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Children tend to have quick movements, high pitched voices, and get places by running, rather than walking. These movements are quite like those of a prey animal in the wild. A dog still retains much of the instincts of his wild ancestors. Many of a dog's play behaviors are based on inherent predatory behaviors. Therefore, they will naturally act excitedly around children, nipping at their heels and trying to knock them down.
Normal play behaviors between your children and your dog are not a problem. However, it's helpful if you do not consistently punish your dog in the presence of your children. If he learns that he's constantly reprimanded around your children, he may start to act defensively. The key is to teach both your dog and your children what behaviors are appropriate when they are around each other.
If your dog behaves aggressively around your children, that is certainly cause for concern. He may have dominance issues and not perceive your children as dominant members of the pack. In that case, seriously consider getting a professional trainer or animal behaviorist to help redirect the behavior in your dog to ensure the safety of your children.