What is the Maths mastery approach?

The mastery approach is a Chinese way of teaching Maths that involves breaking down larger, complex learning goals into smaller, more granular steps. It mostly originated in South Asia and is particularly common in Shanghai and Singapore.

The mastery learning approach in mathematics has actually been around in educational circles for a while. It was the educational psychologist Benjamin Bloom who coined the term “learning for mastery” in 1968, and believed that a learning goal should be broken down into a number of small learning objectives.

Maths Mastery Definition

The mastery approach is a Chinese way of teaching Maths that involves breaking down larger, complex learning goals into smaller, more granular steps.

So for example in a Maths lesson, a goal for a student might be to carry out whole number addition. One objective that would contribute to this goal could be to “add two three digit whole numbers with carrying in the tens”.

In 1983, Robert Ashlock and his colleagues went further, breaking down addition into 23 objectives and subtraction into 24 objectives.

When using the mastery approach in Shanghai, students aren’t broken into separate groups depending on their perceived intellectual abilities. Instead, all students perform the same work at the same time before mastering and advancing to the next concept together.

Need to Know…

  • A mastery curriculum is supported by extensive international evidence and endorsed by the Department for Education (DfE), OFSTED and National Centre for Excellence in the Teaching of Mathematics (NCETM).
  • A mastery approach is characterised by whole class teaching.
  • Depth of knowledge is valued over speed of learning.
  • High expectations are crucial – mastery is built on the belief that all children can achieve.

By contrast, children in the West are often grouped into classes by their learning abilities. Teaching methods are aimed at encouraging students to have a more intuitive understanding of Maths concepts, starting with a broader concept and then breaking the problem down into specific steps.

Since 2014, the Maths mastery approach has been slowly being trialled in UK schools with tremendous results. It is thought that the mastery approach is largely responsible for the UK’s recent advancement in the Pisa league table for Maths.

As curricular understanding of the model grows, more UK schools and education experts believe this approach will help more students increase their mathematical capabilities and has potential for other subjects.

Mastery Maths Goal Orientation

When students find themselves in an achievement situation, they will often be given set goals that give direction to their efforts and act as frameworks, helping teachers to understand how individuals perceive, interpret, and react to achievement situations (Elliot 2005).

Two types of goals have by far received the most attention: mastery goals and performance goals. Mastery goals are aimed at improving one’s own performance and gaining full mastery of the task or subject. Performance goals, meanwhile, reflect the pursuit of outperforming others and displaying superior performance.

Imagine two students with the same class project, but different goal types. Jack’s goal in the class is to learn all of the features of the human body because he is interested in anatomy and physiology and wants to be able to build his base knowledge of these principles. His is a mastery goal.

Meanwhile, Hillary’s goal in class is to identify all of the bones, muscles and tissues in the human body more quickly and better than her classmates. Her’s is a performance goal.

Mastery goals are aimed at attaining a standard of competence defined by self-improvement or skill development. People who hold mastery goals either seek task-related self-improvement or strive to gain task mastery.

 

Mastery goals vs. performance goals

Behavioural researchers agree that mastery goals are more productive than performance goals. This is because when mastery goals are met, a student’s satisfaction isn’t related to external indicators. This means they’re less likely to give up in the face of difficulties or obstacles, and will be more inclined to persevere through setbacks.

Mastery goals are always ‘just beyond reach’. This makes motivation over the long term easier to maintain, as there is always something better to strive for.

People that reach the pinnacle of their skills rarely set performance goals. They’re more interested in competing with themselves and pushing themselves to the edges of their abilities than gaining outside validation. This is what allows them to compete at a higher level over a longer period of time.

One of the key benefits of the maths mastery approach is that it capitalises on these mastery goals. There is always something to strive for – even if it’s as simple as students being better tomorrow than they were today.

