Ann Maguire, 61, was killed at Corpus Christi Catholic College in Leeds, in April 2014.
Sixteen-year-old pupil Will Cornick was jailed for a minimum of 20 years after admitting her murder.
Mrs Maguire's family said due to Cornick's guilty plea the evidence was never fully reviewed.
Mrs Maguire had taught at the school for 40 years and had been due to retire just months after she was killed.
Cornick, who was 15 at the time of the murder, had attacked her from behind, stabbing her seven times in the neck and back, as she was helping another pupil with their work.
Her husband, Don Maguire, said it was important to know whether anything could have been done to prevent her death.
"At the court hearing last year there was a guilty plea and so there was never a full criminal trial which went through all the evidence," he said.
"We believe that a comprehensive, open and independent statutory review examining all the information is crucial to learning lessons from this horrific incident which took place in front of many other pupils in school, traumatising pupils and staff and devastating our family.
"We know an independent inquiry won't bring Ann back but it will give us peace to know whether there was anything which could have been done to prevent her death so that other families don't have to suffer like us in future."
The Department for Education (DfE) said the Secretary of State understood the family's desire for an inquiry into "the tragic events".
"We understand that Leeds Safeguarding Children Board has already begun a two-stage learning lessons review which we trust will be open and full", the statement continued.
No decision would be taken until the review had taken place, the DfE said.

Euro 2016 winners Portugal will now face Chile in the last four on Wednesday (19:00 BST).
Australia went ahead through winger James Troisi, before substitute Martin Rodriguez levelled from close range.
World champions Germany moved above Chile with a 3-1 win over Cameroon and will play Mexico on Thursday (19:00).
RB Leipzig forward Timo Werner scored twice, with Hoffenheim midfielder Kerem Demirbay also on target for the experimental German squad competing in Russia.
Porto forward Vincent Aboubakar netted for Cameroon, who finished bottom of the group, with a draw from their match against Australia their only point.
Group A:
Group B:

The former Doctor Who actress, from Inverness, joins US stars Kevin Hart, Jack Black and Dwayne Johnson, aka The Rock, in the new production.
Her casting follows her securing a bigger role in Guardians of the Galaxy.
Starring the late Robin Williams, Jumanji involves a magical board game and is regarded by fans as a classic.
In posts on Instagram, Hart and Johnson welcomed Gillan, who studied drama at Eden Court in Inverness, to "the Jumanji family".
Johnson wrote:  "I'm proud to announce a girl who's playing the most important role in our movie - the talented, beautiful and down for a Scottish fight at any time, Karen Gillan.
"And yes, this is the girl who is so bad ass she shaved her freaking head for Guardians Of The Galaxy.
"We start production next month in Hawaii and as many of you already know, this isn't a remake or reboot, but a continuation of the awesome Jumanji story we love."
Gillan shaved her head to play blue-skinned space pirate Nebula in 2014's Guardians of the Galaxy.
She has returned to the role for next year's Guardians of the Galaxy, Volume Two. Its director James Gunn said Gillan will have more screen time in the sequel.
The family of a schoolteacher from Leeds who was stabbed to death in her classroom have called for an independent inquiry into her death.
[NEXT_CONCEPT]
Chile qualified behind Germany from Group B to reach the Confederations Cup semi-finals after drawing 1-1 with Australia in their final group game.
[NEXT_CONCEPT]
Scottish actress Karen Gillan has been cast in a new film that has been described as a follow up story to the 1990s box office hit, Jumanji.