Students at a Sydney private school have allegedly been spotted making fun of social distancing rules by deliberately “hugging and high-fiving” each other on campus, a father has reported.

The father, who wished to remain anonymous to protect the school’s identity, said his Year 12 daughter told him “multiple students” were seen embracing each other and “laughing about how it’s nonsense and not something they need to worry about”.

• Read: Schools on the agenda as Victoria relaxes coronavirus restrictions

The claims emerged on Monday as students in New South Wales returned to school for their first day of face-to-face learning.

School will be back for just one day a week for most students in the state, increasing to two days until the end of week three, when the policy will be reviewed.

An exception has been made for Year 12 students, who are allowed to return for an average of three to four days per week so teachers can help them get back on track with HSC preparations.

• Read: Just one new COVID-19 case in NSW, as decline continues

Student attendance is expected to increase over the course of the term, with the NSW government aiming for a full-scale return by term three.

The Sydney father said he had alerted the school about the behaviour of a small group of students and confirmed staff were “dealing with it”.

But the incident has raised concerns over the possibility of students contracting the coronavirus at school and unwittingly infecting their parents or siblings at home.

Nearly one in three Australian parents will not send their children back to school when they reopen or are unsure if they will, a national survey conducted by Cluey Learning tutor service in Sydney revealed.

About 46 per cent of parents surveyed were pleased about school returning, while 39 per cent had mixed feelings and 15 per cent were anxious.

On Monday, Victorian Premier Daniel Andrews announced the government was close to finalising a plan so that face-to-face learning could resume in Victorian schools before the end of term two.

“We had for the purposes of certainty said to parents across the state that they should plan and assume that learning from home would continue for the entirety of term two,” Mr Andrews said.

“We now believe that a gradual, staged return to face-to-face learning is safe, cautious and appropriate, given the testing we’ve done and the circumstances we face.

“Today’s not the day to announce the details.”