In February, a nine-year-old Arkansas boy called Hank asked his uncle if he could head off on his own from their remote camp to hunt a rabbit with his .22 calibre rifle. “I said all right,” recalled his uncle Brent later. “It wasn’t a concern. Some people are like, ‘a nine year old shouldn’t be off by himself,’ but he wasn’t an average nine year old.”

Hank was steeped in hunting: when he was two, his father, Brad, would put him in a rucksack on his back when he went turkey hunting. Brad regularly took Hank hunting and said that his son often went off hunting by himself. On this particular day, Hank and his uncle Brent had gone squirrel hunting together as his father was too sick to go.

When Hank didn’t return from hunting the rabbit, his uncle raised the alarm. His mother, Kelli, didn’t learn about his disappearance for seven hours. “They didn’t want to bother me unduly,” she says.

The following morning, though, after police, family and hundreds of locals searched around the camp, Hank’s body was found by a creek with a single bullet wound to the forehead. The cause of death was, according to the police, most likely a hunting accident.

“He slipped and the butt of the gun hit the ground and the gun fired,” says Kelli.

Kelli had recently bought the gun for Hank. “It was the first gun I had purchased for my son, just a youth .22 rifle. I never thought it would be a gun that would take his life.”

Both Kelli and Brad, from whom she is separated, believe that the gun was faulty – it shouldn’t have gone off unless the trigger was pulled, they claim. Since Hank’s death, she’s been posting warnings on her Facebook page about the gun her son used: “I wish someone else had posted warnings about it before what happened,” she says.

Had Kelli not bought the gun and had Brad not trained his son to use it, Hank would have celebrated his 10th birthday on 6 June, which his mother commemorated by posting Hank’s picture on her Facebook page with the message: “Happy Birthday Hank! Mommy loves you!”

Little Hank thus became one in a tally of what the makers of a Channel 4 documentary called Kids and Guns claim to be 3,000 American children who die each year from gun-related accidents. A recent Yale University study found that more than 7,000 US children and adolescents are hospitalised or killed by guns each year and estimates that about 20 children a day are treated in US emergency rooms following incidents involving guns.

Hank’s story is striking, certainly for British readers, for two reasons. One, it dramatises how hunting is for many Americans not the privileged pursuit it is overwhelmingly here, but a traditional family activity as much to do with foraging for food as it is a sport.

Francine Shaw, who directed Kids and Guns, says: “In rural America … people hunt to eat.”

Kelli has a fond memory of her son coming home with what he’d shot. “He’d come in and say: “Momma – I’ve got some squirrel to cook.” And I’d say ‘Gee, thanks.’ That child was happy to bring home meat. He was the happiest child when he came in from shooting.”

But Hank’s story is also striking because it shows how raising kids to hunt and shoot is seen as good parenting, perhaps even as an essential part of bringing up children in America – a society rife with guns and temperamentally incapable of overturning the second amendment that confers the right to bear arms, no matter how many innocent Americans die or get maimed as a result.

“People know I was a good mother and loved him dearly,” says Kelli. “We were both really good parents and no one has said anything hateful to us. The only thing that has been said is in a news report about a nine year old being allowed to hunt alone.”

Does Kelli regret that Hank was allowed to hunt alone at that young age? “Obviously I do, because I’ve lost my son,” she tells me. But she doesn’t blame Brent for letting him go off from camp unsupervised with a gun.

“We’re sure not anti-gun here, but do I wish I could go back in time and not buy that gun? Yes I do. I know you in England don’t have guns. I wish I could go back and have my son back. I would live in England, away from the guns.”

Spyder, a trailer park manager from Texas, and his daughter Gia, nine. Photograph: Channel 4 Photograph: Channel 4

There is no sign that American kids are going to stop hunting. Consider Gia, another child hunter featured in Kids and Guns. On the nine year old’s Facebook page, she has posted a message: “Zombie hunting at the ranch in lochart in sat. wish us luck.”

She and her dad, Spyder, a Texan trailer park manager, often head off in his Jeep (emblazoned with the words “Zombie Response Team”) to the woods where he has pinned up targets depicting zombies on tree trunks. Gia shoots with an AR-15 rifle using real bullets. She aims for the head: “Shoot it in the arms and legs and it’ll just fall down and get right back up,” she says.

Instead of playing with Barbie dolls, Gia shoots them as target practice near her home. She owns six pistols, a shotgun and a Winchester rifle. Her dad has even more, and says: “There’s an expression in Texas: ‘If you know how many guns you’ve got, you haven’t got enough.’”

Again, Spyder, a single father, considers himself to be a good parent. He teaches his daughter the four rules of gun safety, rule four of which is: Know your target and what is behind it. “I taught her to have her finger off the trigger and point the gun away. That was already ingrained in her by [age] five. If you live in Texas or Oklahoma where there are guns, you’ve got to teach them that part,” says Spyder.

What about those who say that teaching children to use guns is wrong? “Tough shit. That’s what we do.”

To Britons, it may seem that shooting blows American families apart, but some US citizens, at least, believe the opposite: guns can bring families together.

For instance, there’s an interview with a family from the Las Vegas suburbs, filmed on an outing to the Nevada desert where they take turns at machine-gunning the wreck of a car. There’s Ron, owner of the Lock N Load gun store, his wife, as well as kids Jensen, 13, Courtney, 12, and Boo Boo, 16. During the family outing, Boo Boo says: “Those guns were initially designed for killing but we’ve turned them into a recreational sport.”

