At Beamish and Pelton, we have high expectations that all pupils can and will achieve, and this has led to us adopting a ‘mastery’ approach to planning and teaching maths.
Mastering maths means acquiring a deep, long-term, secure and adaptable understanding of the subject. Once a pupil has achieved mastery, this means that their understanding of the maths topic they have been studying is solid and they can now move on to more advanced material.
Some people confuse mastery with Greater Depth but they are two very different things. All children in our federation have access to a Mastery curriculum which is based on the idea of ensuring all children have ‘mastered’ their mathematics and secured a deepened understanding (as mentioned above). Greater Depth refers to pupils who show a higher level of understanding for an area or aspect of learning and are able to challenge themselves further with new concepts and ideas.
The mastery approach is defined by five key principles, which are illustrated in the diagram below:
Lessons are broken down into small connected steps.
Representation and Structure
Representations used in lessons expose the mathematical structures being taught, the aim being that students can eventually do the maths without needing the representation.
We use lots of different equipment and a variety of images to support our learners. Here you can see Part Whole Models, Tens Frames and Bar Models:
If taught ideas are to be understood deeply, they must not merely be passively received but must be worked on by the student: thought about, reasoned with and discussed with others.
Mathematical Thinking involves:
- looking for patterns;
- looking for relationships and connecting ideas;
- reasoning logically, explaining, conjecturing and proving
Here are some of the types of Mathematical Thinking questions we use:
- Always, Sometimes, Never?
- Convince me …
- What do you notice?
- What’s the same? What’s different?
- True or false?
Fluency is the quick and efficient recall of facts and methods and the flexibility to move between different contexts and representations of mathematics.
Procedural fluency is knowing number facts and times tables. It is also being able to carry out methods efficiently.
Conceptual fluency is being able to use mathematical knowledge in different contexts and recognising mathematical concepts in unfamiliar situations.
Variation is twofold. It is firstly about how the teacher represents the concept being taught, often in more than one way, to draw attention to critical aspects, and to develop deep understanding. It is also about the sequencing of the activities and exercises used within a lesson and follow up practice, paying attention to what is kept the same and what changes, to connect the mathematics and draw attention to mathematical relationships and structure.
Click here to read more about the key messages behind the Five Big Ideas.