The dog park is a fascinating place to observe society. At first glance, the dogs are separated by size; large and small. Most people are respectful of the weight limit (installed to protect the dogs); however, there is always the owner who believes that rules don't apply. Meaning: the dogs are separated by size except for the special doberman and it's owner in the small dog run. I happen to go into the "Mighty-Mite" pen, as my 6 lb Chihuahua often seems like bait to the larger breeds.
A handful of pooches run around barking at each other, generally having a great time. They roll around, wag their tails, and genuinely look excited to have the space to run leash-free! Meanwhile, there are other dogs on the sidelines, anxiously licking their lips and waiting to be released from the torture (seriously, such an active place is not always the ideal situation for some). Attempting to bridge the gap and bring others into the game, some of the dogs run to the outskirts of the field, hoping to entice the unwilling. The world needs both kinds of dogs, and each is very much appreciated.
In terms of the owners, some notice their dog's obvious discomfort and stand by, lending their support (and open arms for the small guys!) to their "kids." And of course there are other "parents," who seem more concerned with reliving the previous night than ensuring their pooch's safety. Accidents happen because signals are misread (ie- the lip curling does not mean play!) and supervision is not provided. Of course, one can train the dog in the beginning, so it is able to respond in a favorable manner. Inappropriate behaviors need to be caught in the moment and corrected (with positive reinforcement when possible!). Seriously, the dog park is definitely a microcosm of modern society.
On a playground, there are some parents who do not seem overly concerned with what their child is doing; kids pushing their peers down the slide or jumping into a pile of unsuspecting victims (and of course never having anybody model appropriate behavior). However, some parents are too involved in their child's play and do not allow the child the opportunity to run and jump in an age-appropriate manner. The most effective parenting style is to allow children the freedom to be kids, but catch them in the act when they are not behaving in a style that is socially acceptable. Throwing sand will surely lose many friendships in the sandbox. Much like the dog park, catch the child in the act, use a quick "no" and redirect their actions. Attempt to reward for good behavior (more playtime) and leave the park if they are not getting the message. After all, everyone should feel comfortable; whether in the dog run or on the playground.
Not to mention that your child might be behaving perfectly fine, but another child is monopolizing the equipment, and the caregiver is on the cell phone, unaware of the child's actions. As mentioned in Parent.com, you can firmly remind the child that everyone is taking turns. Although it is not your place to discipline another person's child, pointing out social cues to the child will help him/her in this situation and perhaps in the future.
Of course parents need a break (it is SO hard to be on 24/7!); however, playgrounds are optimal teaching "grounds." If you can instill the values early on, so they become innate behaviors, the rewards will pay off immensely. Children can learn lessons on how to behave, respect others, wait their turn and listen to adults (and peers!), but the skills need to be taught right in the moment. Meaning, regardless of how well behaved (or not) your child is, inappropriate behaviors that are corrected, while in the actual situation, are always the most successful.