Here's a question: name the strongest trade union in Scotland. The GMB? Unison? The BMA? All have a case, in different ways.

But there is a good argument the most powerful organisation representing a group of workers north of the Border is the Educational Institute of Scotland.

For decades, going back even before the time of devolution, when the union representing the majority of teachers has speaks, politicians listen, usually with some trepidation.

So when the EIS criticises the Scottish government in public, as it has done this week, ministers, from the First Minister down, should have cause for concern.

And right now, whatever they may say in public, there is cause for concern in ministerial ranks after the general secretary of the EIS, Larry Flanagan, attacked the plans for schools to return full time on August 11.

What sparked Mr Flanagan's ire was education secretary John Swinney's U-turn on the return to schools after the coronavirus shut-down.

Less than two weeks ago Mr Swinney said 'blended' learning - pupils taught partly in school and partly at home - could continue for the next academic year.

That prompted a spontaneous grassroots revolt by parents, who wanted their children to be back in the classroom at the beginning of the next term. It was not long before Nicola Sturgeon was saying 'blended learning' had only been a contingency.

Mr Swinney then told MSPs this week schools would be back full time in mid-August if COVID-19 suppression continues.

His announcement did not please Mr Flanagan, who said it was a 'political' decision which had not been agreed by the Covid Education Recovery Group (CERG), which consists of unions, councils, parents, the Scottish government and others.

Deputy First Minister and Education Secretary John Swinney. Credit: PA

In a blog for union members, Mr Flanagan wrote: "The critical EIS red-line that a return to school, in any model, can only happen when there is demonstrable evidence that the virus is under control remains in force."

He added: "The EIS is not convinced that no physical distancing between pupils is safe and we are absolutely certain that physical distancing between pupils and teachers remains essential.

"It may be that the actual distance, come August, will have been reduced from the current two metres if the level of infection has dropped further, but there cannot be a social distancing rule for outside of schools and a different one for inside classrooms."

Given the power of the EIS, these comments obviously leave some questions for the Scottish government to answer on delivering on their pledge.

At today's media briefing I asked the First Minister about Mr Flanagan's claim the decision was political. Why was it not agreed by the CERC?

And given Mr Swinney had said there would be no physical distancing, how can the union and government positions be reconciled?

Ms Sturgeon replied: "Only a week ago that questions from journalists like you were demanding to know why we weren't doing more to bring children back full time to school. That's the luxury of a journalist and it's perfectly legitimate to ask the question..."

Now just to explain what happened nest, because this is a virtual briefing, it is hard to come straight back to the First Minister but I did interject at that point: "I am asking you what the EIS said First Minister..."

Credit: STV

The First Minister then told me: "I am going to answer the question. I'm going to answer the question fully.

"First of all, there hasn't been a U-turn. We have planned for a contingency because we have until very recently thought that full time education would not be possible because it wouldn't be safe with the levels of infection. We now think that is a different prospect. So our planning assumption now is full time but we still have a contingency."

There would work done over the summer "to make sure there are the right safety measures in place to make that possible".

The First Minister added: "Full time education in schools makes certain assumptions about physical distancing but if the science tells us that any particular arrangement is not safe, then particularly when we are dealing with children, we will do that."This has to be safe and it has to be predicated on continued suppression of the virus."

Ms Sturgeon continued: "The point I have made previously, when you say something is an ambition or when whether it is media or opposition call for something to be an ambition, that is one thing.

"Turning that into reality is where the hard work of government, with teachers and with local authorities, comes in. That is the hard work we will be doing over the summer. But our ambition, and it is one that will be shared by the majority of parents, is to have children back in full time education because that's in their interest.

"And actually I think it is in their interest if this is safe not to have them in full time education where they are having to stay two metres apart from each other.

"That's the detailed work that we have to do, and that work will be done through the Education Recovery Group."

Credit: pa

So we're back to the group, which the EIS says was not consulted (and the Scottish government has not denied that) to try to reconcile those differences between ministers and the union.

In the middle of all of this are Scotland's children and their parents who might now be asking how this is all going to be resolved, indeed whether it will be resolved.

Reading the First Minister's answers to my question on the EIS position, they may also be asking whether they feel Ms Sturgeon has, to use her words, answered "the question fully".

My instinct is that some will think she has, some will think she hasn't and many will want more information well before August 11.

Seasoned observers of negotiations between the union and the government believe that, in the end, a deal will be arrived at - that if the suppression of the virus continues, schools will be back

But wary ministers are aware that Mr Flanagan knows full well the strength of the hand he holds, derived from his union's power. And that he will drive a very hard bargain.