If you want your daughter to become a mathematician, send her to an all-girls school. Research by Marta Favara has found that girls who attend single-sex schools are more likely to choose to study "masculine" subjects such as maths and science than girls who go to mixed school, even controlling for ability:

Attending a sixth form single-sex school alleviates the influence of gender stereotypes for girls. In the absence of gender pressure, gender stereotypes lessen and choices are based mainly on the maximization of their expected monetary pay-off...Single-sex contexts foster less stereotypical behaviours for girls.

This is probably because of a form of priming effect. Girls who attend mixed schools are surrounded by boys and so become more acutely aware of gender differences than gels at schools like St Trinians, and this leads them to become more feminine.

This is not an isolated finding.It's consistent with Alison Booth's finding that girls from single-sex schools are more competitive - more "masculine" - than ones from mixed schools.And it's consistent with experimental evidence (pdf) which shows how gender differences can arise from priming effects.

I mention this for three reasons.

1. It corroborates Akerlof and Kranton's work, which shows (pdf) how our (self-perceived) identities affect economic outcomes such as career choices.

2. It shows how "nudges" are not just policy levers. Subtle but important influences upon our behaviour are everywhere.

3. It give us another example of how the ideologies that sustain inequality arise inadvertently: studying "girly" subjects tends to lead to lower earnings.The creators of mixed schools had no desire to increase gender stereotypes, but this is what has happened.Unintended consequences are ubiquitous.