In a sample of 380 children, self-esteem as measured by the Coopersmith Self-Esteem Inventory (SEI) became more stable and more highly correlated with school achievement as the children grew older. Subjects taking the SEI at ages 12 and 15 showed greater test-retest consistency (r = .64) than did subjects tested at ages 9 and 12 (r = .42). Correlations between SEI and school achievement scores also increased over the age range from 9 to 15. Children's self-perceptions appear less firmly established, and therefore may be more responsive to intervention, at earlier ages.
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Rosalyn A. Rubin (1978) studied this question.