It used to be thought that young children didn't really play with other children. Before they're about three years old, they engage in what is called parallel play – that is, playing alongside each other, but not interacting directly.
That is true most of the time, but at other times, even very young children interact with each other while playing. Children who have been in group child care from an early age have more experience with peers, and tend to interact more. Siblings, who know each other very well, play with each other even at a very young age. However, when playing with other children they don't know as well, they still play in parallel.
By age three or four, children spend more of their playtime interacting with each other. Some of the interaction is positive: imitating, planning, and executing a plan together, or sharing materials. At other times, the interaction is less benign. One child may snatch a toy away or barge in, disrupting the play.
Although it may seem that these actions are intended to annoy, it's more likely that they represent a child's unskillful attempts to join in the fun. It takes a long time for some children to figure out how to assert themselves without being aggressive. On the whole, children learn best when adults assume that their intentions were good, even if they did not carry them off well. It's more helpful to show a child how to go about taking turns, than to scold him for grabbing toys.
Here are some tips that can help make early play more cooperative: