Where would you shoot a child, the head or the heart?

When it comes to exposing the gross absurdity and big business behind guns, the US is an easy target.

Even the phenomenon of school shootings, a horror so regular that kindergarteners perform preparatory drills in the event of an attack, has become normalised. So unquestioned, in fact, that when Sacha Baron Cohen recently pranked a number of American politicians into enthusiastically advocating a programme to arm toddlers, they barely blinked.

"The only thing that can stop a bad man with a gun is a good child with a gun," chirruped congressman Joe Walsh. "Happy shooting, kids."

Donald Trump’s assessment of the situation, unprompted and unpranked, was just as sensible. “And these teachers are talented with weaponry and guns,” he mused during one rally, “and these teachers would have shot the hell out of him before he knew what happened.”

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This is the belligerent, ballistic logic that Training Teachers to Kill (Channel 4, Monday, 9pm) wishes to tease open. It follows the bullish sheriff Richard K Jones of Butler County, Ohio, who mounts a pressure campaign, via billboards, to arm school teachers in his jurisdiction.

One school, Hamilton High School, has the temerity to resist him and his trigger-happy confederates. Another school, Madison High School, which recently experienced a shooting, is ready to capitulate.

Of all the grimly surreal sights in Kira Phillips’s documentary, one of the most unsettling is a drill conducted by Hamilton High School, undertaken with all the enthusiasm of a high school production. “Be a drama queen,” one smiling student is told moments before shots ring out. “I want you to be totally dead,” another hears.

To some, guns provide a fantasy of control. In the training grounds of Ohio's Tactical Defence Institute, a weepy teacher remembers her feelings of helplessness when her daughter was barricaded in a university during an active shooting and "telling me that she loved me".

To others, like the extraordinarily philosophical 16-year-old Cooper Caffrey - shot by one of his friends in Madison High School's cafeteria – guns are never the answer.

“I feel threatened by it,” he says, vocally and reasonably opposing his school’s looming policy to arm teachers. “Teachers are people too, they can have unhinged moments.”

It’s easy to indent with the gruff exasperation of his father, Marty, whose anger and astonishment is leavened with dry wit. “I don’t know how to give you a stronger argument against arming teachers than a kid who was shot eating lunch who still doesn’t want to arm teachers.”

But gun advocates are emboldened and zealous, backed by dubious charities and powerful lobbies. Some display little evidence of humanity, like a Vietnam vet at the gun range who shows teachers a spurious video entitled "Cubs of Allah", purporting to expose child terrorists among them: or "a couple of these kids from the outside" as he puts it.

There will always be cowards and psychopaths claiming the badge of “good guys” (and the documentary provides ample opportunity to spot them), but the more twisted tragedy here is in the responses of the fearful as they edge towards the unimaginable. Like the teacher and mother asked where she would shoot a child – in the head or the heart?

There is something more encouraging in the intelligence of Cooper, who tries to solicit from the documentary makers, with a sly smile, a list of the teachers who will be packing heat, and whose father could neither be more proud or more raw when a subdued Cooper returns to school on the first day of armed teaching staff.

In another drill, back at the firearms ranch, the teachers conducted a grisly role play game of their own. “Are we the good people?” one of them asked her trainer. The documentary makes it very hard to answer.