Developing the maths mastery approach in a mixed-aged school

In 2014, a new National Curriculum was introduced in England which significantly changed the contents of the maths curriculum in Primary Schools (DfEDepartment for Education - a ministerial department responsible for children’s services and education in England, 2014). The new curriculum effectively increased the level of challenge for primary school children, as some year group’s objectives were moved to the year below. For example, five-year-olds were now expected to learn to count up to 100, compared with just 20 under the previous curriculum (DfE, 2014). I initially began using the maths mastery approach because I was asked to do so in my previous school setting. However, I had also come to recognise that the former methods of teaching maths did not ensure that all children became confident mathematicians. Four years later and I am well on my way to using the maths mastery approach to teach maths. This article is based on the impact of adopting maths mastery at my school, St Michael’s Primary School in East Sussex.

The old method of whole-class differentiation did not seem right and felt like it was creating a huge gulf between the highest and lowest attainers in maths.

What is maths mastery?

Charlie Stripp, head of the NCTEM, (National Centre for the Teaching of Mathematics) struck a chord with me when he said that “the ‘traditional’ way we differentiate – putting children into ability-grouped tables and providing easier work for the less able and more challenging ‘extension’ work for the more able – has ‘a very negative effect on mathematical attainment” (Stripp, 2014). The old method of whole-class differentiation did not seem right and felt like it was creating a huge gulf between the highest and lowest attainers in maths. As such, I began to research the use of maths mastery in primary schools. Maths mastery can be defined as a ‘means of acquiring a deep, long-term, secure and adaptable understanding of maths…achieving mastery is taken to mean acquiring a solid enough understanding of the maths that’s been taught to enable him/her to move on to the more advanced material.’ (NCTEM, 2015, p. 5). Approaches to maths teaching prior to 2014 were very much centred around differentiation for learners. Curriculum content was also often fast-paced and skipped between areas of maths very quickly.

Maths mastery is an approach to maths teaching that is commonly used in schools across East Asia and has at its core the belief that all children can be mathematicians. However, like any new approach in teaching, it has received its fair share of criticism. Initially, critics were quick to argue that it is not possible to emulate the mathematics in East Asia as our cultures are too vastly different. A study was conducted by Professor Mark Boyland and colleagues from Sheffield Hallam University: “The evaluation found positive impacts on pupil KS1 mathematics attainment in those schools most directly involved in the Maths Teacher Exchange (MTE) programme. However, there is no quantifiable evidence from this evaluation that the MTE or implementation of East Asian informed teaching alone is leading to improvements in pupil attainment in mathematics at KS2 in comparison with other schools.” (Boylan et al., 2019, pp. 23 – 24). Whilst the findings from this evaluation are inconclusive, there are other reports showing the efficacy of East Asian informed teaching practices, including when applied in England (Boylan et al., 2018). This is why I chose to adopt the approach in my current school and evaluate its effect on students’ attitudes to maths and their outcomes.

Maths Mastery in my school

Nearly three years ago, I joined a new school where I became the maths coordinator and was sent on numerous maths courses to support me in this role. This included a course led by Helen Hackett and also with the Sussex Maths Hub about what maths mastery was. I was also fortunate to attend training led by East Sussex County Council regarding how to be an effective maths leader. I was keen to make sure that maths mastery worked for our pupils and wanted to introduce it so that staff saw the benefits of adopting this approach. The main challenge was how to develop it in a small village primary school with three mixed aged classes and a Reception class.

I began by trialling some of Babcocks’ (2016) ideas in my year 1 and 2 classroom, alongside my job-share partner. The maths mastery approach was a complete change in teaching style for four out of five of our existing class teachers. Therefore, before implementing it across the school, I felt that it was important to trial the approach in my own class, with my own pupils and fellow job-share colleague to assess its effectiveness. In doing so, I was able to share the realities of teaching maths mastery to colleagues, with the benefit of hindsight and with the knowledge that my job-share partner was also trialling this new approach to teaching. This allowed me to reassure colleagues that, despite an initially lengthy experience planning lessons, as soon as I had become more confident with the approach, planning time had been halved in the space of 14 weeks.

“I was keen to make sure that maths mastery worked for our pupils and wanted to introduce it so that staff saw the benefits of adopting this approach.”

Changes to my own teaching

I began with a few changes initially; developing fluency, reasoning, variation and post-teaching maths. I understood that fluency, reasoning and variation were important elements of maths mastery and I should, therefore, begin with them. In maths, fluency refers to knowing key mathematical facts and methods and recalling these efficiently. I looked at how to build this into the maths session, so that pupils became fluent in their number bond, counting and times table skills. I made a few changes to the lesson structure: counting in 2s, 5s or 10s when children were moving to their places and quick recall of number bonds when children initially sat down for each mathematics lesson.

Reasoning refers to the critical skill that enables a student to make use of all other mathematical skills. With the development of mathematical reasoning, pupils show that they can fully make sense of the maths they are learning and apply it to new contexts. Each lesson now had reasoning questions weaved through them. For example, when learning how to count in 5s, pupils were asked to spot the mistake in a sequence of numbers e.g. 55, 50, 45, 35.

Variation was perhaps the hardest of the three concepts to understand and plan for in my lesson structure, as it required me to think differently about the concepts I was teaching. Variation is when you find out what something is by looking at it from different angles. For example, if fractions are only ever presented as amounts of pieces of pizza, then pupils will become confused when shown a fraction of a square. Equally, if parallel lines are only ever shown in pairs, then when pupils are presented parallel lines as a group of three, they are likely to be unsure of the concept.

