Young girls are fooling teachers that they are good at maths because they get their sums right.
The pages of ticks hide the fact that the girls are using inefficient ways to reach the answer. As the calculations get more complicated, girls continue to persevere with long-winded methods while boys give up and get their sums wrong, highlighting their need for help.
By the time they get to 11, girls who did well at seven have fallen behind their male classmates because they have not mastered the different techniques needed to solve more difficult problems.
This phenomenon has been identified by national numeracy strategy consultants in authorities around the country, which are now attempting to find ways to put the pupils back on track.
In Berkshire a dozen schools have been involved in two programmes, developed by King's College London, which encourage pupils to think and talk about how they solve problems.
The primary Cognitive Acceleration through Maths Education (CAME) programme for 10 and 11-year-olds involves plenty of talking about maths and sharing ideas about how to solve problems. The Let's Think programme for five and six-year-olds has a similar approach.
Karen Sawyer, headteacher at Hungerford primary, said: "We thought girls didn't enjoy maths, but we found that they did but lacked confidence. They were not so keen to stretch themselves and played it safe."
She said the lessons for 10 and 11-year-olds were different from a national numeracy strategy lesson, which typically involves children sitting together and answering questions from a teacher. This year 82 per cent of Hungerford pupils reached the expected level 4 in maths at 11, up from 70 per cent in 2004.
Ms Sawyer said: "We think changing our maths teaching, by spending more time talking about how to solve problems, has contributed to the improvement in our test results this year."
In Lancashire, 10 schools are to be asked to come up with ways to raise girls' achievement in maths.
Shirley Bush, senior mathematics consultant in Lancashire county council's mathematics team, said she was concerned that fewer girls who get level 2c (the lower end of what is expected at KS1) than boys go on to get the expected level 4 at KS2.
She says: "We have girls who have no problem achieving level 4 in English, but they do not in maths. They are intelligent but they are not getting it, when it comes to maths."
Tim Coulson, director of the national numeracy strategy, said: "There are girls who may be weak at maths, but are conscientious. They get the answers through sheer hard work using inefficient methods, such as counting on to add 17 and 18. Boys are typically less inclined to count up, but more likely to look for a sensible strategy or just get it wrong, so it is easier for their teacher to see they don't understand."