The clip, filmed at the Carrara Technical Institute and obtained by local newspaper Il Tirreno, shows one boy leaning over the teacher's desk and repeating: "Don't piss me off... put six [a pass]".
At one point he attempts to grab the teacher's tablet, where marks are registered, as other students snigger.
When the teacher pulls it away and stands up, the boy points at him and shouts: "You haven't understood a thing. Who's in charge here? Who's in charge?
"Get on your knees."
Another video has since emerged of what appears to be the same student donning a motorcycle helmet and making as if to headbutt the teacher, while other yell and laugh. The pupils then dump rubbish bins on his desk.
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The students, all under 18, are under police investigation for their attempt to "bully" their teacher.
The complaint was filed by the institute's headmaster, who said the teacher involved had not reported the incident. Instead head Cesare Lazzari learned of it when the videos were widely shared on social media, he told a local paper, saying that his first reaction was "anger and astonishment".
The students involved are facing suspension for the rest of the school year, meaning that some of them will fail, he told Il Tirreno, who said that the main instigator had already been temporarily excluded on multiple occasions.
Lazzari believes that social media might encourage bad behaviour in pupils, by offering an audience for more and more outrageous stunts.
Teachers all over Italy are facing the same phenomenon. In another video widely shared this week, a student at a technical institute in Rome can be heard threatening to dissolve his teacher in acid, telling him: "I'll put you in hospital, sir".
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The Italian Minister of Education, Valeria Fedeli, called for the schools in both cases to hand out strict punishments, including for the pupils who had filmed the incidents without intervening and for those who shared the videos online.
But teachers say the existing sanctions aren't enough, after a string of attacks on school staff not just by pupils, but in several cases by parents.
A teachers' association launched a petition this month calling for a new law on violence against teachers, punishing those who assault them with "sanctions that will provide an educational example to future generations". So far more than 58,000 people have signed.
At least 24 instances of violence against teachers have been reported in the first four months of 2018. In one case in case in Sicily, two parents fractured a PE teacher's rib for telling off their son, while in Caserta a 17-year-old student slashed his Italian teacher in the face with a knife. In Alessandria, a teacher with motor difficulties was taped to a chair which students then took turns kicking, resulting in the suspension of an entire class.