Last week, thousands of striking NUT members took to the streets brandishing “Gove out!” placards. Just five days later, Prime Minister David Cameron’s reshuffle meant they got their wish sooner than they might have expected.

Many members of the union were united in their glee at the former education secretary’s departure - general secretary Christine Blower admitted that she “broke into a very broad smile” on hearing the news - and were keen to claim credit for their role in his downfall. 

“Well done everyone #proudtobenut #goodriddancegove,” tweeted Oldham teacher Niparun Nessa.

But the unexpected exit of Mr Gove has left the NUT with a major decision to make: what next?

Since the coalition came to power, the union has held a series of national and regional strikes, both alone and alongside other unions, in opposition to the raft of educational reforms introduced by Mr Gove.

But with the union’s leadership yet to meet the new education secretary Nicky Morgan, the NUT must decide whether to press on with its industrial campaign, or whether the time is right for it to make a strategic withdrawal.

Professor Howard Stevenson, of the University of Nottingham’s school of education, expects that, in the final 10 months before the next general election, the new minister will take a less confrontational approach to union relations than her predecessor.

“There’s no question Gove’s a hate figure among a lot of teachers,” he said. “That relationship with teachers has become a liability. I would expect Nicky Morgan to have a very different relationship with the unions and use different language about teachers, and perhaps go on a bit of a charm offensive.”

But this would not necessarily herald a shift in policy, Professor Stevenson added.

“What Gove has done is set these policies in place; what Nicky Morgan has to do is manage them. I doubt there will be a change in direction. The more radical stuff is already done, the Gove revolution is already complete. But I would expect Nicky Morgan to build a relationship with teachers. She is bound to have a honeymoon period.”

And, with Mr Gove’s exit coming hot on the heels of the NUT’s most recent strike action, the union could also be full of optimism for its new relationship with Ms Morgan, Professor Stevenson believes.

“The NUT will feel it has made a significant contribution to toppling Gove; the strikes had a lot more impact than a lot of people imagined they would. An obvious thing for Nicky Morgan to do would be to allow the NUT to de-escalate its industrial campaign.

“The NUT has a record of a getting a few things tactically wrong, but Christine Blower and Kevin Courtney have played a canny game. Through a difficult set of circumstances, the NUT has emerged with its credibility enhanced. There doesn’t appear to have been an obvious backlash against the union; it has been very clever in how it has been able to sustain the campaign.”

But, flushed with the ostensible success of its strikes to date, the NUT must decide whether to twist or stick.

The union’s official position is that it will decide on the next phase of its action once it has consulted members during the autumn term.

Not surprisingly, executive member Martin-Powell-Davies, who challenged Ms Blower for the NUT leadership by demanding more strike action, believes more action is needed. In a blog post titled “Gove’s a gonner - striking works”, he writes:  “[The] reshuffle is further evidence that politicians are most susceptible to pressure in the run-up to a general election. So let’s have a good summer break and then come back ready to strike again.”

But Jerry Glazier, a member of the moderate Broadly Speaking group on the NUT executive, urged caution. “The union is going to consult with its members in September, and it is important that we ensure that all members’ voices are heard,” he said.