It is the first time teachers in the ACT have formalised their opposition to an education minister and signals a complete breakdown of relations between the union and the minister.

he 140 councillors from 86 public schools and the Canberra Institute of Technology expressed deeper reservations about the minister's competence and voted not to continue negotiating their agreement with her.

Glenn Fowler, secretary of the Australian Education Union, which represents more than 3500 teachers, wrote to Mr Barr on Monday, calling on him to remove Ms Burch after two-and-a-half years of "confusion, inaction and poor communication".

He wrote that the union membership had requested "the AEU deal with [Mr Barr] directly whilst Ms Burch retains the Education & Training portfolio, including on matters pertaining to the current Enterprise Agreement negotiations".

While previous chief ministers, including Kate Carnell and Jon Stanhope, were required to negotiate the final stages of particularly acrimonious enterprise agreements with teachers in the past this is the first time the union has passed a motion of no-confidence in an education minister.

Ms Burch told ABC radio on Tuesday that she will not be stepping down from the portfolio and loved being education minister.

"I'm personally surprised and disappointed by this because when I'm out and about in schools...it's not the feedback that I hear from teaching staff and principals and families," she said.

She maintained that her pay offer of 12 per cent over four years leading to more than half the teaching workforce earning $100,000 by the end of the agreement was "a fair and reasonable offer, particularly in the current environment, where you are looking at more federal public service job cuts and in some federal agencies fewer conditions and very little growth".

Ms Burch said she used every opportunity she could to value ACT teachers and believed the no-confidence motion was union leadership "playing politics 101" rather than the genuine wish of the ACT's teaching workforce.

Ms Burch noted that she had continued investment in schools and education had received 6 per cent budget growth. This year ACT government high schools also managed to enrol just over 50 per cent of students – reversing a five-year trend which saw the majority share enrolled in private high schools.

She had "also taken the fight to the feds" in terms of universal access to preschools and seeking Gonski funding.

In response to receiving the letter Mr Barr's office said: "The Chief Minister and the Minister for Education will meet with AEU in due course."

Mr Fowler said Ms Burch's ministership had been a period which had seen "a record depreciation in staff morale, as educators continually question the competence of the minister in administering her portfolio".

He said her tenure had seen a host of issues arise, and the union and its members had "consistently found the minster's ability to resolve those matters sorely lacking".

Teachers had been shocked by her surprise tactics with their pay deal – accusing her of making offers through the media and removing their back pay provisions. Meanwhile, Ms Burch has said she would seek cabinet approval for back pay if the union signed the deal.

"There is utter confusion and the minister has taken to speaking in riddles," Mr Fowler said.

He said there was a wider lack of confidence from teachers over other specific issues. He cited her recent "weeks of inaction on the urgent request by staff in special schools to have nurses returned to schools to deal with the complex medical needs of high needs students, and then her washing her hands of the matter despite it involving schools in her Directorate".

Historically, he cited "her bungling of the process to approve non-government schools in 2013, and her inability to provide new guidelines in the last two years as promised. We have also seen her capitulation to the Abbott government on the flawed school chaplaincy program".

Ms Burch has faced questions over her ministerial competence before across a wide range of portfolio responsibilities. For two years running, the first sitting days of the 2014 and 2015 sitting year saw no-confidence motions raised against Ms Burch by the opposition.

Issues have included her retweeting an offensive description of federal Education Minister Christopher Pyne, her oversight of a controversial Fringe Festival performance that featured a burlesque dancer dressed as Adolf Hitler, her approval of $50 notes in territory poker machines which was then revoked by Mr Barr and her management of roadworks in Canberra's south amid gridlock – forcing her to change temporary arrangements in the area.

She also came under fire when her son visited schools with a youth mentoring group Menslink while he was on bail awaiting sentencing last year. He did not have a Working with Vulnerable People card and Menslink was later fined for the breach.

Mr Fowler said teachers were distressed at the thought of Ms Burch continuing in the job.

"We remain committed to political engagement to ensure our member's views are heard, however the value in continuing political and industrial discourse with the current Education minister has diminished so markedly that our members no longer see any value in continuing that line of communication."