Teachers are determined to press ahead with a second day of strike action in the row over Junior Cert reforms.
Education Minister Jan O'Sullivan (pictured) last night pleaded with teachers' unions to return to the negotiating table.
However, the unions are planning a second day of strike action next month in the ongoing row that saw 700 schools shut yesterday, leaving 350,000 secondary students at home.
Ms O'Sullivan has refused to back down on the issue of requiring teachers to correct their students' work.
She said she is willing to negotiate on a number of related issues, but insisted that a system of partial continuous assessment must be introduced.
"The issue around assessing their own students is central to this. This is about a new type of learning for students," she said.
"It is about valuing things like project work, things like creative thinking and a number of intelligences that are not examined by an end-of-term written exam," she said.
Ms O'Sullivan said she has been in regular contact with teachers' unions in the last few hours.
The minister also indicated that she would be willing to engage in a process led by the Labour Court or Labour Relations Commission (LRC).
She said she hoped a second strike day could be avoided.
The Association of Secondary Teachers of Ireland (ASTI) and the Teachers' Union of Ireland (TUI) said last night: "The feedback from union activists and representatives is that teachers on picket lines received a lot of good wishes and other messages of support from the public."
The executives of both unions are set to meet next week and are expected to consider a date for the second day's strike next month.
Teachers manned picket lines nationwide yesterday. At the Mercy Mounthawk Secondary School in Tralee, they took it in turns in groups of 10 and 12, starting at 8.30am, half-an-hour earlier than their working day would normally begin.
ASTI shop steward and maths and science teacher John Dowling said he believed the integrity and credibility of the Junior Cert would be damaged if the correction of 40pc of the exam was not "state-certified".
St Vincent's secondary school in Cork city had a roster of five ASTI members on rotating picket duty throughout the day.
"We don't want to be here today - we want to be in our classrooms teaching but we will not stand idly by and watch standards threatened," said Rose Ferriter. "We will defend the Irish education system."
A teacher for 33 years, she said the strong support for the protests despite the icy conditions was proof of the scale of anger among Irish teachers.
The ASTI picket outside Colaiste Choilm in Ballincollig was supported by Maeve Murphy, Ian Mulcahy, Hugh O'Callaghan, Sarah Daly and Kieran Shanahan.
All felt teachers were left with no option but to press ahead with industrial action.