Its stance follows an incident at a regional Northern Tasmanian school where a senior teacher was vilified by several students on a Facebook page created specifically to slander her.

The incident was reported to the state's Education Department.

In South Australia last week, a former principal at a Coober Pedy school reached a settlement for an undisclosed amount in a defamation case involving three former students and a Facebook hate page.

The principal, Sue Burtenshaw, told media the comments posted on the webpage had damaged her reputation and caused her humiliation.

Australian Education Union state president Terry Polglase said there seemed to be a growing trend of students slandering teachers on Facebook in Tasmania.

He said tougher action on such behaviour may be needed.

''Actions that occur off-site should be dealt with as if they occurred during school time,'' Mr Polglase said.

''With students of a sufficient age, legal avenues are available to address defamation but it would be seen as a last resort.

''Staff can be severely affected by insensitive, personal attacks and the misuse of media adds another dimension.

''Their job can be quite stressful and immediate supportive action would be expected.''

Tasmanian schools are required to develop their own policies dealing with bullying, cyber-bullying, and internet and mobile phone use.

The Education Department has a program available to schools that addresses cyber bullying, online identity, social networking and digital footprints.

Deputy secretary for early years and schools Liz Banks said behaviour by students that was likely to be detrimental to the health, safety or welfare of staff was unacceptable.

''The Education Act lays down the processes related to sanctions such as suspensions, exclusions or expulsions that a school may apply,'' she said.

''Schools . . . also strive to build environments that teach students how to behave appropriately and parents are critical partners in this work.''