Some dogs get overly excited during a chase....once the object has been caught is when one of two things can happen. If there's a dog you don't know, you should never turn your back on it, run away, or look it in the eyes. Standing your ground puts you both on equal terms for the moment until either one makes a move. The movement will be judged as either a threat or gesture of dominance. Most 2 and 4 year old children have no idea, and they are easily outweighed and overpowered by most medium size dogs and up. Best to you in schooling your children about interacting with dogs. I'm sure there's plenty of scary videos available on the internet to boost your cause.
From this article here: Dog Owner's Guide: Kids and Dogs: A Common Sense ApproachThere are other circumstances that can provoke a dog to bite a child. Running, playing, screaming kids can trigger an instinctive predator-prey reaction in some dogs. Children who rough house and wrestle with dogs unknowingly encourage them to use their teeth. Dogs equate this kind of play with littermates or other dogs where using teeth is allowed. Startling a sleeping dog or petting him when he's eating can also provoke a bite.
What can be done to prevent dogs from biting children? I feel that, first, it's essential to understand that almost any dog will bite under the right circumstances. Second, a dog is a dog, an animal whose behavior isn't the same as humans and can't always be predicted with 100 percent accuracy, no matter how friendly or reliable he is.