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Back now to Newtown itself in the aftermath of the shootings. Many parents with children who survived at Sandy Hook Elementary have been trying to help their kids, while sorting through their own feelings.

NPR's Alix Spiegel spent some time with two Sandy Hook parents.

ALIX SPIEGEL, BYLINE: About a month ago, Declan Procaccini's 10-year-old son woke him early in the morning in a fright.

DECLAN PROCACCINI: He came into my bedroom and said, Dad, I had a horrible, horrible dream. And he was really shaken up. I said, well, tell me about it. And he said that he'd dreamt a teenager came into his classroom at his school and shot all the kids right in front of him.

SPIEGEL: Procaccini's son is a sensitive kid, frequently anxious. So, Declan did what he often does when his son crawls into his bed with a fear or anxiety: He explained why the fear wasn't rational.

PROCACCINI: Look, I totally understand you having those fears. Yes, that has happened at times throughout the world. It's rare that, you know, the chances of that happening here are one in a zillion. We talked about probabilities and possibilities and, you know, is it possible that Godzilla could right now come through the trees? Yes. Is it probable? No. I think we both know that it's not probable. So we had all that discussion and, you know, that kind of calmed him down a little bit. And, you know, and it worked out for a little while there.

SPIEGEL: But what happens when the improbable becomes a reality, when you become the one in one in a zillion? How do people respond?

The day Adam Lanza shot his way through Sandy Hook Elementary School, Procaccini's eight-year-old daughter was in a reading room just down the hall from the principal's office. She had walked herself to her class early and was sitting there with two teachers, when the three of them heard the sound of gunfire coming from outside.

PROCACCINI: They grabbed my daughter by the arm and threw her in the bathroom. There's a little bathroom that's off the reading room, I think it's a single-person - I'm pretty sure. And the three of them just sat in there, quiet, 'cause he came in the room. So - but he left.

SPIEGEL: He left and so Declan's daughter survived. In the days after the shooting, one of the teachers who had actually been at the school and knew them well, reached out to Declan and his wife. She wanted them to know just how terrifying their daughter's experience had been.

PROCACCINI: She said, you need to get your daughter help. I was literally in the same area as your daughter, and I know what she saw and I know what she heard. And I'm going to need help for a long time. You need to get her help.

SPIEGEL: But Declan's daughter has barely talked about what happened, barely registered any emotional distress at all.

PROCACCINI: I don't know if she's just disassociated. I don't know if it's her defense mechanism or I don't know if she just doesn't get it. I truly don't.

SPIEGEL: His 10-year-old son, however, has been struggling. His son graduated from Sandy Hook Elementary last year and now attends Reed Intermediate School, which went into lockdown during the shooting, so the boy had no idea what was happening until Declan picked him up and told him about it.

Immediately, Declan says, his son started crying.

PROCACCINI: I mean, he was crying like a little baby. I haven't seen him cry like that, you know? He was so scared.

SPIEGEL: And as soon as they got home, Declan says, his 10-year-old made a decision: no more school for me.

PROCACCINI: I'm not going, he says. I am not going with you. I am not going.

SPIEGEL: But when Procaccini's family went to see a therapist the next day, one of the things the therapist made clear was that staying away from school was a bad idea. The more school his son missed, she told him, the harder it would be to get him to go back.

And so, on Tuesday of last week, when Reed went back into session, Declan tried to convince his son to go.

PROCACCINI: Come on, I'll drive you. I'll walk you in. I'll show you, you know. And then he just snapped and it was crying and screaming and: I'm not going. You're not leaving me. I'm not going there.

He said to me, if you told me last Friday that I'd be completely safe going to school, you would be wrong. And, I don't know what say.

SPIEGEL: For the rest of the week, instead of attending classes as usual, Declan and his son simply drove to the school and walked together through the halls for hours, Declan's car keys safely tucked into his son's coat pocket so that Declan couldn't drive away by himself.

This procedure was supposed to convince his son that school really was a safe place, but his son doesn't seem to be buying it. And Declan is worried about what will happen after the holiday break.

PROCACCINI: I don't have a plan, really. This is a first. It's going to be really rough.

SPIEGEL: And has your son had another dream?

PROCACCINI: No, he hasn't.

SPIEGEL: Do you have any sense of what you would say to him if he had another dream like that?

PROCACCINI: I would say that I completely understand, especially given what we've all gone through.

SPIEGEL: Would you talk about probabilities and possibilities?

PROCACCINI: No. Nope.

SPIEGEL: Two miles away, I met another parent of a Sandy Hook student, a woman named Zhihong Yang, she calls herself Jen. When I walk in, there's a small pile of papers spread over the table in her kitchen.

What is this?

ZHIHONG YANG: This is a handout distributed in parents' conference, last night at Sandy Hook Elementary parents' meeting.

SPIEGEL: Yang's son Jerry is in the third grade and was at Sandy Hook during the shooting. Unlike some of the other kids who were at the school, he genuinely seems to be doing OK. But for her part, Yang finds herself thinking about things she had never considered before.

YANG: Yesterday, I went to Costco, I can't help but think: If there was a shooter there, what do you do? I went to the supermarket and if something happened there, what do you do?

SPIEGEL: This makes sense, after all, death is all around Yang. Take, for example, her drive to school. Her usual seven-minute route is now lined with families affected by the tragedy.

YANG: At least four families that had victims in that accident and when I drive by, I feel the pain and I do cry.

SPIEGEL: As you can probably tell, Yang is originally from China. She tells me that in college there she studied math, and then suddenly, totally without prompting, I find myself in another conversation about possibilities and probabilities. Jen, it turns out, specialized in statistics.

YANG: Probability and possibilities. When there is a massive data, what the rule of statistics says about the information hidden there.

SPIEGEL: It turns out that in the days since the shooting, Yang has been thinking a lot about possibilities and probabilities, reconsidering her original feelings about them. You see, Yang has always assumed that she was safe because the chance of a shooting happening to her specifically was very, very small. But since the shooting, she's been focused on this one rule of statistics that she learned in college, which she called the large number certainty theorem.

YANG: If the base is big enough, even though the probability is small, things will happen with certainty.

SPIEGEL: By Yang's reckoning, this is how the large number certainty theorem applies. First, we know that many people have guns. Second, we know that a certain number of people have disordered minds or bad intentions. And third, we know that this is a huge country. In other words, the base is big.

YANG: So you know, mathematically, something somewhere will happen with certainty.

SPIEGEL: And so, though previously Yang depended on the idea that school shootings were so rare they probably would happen to someone else...

YANG: I think if this taught me anything that is we should not wait until it actually happen to us to take action.

SPIEGEL: And so, Yang intends to get more involved with fighting for gun control. That seems like the logical thing to do. Still, the logic of many parts of what has happened are not at all clear to her.

YANG: You can safely predict this will happen, but why it particularly happened to that class? To that teacher's room? That particular family?

SPIEGEL: This, obviously, is not a question that math can answer. And for Yang, the lesson is that morally she should not distinguish between it happening to someone else and it happening to her. Probabilities just aren't improbable enough for that. Alix Spiegel, NPR News, Washington.

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