What is maths mastery?

13 Jul 2020 | News & Advice, Primary

Maths mastery is the method of teaching children mathematical fluency without leaning on older, more dated methods of rote learning. Maths mastery also allows children to develop problem-solving skills and in turn, solve non-routine maths problems without having to memorise procedures. But where did maths mastery come from? And how can it be applied to British classrooms? We take a look.


Where did maths mastery come from?

South Asian countries including Hong Kong, China, and Singapore sat at the top of the Program for International Student Assessment (PISA) worldwide rankings in 2015 for mathematics. PISA is a measurement of 15-year-old students across reading, science, and mathematics.


Countries in this area of the world are renowned for their academic ability and China has not finished outside of the top 3 of the International Mathematical Olympiad (IMO) since 1997. In 2019, the United Kingdom hosted the event and finished in the 20th.


Since September 2016, there has been a pioneering exchange programme taking place, sending UK teachers out to Asia to understand what exactly makes them so strong in this subject.


What are the main focuses of maths matery?

The idea is based around whole-class teaching and developing a deep understanding of the basic but fundamental principles within maths. A typical maths mastery lesson is led by the teacher, with all children working on the same topic at broadly the same pace.


It’s a common misconception that Asian children are simply taught by repetition and have more ‘natural ability’ for numbers. While of course there is an element of repetition in the approach, it is also a well-paced, highly interactive environment where children are encouraged to work hard and they will succeed. There’s a mixture of short tasks, explanation, demonstration and discussion during lessons involving maths mastery.


From concrete to pictorial, to abstract

The concrete > pictorial > abstract approach is the basis of the teaching. Children use manipulatives and physical objects like Multilink to represent concepts, alongside standard numbers and symbols at the concrete stages. They will then move onto pictorial representation, which might take the form of pictures of multilink rather than the physical object. This helps children move towards the final


The concrete stage can be returned to at any stage to deal with misconceptions which means that concrete resources can be used even with adults who need to learn basic mathematical principles.


Here is a list of ‘concrete’ resources you can use in the classroom for maths mastery:

How does maths mastery benefit children?

Maths mastery is a method of teaching maths that can be used to teach students of any age. However, primary education has been particularly quick and effective at implementing maths mastery. Schools are able to decide how much they integrate the approach with current teaching techniques, though the DfE is hoping for a more radical overhaul of maths teaching that extends beyond primary education.


Pupils in countries that use this approach currently are noted to be 10% less likely to have ‘functionally innumerate’ children at 15 years-old i.e. unable to perform basic maths functions. If a child struggles with maths, there may be concerns about them taking on whole-class activities, but this certainly shouldn’t be the case with maths mastery.


The DfE says that ‘every step of a lesson is deliberate, purposeful and precise’ – if some children are struggling with a concept that others understand, learning continues until the concept is embedded. The pupils who have understood the concept earlier will move on to a ‘deeper understanding’ section with more challenging questions and principles.


Maths mastery requires pupils to think more deeply about mathematical concepts; a slower pace leads to greater progress because it ensures children secure their understanding. Children are given time to really understand concepts at a deeper level, rather than surface-level learning a set of rules.


Core beliefs and key principles of maths mastery

All schools and educators have the aspiration that they can ensure every child will reach a successful level within mathematics. The maths mastery approach sits these values at its heart:

  • Success in mathematics for every child is possible
  • Mathematical ability can be increased through effort and is not innate
  • Focus on fewer topics in more depth
  • Mastery for all pupils, full understanding
  • Number sense and place value come first
  • Problem solving is central to all learning

Perhaps, most importantly, maths mastery never assumes that someone is ‘not a maths person’, helping to give all children the confidence to have a go and become skilled at the subject.


What is ‘mastery’?

Here is a quote from the founder of the approach to describe what it is to ‘master’ mathematics:

“In mathematics, you know you’ve mastered something when you can apply it to a totally new problem in an unfamiliar situation.” Dr. Helen Drury, Director of Mathematics Mastery

Fill your classroom with all the concrete resources your children will need to master maths.

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