 100
Children will also be taught how to evaluate the efficiency of a method in order to select the most appropriate method for the calculation. It is imperative that children are confident in selecting these methods so as to see the mathematical structure alongside procedures. For example if a child was given the question 200-199 and they began to solve this with column subtraction, it would not be an efficient strategy and would probably cause more confusion due to exchanging whereas a child who was fluent in number facts would recognise that they could count on from 199 to 200 easily.
At Oakthorpe, we want children to develop their fluency and understanding of these key facts rather than just memorising them and not fully understanding their true meaning and purpose. For example, a child who can chant all of their times tables may appear to be fluent but unless they can apply this knowledge into other areas of maths then they are not yet secure in their understanding of what multiplication means.
An important part of teaching this number fluency is to ensure that children are being explicitly taught strategies when solving problems. When a child is learning to add and subtract, we don’t just want them to understand what 3+4 or 7-2 means. We want them to be able to explore what happens when you add or subtract to certain numbers. We encourage children to explore statements such as, ‘You will always get an odd number if you add two odd numbers together.’ Children will then use their number facts to investigate this statement and state whether they think this is true or false. Children will then be able to
At Oakthorpe, we are aware of how important learning times tables is. We expect that all children in Year 2 should be confident in knowing their 2,5,10 and 3 times tables and that all children will have mastered their times tables by the time they reach the end of Year 4. With this in mind, children learn about the different times tables in a range of ways. Children are taught times tables by first chanting in constant steps of the number (3,6,9,12), then by being able to state the answer of how many times a number is (3x4=12) and then by using the associated division facts for that times table (12÷3=4). As well as teacher led activities within the classroom, children have access to Times Tables Rockstars to use in school and outside of school. This can be in the form of an app and through the website. Each child has their own log in details and so teachers are able to set different times tables for children to compete at different times. This enables children to focus on one times table or answers questions from a selection of times tables which they already know.
From 2019/2020 all Year 4 children will be expected to take an online times tables check to ensure that they have met the age related expectation of knowing their times tables from the 2 times tables to the 12 times tables.
Whole school mastery themed weeks
As part of our mastery commitment, we have held whole school themed weeks around one mathematical theme. Recently, we investigated an open ended problem from N Rich to explore a ‘Fraction Feast’. The week began with children being shown a selection of different food items which they were to take back into their classrooms to explore the different ways in which we could share the feast. This was a fantastic opportunity for children to explore the misconceptions around fractions and division. Children across the whole school were able to talk about how they could share the feast and generated their own questions, such as, ‘What if we had 2 breadsticks and 3 people?’ These questions were the starting point for the feast and all children had the opportunity to explore their question.
A Mastery lesson
During a Mathematics lesson at Oakthorpe, you would expect to see:
- A clear objective which is part of a carefully planned sequence of learning which takes the small steps of larger objectives into account.
- Precise, varied and targeted questioning which enables learners to expand on their answer develop their ‘why’.
- ‘Grapple’ problems which give learners the opportunity to explore a problem in different ways to really get ‘stuck-in’ to their learning.
- Children answering questions and developing their reasoning using a range of sentence stems to support the development of their answers in order to give a precise and water tight answer.
- A range of resources for all children to use, throughout the school.
- Teachers and teaching assistants supporting, teaching and assessing children constantly throughout a lesson. Sometimes this is whole class directed teaching or through group work.
- Feedback being given to children through marking and mini-plenaries; 1-2-1, group or whole class.
- Targeted intervention during the lesson where children may be brought together by teacher or teaching assistant to support learning.
- Children have the opportunity throughout different lessons to work independently, in small groups and in larger groups.
- Misconceptions are rapidly picked up on and addressed by teachers and teaching assistants to ensure that children are confident in what they are learning about.
- Complex challenges are directed at children who need to deepen their understanding in different ways.
- Children’s learning is marked using green and orange highlighters. Adults will highlight children’s work to show their successes and any areas which children need to look back at. Marking is done in the moment to provide immediate feedback to the child, this enables children to discuss their learning with an adult. Children develop the skill of editing by looking at any orange highlighting and then looking at the problem again in order to be more accurate.
- Spaced practice is an important part of retaining information and so we use ‘Progress Pit Stops’ as a way of drawing back on previous learning to help children recall facts they have already mastered. The questions on the ‘Progress Pit Stops’ are designed to help children develop an understanding that even though they may be learning about a unit on multiplication, that all their previous learning, like place value, is also still important.
EYFS and the mathematics curriculum
Our EYFS mathematics curriculum has been rigorously designed to ensure that children begin their mathematical understanding by developing an excellent sense of number. It is through a balance of quality first teaching and high expectations in carefully planned continuous provision that children are able to achieve this depth in number. Children are encouraged to explore tasks which help develop and support early mathematical concepts through the enabling environment within each provision area. For example, children have the opportunity to explore measuring in the small world area, capacity through the sand and water area and number lines and real life number problems within the role play.
Alongside the continuous provision, children within EYFS use a range of books and songs to help them retain mathematical information.
What do Mathematics books look like?
All of our maths books at Oakthorpe are designed to show clear learning and progress throughout a topic of learning. In order to show this, children first complete a cold task at the beginning of a unit in order to show what they already know. This task also highlights some of the key areas of learning that will take place. Children will then show their learning journey through a range of activities including fluency practice, games, open ended tasks, grapples, guided maths and independent activities.
Throughout the unit, children will have the opportunity to reflect on previous learning to ensure that this still stays fresh in their minds and that they are able to recall a range of methods, calculations and key facts confidently. When teachers and teaching assistants have worked with children in a lesson, or through an intervention, this will be recorded and shown in the child’s book. There are many opportunities for children to reflect on their maths learning and edit using a pink pen. This gives children the ability to contemplate their solution and develop it with the support of a peer, an adult or after other learning has taken place.
At the end of the unit, children will complete a hot task which will be directly linked to the cold task so that children can show the learning that has taken place. This is a great opportunity for children to show how successful they have been.