She had said that she hoped to "humanize" the space age for children across the country. And she had done it -- in the months before her scheduled voyage aboard the shuttle Challenger, Christa McAuliffe had managed to inject warmth and human spirit into the elaborate space fantasies of tens of thousands of American kids.

Many of those children were watching in classrooms and auditoriums yesterday when McAuliffe died in a flash of fire miles above the Atlantic, and in that instant she humanized for them something terrible and frightful and beyond reason: her own mortality, and theirs.

How can a child mourn such a death -- so vivid, so immediate, so public?

That question was on many minds yesterday. President Reagan tried to answer it during his nationally televised remarks, when he paused to address the American schoolchildren who had watched the shuttle's takeoff. He said that while it might be hard for children to understand, "sometimes painful things like this happen."

McAuliffe had become "a stand-in for everyone's favorite teacher," said James Egan, chairman of the psychiatry department at Children's Hospital. "What makes it especially traumatic for children is that teachers are sometimes stand-ins for moms. That has to raise some anxieties for many children about parental loss, parental death."

Researchers and practitioners in child psychiatry contacted yesterday agreed that the televised deaths of Christa McAuliffe and her six crew mates aboard the Challenger would linger indelibly in the minds of many children.

"Children are excessively vulnerable to trauma because of their intellectual and emotional immaturity," said Yehuda Nir, associate professor of psychiatry at Cornell Medical College in New York. "There's a degree of distortion in their perception. Things that to us seem to be at a distance have an unusual immediacy to a child. For them to see a teacher killed might evoke a feeling that the next day, it's going to happen to their teacher or to themselves."

Research by Nir and others into the reactions of children to traumatic events has identified a class of children who are especially vulnerable: those who have already experienced a loss themselves, such as divorce or death in the family. In the aftermath of the shuttle deaths, such children may experience what Washington psychiatrist Joseph Novello called an "anniversary reaction" -- recollections of grief or sadness first associated with a personal tragedy.

Another class of children at risk, according to Novello, are those who "tend to hold things in and are not very good at expressing feelings. To the casual observer, that kind of youngster may appear on the surface to be handling it very well. But beneath the surface, there may be a fire brewing."

Then, too, there is the matter of the country's pervasive culture of space fantasy, which has become an important part of contemporary children's lives. For an earlier generation, space travel was the blazing of an ultimate frontier, attended by dramatic risks and rewards. But today's children have come to see rocket launchings and space voyages as routine, givens of modern life and seeds of far-reaching fantasies.

"This year, with the comet and everything, there's been a lot of talk about space with third graders and fourth graders especially," Nir said. "This will make it harder to distinguish between fantasy and reality, especially with people as high as the president talking about 'Star Wars.' The explosion is a brutal reality. It's a kind of excessive stimulation to the child, just watching the event on TV . . . TV breaks down our protective barrier."

But the immediacy of seven deaths on live television, while indisputably traumatic, may also offer a chance for children to learn the distinctions between fantasy and reality, Novello said. "We're assuming that youngsters are going to be struck with the enormity of it all, that they may have identified very closely with the seven real people inside the shuttle. But among children raised on television, there may be many of them that don't really perceive this as a real event at all, but just something they're seeing on the screen.

"For those youngsters, it's an opportunity to educate them to the realities of the world. That is, that there were real people on board, that we grieve at their passing and we acknowledge our own mortality. It can be used as a growth experience."

In his nationally televised address on the shuttle tragedy yesterday, President Reagan told the nation's children that "I know it's hard to understand, but sometimes painful things like this happen. It's all part of the process of exploration and discovery. It's all part of taking a chance at expanding man's horizons. The future doesn't belong to the fainthearted. It belongs to the brave. The Challenger crew was pulling us into the future, and we'll continue to follow them."

Novello and other child psychiatrists emphasized, however, that it was crucial for parents and teachers not to be "too quick with reassurances in the face of tragedy. We're too quick to tell kids that this won't happen to them. The youngsters have things they have to get out."

Novello cited four steps that parents and teachers should consider following in the days ahead:

"Number one, they should create an environment for children in which they can express their thoughts and their feelings. Secondly, it is important to listen. Number three, provide the facts. Tell them what happened and why so they have some detailed reference on which to hang their own thoughts and feelings. And four, I would say watchful observation -- you can't assume that you can wrap it up in one neat package or that after a talk of 60 minutes you've said everything there is to say on the subject. Some kids may need a follow-up opportunity to talk about it."

So may we all. The sudden deaths of the Challenger's crew yesterday was an ineradicable instance, as Georgetown University clinical psychiatry professor Edwin Kessler put it, "of something that you count on as being strong, safe and dependable suddenly being found to be vulnerable.

"And it's as if you can't count on the stability of the world around you. It shakes everyone's sense of the predictability of the world. And of course, the world cannot be predicted."