The Minister for Education and Science, Mr Dempsey, should display a more positive attitude towards teachers, according to the new president of the ASTI, Ms Susie Hall.
In her first public comments since assuming the presidency of the country's largest second-level teaching union yesterday, she said she had "no problem" dealing with any Government Minister, regardless of whether Mr Dempsey was moved as part of the imminent cabinet reshuffle.
But as a former teacher himself, she felt Mr Dempsey should have displayed a "better feeling" for the challenges facing teachers.
"I would have to say that I would not be giving him an A plus. I think there were opportunities missed," she said. "I expected a better insight into the difficulties faced by teachers every day, given the under-resourcing, the heavy workload, the overcrowding and the very, very poor physical conditions in which many teachers have to work.
"I felt that a former teacher should have a better feeling for that."
Ms Hall, who officially took over from outgoing president, Mr Pat Cahill, yesterday said her main aim during her one-year term of office was to highlight "the respect and dignity of the teaching profession." And she said she believed the problems of the ASTI which had been highlighted in recent years were now in the past.
"We're looking forward and we're focused on the needs of our members," she said.
"Our members are centre stage and they are going to get all my attention."
But she added that, having attended all 17 of Mr Dempsey's Your Education System (YES) meetings, which took place around the country earlier this year, the issues raised would also form a key part of her presidency.
"I feel that my presence at all the YES meetings gave me a feel for what are the burning issues in education, right around the country," she said.
"The main issues that came up - and consistently came up - were the under-funding of the education system and the serious lack of provision for students with special needs."