The union executive will be influenced by the views of 250,000 school support staff, who are also being asked if they would strike over their latest one-year pay deal.
The executive, meeting next week in London, will also schedule elections for a new general secretary to succeed Steve Sinnott, who died suddenly last month.
The stop-work meetings, one option being considered, mean union members stopping teaching to hold meetings during school hours.
The union's national strike last week has led to conflict with headteachers and local authorities.
The NUT expressed anger at Kensington and Chelsea council officials in London, who advised headteachers that the strike was "technically illegal". A note to headteachers said the council had not been officially informed of the strike ballot or its result, an assertion strongly denied by the union.
Kieran Parsons, secretary of the Kensington and Chelsea NUT, said: "Some teachers were very worried and we had to put their minds at rest that the NUT would never take action if it wasn't legal."
The union also criticised headteachers who used non-striking teachers or school leaders to cover GCSE and A-level classes that would normally have been taught by striking NUT members.
Roger King, the union's Birmingham general secretary, said that these headteachers were undermining the strike.
"Management who asked them to do that are a disgrace," he said.
But John Dunford, the general secretary of the Association of School and College Leaders, said that such emotive language was not being helpful.
During a strike, heads were forced to balance the number of affected children, their age, the proximity of exams and the facilities at their school.
"There is the safety of the children to balance against the refusal of some teachers to supervise them," said Mr Dunford.
School's out, pages 16-17.