In a briefing paper for MSPs, the union dismisses some studies which argued that attainment was higher in larger classes. "The conclusions of these studies are now rarely considered tenable," it says.
Researchers were unable to distinguish the effects of class size from other factors and often used narrow measures of attainment.
The one "incontrovertible" study that supports its campaign is the Tennessee STAR programme, which showed that small classes in the early years of school led to significant long-term improvements. Disadvantaged pupils benefited more than others.
Other states in the US have adopted similar practices and come to similar conclusions, persuading the Federal Government to provide funds to cut class sizes in elementary schools across the country, the EIS reveals.
The union also cites evidence from England, Canada and Scotland which backs its views that only major cuts - not just from 33 to 30 - will make a big difference. Current class size limits were drawn up 30 years ago, when demands were very different.
"Large class sizes are not merely associated with lower attainment: they impact negatively on pupil behaviour, on pupil motivation, on pupil self-image. These qualities are difficult to foster when the teacher must spend most of her time managing a large group," the union states.
A report in 2002 from the SCRE Centre at Glasgow university, quoted by the EIS, says: "Most studies show that teachers of smaller classes report that these are quieter and more easily managed than larger ones. Therefore potential discipline problems are prevented from arising."
Researchers on the STAR programme in Tennessee noted that in small classes basic instruction was completed more quickly and more in-depth teaching was possible. Teachers also were able to focus more on individual pupils.