Longitudinal validation of the Chinese Achievement Emotions Questionnaire-Mathematics: A one-year study using exploratory structural equation modeling

Achievement emotions shape students’ mathematics learning and performance, yet their measurement in young children remains underexamined. Developed from Taiwanese students’ open-ended descriptions rather than through direct translation, the Chinese Achievement Emotions Questionnaire-Mathematics (CAEQ-M) assesses four culturally salient emotions: enjoyment, anger, anxiety, and boredom. However, its simultaneous four-emotion structure has not been evaluated using exploratory structural equation modeling (ESEM), nor has its longitudinal measurement invariance been examined across repeated occasions in young children. Data were collected across four waves spanning one school year from 377 third- and fourth-grade students attending two elementary schools in Mainland China. At each wave, confirmatory factor analysis (CFA) was compared with exploratory structural equation modeling using target rotation (ESEM-T). Longitudinal and gender measurement invariance were subsequently tested. ESEM-T fitted better than the oblique four-factor CFA at every wave and on every index. Constraining cross-loadings to zero inflated the latent factor correlations: under CFA, the correlation between anger and boredom ranged from 0.88 to 0.95 across waves, compared with 0.73 to 0.80 under ESEM-T. The oblique four-factor model showed invariance of thresholds, loadings, and intercepts across the four waves and across gender at each wave. Repeated measures ANOVA revealed that only boredom increased significantly across the four occasions, with pronounced elevation at Time 4. The CAEQ-M shows a stable four-factor structure in Chinese elementary school children, invariant across one school year and across gender. Modelling cross-loadings is necessary: under a confirmatory model, anger and boredom appear almost redundant. These two emotions remain the least well differentiated pair throughout, and the anger scale is the weakest of the four, indicating that its measurement would benefit from revision. Boredom rose significantly across the academic year.