As the new school term commences in Switzerland, the teachers will be advised by experts on the potential signs of jihadist leanings, reported newspaper Tribune de Genève on Tuesday.
Those could include a female student suddenly wearing a headscarf, or a male pupil refusing to shake the hand of a woman, said the paper.
Nearby Zurich will take the same steps, despite not having any concrete cases of radicalization.
The city's office for the prevention of violence is set to publish a paper this October with recommendations for teachers to follow should they notice any worrying signs among their students.
While the Zurich canton teachers' association supports the move, their colleagues in French-speaking Switzerland are less convinced.
Speaking to the Tribune de Genève, president of the Romandie teachers' union (SER) Georges Pasquier said he found the move “bizarre”.
Given one of the purposes of school is to develop students' social skills, any unusual behaviour among students would be picked up as a matter of course, he said, without the need for special training.
“When one of them starts behaving strangely we try, with the support of specialists and parents, to identify the source and sort out the problem. A special programme seems inappropriate.”
He added that to his knowledge, “no school in Switzerland has experienced the phenomenon of systematic radicalization”.
And in any case, if a student is displaying signs, it's probably too late anyway.
“We must act before then,” he said.
Bilal Ramadan, a member of a Geneva teaching union, agrees, and fears such a move could lead to stigmatization of Muslims.
“We are far from experiencing the problems seen in French schools,” he told the Tribune de Genève.
“Such an initiative would only add fuel to the fire.”
But an anti-terrorism specialist in Geneva sees merit in the Winterthur scheme.
“Potential recruits for groups like IS are getting younger and younger,” said Jean-Paul Rouiller of the Geneva centre for training and analysis of terrorism (GCTAT).
“Giving teachers and educators the tools to detect such a dramatic change seems sensible to me.”