This study explored how young children interact with their peers in the computer area of a public kindergarten classroom. Children's social interaction, as defined in this study, is the action of giving and taking information that results in children's knowledge construction and cognitive development that can be accomplished through peer-to-peer interactions. This kind of social interaction is referred to as "Cognitively Effective Social Interaction (CESI)" in this paper. Patterns of young children's social interaction with peers in the computer area of this classroom were discussed. Two teachers and 28 children in a full-day kindergarten classroom were observed and interviewed. The patterns of young children's social interaction that occurred in the computer area were described as parallel play, verbal conflicts, sociable interaction, knowledge construction through positive and negative processes, and non-verbal communication.