At Lovelace, we believe using key principles that enable teaching for mastery is the most effective approach in order for our children to become confident and proficient mathematicians. As the NCETM (National Centre of Excellence in Teaching Mathematics) states, “Mastery means pupils of all ages acquiring a deep, long-term, secure and adaptable understanding of the subject. The phrase ‘teaching for mastery’ describes the elements of classroom practice and school organisation that combine to give pupils the best chances of mastering maths.”

Pupils are taught through whole-class interactive teaching (involving demonstrations, explanations, questioning, discussions and short tasks) where the focus is on all pupils working together on the same lesson content at the same time. This ensures that all can master concepts before moving to the next part of the curriculum sequence, allowing no pupil to be left behind. This approach develops deep and sustainable knowledge and understanding that enables pupils to be able to reason about a concept, make connections and have conceptual and procedural fluency. 

Teaching for mastery is about:

• The belief that all pupils can achieve in maths
• Keeping the class working together so that all can access and master mathematics
• Development of deep mathematical understanding before moving on
• Development of factual, procedural and conceptual fluency
• Spending longer on key topics, providing time to go deeper and embed learning
• Children working in mixed ability pairings with differentiation occurring via the support and intervention provided. Quick identification of children who have not grasped a concept or procedure and ‘Keep Up’ interventions utilised.  

There are five big ideas which underpin teaching for mastery: coherence, representation and structure, variation, fluency and mathematical thinking. 

Coherence – Small steps are easier to take. Focussing on one key point each lesson allows for deep and sustainable learning. Certain images, techniques and concepts are important pre-cursors to later ideas. Getting the sequencing of these right is an important skill in planning and teaching for mastery. When something has been deeply understood, it can and should be used in the next steps of learning.

Representation and structure – The representation needs to pull out the concept being taught, and in particular, the key difficult point. It exposes the structure of a concept being taught and acts as a scaffold. In the end, the children need to be able to do the maths without the representation. A stem sentence describes the representation and helps the children move to working in the abstract. There will be some key representations which the children will meet time and again. Pattern and structure are related but different: children may have seen a pattern without understanding the structure which causes that pattern.

Variation – The central idea of teaching with variation is to highlight the essential features of a concept or idea through varying the non-essential features. As stated by Mike Askew in Transforming Primary Mathematics (2001), Awareness, according to Marton and Booth (1997), has a structure to it. By this they mean that the amount of sensory data that we are subject to cannot all be dealt with at once; some things have to be to the foreground of our awareness, others will not. We must try and help learners focus their awareness on critical features.

Conceptual variation – When giving examples of a mathematical concept, add variation to emphasise: What it is (as varied as possible) and what it is not. 

• Procedural variation – When constructing a set of activities/questions, consider what connects the examples; what mathematical structures are being highlighted? Variation is not the same as variety – careful attention needs to be paid to what aspects are being varied (and what is not being varied) and for what purpose.

• Fluency – Fluency demands more of learners than memorisation of a single procedure or collection of facts. It encompasses a mixture of efficiency, accuracy and flexibility. Quick and efficient recall of facts and procedures is important in order for learners to keep track of sub problems, think strategically and solve problems. Fluency also demands the flexibility to move between different contexts and representations of mathematics, to recognise relationships and make connections and to make appropriate choices from a whole toolkit of methods, strategies and approaches.

Mathematical Thinking – Mathematical thinking is central to deep and sustainable learning of mathematics for all pupils. Taught ideas that are understood deeply are not just ‘received’ passively but worked on by the learner. They need to be thought about, reasoned with and discussed. Mathematical thinking involves: 

1. Looking for patterns in order to discern structure; 
2. Looking for relationships and connecting ideas; 
3. Reasoning logically, explaining, conjecturing and proving.

We believe that following these key principles enabling teaching for mastery allows our pupils to become confident, ambitious and successful mathematicians who are able to: use prior learning as stepping stones to build coherence; use mathematical vocabulary to articulate and support their learning; demonstrate quick and efficient recall of key facts and procedures; reason logically, explain, conjecture and prove mathematical concepts.