The Minister for Education, Mr Dempsey is likely to receive a frosty reception when he appears at the three main teaching union conferences this week.
Mr Dempsey only agreed to speak at the final of the three meetings last week after long-running negotiations.
The "on-off" saga about his attendance at the events has angered the teaching unions, with some representatives accusing Mr Dempsey of being too fussy.
The minister called for change in the traditional conference format where the set-piece ministerial address is followed by a speech from a leading union figure.
He labelled this format "dated" and wanted it replaced with a debate modelled on the Your Education System public meetings, which have taken place at 17 venues across the country over the past two months.
The Department of Education claimed the new format allowed for more real communication on education issues, but Mr Dempsey later agreed to deliver a speech at the events.
The minister will address the Irish National Teachers' Organisation conference tomorrow, before appearing at the Association of Secondary Teachers Ireland (ASTI) meeting that evening.
He will be involved in a discussion with Teachers' Union of Ireland president Mr Derek Dunne at the body's conference on Wednesday.
ASTI president Mr Pat Cahill has accused Mr Dempsey of demoralising the teaching profession.
In a pre-conference attack on the minister, he said Mr Dempsey had established little rapport with teachers and had caused widespread anger by sending inspectors in to ensure schools did not close two days early before Christmas. "He has left us feeling demoralised and alienated," Mr Cahill said.
PA