Children's numerical skill and judgments of confidence in estimation

This study investigated how children's fluent use of a basic numerical skill is related to their perceptions of confidence on a task of quantitative estimation. One hundred four 10th graders (age 15.7 years) were categorized according to level of numerical fluency as assessed by timed tasks of counting in various nonunity increments. They then made estimates of large numbers of dots and rated how confident they were on each trial. The estimation task varied according to two within-subject factors of task difficulty. It was found that counting skill was related not only to accuracy in estimating, but also to the appropriateness of the children's confidence in their responses. Skillful children made judgments that corresponded with actual task difficulty. A derived calibration score corroborated ANOVA findings of the interaction of skill level and task difficulty on confidence ratings. It also revealed that while girls were less confident than boys, they were actually more realistic in their judgments. Findings are discussed in terms of (a) the effect of stimulus knowledge on awareness of task difficulty and (b) sex differences in achievement-related expectancies.