Mastering Mathematics

I have read a very interesting, informative and succinct book this weekend by Dr Helen Drury. The main premise is that a mastery approach to the maths curriculum can enable teaching to transform achievement.

Below are some of the key points that Dr Helen Drury makes.

This is a re-blog post originally posted by Tim Clarke and published with kind permission.

The original post can be found here.

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In mathematics, you know you’ve mastered something when you can apply it to a totally new problem in an unfamiliar situation.

Mastered through: exploration, clarification, practice and application over time.

A learner who has mastered a concept or skills can:

  • Represent learning in a variety of ways
  • Has the mathematical language to communicate
  • Can think mathematically with the concept to apply independently to a new problem

Every child can succeed in mathematics as long as they are given appropriate learning experiences.

Create flexible groupings based on pupils’ current depth of understanding of the specific concept or skill.

Where a pupil doesn’t fully grasp a new concept at first the teacher persistently tries alternative explanations and approaches.

  1. Every child: higher expectations for potential low attainers.
  2. High expectations: greater proportions of children excelling in mathematics.


A cumulative curriculum, with sufficient time for every child to access age-appropriate concepts and skills.

Supporting and challenging pupils through depth: mathematical thinking, multiple representations, communication.

Purposeful planning: clarity as to content to be: explored, clarified, practiced and applied.

Transformational whole-school leadership: commitment to achievement, shared approach to teaching and observation, quality training and professional learning, resourcing, planning and mathematics celebrated.

Every child in a year group studying the same concepts and skills…ensure they have time to really master key mathematical ideas and understand them in depth.

Teachers must have a very clear purpose for each task, for each lesson…every moment of every lesson is extremely important, but important as part of a coherent long-term learning experience.

Taking things slower for everyone – spending longer with new concepts.

Not accelerating relatively high attainers by rushing to cover content.

Dimensions of depth

  • Deepening conceptual understanding through use of physical and diagrammatic representations and making connections
  • Developing communication through explicitly teaching pupils to discuss mathematics in grammatically correct full sentences with accurate terminology: explaining and justifying
  • Encouraging pupils to think like mathematicians through opportunities to seek patterns and rules, ask and answer open questions, sorting and comparing.


Multiple representations: grasp underpinning concepts through concrete experience, gain a more complete and connected perspective, give abstract mathematical concepts meaning and relevance.

Language and communication: every single lesson has time set aside for conversation about mathematics, articulating ideas brings about reflection and refinement, listening to others modifies your own thoughts, explicit modelling of mathematical talk, insistence on complete sentences.

Thinking mathematically: generalise, seek patterns and connections, make choices, ask questions, make and learn from mistakes, organised, systematic.

Purposeful learning for mastery

  • Learners explore mathematical concepts and techniques
  • Learners clarify meanings and methods
  • Learners practice techniques
  • Learners apply concepts and techniques to solve non-routine problems

Adapting tasks for exploration, clarification, deliberate practice or application

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About Tim Jump Clarke 20 Articles
HT at Cornerstone CE Primary (Hampshire).

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