TOTS IN TRAINING

They bring their Olympic dreams here. At the superbly equipped Sport Club of the Moscow Trade Union Council, nine- and 10-year-old girls race down a long mat, turn four neat handsprings, and land in a pit of foam rubber. Do they enjoy their training? They look at each other and giggle. ``Of course,'' says one. ``It's fun here - we're with our friends.''

Grueling fun. The day opens with limb-stretching exercises that bring tears to these tiny athletes' eyes. ``Does it ever hurt?'' one little girl is asked. ``Sometimes,'' she says, in courageous understatement.

For would-be Soviet gymnasts, the path to the Olympics invariably starts in club schools such as this. The government pays all expenses, and the trainers receive regular teacher's salaries. The trade union school is a very ordinary one, head trainer Victor Vasiliyevich explains. ``There are schools like this in every region of Moscow, and all over the Soviet Union,'' he says. His school hasn't yet produced any champions, as have others, like Moscow's venerable Central Army Sports Club. But, like his students, he is hopeful.

The gifted children selected for this four-year-old school train four hours a day, six days a week. The staff appears to be tough, but compassionate; Mr. Vasiliyevich says the school's main goal is to make the children healthy and to teach them to love gymnastics.

Nevertheless, the practice of engaging young children in such intensive physical training has its critics.

After the 1980 training accident which left one Soviet hopeful, Yelena Mukhina, paralyzed, some Soviets began to speak out against the pressure on child gymnasts. The youngest children in the trade union school are, in fact, only six. Some of them have trouble telling their right leg from their left.

Vasiliyevich counters that ``unlucky accidents'' can happen in any sport, and that the children ``don't feel a burden.''

``Sport is youth,'' he says.

At the end of the session, the girls are bundled away, weary and exhilarated, by waiting grandmothers.