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.