The Mathematics Curriculum
How maths is organised in school
All cohorts follow the National Curriculum for maths Age Related Expectations (ARE) based around the aims of fluency, mathematical reasoning and problem solving. The National Curriculum places higher expectations on pupils and teachers. It requires teaching to mastery. The Singapore approach to teaching mathematics that we use at St Philip’s unpacks mastery and ensures deep learning. In all key stages, pupils who grasp concepts rapidly are challenged through rich and sophisticated problems before any acceleration through new content and those who are less secure are supported to consolidate their understanding before moving on.
A typical Singapore maths lesson
Our children’s curiosity is ignited through exploration of a really good problem that is easy to enter but difficult to leave. Deep learning takes through challenge, consolidations with the use of variance of context. Children make links and connections using a blend of practical apparatus, moving from using concrete resources to visual representations (picture form) and then progressing to the abstract form.
Every lesson includes:
- An anchor task: A rich and sophisticated problem that is explored by using concrete resources. Children identify methods to tackle the problem which are then recorded in the child’s journal. Journaling allows the opportunity for children to record their chosen methods and challenge themselves by thinking of the most efficient method and other possibilities.
- Let’s learn: This allows the teacher to model and explain key methods for solving the problem.
- Guided Practice: This part of the lesson allows the teacher to scaffold the children’s learning which then supports all learners ready for independent work.
- Independent workbooks: Children apply the skills that have been taught independently.
- Challenge / Support: Some children may progress through their independent activity quicker than others therefore challenges are set to extend their thinking further. Challenges extend the child’s thinking by applying their knowledge creatively to word problems, writing explanations, thinking of their own problems, thinking of other possibilities and combinations of methods and number facts. Other children may require additional support during lessons, this is provided by a teacher or teaching assistant, through the use of practical resources or through sitting in mixed ability groups as the children develop their ability to coach each other’s learning.
- Pre learning/ Post learning: Children may take part in pre learning activities which give children the opportunity to work closely with a teacher or teaching assistant to have a preview of area they will then be engaging in in class. Post learning may take place to recap areas of learning or if children need additional support to grasps certain methods or concepts.
Differentiation will be evident in how the teacher helps all pupils in the class to understand new concepts and techniques. The blend of practical apparatus, images and representations within the Singapore Model may be different for different groups of pupils, or pupils might move from one to the next with more or less speed than their classmates. Skilful and carefully planned questions are key, as is creating an environment in which pupils are unafraid to grapple with the mathematics. Challenge comes through more complex problem solving, not a rush to new mathematical content.
A Mastery Approach to Teaching and Learning
A Mastery approach to teaching mathematics requires all children to develop a deep understanding of concepts. Depth of understanding is demonstrated by ‘unpicking’ concepts so that children can recognise and apply their knowledge creatively in different contexts and situations. Children have experience of and understand a concept in a variety of ways and develop fluency by making links between their knowledge of number (e.g. 7 x 3 = 21 leads to knowing 70 x 3 = 210 and 3 x 70 = 210 and 3 x 7 x 10 = 210).
Depth and mastery embeds a deeper understanding of maths by utilising a concrete, pictorial and abstract approach so that pupils understand what they are doing rather than learning to repeat routines without grasping what is happening.
Feedback and Marking
Feedback underpins the lesson delivery. There is continuous dialogue between teachers and children through reasoning and explanation. In the work book you will see correct answers with a tick. This book is used for the child to practically apply the concepts that they have explored through reasoning and the use of manipulatives at the start of the lesson. In the journal you will find that children use this to explain their thinking and teachers may challenge this further through written or verbal feedback. Children will respond to this dialogue by revisiting concepts, attempting challenge tasks and correcting misconceptions in red pen when responding to the teacher.
A Growth Mindset in Mathematics
The Singapore approach aims to support children’s understanding using a variety of methods and build upon their knowledge in every lesson. It is important that children become resilient learners and through tackling a variety of problems, children will become equipped to explore a range of methods and have an open mind to others’ ideas. Reflecting on their own learning is important, and teaching children to have a positive attitude to learning will encourage them to challenge themselves further. Rather than thinking “I cannot do this,” they should be encouraged to think “I cannot do this yet but I will persevere and tackle this in a different way,”. With the tools the Singapore approach provides, children will become fully equipped to tackle any problem given to them therefore taking a positive mindset towards their learning and mathematics.
Assessment and Progress
Pupil attainment will be assessed through the use of tests and teacher assessment linked to the Age Related Expectations (ARE).