All you have to do, they were told, is observe the correct posture, tilting the page towards your writing hand, pencil held at an angle away from your body, between a tripod of thumb, forefinger and middle finger. You then start writing, linking most - but not all - letters.
"Down, down, down," Mr Gourdie said in his well moderated tones as he illustrated the emphasis that should be placed within the hand movements. He went on to show how the links should come from easily positioned "entry" and "exit" strokes.
There are some breaks, however. "Handwriting is like speech. It has to have breathing spaces. If I kept speaking without taking a breath I'd soon drop. So you have to observe a break now and again to allow your hand to move along, " he told the children.
One boy struggled awkwardly as he wrote out the name of his school. Mr Gourdie spotted the problem. Adam Norton, aged nine, was holding his pencil with his whole hand, not with the more comfortable tripod grip, and he was not tilting his pen. As a result, his letters were too upright.
Mr Gourdie advised: "You are looking for a running pattern. And if you are running in the playground you lean forward." Once corrected, Adam's writing began to show the fluency that is the hallmark of the Simple Modern Hand. He is keen to improve and to follow the school's tradition of entering the national BBC handwriting competition.
Vivien Payne, aged 10, felt that the "Gourdie hand" helped the creative processes in her stories, her favourite form of writing. "It's got a flow to it," she said.
Simple Modern Hand, which is a form of the "cursive" style of writing now favoured by government advisers, has been taught in Largoward primary for four years. Elaine Salmond, the headteacher, is a former pupil of Mr Gourdie at Kirkcaldy High, where he taught art and writing.
Mr Gourdie, an italic handwriting expert, first developed his Simple Modern Hand in the late 1950s as a form of remedial exercise against bad habits created by print script writing. At the age of 82, he has seen his methods adopted in Scandinavia, New Zealand and parts of Australia and North America. "It has taken me all over the world. I don't think there is a city in the United States I have not been to and now the latest place is Largoward primary," he told a mesmerised class.
The method is in use in Glasgow, Lothian and Fife, as well as other parts of Scotland. But Mr Gourdie continues to campaign with the Scottish Office to have his method universally adopted. One piece of correspondence bears the handwritten greeting and signature of a former education minister. Analysing the hand of Michael Forsyth, Mr Gourdie commented: "For a man who is very busy the writing is not at all bad. But I think he can learn a thing or two. I'd very much like to meet him."