Girls to the power of x2
The sea of girls may know the answer to the maths equation, but their arms remain stubbornly at their sides. It is the boys who wave their hands in the air - eager to impress even with the wrong answer.
Such images may pander to gender stereotypes, but it is a recognisable issue at Queen's Crescent Primary School in Chippenham, Wiltshire. "We had a problem with passive girls," explains Gen Tatters, a Year 6 teacher.
"The girls' hands were never up. They would never volunteer and had to be pushed to take part. There was a significant gender difference in terms of key stage 2 results - the girls just weren't achieving at level 5."
This lack of confidence among girls is not an isolated problem. In a 2007 study called Questioning the Gender Problem in Mathematics, Paul Ernest, emeritus professor of mathematics education at Exeter University, found that 66 per cent of girls - almost twice the proportion of boys - said they would not continue studying maths after GCSE because it was "too difficult". Just 40 per cent of those who took A-level maths in 2009 were girls (see box, bottom right).
But while much attention has focused on ways of encouraging boys to read, the problem of getting girls interested in maths has been comparatively overlooked. One reason may be that, unlike boys in English, girls do well at maths. They are just not that keen on it.
Although boys get better grades on average in maths at key stage 2, girls have outperformed boys at GCSE level in every year bar one since 1997.
The exception was last year, when boys nudged ahead of girls by 0.6 per cent - a shift widely attributed to the removal of maths coursework, where girls tend to outshine boys. The problem, it seems, lies not in performance, it is in take-up.
It was in response to these concerns that Wiltshire local authority invited six teachers from different primary schools to join a working group to look at ways of helping more girls reach the top level 5 in maths at key stage 2.
"It was clear from the beginning that there was no excuse whatsoever for them to underperform in the way they were," says Fred Angus, the authority's maths adviser. While attainment at level 4 was roughly the same between the sexes in Wiltshire, the gap between girls and boys at level 5 had been widening year on year. By 2008 it stood at 8 per cent.
The group looked at teaching more extended activities and encouraging greater discussion. Although this approach aimed to benefit all pupils, girls were a particular target.
While boys often have the confidence to "have a go", girls are considered less likely to put themselves in the spotlight, especially if they feel unsure about their answer. The assumption behind the Wiltshire pilot was that if pupils are given the opportunity to discuss the possible solutions beforehand, some of the risk is removed and girls will be more likely to get involved.
The teachers needed a dose of confidence, too. In order to build in more discussion, they planned in pairs, observed each others' lessons and reflected on their performance.
But initial results were disappointing. Despite switching from looking for right or wrong answers to focusing on whether any given statement was "always, sometimes or never" correct, girls were still not volunteering any answers, says Ms Tatters.
So she and her partner teacher, from nearby Holy Trinity in Calne, drew up a set of rules emphasising the need to discuss possible solutions thoroughly with a partner. It was then that things began to change. The difference it made to the pupils was "remarkable", Ms Tatters says.
"I was so surprised that the new approach worked as well as it did," she adds. "I couldn't believe the difference. By the end of the project, all the girls were more willing to give suggestions and explanations about their investigation."
At the beginning of the project, pupils described a good mathematician as someone who knew their times tables, multiplication and division. By the end, their responses were more reflective, referring to problem-solving, being able to explain concepts to others and investigating different methods.
This also translated into results. Of the six girls identified as being capable of scraping a level 4 at Queen's Crescent, all got a level 5 in last year's Sats.
They were not the only ones to benefit. In a class of 35 pupils, just two missed out on a level 5. Across the authority as a whole, the gender gap at level 5 fell from 8 per cent to 4 per cent.
This exploratory approach to teaching maths is the key to raising standards, believes Jane Imrie, executive director of the National Centre for Excellence in the Teaching of Mathematics. It also has a special resonance for girls.
"Girls in particular like to feel involved in their learning," says Mrs Imrie. "They need to discuss it, debate it, play with it, and make it a more social experience, as opposed to a hard and fast set of rules.
"At the moment, a lot of maths teaching is like trying to teach a pupil to swim with them standing on the side. Girls need to jump in and have a go."
This is just as true at secondary level. At Bishop Challoner Catholic College in Birmingham, pupils are given the chance to take a more active role by teaching younger children. Year 9 pupils teach children at local primary schools, while Year 12 students support key stage 3 lessons.
While the approach has been effective in getting boys interested in the subject, it has been especially influential in encouraging girls to take part in lessons. Girls realised that they knew more than they thought, and enjoyed using that knowledge to help others.
The school has also experimented with a "no hands up" strategy to try to prevent boys from dominating in class, says James Coughlan, a maths teacher.
"At this school, girls love maths," he explains. "There's a real buzz about it. It's not seen as geeky; it's seen as something that teachers and pupils can be passionate about."
But Bishop Challoner's drive to get girls interested in maths is unusual, says Jo Boaler, professor of maths education at Sussex University. She believes the relative parity of GCSE achievement hides the variation in opportunities for girls and boys.
"Some people believe that low participation rates merely reflect the `natural' inclination of the different sexes," she says.
As a result, teachers are more likely to encourage boys to continue with maths after GCSE, rather than girls.
But this attitude starts well before school. Professor Boaler believes it originates in a generation of "traumatised women", who tell their daughters how poor they were at maths as schoolgirls. "That comment has a terrible effect on girls, who use it as permission to switch off," she says.
The low take-up of A-level maths feeds through into higher study. Just 39 per cent of maths undergraduates are women. And for evidence that this is not a case of natural aptitudes, Professor Boaler points to the US, where the equivalent figure is 48 per cent.
At Parkside Federation, which runs Parkside and Coleridge community colleges in Cambridge, teachers have tried to overcome the gender bias in maths through ensuring pupils work collaboratively every time. All classes are also mixed ability, reducing the stigma of a top set dominated by boys who are "good" at maths, and a bottom set of girls who are not.
"Girls are happier and more confident in our environment than in a traditional maths classroom," says Fran Wilson, director of maths and computing.
"We think this is due to the lack of barriers and limitations so pupils don't lose confidence from not being in the top group."
The results speak for themselves. At Parkside, almost all GCSE pupils - girls as well as boys - take the harder, higher tier of maths exam. It is this relentlessly high expectation of both sexes - plus a structure that encourages participation and self-belief - that drives standards up, Ms Wilson believes.
School staff can do the maths for themselves. If teaching and learning are not adapted to meet the specific needs of girls in mathematics, the participation rates between the sexes will never add up.