In a recent Café Scientifique at the Royal Society, Matthew Inglis (Loughborough University) discussed evidence in favor of both views.
For centuries, mathematicians have maintained that studying mathematics makes you better at a whole range of other logical and problem-solving tasks, so that studying mathematics should be encouraged in all people, not just those who want to become mathematicians. Educational psychologists, however, have traditionally struggled to find evidence of these claims in actual studies: it seemed as if studying mathematics only made people better at mathematics, and little else.
So who’s right? In order to find out, Inglis and his colleague Nina Attridge decided to run a new set of experiments based on conditional inference (that is, the process used to answer questions like “if A is true, is B also true?”). They selected two groups of British 16-year-olds, and followed them through their second-to-last year of pre-university education. For one group, mathematics was a substantial part of the curriculum; the other didn’t study any mathematics at all, but received advanced education in other areas such as English literature.
The first interesting result was that the two groups were essentially indistinguishable at the start. This dispels one of the most frequent stereotypes: that smarter people all study mathematics, and that only students who can’t “handle” it choose other studies.
During the one-year experiment, however, the situation changed. Not surprisingly, the performance of the non-mathematicians on mathematical tasks didn’t significantly improve. That of mathematicians, also not surprisingly, did change, but in a less intuitive way: two years of mathematics made better at scooping flawed arguments, but didn’t significantly improve their judgement of correct arguments, making them overall more skeptical and harder to convince, whether of a right or a wrong argument.
It is interesting to reflect on the implications, and how to reconcile them with the statement supported by so many math professionals, that their studies have dramatically changed the way they think. The way mathematics affects thinking is seemingly by making students more skeptical, more wary of a problem’s complexity. The mathematics students in the experiment were somehow more reluctant to agree with an argument, even when that argument was in fact correct, arguably fearing that there could be more than met the eye.
Socrates is believed to have said that those aware of their own ignorance are wiser than those who aren’t, as they at least know that they do not know. Is this the sense in which mathematics improves the thinking processes of those who study it? Has math just made them more alert to what may be beyond their horizon?