The school in the movie is William Dawes Elementary. William Dawes was one of the riders who, like Paul Revere, warned the minutemen that British troops were coming, just as a child at his namesake school was trying to warn people what was coming.
The perceptual phenomenon of people looking for patterns in randomness (number strings, faces in trees, shapes in clouds etc.) is called Apophenia.
The predicament of being able to see future disaster and fearing no one will believe you is called "The Cassandra Complex", after a Greek myth.
A somewhat similar derailment on the New York City Subway's #4 line depicted in the movie happened in real life. On August 28, 1991, a #4 Express train derailed at a rail switch and crashed before the 14th Street-Union Square stop. The severity of the crash caused five out of the ten cars to be destroyed, and one car was split in two. Five people died and 161 were injured. The crash was caused by the motorman, who was intoxicated at the controls and had been speeding when the train passed over a switch. The motorman was sentenced to 5 to 15 years in prison for manslaughter and assault. He was released in April 2002.