Research School Network: Our ​‘Master’s Glasses’ A research-based approach written from the perspective of a teacher

Nicol Winfield, Maths Research Lead for the Derby Research School

‘Mastery’ in mathematics – everyone is talking about it! It would seem that, rightly or wrongly, the term has been adopted as the latest fad in the world of mathematics education, yet Mark McCourt highlights that the idea of teaching for ​‘mastery’ can be seen to date back to the early 20^th century. So how do we enable people to begin to make sense of it in the modern day?

The National Centre for Excellence in the Teaching of Mathematics (NCETM) states that ​‘mastering maths’ simply means ​‘pupils acquiring a deep, long-term, secure and adaptable understanding of the subject’ and that underpinning this is the belief that ​‘by working hard, all children are capable of succeeding at mathematics’. Many of us confidently say that we share this belief, but what do we really perceive ​‘success’ to mean? In the words of Carol Dweck, do we praise our pupils for the process they engaged in or do we praise our pupils for their intelligence? And are we aware of the implications stemming from how we portray success on the mindset of our pupils?

When Wyndham Primary Academy first began to develop their thinking around this, they spoke to those children who rated maths poorly in comparison to other subjects, questioning their reason for this. The children explained that they did not feel a sense of success in maths, and when asked why, they spoke about the length of time it took for them to arrive at a solution to a given problem in comparison to their peers. 

The NCETM states that if a pupil really understands a mathematical concept, idea or technique they can:

• describe it in his or her own words
• represent it in a variety of ways (e.g. using concrete materials, pictures and symbols – the CPA approach)
• explain it to someone else
• make up his or her own examples (and non-examples) of it
• see connections between it and other facts or ideas
• recognise it in new situations and contexts 
• make use of it in various ways, including in new situations

… no mention of ​‘arriving at an answer quickly’. 

And so my team and I realised that we needed to make the implicit explicit to change the way staff and pupils viewed success in mathematics. This led to the birth of the ​‘Master’s Glasses’.

The idea seemed simple. Children would be encouraged to independently use the Master’s Glasses throughout each maths lesson to demonstrate their depth of understanding. They would first look to ​‘explain’, ​‘prove’ and ​‘use’ their thinking before working to evaluate their approaches taken and help others to realise their misconceptions. The emphasis was less on the ​‘end result’. 

After piloting their use within my own classroom and seeing the impact on children’s attitude towards maths, my principal, Paula Baines-Chambers, invested in different coloured party glasses, encouraging children to put them on when they were demonstrating their abilities. Soon there was a real ​‘buzz’ around school – children were enthused and we were enthused.

Months passed and I became deflated seeing that the children in other classrooms had started to neglect the Master’s Glasses. However, I understood that there must be a reason for this and looked to question my approach to implementation.

Reverting back to the evidence base, specifically the EEF’s guidance report for Improving Mathematics in Key Stages Two and Three, I realised that developing metacognition (the ability to independently plan, monitor and evaluate our thinking and learning) was not as straightforward as I first thought and there were some important challenges I had failed to consider. Recommendation 5, ​‘develop pupils’ independence and motivation’, explains that metacognitive strategies must be explicitly taught and the thought processes of an expert learner must be modelled to help children develop their metacognitive skills. Moreover, schools should support teachers to develop knowledge of these approaches, ensuring that they do not detract from concentration on the mathematical task itself which can be the case when children are expected to do too much, too early, without effective scaffolding from their teacher. I recognised the need to lead professional development for staff around this and grant time for children to imitate, internalise and independently apply… 

As I walk round Wyndham Primary Academy three years on, I see self-regulated learners who deploy crucial metacognitive strategies and who feel successful in mathematics, which I deem to be the result of taking a research-based approach.

Putting this new approach into practice highlighted to me that, in the words of the EEF’s guidance report, Putting Evidence to Work: A School’s Guide to Implementation: ​‘it doesn’t matter how great an educational idea or intervention is in principle; what matters is how it manifests itself in the day-to-day work of people in schools’. In the words of Thomas Edison, a ​‘vision without implementation is hallucination’.