Tamsyn, the youngest of four siblings, is the daughter of Sarita and Patrick Whiteman.
The first day back from the school holidays had been a difficult one for many students, Vaughan said.
"It has been a huge day for us at the school and obviously our priority was the welfare of the students and the staff, to make sure that everyone is well supported.
"We follow the same Ministry guidelines about the steps to take in providing due care for our students and staff and that's exactly what we've done today,'' he said.
"We've tried to keep things as normal as possible for students. We've kept them in their class routines.
"We've had qualified counsellors available from 7 o'clock this morning and are on-site all day tomorrow and the day after.
The school has approximately 170 students from Year 3 to Year 13.
School management and staff were helping youngsters cope with the situation but he acknowledged that because all pupils were from the Plymouth Brethren community, their families were already supporting each other following the death.
"A lot of the senior students were able to go and sit in the junior classroom where Tamsyn was and able to provide some comfort and support for those students.
"It's such a tragic event and it is just amazing to see how resilient young people are and how they step up in these circumstances. And that's really encouraging."
The circumstances of the death are not yet known and police said it was too early to say whether a medical event or other accident had happened.
A police spokesman said another official update about the incident would be released tomorrow.
The death has been referred to the Coroner.
