What is teaching for mastery in maths?

I was very interested to read the item in last week’s Schools Week that suggested pupils in one primary school were being prevented from reading books ‘above their level’ because of a ‘mastery’ approach to English teaching.

Teaching maths for mastery involves employing approaches that help pupils to develop a deep and secure knowledge and understanding of mathematics at each stage of their learning, so that by the end of every school year or Key Stage, pupils will have acquired mastery of the mathematical facts and concepts they’ve been exposed to, equipping them to move on confidently and securely to more advanced material.

First, I need to state two fundamental points: (1) Acquiring mastery of mathematics is something for all pupils. (2) Teaching for mastery approaches can enable all pupils (with only a tiny proportion of exceptions) to succeed in maths.

But, when any new word rapidly gains wide currency, as has happened here, competing interpretations will emerge and spread, before a common understanding establishes itself. This is even more likely when the word itself is already widely used in other contexts. Unhelpful examples of this include the concept of a ‘master chess player’ or an accomplished person in any field giving ‘masterclasses’.

The mastery that we envisage pupils achieving in mathematics at primary and secondary school does not fit either of these templates. It is, rather – I repeat – something to which all children can and should aspire, and something which their teachers should believe all their pupils can achieve.

Against that background, let’s try to unpack what mastering mathematics, at any age, looks like. A key word here is ‘depth.’

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.

Vitally, because maths continually builds on itself, it will mean they will have developed secure, lasting mathematical understanding on which they can build more advanced mathematical ideas at the next stage in their learning.

It’s important to note that, for this level of mastery to be achieved, it is necessary for the learner to have acquired rapid and accurate recall of fundamental mathematical facts and concepts (e.g., at primary level, times tables and that division is the reverse of multiplication).

Teachers in hundreds of schools are developing expertise in teaching approaches that help children along this path.

But we acknowledge that there’s a widely-held misconception that sees teaching for mastery as, in some way, holding back high-attaining pupils, because they have to wait for the whole class to ‘get’ something before they can tackle the ‘more difficult’ stuff.

The teachers we work with make two points addressing just this concern. First, the ability to race through pages of pages of questions, demonstrating speedy and accurate ability to do mechanical calculations does not mean a pupil has developed secure grasp of the mathematics concerned – many pupils who appear to shine in this way often struggle when challenged to apply knowledge outside the parameters of routine exercises.

And second, these high-attainers thrive and advance even more in their understanding when exposed to tasks and activities that explore and develop deep understanding. Far from being held back, these pupils are building more secure and transferable understanding.

Achieving this sweet spot of teaching in a maths classroom, so that all pupils, however quickly they appear to grasp concepts and processes, are supported in deepening their learning, whilst moving through the curriculum at the same pace, requires highly skilled teaching.

Bringing these approaches to every classroom in every school won’t happen overnight, but we’ll continue to do our best to help more teachers help more children to acquire the mastery in mathematics that will benefit them throughout their education and beyond.

Charlie Stripp is Director of the National Centre for Excellence in the Teaching of Mathematics