On 14 January 2005, Lawrence Summers (right), president of Harvard University spoke of the reasons behind the disproportionate lack of women in top-end science and engineering jobs. Avoiding suggestions of discrimination, he offered two explanations – unwillingness to commit to the 80-hour weeks needed for top level positions and, more controversially, a lower “intrinsic aptitude” for the fields. According to Summers, research showed that genetic differences between the sexes led to a “different availability of aptitude at the high end”.
For years, scientists have battled over the evidence for sex differences in scientific ability, using genetics, psychology and social sciences as their weapons. But often, they forget that this debate does not rage on in isolation – it is heard and processed by scores of young female scientists trying to make their mark in the field. A year after Summers’ incendiary remarks, a psychological study showed just how pernicious comments like these can be on this group of listeners.
Stereotypes famously reinforce themselves because people respond to them by acting out the stereotype. Black Americans perform worse in intelligence tests if their race is drawn to their attention. And in the UK, the media portrayal of our teenagers as boorish hooded thugs risks driving them further down that route.
But Ilan Dar-Nimrod and Steven Heine at the University of British Columbia reasoned that stereotypes are even more catastrophically self-fulfilling if genetics are thrown into the mix. Regardless of what geneticists know, a large proportion of the public still view genes as inescapable agents of pre-determination, setting your life and actions down a course you have little say over.
You all know the score. A train leaves one city travelling at 35 miles per hour and another races toward it at 25 miles an hour from a city 60 miles away. How long do they take to meet in the middle? Leaving aside the actual answer of 4 hours (factoring in signalling problems, leaves on the line and a pile-up outside Clapham Junction), these sorts of real-world scenarios are often used as teaching tools to make dreary maths “come alive” in the classroom.
Except they don’t really work. A new study shows that far from easily grasping mathematical concepts, students who are fed a diet of real-world problems fail to apply their knowledge to new situations. Instead, and against all expectations, they were much more likely to transfer their skills if they were taught with abstract rules and symbols.
The use of concrete, real-world examples is a deeply ingrained part of the maths classroom. Its advantages have never really been tested properly, for they appear to be straightforward. Maths is difficult because it is a largely abstract field and is both difficult to learn and to apply in new situations. The solution seems obvious: present students with many familiar examples that illustrate the concepts in question and they can make connections between their existing knowledge and the more difficult concepts they are trying to pick up.
The train problem is a classic example. Another is the teaching of probability with rolls of a die, or by asking people to pick red marbles from a bag containing both blue and red ones. The idea is that, armed with these examples, students will recognise similar problems and apply what they have learned. It’s a technique deeply rooted in common sense, which is probably as good an indicator as any that it might be totally wrong.