Teaching for Mastery

At Shap CE Primary School, we believe that all children can succeed in mathematics. Our approach is underpinned by the principles of Teaching for Mastery and is designed to develop children who are confident, curious and resilient mathematicians.

Teaching for mastery does not mean that every child works on exactly the same task or progresses at exactly the same rate. It means that we have high expectations for all children, carefully break learning into connected steps and provide the support, representations and challenge children need to develop secure mathematical understanding.

Our Maths Subject Leader is an NCETM Primary Mastery Specialist and works with the North North West Maths Hub as a Local Leader of Mathematics Education (LLME) and Professional Development Lead. This expertise supports the continued development of teaching for mastery across our school.

The Five Big Ideas

Our teaching reflects the Five Big Ideas in Teaching for Mastery identified by the NCETM:

Coherence • Representation and Structure • Mathematical Thinking • Fluency • Variation

These principles work together and can be seen throughout maths teaching at Shap.

Coherence

Mathematics is taught in small, connected steps, allowing children to build new learning securely on what they already know.

Teachers carefully consider the important mathematical ideas within each lesson and how these connect to previous and future learning. Our mixed-age curriculum is carefully sequenced so that children develop the knowledge and understanding required for their own year group while making meaningful connections between mathematical concepts.

Teachers continually assess children's understanding and adapt the pace, support and depth of learning accordingly.

Representation and Structure

Children use a range of concrete resources, images and representations to help them see and understand mathematical structures.

These might include manipulatives such as counters, cubes, place-value equipment, bead strings, number lines, arrays and fraction models.

Resources are not simply used to help children who are struggling. They are an important part of mathematical thinking for all learners, helping children to explain relationships, make connections and move towards increasingly abstract mathematics.

Teachers carefully choose representations which expose the mathematics and help children understand why a method works, rather than simply memorising a procedure.

Mathematical Thinking

We want children to do much more than find an answer.

Children are encouraged to notice patterns, make connections, explain their thinking, justify their ideas and prove whether something is always, sometimes or never true.

Mathematical talk is an important part of our classrooms. Teachers model precise mathematical vocabulary and use questions, stem sentences and discussion to help children express increasingly sophisticated ideas.

Children learn that different approaches can be valuable and that explaining how they know is an important part of being a mathematician.

Fluency

Secure number sense and fluency give children the foundations they need to reason and solve problems confidently.

We develop fluency through regular opportunities to retrieve, practise and apply important number facts and strategies. This includes number bonds, additive relationships, multiplication facts, mental calculation and efficient written methods.

Our youngest children develop strong foundations in number through Mastering Number, while Mastering Number at KS2 supports the continued development of multiplicative thinking and fluency as children progress through school.

Times Table Rock Stars and carefully planned arithmetic and retrieval practice provide additional opportunities to strengthen important knowledge so that children can recall and use it efficiently.

Importantly, fluency is not simply about speed. We want children to develop flexibility with number and to choose efficient strategies because they understand the relationships involved.

Variation

Teachers carefully select examples and questions so that children notice what is changing, what remains the same and which mathematical structures are important.

Rather than completing large numbers of almost identical calculations, children encounter examples which encourage them to compare, notice, predict and generalise.

Questions may vary one element at a time or present the same mathematical idea in different ways. This helps children develop deeper understanding and recognise when their knowledge can be applied in a new context.

Keeping the Class Together

Wherever possible, children explore the same important mathematical idea together.

Children who need additional support are given carefully chosen scaffolds, representations, additional practice or adult support so that they can access the learning. Where earlier gaps in understanding are identified, these are addressed explicitly rather than allowing misconceptions to become embedded.

Children who grasp concepts quickly are challenged to explore ideas in greater depth through reasoning, proof, generalisation and more complex applications rather than simply racing ahead to new content.

This means that support and challenge look different according to children's needs, while maintaining high expectations for everyone.

Retrieval, Assessment and Responsive Teaching

Assessment is an ongoing part of every maths lesson.

Teachers use questioning, discussion, children's work and short retrieval opportunities to identify what children know, what they have remembered and where misconceptions or gaps remain.

Learning from previous weeks, terms and year groups is deliberately revisited so that important knowledge is remembered over time, rather than only being successful within one unit of work.

Teachers use this information to respond to children's needs: revisiting prerequisite knowledge where necessary, adjusting representations and explanations, providing additional practice or increasing the level of reasoning and challenge.

Mistakes Matter

At Shap, we want children to feel safe enough to have a go, make mistakes, change their minds and learn from one another.

A wrong answer can reveal an important misconception; an unexpected method can begin a valuable mathematical discussion; and a difficult problem can provide an opportunity to persevere.

This reflects our school vision of providing “A Safe Branch from which to Soar.” Children develop confidence not because mathematics is always easy, but because they learn that they have the strategies, support and resilience to tackle something they do not yet understand.

What does a mathematician at Shap look like?

A mathematician at Shap:

• notices patterns and relationships;
• explains their thinking using precise mathematical language;
• represents ideas in different ways;
• makes connections between previous and new learning;
• chooses efficient strategies rather than simply following a procedure;
• reasons and justifies their ideas;
• learns from mistakes and is willing to try again;
• and develops the confidence to say, “I don't understand this yet.”

Our aim is not simply for children to be able to do mathematics. We want them to understand it, talk about it, make connections within it and enjoy thinking mathematically.