Delegates at the NUT annual conference in Brighton passed a motion calling for the development of “alternative strategies to safeguard children and identify risks" to young people.
The vote comes after TES revealed that the number of people referred by education institutions to Prevent has exceeded the number of tip-offs from the police for the first time.
The surge, from October to December last year, coincided with the introduction of a new legal duty to “prevent young people from being drawn into terrorism”.
At the conference this morning, delegates also voted to call on the government “to conduct urgently” an independent review of the Prevent Strategy with the involvement of teaching unions.
The call follows a conclusion by David Anderson QC, an independent reviewer of the terrorism legislation, who said that “if wrong decisions are taken, the new law risks provoking a backlash in affected communities'.
He said it could lead to "hardening perceptions of an illiberal or Islamophobic approach, alienating those whose integration into British society is already fragile.”
Alex Kenny, an NUT executive member, said: “We want to keep children safe from those organisations that promote hatred and violence. But there are limits to what we can do, and as we predicted a year ago, Prevent is making that harder. It is leading to cases of overreaction of teachers and schools.”
He added: “It is leading to a situation where teachers are finding it more difficult to seize opportunities to discuss important issues that may help students make sense of the world.”
Gary Kaye, a teacher from North Yorkshire, told delegates that training on the Prevent strategy “has been genuinely crude and often involves lazy stereotypes.”
He said: “What the Prevent strategy has so far achieved has been suspicion in the classroom and confusion in the staffroom.”
He urged delegates to “stop education professionals being the secret service of the public sector.”
Following the debate, Christine Blower, general secretary of the NUT, said the union believes "there is a moral obligation on schools and teachers to protect children and young people against extremism of whatever nature.
"The union does, however, have some concerns regarding aspects of the current Prevent Strategy."
She added: “Evidence shows that grooming by extremist groups happens mainly on social media sites, not on school premises. Schools’ best contribution to countering any behaviour that could be a problem is by encouraging discussion.
"Some aspects of Prevent inhibit this and it is for this reason that we need a review of the strategy to find the right, and best way to protect children and young people."
Next week, at the ATL annual conference in Liverpool, delegates will consider a motion calling for the union to take a position of non-cooperation with Prevent.
A government spokesman said last week that it made “no apology” for protecting children and young people from the risks of extremism through the strategy.
They added: “Prevent is playing a key role in identifying children at risk of radicalisation and supporting schools to intervene.”