Math Self-Concept, Grades, and Achievement Test Scores: Long-Term Reciprocal Effects Across Five Waves and Three Achievement Tracks

This study examines reciprocal effects between self-concept and achievement by considering a long time span covering grades 5 through 9. Extending previous research on the reciprocal effects model (REM), this study tests (1) the assumption of developmental equilibrium as time-invariant cross-lagged paths from self-concept to achievement and from achievement to self-concept, (2) the generalizability of reciprocal relations when using school grades and standardized achievement test scores as achievement indicators, and (3) the invariance of findings across secondary school achievement tracks. Math self-concept, school grades in math, and math achievement test scores were measured once each school year with a representative sample of 3,425 German students. Students' gender, IQ, and socioeconomic status (SES) were controlled in all analyses. The findings supported the assumption of developmental equilibrium for reciprocal effects between self-concept and achievement across time. The pattern of results was found to be invariant across students attending different achievement tracks and could be replicated when using school grades and achievement test scores in separate and in combined models. The findings of this study thus underscore the generalizability and robustness of the REM.