I was at a parents night in my son’s primary school yesterday and the teacher who was talking on the maths curriculum said something that made me think of Steven Pinker’s paper on the ‘cognitive niche’. Pursuing arguments first made by Alfred Russel Wallace, Pinker asks the question:
“Why do humans have the ability to pursue abstract intellectual feats such as science, mathematics, philosophy, and law, given that opportunities to exercise these talents did not exist in the foraging lifestyle in which humans evolved and would not have parlayed themselves into advantages in survival and reproduction even if they did?”
Pinker proposes these feats are just by-products (‘spandrels’) of evolution, just as many others have suggested that religious belief is also a spandrel.
Pinker suggests that humans’ enhanced ability to think (but not necessarily in an abstract manner), and to cooperate, gave them a survival advantage. On the whole question of abstract thinking he says
“Humans do not readily engage in these [abstract] forms of reasoning. In most times, places, and stages of development, people’s abilities in arithmetic consist of the exact quantities “one,” “two,” and “many,” and an ability to estimate larger amounts approximately. Their intuitive physics corresponds to the medieval theory of impetus rather than to Newtonian mechanics (to say nothing of relativity or quantum theory). Their intuitive biology consists of creationism, not evolution, of essentialism, not population genetics, and of vitalism, not mechanistic physiology. Their intuitive psychology is mind-body dualism, not neurobiological reductionism. Their political philosophy is based on kin, clan, tribe, and vendetta, not on the theory of the social contract. Their economics is based on tit-for-tat back-scratching and barter, not on money, interest, rent, and profit. And their morality is a mixture of intuitions of purity, authority, loyalty, conformity, and reciprocity, not the generalized notions of fairness and justice that we identify with moral reasoning.”
Anyway, to get back to the maths teacher…
While most of what she said was reassuringly sensible and ‘traditional’, there were was one point that she made about early stage maths teaching that got me thinking. She suggested that it is better to avoid making mathematics too abstract too early. And so, the classroom we visited was filled with all sorts of maths ‘toys’. I would have scoffed at this just a few weeks ago because in general I dislike gimmicks and I have a fairly traditional outlook when it comes to education. But if abstract thinking doesn’t come easily to us as a species, perhaps only some of us will take to it. So maybe we need to be careful about diving too deep too quickly and causing many pupils to drown, only to be left with a minority who, by chance, have been born with a natural aptitude for abstract thinking.
More broadly, maybe we have to accept that not everything to do with maths is cultural or even pedagogical – perhaps mathematics presents problems that are biological in origin.