The union may also hold stop-work meetings, where teachers abandon lessons during the day.
Rolling strike action and stop-work meetings could take place in September. The NUT executive will decide next week. But this time 250,000 school support staff are also being balloted.
Last week's action has led to conflict with heads and local authorities in some parts of England. The NUT expressed anger at Kensington and Chelsea council officials in London, who told heads the strike was "technically illegal".
The union has also criticised heads who used non-striking staff to cover GCSE and A-level classes.
But John Dunford, general secretary of the Association of School and College Leaders, said "There is the safety of the children to balance against the refusal of some teachers to supervise them."
In Wales there was little negative reaction from other unions or local authorities. Five hundred schools closed and 900 others were affected.
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