IT is a rite of passage rather than a mere game.

Andy Murray is hitting with his mum on the Dunblane courts just before he heads for another tournament far from home.

The grand slam winner is far from impressed. "You used to be good," he tells mum. "And you used to be 10 years old," she replies, making the point that a grand slam winner now plays a game that few can accommodate, even someone who was and is a mentor.

A couple of years later, and a few miles up the road, Judy Murray tells another youngster: "You should be on the Tour." The boy, glowing from the compliment while perspiring at the effort in achieving it with a stretched volley at the net, is one of 40 children who have been chosen by Adam Brown, head coach of the Gleneagles Arena, to benefit from what can only be called a masterclass.

After all, how many sessions in Britain are jointly run by Judy Murray, captain of the Federation Cup team, and Leon Smith, captain of the Davis Cup team.

But this session is not elite in terms of participants and observers. The players, boys and girls from 10 to 18 years of age, and the watching coaches, from clubs throughout Scotland, have been brought together not to concentrate on producing the next Scottish grand slam champion but rather to develop both the sport in the country and the ability of those who play at a level below the very top.

The theme in Gleneagles is how to think one's way to success on court. The rudimentary Dunblane courts where mother and son hit for years remain but the Gleneagles Arena is only just open, pristine.

Yet the link with thinking and Murray, Wimbledon champion and Olympic gold medallist, is made obvious to children who may have more modest ambitions considering the sport.

Smith, Murray's first coach, points out that one of his duties with his former protégé at the Australian Open was to download quiz apps and have a competition with the world No.3.

''He likes to keep his brain active before matches," says Smith. "He wants to be alert and ready for whatever faces him on court. He has his own team but I am drafted in for the quizzes."

This impression of tennis as a puzzle is enhanced when Judy Murray invites the children to play games that involve lateral thinking. She is also an advocate of draughts and dominoes for competitors.

"The aim of this session was basically to develop all these kids as players but specifically to make them think for themselves on court," she says while overseeing a series of drills that do precisely that. The emphasis is not on power but on the poise occasioned by having the right thought and executing it precisely through shot or movement, or both.

"There is a danger of kids nowadays being over-coached and not thinking for themselves," says Murray. "This is a cerebral sport. You must learn to think before you can expect to win."

Most of the children were taken from areas where there are few indoor facilities. They were not the "elite" band of those expected to make a substantial living from the game. The emphasis was on working with a large group of kids - about 20 in two sessions spanning the day - to show how players can be handled by just one coach while taking part in a series of drills that had a definitive purpose but a distinct level of enjoyment. Both Murray and Smith believes that children who will form the level of county players in the future are crucially important to the development of the sport in Scotland.

Space is restricted at the very top of tennis. The aim is to increase the base, providing a generation of players who will remain in the sport and pass that commitment on, so building a stable foundation for Scottish tennis.

"We must keep challenging players and coaches," says Murray. "We must make this a stimulating sport so that inspires people to keep playing it."

Here exercises in the Gleneagles Arena were clever yet simple. They involved 20 players under the direction of one or two coaches. Everyone was keep involved, everyone was having fun. But Murray, in thought and word, made sure there was a focus. "If kids are just taught in drills then there are not going to be good match players," she says. "They have to learn to think themselves out of trouble."

It is an attitude that exists most conspicuously in her son, who comes back from every defeat strengthened by what he has learned.

"He is a thinking player," says his mother. "He is quick, he anticipates but he reads the game incredibly well. Because of the way he was taught when he was young he has so much variety. He can change pace, direction. He can do everything. If you can work out the right tactic to defeat a specific opponent, he can execute it because of the range of his weaponry."

All this was said with some graciousness considering the hit, and the putdown, on the Dunblane courts a couple of years ago is the last time they played together.

Murray, the coach, concedes that some players have an intuitive grasp of how to solve the puzzle of tennis but she insists that solutions can be taught too.

One of the most obvious traits of more than hours of coaching yesterday was the imperative to present a problem to a player and teach him or her to find their own way out.

"There are three aims in my coaching," says Murray. The first is how to cause trouble to an opponent. The second is how to avoid trouble, simplistically, for example, how to play to Rafa's backhand rather than short to his forehand. And thirdly how to get out of trouble. I always ask players what is causing them trouble and I want to hear their solutions about how to nullify, say, a high shot to the backhand."

These certainties prevail on a Dunblane outdoor court, in a plush Gleneagles interior, or, later this month, on the red clay of Roland Garros.

She says of her son who has started his preparations for the French Open by winning his first tournament on clay in Munich this week.

"He has always been self-driven. He has always had a belief in himself. You have to adapt in tennis. It is not like running the 100 metres. That is always going to be the same distance, in a straight line, on a similar surface. Coaches must understand how to develop thinking play. And then players can think for themselves."

Murray, approaching his 28th birthday later this month, has developed by winning on clay. So what of his prospects at Roland Garros?

"Winning in Munich was a big milestone for him. He is in good shape, physically and mentally. But it is a very tough thing to do, to win a slam," says Murray.

It is beyond all but the extraordinary few. But sport still offers its substantial consolations. The deft shot at the net that occasioned the effusive but genuine Murray praise was performed by Scott Docherty, a 16-year-old from Strathgryffe Tennis Club in Renfrewshire.

He may not sparkle on the tennis tour but he later affirmed a personal ambition. "I just want to see how far I can take it," he says. ''I just want to keep playing. I love it."

On a day of reflections on tennis, this was the perfect thought for the day.