The union has concerns about the Smith Group, the schools-business partnership set up by former first minister Jack McConnell to tackle the issue of youngsters not in education, employment or training (Neet).
Andrew Fullwood, South Lan-arkshire EIS member, told the union's annual conference that he had become "increasingly worried" about how education policy was being made. He pointed to a report in The TESS last November where Willie Haughey, a member of the Smith Group and the entrepreneur behind Glasgow business City Refrigeration, suggested raising the leaving age for some pupils to 18.
"Two days later Jack McConnell reveals it as Labour Party policy," said Mr Fullwood. "What type of democracy is it where that's how policy is made, where millionaires are making education policy? They seem to be having an inordinate type of influence."
Fellow South Lanarkshire EIS member Michael Dunn said: "Will the new education minister (Fiona Hyslop) listen to a shadowy group like this more than she listens to a teachers' trade union of more than 70,000 members?"
There was an overwhelming vote in favour of a motion from the union's South Lanarkshire association calling for the EIS council "to investigate and report on the Smith Group with reference to Scottish education".
Sir Robert Smith, chairman of the Smith Group, told The TESS that it was an "open book" and that anyone from the EIS was welcome to get in touch to find out more about its aims.
He stressed that, far from being exclusively for wealthy businessmen, its members also included education directors and the headteachers at Trinity Academy, Edinburgh, and Langside Primary in Glasgow.
"It's a group of well-meaning people who come together to try to help, but I don't think the business people round that table have all the answers,"
Sir Robert also stressed that the views expressed by Mr Haughey on raising the leaving age were personal, and that there was likely to be a range of opinions on that issue within the Smith Group.