By age six, girls are less likely than boys to view their own gender as brilliant and express interest in activities described as for "really, really smart" children, according to new research published in Science.

Many media outlets reported these findings. But most of the coverage overlooked another key finding from the same study: Boys were less likely to say their own gender gets top grades in school.

The beliefs of children matter because they could shape students' interests and achievements over time, other research suggests.

For instance, one 2013 experiment found that telling elementary school children "girls do better than boys" in school made boys - but not girls - perform worse on a series of academic tests.

These expectations can work both ways: When researchers told children that boys and girls would perform the same, boys' academic performance improved.

There are real and persistent gender achievement gaps in the US.

For instance, boys tend to get worse grades than girls, but girls are few among top scorers on standardised maths tests. While much research has studied how stereotypes about achievement can make girls underperform, the gaps where boys do worse have often been historically overlooked. But stereotypes can harm boys too - just in different ways.

WHO GETS THE GRADES, WHO'S SUPER SMART?

In the new Science study on children's views about brilliance, developmental psychologists asked 144 children aged five to seven a series of questions about school achievement. For instance, the children had to guess which of two unfamiliar boys and two unfamiliar girls got "the best grades in school".

Kids tended to favour their own gender, but boys did so to a lesser extent. Among seven-year-olds, 79 per cent of girls selected girls as the better student, but 55 per cent of boys selected boys.

These results sharply contrasted with those about brilliance. When asked to guess who was "really, really smart", girls instead expressed less confidence in their gender. Among seven-year-olds, 55 per cent of girls selected girls as being super smart, but 66 per cent of boys selected boys.

In other words, these young children overall held positive beliefs about their gender. But boys were less certain about their gender getting good grades and girls were less certain about their gender being super smart.

Other research has found that, by fifth grade, both boys and girls say that girls work harder in school, want to learn more, listen better, follow instructions better, are more polite and - perhaps as a result - perform better in school.

REALITY OF GENDER ACHIEVEMENT GAPS

Children's stereotypes reflect reality to an extent. For instance, girls have got better school grades in all subject areas for nearly a century, according to a recent synthesis of 308 studies that included over one million students.

Girls get better grades, even in maths and science - two subject areas often assumed to favour boys. Women now earn more bachelor's, master's and, since 2007, doctoral degrees than men in the US.

Despite their advantage in grades and degree attainment, girls are under-represented among the highest scorers on standardised maths and science tests. For instance, boys typically outnumber girls by between two and four to one among the top 1 per cent or higher of maths scorers. But girls tend to slightly outnumber boys among top scorers on standardised reading and writing tests.

Children's views about who is "really, really smart" therefore partly match the reality of who gets top scores on maths (but not reading or writing) tests.

SELF-FULFILLING STEREOTYPE

But children's stereotypes may do more than merely reflect reality: They may help create that reality through self-fulfilling prophecies. For instance, if girls doubt their gender can be brilliant, girls might avoid "super smart" activities like advanced maths summer camps and then not develop precocious maths talent. In other words, stereotypes and reality could mutually strengthen each other.

Consistent with these hypotheses, the new Science study also found that, by age six, girls expressed less interest than boys in games described as for children "who are really, really smart" (though more research is needed to see if stereotypes directly caused this gap in interest).

Stereotypes could negatively affect boys too. As experiments on elementary schoolkids suggest, beliefs about boys' academic inferiority or poor reading ability could make boys underperform on evaluative academic tests.

Teachers' stereotypes also matter. For instance, teachers' beliefs that girls are better readers predict declines from grade five to grade six in boys' - but not girls' - confidence in their reading skills. Researchers also find that teachers often view boys as "lazy, disruptive, unfocused, and lacking motivation". This stereotype could negatively affect teachers' perceptions of boys' learning, one experiment found.

These results suggest stereotypes contribute to gender achievement gaps, but they certainly are not the only factor at work. The girls' advantage in grades might be tied to actual differences in classroom behaviour or activity level.

MAXIMISING ALL CHILDREN'S POTENTIAL

Stereotypes could therefore hold back both girls and boys, but in distinct domains. Beliefs about brilliance might deter girls from top intellectual pursuits, but beliefs about grades and classroom behaviour might harm boys in school more broadly across the achievement spectrum.

Both sets of findings are important. However, people often appear much less concerned with stereotypes negatively affecting boys than those affecting girls. For instance, several tweets about this new study described its results about brilliance as "sad" and "depressing", but its results about grades went largely unnoticed.

Data on boys' underachievement has often been historically overlooked in media attention and educational policies. Some writers even argue that boys' educational struggles are not "worrisome" because "the workplace is still stacked against (women)".

But it is not constructive to pit one gender against the other. Recognising contexts that favour females does not erase biases against them elsewhere. More importantly, the goal of education should be to maximise all students' potential and remove obstacles in their way. Regardless of the individual strengths students bring to school, stereotypes should not determine how far they go.

Realising that goal requires identifying and mitigating how stereotypes can also hold boys back in school.

•The writer is a doctoral student in psychology, Northwestern University.

•This article first appeared in The Conversation http://theconversation.com , a website which carries analysis by academics and researchers.