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This study examined the accuracy with which parents can judge their children's cognitive abilities, as well as the relation between parental accuracy and the level of the child's performance. Subjects were 50 second- and fifth-grade children, their mothers, and fathers. Each child responded to five cognitive tasks, and each parent predicted both how his or her child would perform and how children in general would perform on each task.
Miller et al. (Fri,) studied this question.