Why do we teach maths in schools?

a) To create the research mathematicians of the future

b) To empower ALL of our children to take their place as mathematically literate members of society

c) To instil in our citizens an appreciation of mathematics as a thing of beauty and truth

If we create a mathematics curriculum that allows everyone to reach a minimum standard of mathematical understanding (functional numeracy, perhaps) but also allows a generation to leave school without any appreciation for the wonder and pleasure of doing mathematics, then we have failed. But at the same time, if the system identifies and nurtures superbly talented mathematicians who go on to win Field’s Medals, while allowing some children to slip through the net and leave school innumerate, we have also failed.

If we work towards c) however, and see the job of school mathematics lessons as teaching all children to think mathematically (and to understand what we mean by thinking mathematically), I think we will go a long way to achieving the other two objectives – they needn’t be mutually exclusive. In classrooms where high-level mathematical reasoning is the norm, a good level of mathematical literacy becomes the currency for convincing others of your ideas, so pupils are given a motivation for wanting to become more skilled in mathematical procedures. If thinking mathematically is the expectation, those children who enjoy the pedantic* process of convincing themselves and others of the truth of a conjecture will discover themselves to be mini-mathematicians and will be more likely to embark on the process that could lead them to fame, fortune and Field’s Medals. As soon as our curriculum aims to do anything other than exposing young people to mathematical thinking, we risk doing at least some of the children in our care a great disservice.

*I do not use this term in a pejorative way. I took great delight in being exceedingly pedantic throughout my secondary school career.

Good comments. We can apply similar arguments right through to A-level and beyond. Even at university, there is a semi-unwritten assumption that the mathematical stars of the future will hit the ground running in the first year, so there is no real need to pay too much attention to the lower achievers. This, of course is untrue. I wonder how many potentially great achievers lost their way aged 18 or 19?

You speak wisely, Alison.

I like the way you refer to ‘the pedantic process of convincing themselves and others of the truth of a conjecture’. I had a good discussion with primary teachers at a school I was at this time last week about how ‘picky’ we should be when encouraging children to justify and explain their thinking. One teacher commented that when he had watched my session with the children, he was surprised by how demanding I was in terms of encouraging them to be precise. He worried that sometimes the pace of the lesson might be lost but having high expectations is important, I think …

Yes I think as teachers sometimes our instinct is to step in and provide the rigorous explanation as soon as we see that the child has the beginnings of a justification, rather than teasing a precise proof out of them, not just because of concerns about pace, but also because it’s uncomfortable to watch a child struggle. But the joy that comes from constructing a watertight argument that convinces a sceptic has to be worth investing some time in!