At the centre of the Guardian Angels mastery approach to the teaching of mathematics is the belief that all pupils have the potential to succeed.  Developing a 'Mathematical Mindset' in every child enables them to proactively self-regulate and take ownership of their learning through metacognition. They should have access to the same curriculum content and, rather than being extended with new learning, they should deepen their conceptual understanding by tackling varied and challenging problems. Similarly with calculation strategies, pupils must not simply rote learn procedures but demonstrate their understanding of these procedures through the use of concrete materials and pictorial representations to ensure fluency and depth of understanding.

The principle of the concrete-pictorial-abstract (CPA) approach is that for pupils to have a true understanding of a mathematical concept, they need to master all three phases. Reinforcement is achieved by going back and forth between these representations. Pupils who grasp concepts rapidly should be challenged through rich and sophisticated problems before any acceleration through new content. Those pupils who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on