So how can you help calm their fears? The Early Show co-anchor Harry Smith asked child psychologist Robin Goodman, who outlined steps parents could take.
The first thing is to recognize that your kids even are feeling the impact.
"When there's a change in behavior, you can usually tell that something is up," Goodman told Smith. "You also should realize there are certain kids who will just be more affected by this. If their parents have relatives or are concerned about people in that part of the world, then the kids will be picking up on that. Or if a kid possibly had some other recent experience that maybe triggered a reminder, something scary that happened in the water or on an airplane, then you know they might be a little more sensitive to what they're seeing and feeling around them."
Goodman says fears may be exacerbated by the fact that so many children have been victims of the disaster. "What you want to do is look at how the child is personalizing it to them," Goodman advises. "So that when a child looks upset or is asking a question, a parent wants to find out what is their real question. Is it, 'Are we going to be able to go to the beach this summer?' Or 'Where are you going when you're leaving the house?' It's about what is happening immediately in their world. When the older kids go back to school next week, you might start to hear a lot more talk about it when it's brought up in science and history classes."
So what do you say if kids ask whether this could happen to them?
"Well," Goodman responded, "little kids, you really can reassure them, saying, 'No, this is a very rare thing and it happened very far away.' Older kids, you can really start to talk about the science of it and what happens in rare events, and say, 'This really has never happened before in our lifetime. So it will be another number of lifetimes before anything so tragic ever happens again.' "
"Little kids should not be watching this," Goodman cautioned. "Even adults should not be watching it all of the time and neither should, you know, any child. Because what happens is, when we see it over and over again, the numbers are changing but the event is over, and kids may not understand it. So parents also want to help everyone understand."
Goodman says it's "great" if kids voice the urge to help: "The holiday season is a typical time when people do things for other people. Someone in the world every day needs help, and if parents want to donate their time or money, then they should get the child involved. Do research on the Internet together. Go to the local food bank or go to the Red Cross Web site. Find out and have the child involved."