'Maths mastery makes setting according to ability irrelevant'

Maths mastery allows classrooms to become places where struggles and mistakes are seen as normal and in the end become a positive sign that good learning is taking place, writes one education academic

Professor Pete Boyd

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Many schools are exploring "mastery" approaches to teaching and learning. A mastery approach generally means that, as a class, we work collaboratively on a topic or key idea until everyone has "got it".

In mathematics, some of the mastery approaches being developed in UK schools are informed by South Asian approaches to teaching – in particular, Shanghai Maths and Singapore Maths.

There is some evidence of modest learning gains from mastery maths and South Asian approaches, based on test results in large-scale randomised control trial research studies.

We wanted to find out what impact mastery approaches had on teachers. A small-scale collaborative study with teachers in the Deep Learning Alliance on Merseyside has focused on significant changes in teachers’ underlying beliefs during their adoption of the Maths – No Problem! Singapore Maths mastery programme.

Seven teacher researchers captured classroom video during a mastery maths lesson and were subsequently interviewed to discuss their teaching strategies. Pupil interviews and teacher focus groups provided further insight, including into the role of the textbooks.

There is a strong cultural belief in Britain about the need for schools to put children into in-class groups or different sets according to their "ability". This belief has persisted despite the research evidence that shows grouping or setting has little or no beneficial impact on children’s learning and is damaging for children placed in lower groups or sets. This belief about grouping is shared by many teachers, school managers, parents and even government ministers, and is particularly strong in the subject of maths.

The benefits of a collaborative approach

However, this new study has shown that being involved in the whole-class, collaborative and exploratory approach of the mastery maths scheme seems to be changing the underlying beliefs of the teachers. They are rejecting in-class grouping as simply being no longer relevant due to their new mastery approach and they tend to use mixed pairs of children for work on maths activities:

"That’s a big shift from the way I would have taught maths before and did with this class before, it would be very much separated into, you know, ‘You can only do this because you’re low ability, middle and high’. Whereas now I feel like the high or middle-ability children can help the other children by showing them the equipment and talking to them about it. I think the reasoning and the talking from the high or middle-ability children helps them as well to distill what they’re thinking by explaining it to somebody else."

The teachers are very aware of the need to stretch higher-attaining children during the first half hour of each lesson, within which the class work together and in pairs to collaboratively explore the maths underpinning the "anchor" problem for the lesson. The teachers spend time training the children so that they are able to collaborate effectively and support each other’s learning.

The teachers in this study created a maths classroom where struggle and mistakes were seen as normal and as a positive sign that good learning is happening. The teachers seem to enjoy the mastery approach because it allowed them to model struggle and mistakes themselves rather than feeling under pressure to model slick solutions to maths problems:

"I’m far happier to be the person making mistakes at the front or not getting things right and I’m less frightened about mistakes in the lesson.  It doesn’t worry me now if things aren’t going the right way.  If they’re not going the right way and we use that within the lesson."

Welcoming struggle and mistakes as opportunities for learning is a key step in helping children to develop a growth mindset; a positive belief that the harder you work, the more intelligent you become. In the study, teachers showed signs of developing their own mathematical growth mindset, as well as projecting a growth mindset by setting high expectations for all children:

"With maths you’re continually learning: different ways, different methods. You’re always learning and your intelligence is not capped."

There is a general consensus that many school textbooks are dull and may lead to low-quality teaching and learning. In the research, the Maths – No Problem! textbooks were usually not brought into use until halfway through the lesson. After an initial period of exploring the anchor problem, the children share their different solutions and complete a journal entry to record and reflect on their learning. The textbook is brought out and provides some example solutions and then some carefully designed practice problems for the children to work on.

The textbook scheme includes teacher guidance, and the teachers report that their lesson preparation mainly focuses on the maths underpinning the lesson. This is because with an open-ended anchor problem, the children might take the maths in different directions and the teachers feel the need to prepare for most, if not all, eventualities. The textbooks seem to be very successful and are highly valued by the teachers but have the mastery approach built-in so that they avoid the dullness of lessons based on more traditional textbooks. 

Professor Pete Boyd is a principal lecturer at the University of Cumbria

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Professor Pete Boyd

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