Because of the lack of error-free, on-task performance by young children, cognitive modeling has not generally been considered an appropriate technique for characterizing computer use by young children. It is argued that cognitive modeling can be a useful strategy for organizing data on children's performance when the domain being studied is appropriately defined. The domain of interface devices for computer control and their demands on young children as computer users is used in this example, which reviews the results of several studies of children's use of a variety of different input devices conducted at the Children's Television Workshop. The cognitive modeling hypothesis suggests that for young children the degree to which cursor movement devices resemble natural motions (such as pointing) makes use easier. The more rules of use a device requires, the more difficult it will be for the child to use because working memory will be consumed in a manner similar to the use of the device itself. The model assumes that the demands of cursor control and device rules are additive. The model is applied to children's task performance in several studies. The current model shows promise as a framework for analyzing children's performance with different input devices and explaining and predicting differences in competence across devices and across children. Two tables illustrate the discussion. (Contains 12 references.) (SLD)