The use of mastery in education has been around since 1968, when psychologist Benjamin Bloom suggested that learning a subject is done best when broken down into small learning objectives. Accomplish each one on a deep and thorough way, helping you accumulate each small objective on your way to mastering the overarching topic.
A pupil is said to have mastered a mathematical concept when they can display that concept in multiple different ways and apply that concept to a new problem which they are unfamiliar with. Ultimately, maths mastery focuses on depth over speed. Pupils are encouraged to demonstrate a deep understanding of mathematical concepts, slowly building their knowledge over time.
“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
Introduced into UK schools in 2014, the mastery method is said to be responsible for the UK’s rise up the global Program for International Student Assessment (PISA) rankings for maths. In 2019, the UK had risen from 27th to 18th.
Maths mastery definition
The subject of maths is broken down into numerous small, granular objectives. Pupils learn a deep and thorough understanding of each concept before moving onto the next together. Each objective accumulates their knowledge in order to master the overarching subject – maths.
South Asian countries including Hong Kong, China, and Singapore sat at the top of the 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 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 – leading them to the mastery method.
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
- Mathematical ability is not innate
- Focus on fewer topics, covered in more depth
- Mastery for all pupils, with 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.
The idea of maths mastery 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.
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.
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 is 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.
Concrete: Pupils are encouraged to use concrete objects to symbolise mathematical concepts.
Pictorial: Pupils build on their concrete understanding by using illustration, using imagery to reinforce and deepen their understanding.
Abstract: This foundational work allows pupils to embrace key mathematical concepts on an abstract level. This is where they are able to master the concept.
There are many things you can use as concrete resources in the classroom to lay the foundations for maths mastery:
- Bead strings
- Fraction towers
- 100 grids
- Cuisenaire rods
- Number lines
- Multilink cubes
- Dienes blocks
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.
There are plenty of ways in which children benefit from a mastery-based approach to maths:
- Pupils are required 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
- Smaller steps lead to children not becoming overwhelmed too fast
- A “faster isn’t always better” approach ensures everyone can gain a deeper, more embedded level of understanding
- Mastery promotes a “can do” attitude that builds confidence in pupils
Aside from the UK’s improvements in the PISA rankings, other research has shown how the mastery approach is improving maths proficiency in our schools.
A 2015 study from UCL Institute of Education and Cambridge University found that children who benefitted from maths mastery made on average a month of extra progress per year over those who didn’t. The research also suggested that these pupils could boost their earnings potential in adult life by up to £200 a year.
Now you’ve got a handle on the tenants of maths mastery, how does a teacher best maximise the approach and boost class knowledge? Here are a few starting points that can help you formulate lesson plans:
- Plan, plan and plan
Maths mastery is all about breaking down a big objective into smaller ones. As the teacher, it’s your job to formulate what these units look like and decide how to tackle them. Put the time in beforehand and plan a learning objective for each unit.
- Decide on evaluation techniques
Formative assessment strategies are often preferred as you work through a maths mastery lesson. Plan in advance how you will evaluate the success of each unit.
- Focus on guiding pupils
Maths mastery aims to facilitate a learning environment where pupils can think for themselves, rather than a teacher telling pupils what to do and how to do it. Peer discussion and mixed-ability group activities are key to mastery teaching, so look to incorporate these aspects where you can.
- Change your differentiation for higher and lower achievers
Maths mastery is a move away from a tiered approach to work. Instead of using different worksheets for different skill levels, challenge higher learners with questioning that challenges them to apply their knowledge in a different way. Not only does this lessen planning time, it also boosts the confidence of lower ability children.
- Define your lesson non-negotiables
For each lesson in your maths mastery plan, think about where your class needs to be by the end of that session. What concepts should they know? What would mastery of the concept sound like? What misconceptions or common holes might their knowledge have, and how can they be amended? What terminology do they need to know and carry forward?
Ask yourself these questions and use the answers to develop a list of benchmarks you need to hit by the end of each lesson.