A judge in London will hear the judicial review action brought by Ann Maguire's husband Don, children and nephews.
Wednesday's hearing before Mr Justice Holroyde follows an earlier ruling that the family had an "arguable" case which should be fully aired.
Mrs Maguire, 61, was stabbed to death by a 15-year-old pupil as she taught a Spanish class at Corpus Christi Catholic College in Leeds in April 2014.
Will Cornick was later sentenced to life by a judge who ordered that he must serve at least 20 years, and warned that he may never be released.
An inquest into Mrs Maguire's death is due to take place before a jury at Wakefield Coroner's Court in November.
At an earlier hearing at the High Court, Mrs Justice Lang granted Mrs Maguire's family permission to challenge a "blanket" decision made by Assistant West YorkshireCoroner Kevin McLoughlin not to hear evidence from students who had contact with Cornick "immediately prior to the murder".
She said the coroner decided "not to call as witnesses" those students who were aware prior to the murder that Cornick had a knife and planned to kill the teacher.
The coroner concluded the "risk of psychological harm outweighed the potential benefit", particularly given the length of time since the murder.
Mrs Justice Lang ruled: "In my judgment the claimants have raised arguable grounds for judicial review of this decision."
The family's barrister, Nick Armstrong, told the court it was the "only occasion on which a teacher has been killed by a pupil in a British classroom", and part of their case was that "it flows from this alone that all lesson-learning that can be done, should be done".
It was the "first time something of this magnitude has happened, and it occurs against a background of increasing public concern about knives in schools, and a public debate about how best to respond to that".
Mr Armstrong told the judge: "All, including the assistant coroner, accept that student knowledge of school policies and rules on reporting weapons and behaviour is properly within the scope of this inquest.
"Understanding how this impacted on the absence of any report of Cornick's repeated intentions, and his possession of the knife, is obviously crucial to any lesson-learning that may be done. Can the policies be improved? Can they be communicated better?"
The family said in a statement after their action was given the go-ahead: "We hope this will be the first step on the road to establishing the true circumstances surrounding the murder of Ann Maguire."