But their extensive private arsenal is also ready to be deployed to repel, or more likely slay, intruders to the family home. “If something ever happens in this house, we’re going to be prepared. We’ve had our conversations and those boys and Courtney have to be prepared to do what they have to do,” says Ron.

“As Americans we have that right. A lot of other countries don’t have that right but we do and it’s such a precious right that so many responsibilities come along with it.”

Jensen, 13, from Las Vegas. Photograph: Channel 4 Photograph: /Channel 4

One of those responsibilities, such American parents feel, is to teach their children the way of the gun. JD, for instance, a US army veteran and triple amputee who lost his legs and an arm when he stepped on an improvised explosive device on duty in Afghanistan in 2010, regards teaching his daughter how to use guns as an essential part of his job as a father – even though Kaylin is only four. “I woke up and I realised I had lost both my legs and my right arm and I was just kinda, what’s my purpose now?” he says. “But as soon as I heard my wife and daughter’s voices I knew exactly what I had to do – bringing her up being able to spend quality time together and teaching everything about being a hunter.”

His wife, Ashlee, says: “With everything that’s going on in the world I think it’s very important she knows how to take care of herself and use guns safely.”

JD agrees: “My dad made it a point in our family to have weapons in the house so if somebody does break in we all knew how to protect our family.”

JD has a dream that his daughter will be the “first four year old in the world to hunt and kill a hog”. “I have to be with her for her very first kill,” he says. “Can’t take that away from me, you know. It’s going to be a huge accomplishment that her dad’s a triple amputee with one arm and he’s got her to where she can hunt herself.”

Clearly, JD is struggling to come to terms with his disability, but he isn’t the only one. When he got back from Afghanistan, he says, the person apparently most affected by his injuries was his dad. “He lost a big part of his life when I lost my legs, you know?”

JD used to go hunting with his father, but those days are over. As compensation for the loss of that father-son rite, perhaps, JD is determined to raise his daughter in the family hunting tradition.

But, as Kids and Guns shows, there’s a slight problem: Kaylin is not keen to learn to shoot. In the film we see JD training his daughter to shoot at a turkey pinned on a fence in the family garden. She sits on his lap as he, sitting in his wheelchair, helps her squeeze the trigger. Her first shot puts a hole in the turkey’s neck. But the rifle recoils into Kaylin’s face, leaving her complaining about her hurt chin and not keen to carry on. “She doesn’t want to shoot?” says JD sternly at one point. “She’s going to learn to shoot whether she likes it or not.”

Later, though, JD calls his dad for advice on how to encourage his daughter to enjoy shooting as much as they both do. His dad counsels that JD remember his daughter is only four and that by pushing her too hard to take up shooting he may traumatise her and put her off altogether.

So instead, JD takes his daughter to witness a squirrel hunt with him and his buddies. After JD shoots a squirrel from his wheelchair, he encourages her to hold the corpse by the tail for photos and watch it being skinned. So far, Kaylin hasn’t killed anything herself, although father and daughter did recently go on a bear hunt.

What’s striking about Francine Shaw’s film is that she doesn’t judge the parents she interviews. “I come from a culture where all this is completely alien, but I have gone into it with an open mind trying to understand.”

She came away impressed by the loving nature of the parents she met. “When I was interviewing Spyder, it became very clear that he’s a very loving parent. He does homework with her, is very attentive to school work and is proud that she’s on the honour roll at school.”

Could Shaw have made this programme anywhere other than the US? “Well, in other countries there are lots of issues with kids and guns – child soldiers, competitive shooting events for children and countries where hunting is a family hobby, but American attitudes to guns are different to anywhere else.”

Shaw’s film doesn’t tackle one especially vexed part of the issue with with children and guns – a sharp acceleration in cases of gun-related violence at American schools and colleges. In June, when a 15-year-old boy armed with a rifle killed a student at a school in Oregon, injured a teacher and then apparently shot himself in a bathroom, it became the 31st firearms attack at an American school in 2014. In the 18 months since 20 school children and six adults were killed in the December 2012 massacre at Sandy Hook Elementary in Connecticut, there have been 41 deaths in 62 documented incidents at US schools – and often the shooters are children or young adults.

“School shootings are part of a much bigger problem,” Dan Gross, president of the Brady Campaign to Prevent Gun Violence, told the Los Angeles Times. “There are 86 people who die from bullets on an average day.”

Gross argues that many cases of gun deaths go unreported. Each year, he says, about 2,000 teens and young children

commit suicide

with guns at home. He contends that the power of the gun lobby makes it difficult to limit gun ownership. A recent bill, for instance, barring gun ownership for anyone with a history of alcohol abuse and drunk driving arrests, was recently vetoed by California’s governor, Jerry Brown.

Francine Shaw declines to say if she came out of making the programme more sympathetic to the gun lobby or convinced that teaching kids to shoot is, in the US at least, right. But she does point out that there is a huge divide in American society between parents who oppose even buying their children toy guns, and others who are teaching their kids to use the real thing. And Shaw says that she doesn’t despise parents who make the latter choice. On the contrary. “I spent a lot of time with these families seeing how they raise their children and they do love their kids. I liked the families I was with. I didn’t expect to, but I did.”

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Kids and Guns is on Thursday 31 July at 10pm on Channel 4