I have read widely around the maths mastery approach (including books, blogs, research papers and practitioner articles), but it was Bloom’s much earlier research which was the most powerful in influencing my thinking. Bloom (1971, p. 48) suggested that ‘weaker students required approximately 10-15% additional time to achieve the same results as their peers’. He also suggested that over time the gap closed “so that students became more and more similar in their learning rate until the difference between fast and slow learners becomes very difficult to measure” (Bloom, 1971, page 48). After reading Bloom’s research and through discussions with colleagues, it was apparent that we needed to give pupils additional time to help close the gap with their mathematical understanding.

I chose the changes above to begin with as they were important components of the ‘5 Big Ideas of mastery’ highlighted by the Sussex maths hub in a training session. They were important elements of maths mastery and therefore it felt important to embed these centrally in lessons.

Changes to the whole school

As a whole team, we looked to White Rose More Detailed Plans (www.whiterosemaths.com), NCTEM’s Teaching for Mastery (Askew et al., 2015) and NRICH Maths activities (www.nrich.maths.org) to plan and create our daily lessons. Initially, this took the largest amount of time and there was much frustration along the way as we all grappled with a new way of teaching, planning and assessing maths. Two years later, the process of planning these aspects of mastery in lessons had become a lot easier and staff were all feeling more confident and enjoying teaching maths.

Manipulatives are another central aspect of Maths Mastery. Discussions with pupils showed that Key Stage 2 children were less likely to use manipulatives in lessons, as they considered that it somehow linked to low attainment in maths. In total, all of our Key Stage 2 children were questioned (fifty at the time) and observations were made by the two different class teachers to discern how often manipulatives were taken using a child’s initiative. The focus, therefore, turned to all staff receiving CPD in using manipulatives to support maths teaching. We found relevant maths courses led by East Sussex’s education department and I myself led several staff meetings addressing how to use manipulatives in a lesson. I led seven staff meetings focussed on: what is maths mastery, how to use mastery resources, an exploration of the NCTEM website, lesson design, developing problem solving in the classroom, re-cap on the 5 big ideas of mastery and developing bar modelling.

Additionally, staff were all given access to maths mastery based training. Staff attended subject specific work, fractions for example, or attended sessions focussed on the new teaching approach in maths. Additionally, in September 2017, I found an opportunity to join our school with a mastery teacher research group, facilitated by the Sussex Maths Hub, based at St Paul’s Catholic College, Burgess Hill. Myself and a second staff member attended termly sessions led by a mastery maths specialist. We got the opportunity to see maths mastery lessons in a mixed aged setting to help us use the approach within our own school.

The pre-and post-teaching of pupils continued. Post- teaching took place during the afternoon assembly slot and involved different children each day. It focussed on children that had struggled with that day’s teaching content and the sessions showed that morning’s maths content in a different way to help to fully understand that day’s learning.

“The old approach of differentiating a lesson three ways for high, middle and low attaining pupils has been replaced by a more effective use of pupil questioning and small-steps to help all children achieve.”

Evaluation

As part of our mastery journey, I wanted to understand how mastery had impacted on pupils’ enjoyment of maths. As such, I questioned 15 pupils, who were randomly chosen, (one-sixth of the school population) at the beginning and the end to see if or how their attitudes towards maths had changed.

The pupils ranged from children aged 4 through to children aged 11 and were taught by five different teachers (including myself). Although the 15 pupils had differing levels of attainment, all participants were feeling happier about learning maths. Our results for the whole school in maths in June 2018 showed that for each year group there has been at least a 10% increase in children attaining age-related expectation (ARE) since September 2017, although of course there may have been a number of reasons for this.

Conclusion

Two years of teaching using the mastery approach has been a journey. In early months, I frequently asked myself, ‘why am I doing this? Is there a better way?’ The whole approach is now far less time-consuming the plan for and the benefits can be seen in our pupil progress. In its second year, all pupils at St Michael’s are visibly more confident in approaching reasoning and problem-solving questions. This was evident in termly lesson observations in maths. The old approach of differentiating a lesson three ways for high, middle and low attaining pupils has been replaced by a more effective use of pupil questioning and small-steps to help all children achieve. It has been hugely rewarding to see pupils being more positive about maths lessons and engagement in lessons has risen too. Long sessions crafting lessons have slowly diminished over time and we are all more confident as staff in teaching using the mastery approach. Experience has taught me that the more children enjoy a subject the more likely they are to be confident participators in a lesson.

I can now see the impact of using a mastery approach in teaching maths. With carefully crafted lessons, children were able to make better progress, aided by a change in mindset that all pupils can be mathematicians and the role of all teaching staff was integral to this. In a small setting with budgetary constraints, using a small step approach has had the greatest impact on closing the gap in mathematical attainment.

The five big ideas have brought successes for pupils as they have been slowly and carefully exposed to the structure of new mathematical ideas. Through using a maths mastery approach, concepts are taught carefully, slowly and with great thought given to pupil’s previous learning and the bigger picture. Effectively it helps to close the gap for pupils, who in the previous curriculum, would have not have been given access to whole class content. In effect their progress was capped because they were only ever given access to ‘lower ability’ content.

Final Thoughts

Implementing maths mastery in a mixed-aged setting has not been an easy process and there have been no quick fixes. It has taken time to embed with staff, but all staff are thoroughly enjoying teaching using the approach. Pupils in our school are benefiting from a mastery approach and we can see that results are slowly improving and gaps in attainment are beginning to close.

We are now in the third academic year of using the mastery maths approach at St Michael’s and it will be interesting to see how this impacts on pupil attainment and attitude in maths over the next few years. Mastery maths is still in its foundation stage and there is still work to be done, however, our experience suggests that if mastery is going to be successful in mixed-aged classrooms it needs time to develop. We are fortunate to have a group of teachers who were curious and inquisitive enough to change the way they teach maths and our pupils are now reaping the benefits.