Benefits of Teaching Mastery Maths

The mastery approach to teaching has been steadily gaining attention in the UK. In 2015, 30 teachers from Shanghai, China, were flown to the UK by the Department for Education to teach the mastery approach to English teachers.

The Guardian detailed the experience of one London school, Fox School, in which teacher Lilianje Lu brought the mastery approach into a classroom of 7- and 8-year olds.

Lu first asked the children one by one to read out the fractions on screen, with the rest of the children repeating after each one. At the end of the session the children were invited to give themselves a ‘clap’ – five claps rhythmically – before they were asked to read out the fractions all over again. Lu then moved on to teach them how to write fractions.

Though this chanting and recitation can seem formulaic by English classroom standards, it has been shown to be effective at encouraging understanding. A 2015 study of 140 schools in the UK by the UCL Institute of Education and Cambridge University found that the mastery approach improved the speed at which students learned maths skills.

Lessons taught using the mastery approach are also much shorter than most lessons in the UK, with about 35 minutes of learning time followed by 15 minutes of playtime.

The mastery approach has also had wide support from other education experts in the UK…largely due to the academic efficiency of countries using the method.

Countries at the top of the table for attainment in mathematics education employ a mastery approach to teaching mathematics.

Charlie Stripp

“Countries at the top of the table for attainment in mathematics education employ a mastery approach to teaching mathematics,” said Charlie Stripp, Director of the UK’s National Center for Excellence in the Teaching of Mathematics.

“Teachers in these countries do not differentiate their maths teaching by restricting the mathematics that ‘weaker’ children experience, whilst encouraging ‘able’ children to ‘get ahead’ through extension tasks,” he continued.

Chinese Maths classroom

Chinese primary school students in a Maths lesson.

Indeed – the 2012 PISA table (Program for International Student Assessment) showed that Asian countries that implement the mastery approach hugely outperform the UK and US in Maths.

Additionally, more recent PISA results released in 2018 showed a massive improvement for UK schools, which jumped nine places from 27th to 18th place. This was after the British government announced in 2016 they were investing £41m over four years to support half of English primary schools in adopting Maths teaching methods from Asia.

Experts believe that it is this adoption of the mastery approach that is likely to have driven up the UK’s test results.

Mastery Maths Programmes

There are currently a number of mastery maths programmes in the UK that hone in on the method of teaching mastery maths and achieving the most effective learning outcomes.

  • Mathematics Mastery – a non-profit organisation prioritising teacher collaboration and knowledge sharing
  • Teaching for Mastery – a Government-backed programme aimed at empowering and equipping teachers to improve students’ attainment and understanding in maths.
  • Maths No Problem – an evidence-based approach to teaching maths. Those interested can request a free demo to see how to implement the mastery learning approach in their classroom.
  • Education Endowment Foundation – a scientifically-proven whole school approach to teaching mathematics, aimed at deepening students’ conceptual understanding of key mathematical concepts.

Limitations of the mastery approach

Despite the high acclaim for the mastery approach’s success, the teaching technique does come with a few limitations.

According to Steve Chinn, visiting professor at University of Derby, teaching in this way could handicap learning because the whole process can take some time; therefore students may forget the earlier stages if and when they reach the later steps.

Also, it is said the detailed nature of the structure means children who are perhaps lagging behind would struggle to catch up. A focus on broader maths concepts may be more beneficial for all learners, which would then support memory.

There are also concerns about an over-emphasis on the idea of ‘mastery’. If the level of mastery is defined, as the word implies, as 100% performance, then many students may never achieve that level and this can place unnecessary pressure on learners. Similarly, if full mastery is required in order to progress to the next stage, then this could mean some students may not progress.

Chinese maths lessons

It is also important to note that all children learn differently, so applying a strict hierarchy in the process of learning may not be beneficial for everybody. Ann Dowker, research lecturer at Oxford University, explained that a child may perform well at a difficult task while performing poorly at an easier one. Limiting progression to a specific hierarchy of steps could lead to many children being denied success in maths.

