Professor Andrew Wiles, the Princeton researcher who in 1994 solved the world’s most famous maths problem, Fermat’s last theorem, once compared doing mathematics to entering a dark mansion in which each room has to be explored by stumbling around for a while, bumping into the furniture.

This has a familiar ring to many schoolchildren. The big difference is that professional mathematicians eventually find the light switch. After years of schooling, many children still remain in the dark with only the vaguest notion of what is inside the first few rooms of the mathematics mansion.

Large classes containing children with a wide range of aptitudes and a teaching pace imposed by a crowded syllabus combine to ensure that most children are shepherded through those first few rooms without ever finding a light switch. It doesn’t have to be that way.

Highland Council has been training primary and secondary teachers in methods that can illuminate an entire class. These have been developed by education consultant and former maths teacher Peter Patilla.

It has also produced a video of the methods, which so impressed HM Inspectorate that they bought the copyright. Now a copy has been distributed to every primary school, every secondary maths department and every special school in Scotland, says George Gibson, the maths adviser who was responsible for production of the video.

Peter Patilla Counts is an edited account of an in-service training day for teachers from all over the Highland area, but still lasts almost two-and-a-half hours. At first sight the hero of the piece seems to be Mr Patilla but it soon becomes clear that, charismatic and entertaining though he is, the techniques he advocates are the real stars.

“When we analysed the problems children were having in mathematics,” he says, “many seemed to boil down to a lack of confidence and competence in basic mathematical skills.

“A particular problem is anxiety, which can be made worse by how a teacher tries to develop the skills, such as going around the class and asking individual children to respond in front of other children.

“That can be quite threatening. So over the years I’ve been working hard on ways to get children to engage with teachers in whole class mathematics that remove the fear and bolster children’s confidence.”

The essence of his approach is a set of teaching techniques which embody differentiation and support for weaker pupils while at the same time being entertaining for children, useful for teachers of all stages and applicable to a variety of mathematics topics. The methods focus on the direct, interactive and participatory style of teaching shown to be effective by research and recommended by school inspectors.

The techniques include unison response, which lets the teacher control children’s thinking time without putting the spotlight on individuals; “show me”, which can be used with a variety of mathematical aids from pencil and paper to counting sticks; and problem of the week, which is especially valuable for pupils who like to stay blamelessly off-task by sitting with their hand up waiting for help.

Perhaps the most interesting and useful of all the techniques is “The answer is I What is the question?” While this may sound like a variation of a quiz show, it is in fact a versatile and enjoyable way of sparking the creativity and enthusiasm of a class while reinforcing familiar ideas and introducing new ones.

“The children will often become very imaginative,” says Mr Patilla. “And once they have begun ‘What is the question?’ they usually don’t want to stop. How often does that happen in a maths lesson?” The video has been well received in schools - and not only those in Highland, where teachers have been attending in-service training from Mr Patilla for years.

“A lot of the techniques involve children physically, which means they are more likely to be involved intellectually,” says Linda Fleming, director of studies in the junior school at George Watson’s College in Edinburgh.

“Peter Patilla is a charismatic teacher, but it’s not all about charisma. It’s mainly about the craft of teaching.

“We primary teachers are involved in a plate-spinning exercise and when one starts to slow down you have to come back and give it a spin again. That’s what this does really well with maths.”

The video has also been distributed to universities that provide initial teacher education. At Strathclyde, it is already being used for pre-service and in-service training. Jennifer Moffat, senior lecturer in the faculty of education’s maths department, says it contains “excellent illustrations of teaching methods which stimulate enthusiasm and develop confidence”.

Copies of Peter Patilla Counts: A teacher’s guide to the video, produced by Highland Council, cost pound;6. Contact George Gibson, tel 01349 863441