Research School Network: Guest Blog: Maths mastery: a blessing or a curse?

If you had gone into a maths lesson even 6 years ago, things would have looked mightily different. I can remember the day we had an SLT meeting at my previous school and I was asked as the then Maths Coordinator to define ​‘Maths Mastery’ and my response was at the time less than articulate and a little bit jumbled. I would say I was embarrassed but to be honest, we were all wrestling with what it meant, what it looked like and how it would impact on our daily practice. The journey has been interesting and has challenged my thinking along the way. The EEF Teaching and Learning Toolkit places​‘Mastery Learning’ as a big hitter with a +5 months impact size and so our desire to take that principle and translate it into practice in our settings with that real impact on outcomes has driven many of us along the way. It’s brought lots of new thinking about how and why we teach Maths, and in turn made us reflect and question. Dave Benson, Mathematics Education Coordinator and Senior Lecturer at Derby University, explores this further in a guest blog, asking if Maths Mastery has been a blessing or a curse.

Tammy Elward, Director of the Derby Research School, Research Lead

Maths mastery: a blessing or a curse?

Dave Benson, Mathematics Education Coordinator at the University of Derby.

‘Mastery in Mathematics’ has been adopted as a term by the National Centre for Excellence in the Teaching of Mathematics (NCETM) since 2014. It has many roots in well-established pedagogical approaches in high-achieving East Asian countries. The Centre has sought to define it and establish principles for teaching mathematics which help to raise standards in achievement across the primary and secondary sectors in the UK.

What is mastery of maths?

Defining ​‘mastery in mathematics’ is in itself a complex business. In his Schoolsweek blog (20÷04÷16), Charlie Stripp (Director of NCETM) offers insights into his interpretation when he writes,

If understanding in any mathematical area is deep (not superficial) then it will mean the learner has recognised and grasped connections between the concept in question and concepts in other areas of maths. It will mean they can explain why something in this mathematical area works, and why, perhaps if just one parameter changes, it doesn’t work.

Helen Drury (2015: 9) reinforces this definition when she writes:

A mathematical concept or skill has been mastered when, through exploration, clarification, practice and application over time, a person can represent it in multiple ways, has the mathematical language to be able to communicate related ideas, and can think mathematically with the concept so that they can independently apply it to a totally new problem in an unfamiliar situation.

So, ​‘mastery’ of a mathematical concept would suggest that we understand it at a deep level. In this context, ​‘deep’ is obviously a relative, complex and even subjective term. What is deep for one person may be shallow for another! That said, if a concept has been ​‘mastered’, one would expect the learner to be able to apply their knowledge and skills effectively to solve new problems and also to demonstrate a growing ability to explain as well as justify their thinking.

Although complicated to define, many would argue ​‘maths mastery’ is still persuasive as an idea and potentially supportive to both primary and secondary school practitioners. For example, in the light of new-style Key Stage 2 SAT and GCSE papers which are expected to assess pupils’ ability to use and apply skills more rigorously, an emphasis on secure understanding, confident reasoning and problem solving skills rather than on mechanical application of mathematical procedures certainly feels like a positive and wise aspiration. For me, despite its potentially divisive label, there is something positive and pedagogically persuasive in the intentions of the idea of ​‘mastery’. Its emphasis on depth of understanding, over breadth of knowledge and procedural approaches to learning, for example, chimes with my personal philosophy for teaching and learning mathematics.

For some time, however, my sense has been that we need to move on from a debate about definition of ​‘mastery’ to the much more interesting and challenging idea of classroom implementation and evaluation of experiences. Only that way can we begin to ascertain the potential benefits and shortcomings of a ​‘mastery’ approach in our primary and secondary schools. With this in mind, since March 2016 I have worked with more than 100 teachers and 20 schools to explore with them ideas for implementing a ​‘mastery’ approach in their classrooms. Throughout my research with these teachers, I have seen both the pros and cons to ​‘mastery maths’.

The pros of ​‘mastery maths’:

• Teachers feel less constrained by planning structures and are at ease with the idea of carrying more in their head with less detail in their written plans.
• Participants see the value of ​‘dwelling on’ topics for longer periods as beneficial because it helps provide a more secure base for learning.
• The balance between ​‘pacey’ activities to support fluency and richer exposition and tasks which demand more reasoning and problem-solving skills could be beneficial to pupils’ progress.
• Teachers have developed their own subject knowledge by engaging with a mastery approach.
• Many have experimented with grouping pupils in alternative ways. Although grouping by ability is still used, many have begun to recognise the potential benefits to learning of mixed ability groupings.
• Generally, participants report that pupils are strengthening verbal reasoning skills more obviously than developing confident written explanations of their thinking.

The cons of mastery of maths:

• Losing the awe and wonder of learning mathematics.
• Providing adequate intervention.
• Dealing with differentiated learning needs.
• Managing pace of lessons and learning.
• Maintaining variety and creativity in pedagogical approaches.

The question of how to provide intervention for those pupils falling behind the expected pace of learning has persisted amongst the teachers I have worked with. In addition, concerns surrounding headteachers’, parents’ and Ofsted’s views of the changes in approach also remain uppermost in participants’ minds. Understandably, they wonder whether the rationale for and intentions of the changes will be shared and understood, particularly with regard to differentiation and grouping of pupils. Paradoxically, they sense progress in their professional practice yet feel concerned about how they will be judged, particularly if outcomes for their pupils who do not improve.

So, would I see ​‘Mastery in Mathematics’ as a blessing or a curse? With its emphasis on conceptual understanding of mathematics as a complement to confident procedural skills, I would probably go more with the former than the latter. However, a reading of key figures in the history of educational thought on the learning of mathematics, would suggest that Mastery is far from a new idea and that similar principles have underpinned much academic writing for more than 40 years! The ​‘Curse of Mastery’ could be the way in which it has become yet another educational initiative which seeks to control rather than liberate the potential of professional practice. With their plethora of strategies for improving outcomes in mathematics across the primary and secondary sectors, recent governments have, as far as I can see, tended to de-professionalise teachers by denying them genuine opportunities to exercise professional judgement and, instead, creating cultures of fear in which teachers feel constrained to be seen to be engaged in expected practices. Although well-intended and, in my view, fundamentally persuasive at heart, if Mastery becomes regarded as some kind of perfect ​‘recipe’, official directive or panacea for teaching mathematics, we shall once again find ourselves in a position where the potential to promote children’s learning in mathematics will be lost.

References

Drury, H. (2015) Mastering Mathematics.Teaching to Transform Achievement. OUP: Oxford

Mathematics Mastery: a blessing or a curse?