Children's performance on cognitive tasks is often described in categorical terms in that a child is described as either passing or failing a test, or knowing or not knowing some concept. We used binomial mixture models to determine whether individual children could be classified as passing or failing two search tasks, the DeLoache model room task and the Berthier et al. door task. The data support categorical classification of the children and suggest that the increase in average proportion correct with age is the result of an increasing proportion of children who can solve the tasks. Performance on the two tasks was concordant, and improving performance could be due to advances in a single psychological ability, such as cognitive control.