How gum moves from a child's mouth to his hair will forever remain a mystery. Maybe the school bully put it there. At any rate, chewing gum sticks to everything, so trying to tease it out of hair with just your fingers will end up being a sticky mess.
What works? Apply petroleum jelly to the stubborn piece of gum. Using your fingers, work a large amount of jelly into the tangle, but make sure to coat the gum more than the hair. Soon the gum will slip right out.
Adapted from "Amazing Uses for Household Products: Toothpaste" © 2009 Publications International, Ltd.