According to a study published recently in the American periodical Science, by the time they are six years old, girls already think that they are less capable than boys. At school it is girls who on average achieve more highly, and yet from the very first year of primary school they assume that boys are better than them.

How is this possible? Who has put into their heads the idea that boys are superior, despite all evidence to the contrary? Think for a moment about the children’s books that you have at home, and the animated films you watch with your children. No doubt there will be some classics featuring enterprising and brave girls, such as Pippi Longstocking and Matilda. There will be wonderful, more recent books such as Andrea Beaty’s Ada Twist, Scientist and Jacqueline Kelly’s The Evolution of Calpurnia Tate, in which girls are the protagonists of amazing adventures.

But look a little further and start counting. How many of the books for children in your local bookshop have female protagonists? And when they do have them, what do they actually do? Do they speak? Do they work? Or do they stand there waiting for someone to rescue them, or at best provide assistance to the usual male hero?

You probably think we are talking about traditional fairytales in which sleeping princesses await deliverance at the hands of a prince, and that surely books for children are very different these days. So let’s have a look at a few statistics regarding books for children and children’s television – a snapshot of children’s media in the last 50 years.

The most recent study of gender stereotypes in children’s literature was carried out at the University of Florida, and surveyed a range of books published between 1900 and 2000. Every single one of these books had at least one male character, 25% had no female characters whatsoever, and 37% had no female characters who spoke.

Things get even worse with films, particularly cartoons. According to a recent study by See Jane, the institute set up by the American actor and producer Geena Davis to investigate gender stereotypes in the media, only 18.5% of cartoons have female characters who have a job or professional ambition, compared with 80% for male characters.

Take Finding Nemo – one of the most-loved animated films of recent years. Nemo’s mother dies in the first five minutes of the film, and from that point onwards the only other female character he encounters is the neurotically forgetful Dory. In the entire ocean, enormously vast and unexplored by definition, Nemo does not encounter a single other creature of the female sex.

Or look at a classic feature film such as ET The Extra-Terrestrial, the marvellous story about a space traveller who comes to Earth and is welcomed by a family with a mother and three children: two boys and a girl. The children become his friends and share amazing adventures with him. And yet in the end it is only the two brothers who help ET in the exciting feat of getting back home, flying across the sky on their bicycles. Their sister – who up until this point in the film has shared in every adventure – is suddenly out of the picture for the finale.

Children use stories to construct their own view of the world. Through stories, they understand how things work and what their place is in the scheme of things – their role in the world. What kind of a vision of the world is generated, then, by a children’s media that is so limited with regard to girls? One in which – by all accounts – if you are a female, you will think yourself inferior by definition to boys by the time you are six years old?

The Oscar-winning film Zootopia. Photograph: Allstar/Disney

Fortunately there are encouraging signs that things are changing. Many parents are now aware of these limitations, and are actively seeking books and films that do not merely advocate princesses and ballet dancers as role models for their children, and which teach their sons that it is possible to become engrossed in stories in which girls are the protagonists.

Have many of us not grown up identifying with Pinocchio, Superman, Inspector Gadget, Gulliver and Mowgli? Why should we not expect from boys the same capacity for cross-gender identification? Children are not born thinking girls are inferior to boys. We teach them to think that way – when, for instance, we decide that it is all right to buy a blue T-shirt for a girl but would not countenance buying a pink one for a boy; and when we read books devoid of female protagonists to our girls without even realising it, yet immediately worry that a boy might feel excluded if the protagonist of a story is a female pirate, simply on account of the fact that she is a woman.

Female characters don’t sell: we often hear this repeated by those who work in media and publishing. Yet consider the box office success of the film Hidden Figures. It tells the previously little-known story of three African American women who worked for Nasa in the 1960s, and who, despite racial segregation, at a time when there were black- and white-only bathrooms in the offices of Nasa itself, succeeded in playing a determining role in the missions that put the first small ships into space, and then Apollo 11 on the moon.

Another game changer is Zootopia, voted best animated movie at this year’s Oscars, with an intrepid and courageous female bunny in the lead role, determined to fulfil her personal dream of moving to the big city to become a cop. To realise her ambition, she needs to overcome her own fears and then prove herself by challenging the stereotypical preconceptions shared by her family and colleagues.

Disney is also attempting to expand horizons, on one hand investing in the live-action remake of Beauty and the Beast, while on the other backing an absolute outsider, Queen of Katwe, based on the true story of a girl raised in the slums of Kampala in Uganda who becomes a chess champion.

The truth, of course, is that there are myriad stories and human experiences that haven’t yet been told. This is largely due to the fact that modern readers and audiences no longer accept being treated as passive spectators or merely as objects of desire. Nowadays people want to see themselves represented as strong and complex personalities. As the 18th-century Chinese astronomer and poet Wang Zheng put it: “Daughters also can be heroic.” Many of us are starting to recognise this.

• Translated by Erica Segre and Simon Carnell