Mastery in Maths – Time to reflect


Mastery is a hot topic in both primary and secondary mathematics education in England. The definition is debated in blogs, independent evaluators have questioned the impact and the government continues to back it with both words and money.

The DfE funded National Centre for Excellence in the Teaching of Mathematics (NCETM) have been promoting ‘mastery’ to improve results in mathematics since 2014.

Whilst the exact definition of ‘mastery’ is the subject of debate it is fair to say that the NCETM themselves are promoting 5 big ideas that they believe underpin their version. As part of the programme I recently joined thirty teachers to observe a Year 7 maths lesson taking place in an English secondary school. The lesson (the sixth in a series of seven) was organised by a local Maths Hub and taught by a visiting teacher from Shanghai with the intention of demonstrating ‘mastery’ and the 5 big ideas.

To lay my cards on the table I left the lesson (and surrounding discussions) feeling bitterly disappointed. As I have tried to process my disappointment and frustration, I reflected on three areas – the experience of the students, the failing of the explicitly stated message and the dangerous implicit message.



Our first concern after observing a lesson should always be to consider our students.

This is inevitably quite subjective, but my feelings are based on listening in to student conversations during the lesson and speaking to students at the end of the lesson. Unfortunately, I witnessed widespread confusion, an over-reliance on procedural understanding, misconceptions and most worryingly – boredom. In this case, thirty passive students mindlessly trying to do what they were asked but struggling to make sense of it means that this lesson failed the students.

The next source of my frustration is in considering whether the NCETM are even demonstrating the very things they say are important.

This is again subjective, but within the lesson there was no evidence of 4 of the 5 big ideas that they are claiming to promote! Nothing. The fifth (coherence) may arguably have been intended but it wasn’t clear and it certainly wasn’t successful. Irrespective of whether these ideas are the correct ones to promote, it should be unthinkable that they’re not being demonstrated in a lesson set up to demonstrate them! Teachers I spoke to left questioning the relevance of the ideas, the work of the Maths Hubs and of ‘mastery’ itself. This lesson fell short in modelling the explicit ideas of the NCETM.

Thirdly I had a feeling of unease about the implicit messages the demonstration lesson created.

The explicit message was that creating small coherent steps in understanding means that the whole class cannot fail but to proceed together. However, if a significant proportion of a class have not understood the small steps (as happened in this series of lessons) then just ploughing on is madness. The implicit message created is that small steps are sufficient for progress and that there is no need to worry about assessment for learning or intervention. That is a dangerous message.


Final Thoughts

Granted these thoughts are based on one lesson and others may have had far more positive experiences at other exchange lessons.

However, the fact that this lesson has happened should be a cause for reflection. I left the lesson fearing that students are being harmed, that the explicit message of ‘mastery’ is being harmed and that implicit misunderstandings are being allowed to grow.

If the teaching is failing the students and the lesson is failing to illustrate the very ideas an organisation is trying to promote then someone needs to be brave enough to do something about it. That might be the class teacher putting the interests of their students first, the Maths Hubs caring about local teachers, or even the NCETM realising that they’re accountable for their own message.

As the Chinese philosopher Confucius said, “by three methods we may learn wisdom: first, by reflection – which is noblest; second by imitation – which is easiest; and third by experience – which is the bitterest”.

Perhaps there has not been enough of the first in this exchange programme, too much of the second and now we are experiencing the third.

Matt Woodford

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