The mastery approach to teaching maths has gradually taken root in many primary schools, thanks to enthusiastic and committed teachers leading it, and a well-funded support network.
But myths still persist in the delivery. I don’t seek to denounce the mastery approach but question some of the assumptions and recommended practices, and, in particular, their application to the UK educational model.
Having evaluated the mastery recommendations, at my school we plan to end up with a flexible, blended approach, which combines much of the thoroughness of mastery (especially in lower years and lower-ability groups) with the inspiration provided by letting children explore maths in real-life situations, hopefully instilling in them a passion for the way they apply the incredible concepts they have discovered.
Difficulties in delivering maths mastery in primary schools
Here are some of the most common issues we have found:
1. The method problem
Mastery focuses on the long-term embedding of concepts and techniques, with long periods of time spent on alternate framings of single concepts. A key assumption seems to be that after this all children retain each concept (at least until the following academic year).
This ignores the fact that some children show improved learning from a “teach, practise and repeat” approach, where a topic is revisited several times. Many children benefit from this steady drip-feed of concepts, revised and solidified at regular intervals through the school year.
2. The ability problem
Mastery teaching is delivered in single, mixed-ability classes (typically the child’s own class, delivered by their own class teacher), with the material differentiated to allow more able mathematicians to explore in more depth. However, in a typical larger primary school, it is possible to structure maths teaching (mastery or otherwise) to reflect different abilities.
A higher-level maths set might have one well-qualified teacher, with a middle set having more TA support, and a development set having lots of adults to encourage the children who struggle. Regular movement between the groups gives schools flexibility, and gives parents reassurance that their child is being appropriately supported. Schools that have invested in more than two maths sets also show excellent results.
At its best, mastery teaching means all children are suitably challenged by the excellent materials and committed staff available. At its worst, the less-able children still struggle, and the brightest mathematicians are not challenged or find themselves as unofficial unpaid tutors to their peers.
3. The results problem
The original funding for mastery seemed to be a reaction to the position of the UK in a number of international league tables of pupil performance.
Apart from the vagaries of measuring such attainment, league tables obscure some of the desired teaching outcomes for young children, namely motivation and a love of learning, and the potential for a lifelong commitment.
Mastery implementation is still in its infancy and there is little concrete evidence yet that its original (results-focused) objectives are being met.
4. The teaching problem
One of the showcase features of mastery training is when teachers from Shanghai perform model lessons for a group of admiring British teachers. These are what they are – show lessons, prepared weeks in advance by professionals with up to five years’ mathematics training to university level, whose specialist daily teaching load is perhaps one-third of that of a generalist UK primary teacher.
Our impression of these lessons was that they were meticulously prepared and beautifully structured, and reflected the time and training available to those who produced them. Good lessons always require these levels of input, whatever the underlying philosophy. Outstanding lessons additionally require the creativity, practicality and cross-curricular brilliance that should make maths so compelling for everyone.
5. The curriculum myth
UK primary schools are required to deliver a “broad and balanced” curriculum. We often hear about the erosion of this, largely due to the breadth of the curriculum and the time available. But breadth is vital. To enthuse our children, to instil in them a love of learning, and for them to emerge from primary school with general knowledge and a world view is fundamental.
Some of the mastery recommendations – which refer to children being required to catch up on maths during the afternoons – are entirely inconsistent with this and, indeed, may have the opposite effect to that which is intended. Not only may children miss out on developing their other skills in music, art, PE or history, they may also be put off maths for good.
The elephant in the room
Less a myth, but certainly a very large elephant in the room, is the assumption that it is desirable for children to learn in this way. Although the “concrete, pictorial, abstract” progression is fundamental to mastery teaching, there seems to be little space for practical, daily life mathematics.
It is recommended that children sit in rows and stand up when they answer a question, for example. Over the past 18 months, we have seen children’s mental health decline markedly over multiple lockdowns. It is surely more important than ever now that primary education is nurturing and supportive.
Dr Rupert Loader is a primary maths specialist at Sonning Common Primary School in Reading