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Bridging the gap: Trainee and Teacher knowledge in Primary Maths and its impact on children’s understanding. How will the commitment to Maths Mastery fit in around this?

Robert Newell

This article argues that the valid pursuit of Mastery style Maths teaching could lead to deeper understanding in children and is a worthy goal. However, it will not be achieved fully without greater government support and funding to equip primary teachers with suitable confidence levels and understanding themselves. A significant minority of primary school teachers, in England, acknowledge that although they achieved the required pass grade in GCSE Maths their knowledge isn’t deep and they don’t feel equipped to probe deeply into fundamental maths to assist children in understanding the maths they are being required to do.

“If, as is widely suggested, there is a ‘problem’ of some kind with teachers’ mathematics subject knowledge the nature of this knowledge has to be understood” (Rowland, 2008)

Seemingly the interest and understanding of a number of children is compromised by the resulting interactions that take place. This is only partly compensated for by the teaching they receive from other teachers who feel both secure and upbeat about their teaching knowledge. Observing responses to lectures and workshops with primary PGCE trainees and Teach First participants, I pick up that a significant minority are comfortable about both their knowledge and how a lot of maths is interconnected. Many others, often with sound academic profiles, are not. Trainees expressed concerns reflect both a lack of fundamental understanding in mathematics and a lack of confidence about how to use knowledge that they possess.

Thus, they shy away from more complex but crucial discussions with children to unlock understanding, including engaging in meaningful discussion with children about mathematical reasoning and deduction: Often they feel ill equipped to front discussions to separate the relevant from the irrelevant. It is the inability to teach for , “Relational & Instrumental” understanding (Skemp,1976) that led to the Williams Report of 2008 that sought to ensure one teacher in every primary school with “deep understanding” in mathematics, to support development in subject , content and pedagogic knowledge, (Shulman, L, 1986). The report, in the main was ignored by the incoming coalition government although the issue remains. Committed though the vast majority of PGCE Primary trainees are, the PGCE year itself scratches at the surface relating to trainees knowledge to teach; generating a little belief, maybe, that the less confident as well as the fearful can overcome the perception that they aren’t equipped to teach for understanding.

The National funding to train teachers in the Maths Mastery approach, seen as being at the centre of success in maths teaching in high achieving countries such as Singapore and China, will, I believe, provide some impact on maths achievement. The NCETM (National Centre for Excellence in Teaching Maths) definition of mastery lays emphasis on whole class teaching. It demands factual fluency, seen as a crucial prelude to deeper teaching and learning in maths will provide a real challenge for some teachers and therefore children. The opportunity for those children who are more secure to achieve the deeper mastery classification may be achieved by some. I have yet to see a plan that will ensure a wide range of trainees as well as new and experienced teachers will be able to develop Mastery understanding in a range of children.   Funding has been made available for Mastery Trained specialists here in England (Gibb, N, 2016). This is having some impact but the numbers are, as yet, small. Maths Leads in schools are resourceful. Teachers working together can become the sum of their parts. Will this bridge a gap in teacher confidence and knowledge (the likely roots identified earlier in the piece)? Only in part, I feel.

More investment is needed. Our more confident primary maths teachers are likely to make the transition to Mastery style teaching with enthusiasm. However, course audits and discussions with trainees during training show huge disparities. As well as Mastery Training for selected teachers the government must fund support for the identified teachers who lack confidence and understanding, many citing limitations in the teaching they themselves received. It also needs to track a range of teachers as they complete training to identify what impact the Mastery Training is having in terms of how effectively less confident teachers are learning to deepen children’s understanding. The latest Trends in Maths (TIMMS, November 2016) has England in 10th place in the world.



Skemp R.:1976,- ‘Relational and instrumental understanding’, Mathematics Teaching 77, 20–26.

Hansen, A. – Children’s Errors in Mathematics, 2014

Shulman, L 1987, Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.

Williams Report ,2008, Independent Review of Mathematics Teaching in Early Years Settings and Primary Schools, DCFS

Rowland,T in Joubert, M. (Ed.) Proceedings of the British Society for Research into Learning Mathematics 28(2) June 2008