Though the mastery approach has been cited as the reason for the UK’s progression in the PISA league table for Maths, not all education professionals are convinced.

Ruth Merttens, professor of primary education at University of St Mark & St John, thinks that pointing solely to the mastery approach as the reason for high achievement ignores other factors that may be at play.

Speaking to The Guardian, she said: “We don’t know what elements of Shanghai’s education produces good mathematics education. One thing to note, however, is that Chinese teachers have a five-year education training specifically targeted at teaching primary children, whereas we have systematically cut the time we give to trainee teachers.”

There are also experts who say that Chinese students’ success with standardised testing is not necessarily direct evidence that Chinese students are overall more successful than students in other countries.

 

Implementation is important

However, Dan Polak, Deputy Headteacher in the UK and Mastery Specialist, warns of the potential errors in judgement that can occur when implementing the mastery approach to teaching.

While some teachers and experts may attribute the outcome of mastery to the method itself, Dan explains that the success or failure of the approach can be all to do with how it is implemented.

Schools are all at different stages when considering Mastery Mathematics and it's imperative that any change happens in a considered way.

Dan Polak, Deputy Headteacher & Mastery Specialist

“The shift to teaching for mastery is a complex and nuanced change in practice for many,” he says. “Schools are all at different stages when considering Mastery Mathematics and it’s imperative that any change happens in a considered way.

“The implementation of any new idea, if not understood in its entirety, can be ditched on false premises. All new changes need to account for what has gone before, and this doesn’t relate specifically to mastery – but of course we see it a lot in mastery.

“If people just switch to mixed attainment without considering the specific impact on their cohorts, for example, they normally switch back and abandon ‘teaching for mastery’ unfairly. If you adjust the rug, you can move a lot of furniture at once.”

Rather than implement teaching for mastery practices overnight, Dan recommends first considering how the teaching style will be rolled out, and how various pupils could respond. That way, any possible difficulties can be planned for ahead of time, and prevent schools or teachers from dismissing the mastery approach entirely.

He concludes, “Mastery requires careful discussion about anticipating likely responses from children, and this will change from class to class. Giving time to scrutinise and challenge ideas will help any new initiative take root, without the false starts that accompany knee-jerk mass changes in practice.”

Mastery approach in uk schools

Conclusion

As with all models, the mastery approach may work for some students, but not for all. There is currently no data on which profiles of children may benefit most from this teaching method, but experienced professionals believe it may be more suitable for children without pre-existing learning difficulties or that don’t already struggle with maths.

How teachers can implement the mastery approach

As industry knowledge and awareness of the mastery approach increases, it is only natural that more and more teachers are growing curious about its potential benefits in their classroom.

Learn more about the mastery learning process below, as well as pointers for implementing the model with your students.

 

The mastery approach to teaching

When teaching with the mastery approach method, teachers should break up their curriculum into a series of skills or instructional units. Then they will usually teach a topic before carrying out an evaluation to see how well the students understand that topic.

Students who have mastered the unit can go on to do enrichment activities while students who didn’t meet learning goals are given additional time to practice their skills.

Strategies for implementing the mastery approach

  • Take time to plan your curriculum and break it down into units, writing down learning goals or objectives for each one. Make sure the units are planned in a sequential manner and that adequate time is given to develop critical skills.
  • Plan out how you will evaluate the relevant skills. Formative assessment strategies can be used to give an effective evaluation.
  • For students that meet their learning goals, think of various enrichment activities that could be used to take their learning further. Some ideas are games, working in pairs or group projects.
  • For students who struggle to meet learning goals, give them activities that will help them further practice their skills. The activities should be different to the original ones that help accommodate a greater range of learning styles such as visual, auditory and kinesthetic. Afterwards, reassess these students to evaluate mastery of skills.

Thanks to computers, the internet and technology, mastery learning is becoming easier and more practical to utilise for schools everywhere.