The research, led by Xia Zheng of Nanchang University together with colleagues from institutions across China and Spain, focused on the Chinese Achievement Emotions Questionnaire-Mathematics, abbreviated CAEQ-M. Unlike many psychological instruments that are translated directly from English originals, this questionnaire was built from the ground up using open-ended descriptions of classroom emotions written by Taiwanese students. That approach allowed the instrument to capture four emotions the researchers identified as culturally salient in Chinese mathematics classrooms: enjoyment, anger, anxiety, and boredom. The questionnaire draws on the broader framework of the Achievement Emotions Questionnaire, which itself rests on the Control-Value Theory of achievement emotions, the influential account developed by Reinhard Pekrun that links students’ emotional experiences to their sense of control over outcomes and the value they place on academic activities.

What made the new study distinctive was its combination of two features that are rarely tested together: a longitudinal design spanning an entire school year and a modern statistical approach known as exploratory structural equation modeling, or ESEM. The researchers recruited 377 third- and fourth-grade students from two elementary schools in Mainland China and surveyed them at four separate waves across one academic year. Because achievement emotions are thought to fluctuate with classroom experiences, the team wanted to know not just whether the questionnaire worked at a single moment, but whether it measured the same constructs in the same way across repeated occasions, a property psychometricians call longitudinal measurement invariance.

The statistical heart of the study lay in a head-to-head comparison between confirmatory factor analysis, the traditional workhorse of questionnaire validation, and exploratory structural equation modeling with target rotation, known as ESEM-T. The difference between the two approaches may sound technical, but it has profound consequences. Confirmatory factor analysis forces each survey item to load on only one emotion factor, treating any relationship between an item and other emotions as statistical noise to be discarded. ESEM-T, by contrast, permits small cross-loadings, acknowledging that a single statement about math class might tap more than one emotion at once. Human emotions are messy, the argument goes, and measurement models should reflect that messiness rather than deny it.

The results were unambiguous. At every one of the four waves and on every fit index examined, the ESEM-T model fit the data better than the oblique four-factor confirmatory model. More striking still was what happened when cross-loadings were forced to zero. Under the confirmatory model, the latent correlation between anger and boredom ballooned to between 0.88 and 0.95 across the waves, figures so high that the two emotions would appear nearly indistinguishable, almost redundant. Under ESEM-T, the same correlation dropped to a more interpretable range of 0.73 to 0.80. In other words, the apparent overlap between anger and boredom was largely an artifact of the restrictive modeling strategy, not a genuine feature of children’s emotional lives. For anyone who has ever used confirmatory factor analysis to validate an emotions questionnaire, the implication is sobering: the standard method may systematically exaggerate the similarity of negative emotions.

Even with the more flexible model, however, anger and boredom remained the least well differentiated pair of emotions throughout the study, and the anger scale proved to be the weakest of the four subscales. The authors conclude that the measurement of anger in this instrument would benefit from revision, a candid admission that is relatively rare in validation studies, which more often emphasize what works rather than what does not. For researchers planning to use the CAEQ-M, the practical message is clear: the enjoyment, anxiety, and boredom scales can be used with confidence, while anger scores should be interpreted with caution until the scale is refined.

The invariance testing provided the study’s second major contribution. Across the four waves, the researchers found that the four-factor model held with invariant thresholds, loadings, and intercepts, meaning that children interpreted the questionnaire items in the same way in autumn as they did at the end of the school year. The same invariance held across gender at each wave, indicating that boys and girls responded to the instrument equivalently. This is a critical foundation for any longitudinal claim, because without invariance, apparent changes in scores over time could simply reflect changes in how the instrument functions rather than genuine changes in children’s emotions. With invariance established, the researchers could legitimately ask whether emotional experiences shifted across the year.

They had, and the answer was both simple and troubling. Repeated measures analysis of variance revealed that only one of the four emotions changed significantly across the four occasions: boredom. And it did not change in a promising direction. Boredom rose steadily across the school year, with a particularly pronounced elevation at the fourth and final measurement point. Enjoyment, anxiety, and anger, by contrast, remained statistically stable. The finding resonates with a growing international literature suggesting that boredom is among the most corrosive of achievement emotions, associated with reduced attention, shallower learning strategies, lower motivation, and poorer grades. If boredom accumulates as the academic year progresses, classrooms may be quietly losing children’s engagement long before final examinations arrive.

Why might boredom climb? The study itself does not test explanations, but the pattern invites several hypotheses consistent with Control-Value Theory. Boredom arises when students perceive an activity as lacking value or when their sense of control is undermined by tasks that are either too repetitive or mismatched to their skill level. A mathematics curriculum that becomes more demanding or more monotonous in the later months of the school year could plausibly push more children into this emotional state. Alternatively, the cumulative fatigue of a long academic year, with its cycle of drills, homework, and assessments, may erode the novelty and perceived meaningfulness of math lessons. Distinguishing among these possibilities will require future studies that pair emotion measurements with detailed records of classroom activities and instructional practices.

The study’s strengths lie in its design: four measurement occasions, a sample of young children who are often overlooked in emotion research, a culturally grounded instrument, and a modeling approach that many psychometricians argue should become the default for multi-item emotion scales. Its limitations are those of any single-region study; the participants came from two elementary schools in Mainland China, and generalization to other regions, age groups, and subjects remains to be demonstrated. Still, the implications reach well beyond psychometrics. For educators, the steady rise of boredom across the year is a signal worth heeding, a reminder that emotional engagement is not a fixed trait but a resource that can be depleted. For researchers, the work is a methodological wake-up call, demonstrating that the choice between confirmatory and exploratory modeling is not a technical footnote but a decision that can reshape what we believe about the emotional lives of students. As mathematics classrooms around the world grapple with declining engagement, knowing how to measure the emotions involved, accurately and over time, is an essential first step toward addressing them.

Subject of Research: Longitudinal psychometric validation of a mathematics achievement emotions questionnaire in Chinese elementary school children

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

Article References: Zheng, X., Chen, J., Fu, Q.-L., Wang, H., Zhou, Y., Liao, X.-L., Chen, N., Chen, I.-H., & Malas, O. (2026). Longitudinal validation of the Chinese Achievement Emotions Questionnaire-Mathematics: A one-year study using exploratory structural equation modeling. BMC Psychology. https://doi.org/10.1186/s40359-026-05706-9

Image Credits: AI Generated

DOI: 10.1186/s40359-026-05706-9

Keywords: achievement emotions, mathematics education, psychometrics, exploratory structural equation modeling, measurement invariance, boredom, anxiety, elementary students, Control-Value Theory, questionnaire validation, longitudinal study, educational psychology