Joshua was a year nine pupil at Christchurch Boys High School. His death was a "headmaster's worst nightmare", said headmaster Trevor McIntyre.
Mr McIntyre said he occasionally spoke with Joshua when he came across him on the school grounds and he was very friendly and had a "lovely smile".
"And he had a bit of a spark to him. He will be sorely missed."
A room had been set up at the school, with a photo of Joshua, where his friends could gather and speak about him or write messages about him.
Guidance counsellors were on hand to help those struggling with their loss.
Police have spoken to the driver of the car, and to a number of witnesses, but are appealing to anyone who saw the incident to contact police. Mr Quested said it was too early to determine whether any charges would be laid.