Ceri Morgan of Ofsted, the UK's official body for inspecting schools and standards in education, explains some of the counterbalancing tensions in maths education, ahead of the British Council's Mathematics Matters conference in December 2013.
Maths education is like a suspension bridge. There are lots of beautiful gentle curves right next to the sudden drama of a huge drop, and the whole thing is held together by a string of tensions.
Let's think about these tensions. How much 'basic' mathematics do we need to drop from the curriculum, because we now have technology that can do sums faster and more accurately? This debate is not new and won’t go away. It's a tension within the subject, and it's likely to get more taut as technological developments increase in pace.
First tension: Should we only teach 'useful' maths?
For example, there's a tension between teaching maths for the beauty and integrity of the subject in itself, and the pragmatic requirements of teaching only the 'useful bits' of maths. If we only focus on the latter, then how do we decide who maths must be useful for, and which bits of maths are most useful?
Do we always need to think about what 'business needs' are? If so, how do we know what companies' business needs will be in 20 years' time, when the children being born now leave school and enter the workplaces of the future?
Second tension: What do we first look for in maths teachers?
Another tension is how we should train mathematics teachers for their task. Do we ensure they are excellent mathematicians first and foremost, and consider their teaching skills to be of secondary importance? Or do we go for teaching skills first and subject knowledge second? And if we need both – which clearly we do – how do we go about finding the balance?
There is plenty of evidence that our strongest young mathematicians enjoy the challenge of exploring problems and love to talk about the subject. However, sometimes they don’t see the need to commit to writing down how they go about solving a maths problem. The process goes on way faster in their heads, so they think, 'why bother?'. But there is always going to be a tension between what needs recording, and what can always remain at the conceptual, or 'thinking' stage.
Then there's the tension between the need to have a shared language of mathematics (for example, we all need to know what a cube is) and the need to continually develop a new one, which is also obviously useful - think about the whole new vocabulary built around computers in the past several years.
How these tensions inform the debate on standards
My point is this: these tensions are sometimes seen as part of the problem in 'raising standards', but in fact they are holding the whole structure around mathematics teaching together, preventing collapse – apart from the huge imminent collapse if the debate ossifies. These discussions are what keeps the subject dynamic, interesting and responsive to new ideas.
Whilst all these useful tensions are holding the whole edifice up, the bridge is always of course subject to buffeting cross winds. We could usefully characterise these unpredictable winds as 'the future of mathematics'. We can't always tell which direction they are blowing in, but the subject needs to take account of them. I have of course stretched the analogy way too far already, but as we make our journey across the bridge towards the promised land of high standards in mathematics, let's just be thankful for the continued tensions pulling above our heads. They are what's stopping us from getting our feet wet.
Find out more about Mathematics Matters, a three-day conference on current trends in mathematics education, taking place at the University of Warwick on 11-13 December 2013.