"one shift in activation that occurs as children develop is from diffuse, larger areas to more focal, smaller areas. this shift is characterized by in which, areas of the brain not being used lose synaptic connections and those being used show an increase in connections"

The answer would be synaptic pruning.

The brain in children will have a much more synaptic connection than adults. This connection is important for learning process in the early stage of life. More synaptic connections allow multiple parts the brain areas to be connected even if there is a damage in one area. 
The synapse will be cut down later in a process called synaptic pruning. Only the area that frequently used will be preserved.