Mrs Maguire, a 61-year-old Spanish teacher, was stabbed to death by Will Cornick at Corpus Christi Catholic College in Leeds in April 2014.
The school pupil, who was 15 at the time, admitted murdering Mrs Maguire and was given a life sentence later that year.
Since then, some of Mrs Maguire’s family have campaigned for further investigation into her death as they believe more could have been done to prevent the tragedy.
They instructed law firm Irwin Mitchell to represent them at the inquest and have battled over the past year for more evidence to be made available at the hearing.
In August, the High Court rejected the family’s application for a judicial review of assistant West Yorkshire coroner Kevin McLoughlin’s decision that the inquest would not hear from pupils who had contact with Cornick immediately before the killing.
Then, last month, the Court of Appeal turned down a challenge from the Maguires to August’s ruling.
Mrs Maguire’s widower, Don Maguire, said: “While we are disappointed that certain evidence will still not be reviewed at the hearing we hope the inquest can shed further light as to whether Ann’s death could have been prevented and whether lessons can be learned from this.”
The inquest is listed at Wakefield Coroners’ Court for the next two weeks.
Yogi Amin, a partner at Irwin Mitchell, said: “While hearing evidence about Ann’s death will no doubt be difficult for the family, they remain committed to finding out exactly what happened on the day she was killed and the lead up to it.
“They believe it is the only way that lessons will be learned from the incident.”