More than 3,000 classroom assistants across NI resumed a strike over pay and conditions on Thursday.
Nipsa members have been taking industrial action
Nipsa union representatives are to take two days of action each week until at least Christmas.
Hundreds of special needs pupils had to stay away from school. An offer allowing parents to act as classroom assistants was largely ignored.
Education Minister Caitriona Ruane had urged an end to a strike which "risks" the education of "vulnerable children".
Last month, a 10-day strike by classroom assistants shut more than half of special schools.
Subsequent talks with employers at the Labour Relations Agency failed.
Classroom assistants walked out on Thursday and will do so again on Friday, and on Monday 18 and Tuesday 19 November.
Nipsa General Secretary John Corey said: "Not one single Nipsa member has voted to accept the employers' offer.
"Members have also made very clear their determination to resume strike action."
Caitriona Ruane has called for an end to the strike
Assistants belonging to the smallest union involved, T and G Unite, did not go on strike.
A union official said members were split about 50/50 and that was not seen as a mandate for strike action.
However, the union says the vote does not mean it accepts the current deal on offer.
Two teachers unions instructed their members not to tolerate pupils' parents or carers in the classroom.
They were told not to teach and to withdraw to the staffroom.
Education Minister Ms Ruane said: "Whilst I understand the frustration of classroom assistants that the job evaluation exercise has taken so long, I had hoped that Nipsa would follow the example set by other unions and exempt special schools from strike action.
"Three of the unions involved have decided to ballot their members on the latest offer. However, I am disappointed that we are left in a position where special needs children will suffer through no fault of their own."