No Maths Mastery lesson should be the same, as all should be planned according to the needs of the class with a focus on our core principles.
The first and most important message is that there is no such thing as a Mathematics Mastery lesson. All lessons should be planned according to the specific context of the school and class, and therefore teachers should never feel compelled to ‘stick to’ specific lesson structures or ‘off the shelf’ activities. While lessons always vary, there is an expectation that lessons reflect the core principles of Mathematics Mastery. As such, teachers should use the planning resources to support them to apply the approach in a way that suits their class
All students will benefit from receiving a curriculum underpinned by a focus on C-P-A representations. Reinforcement of learning is achieved by going back and forth between these representations, and seeing them used in parallel.
- Concrete - the doing - At the concrete level, tangible objects are used to approach and solve problems. Almost anything students can touch and manipulate to help approach and solve a problem is used at the concrete level. This is a 'hands on' component using real objects and it is the foundation for conceptual understanding.
- Pictorial - the seeing - At the pictorial level, diagrams and other visual representations (e.g. bar models, number lines, diagrams, charts and graphs) are used to approach and solve problems. These can often be pictorial representations of the concrete manipulatives, in which case it is important for the teacher to explain this connection.
- Abstract - the symbolic - At the abstract level, symbolic representations are used to approach and solve problems. These representations can include numbers or letters. It is important for teachers to explain how symbols can provide a shorter often more and efficient way to represent mathematical relationships and operations.
Concrete manipulatives enable students to engage with the mathematics without the need for abstract representations. Even the most challenging algebraic concepts can be demonstrated using cubes and counters. Using these encourages students to really consider the underlying mathematics and develop their problem solving skills. Students should be asked to explain, justify and talk about what they are doing and how the manipulatives help them to do this.