Children's Skills and Self-Perceptions in Mathematics.

Abstract

Two studies were carried out to investigate the relationship between children's mathematics skills and self-perceptions. Both employed the same sample of children. Study 1 was a longitudinal analysis of the children's achievement and self-ratings of ability in mathematics across grades 2, 5, and 10. Causal modeling showed that between grades 2 and 5, math achievement is causally related to self-ratings of ability. There was evidence that between grades 5 and 10 this causal relationship diminishes. The accuracy of children's self-ratings increased between grades 2 and 5, and there was no appreciable change after that. Math achievement showed high stability from year to year, whereas stability of self-ratings was considerably less. Study 2 investigated how children's fluent use of basic numerical skills was related to their perceptions of confidence on a subjective task of quantitative estimation. Tenth graders made numerical estimates and confidence ratings of the estimates. Fluency was assessed on tasks of counting and arithmetic fact retrieval. It was found that these skills were related not only to accuracy in estimating, but also to the appropriateness of the children's confidence: skillful children made judgments that corresponded with actual task difficulty. Girls were less confident on the estimation task than boys. A derived calibration score corroborated ANOVA findings of the interaction of skill level and task difficulty on confidence ratings. It also revealed that while all subjects tended to be overconfident in their estimates, girls were more realistic, i.e., less overconfident, than boys. Findings are discussed in light of developmental research that shows the effect of stimulus knowledge on awareness of task difficulty in recall situations. Together, the two studies emphasize the role of children's early skill development in mathematics--in one case, on general perceptions of academic ability and in the other, on perceptions of confidence on a novel, non-academic task.