There were "missed opportunities to share and record problem behaviour" before a teenager murdered teacher Ann Maguire in a classroom, an inquest jury has said.
Mrs Maguire, 61, was stabbed to death by 15-year-old Will Cornick at Corpus Christi Catholic College, in Leeds, in April 2014.
A jury at Wakefield Coroner's Court returned a conclusion of unlawful killing on Wednesday.
The jury added: "Overall communication leading up to the incident was inadequate.
"There were missed opportunities to share and record problem behaviour. "
It also said: "The safeguarding policy was not followed as no 'cause for concern' was recorded around the pupil's use of alcohol."
Coroner Kevin McLoughlin said he now wanted Facebook and other social media companies to introduce contracts to make parents responsible for their children's messaging.
Mr McLoughlin said he will write to the digital minister Matthew Hancock to suggest social media platforms require any 13 to 18-year-olds have a named parent on their application to open an account.
He said parents should have the right to monitor their children's activity.
Mr McLoughlin said: "Any parent's responsibility transcends any teenager's entitlement to privacy."
The coroner's remarks follow the evidence that Cornick exchanged a series of Facebook messages with a friend outlining his hatred for Mrs Maguire and his plans to harm her.
After the inquest, Ann’s husband Don Maguire, said: “The jury has now started the process of learning lessons which should have been started three and a half years ago. We want to thank the jury for their careful consideration of the evidence presented. The next step has to be to dig deeper and find out more.
“We still believe there is more to learn and we are disappointed that there is still evidence that has not been heard. During the inquest, we have heard teachers, police officers and Ofsted inspectors all trying to speculate why no student reported the fact of a 34cm knife being brought into school accompanied by threats to kill a teacher. None of those adults have been able to explain why it was not reported.
“We don’t seek to blame anyone, simply to understand what went wrong on that day to prevent it happening again”.