Definition

Maths mastery is an approach to teaching that gives pupils a deep, long-term, secure and adaptable understanding of mathematics.

The concept of mastery has its roots in the mastery model developed in the late 1960s by Benjamin Bloom, an American educational psychologist.

The mastery approach currently being promoted in structured approaches to teaching Mathematics shares some features with Bloom’s mastery model, such as the focus on a uniform degree of learning for all pupils and the desire for students to achieve a deep understanding of mathematical concepts.

However, a stronger focus on structure, early intervention and the consistent use of representations differentiates structured approaches from other models.

The core elements of the structured approach to mastery, as succinctly outlined by the UK National Centre for Excellence in the Teaching of Mathematics, are coherence, representation & structure, mathematical thinking, fluency and variation.

What are the Five big Ideas: 

Coherence

Teaching is designed to enable a coherent learning progression through the curriculum, providing access for all pupils to develop a deep and connected understanding of mathematics that they can apply in a range of contexts.

Representation and Structure

Teachers carefully select representations of mathematics to expose mathematical structure. The intention is to support pupils in ‘seeing’ the mathematics, rather than using the representation as a tool to ‘do’ the mathematics. These representations become mental images that students can use to think about mathematics, supporting them to achieve a deep understanding of mathematical structures and connections.

Mathematical Thinking

Mathematical thinking is central to how pupils learn mathematics and includes looking for patterns and relationships, making connections, conjecturing, reasoning, and generalising. Pupils should actively engage in mathematical thinking in all lessons, communicating their ideas using precise mathematical language.

Fluency

Efficient, accurate recall of key number facts and procedures is essential for fluency, freeing pupils’ minds to think deeply about concepts and problems, but fluency demands more than this. It requires pupils to have the flexibility to move between different contexts and representations of mathematics, to recognise relationships and make connections, and to choose appropriate methods and strategies to solve problems.

Variation

The purpose of variation is to draw closer attention to a key feature of a mathematical concept or structure through varying some elements while keeping others constant.

• Conceptual variation involves varying how a concept is represented to draw attention to critical features. Often more than one representation is required to look at the concept from different perspectives and gain comprehensive knowledge.

• Procedural variation considers how the student will ‘proceed’ through a learning sequence. Purposeful changes are made in order that pupils’ attention is drawn to key features of the mathematics, scaffolding students’ thinking to enable them to reason logically and make connections.

Credit for information to https://www.ncetm.org.uk/teaching-for-mastery/mastery-explained/five-big-ideas-in-teaching-for-mastery/