Broadening the Assessment of Mathematics-Related Achievement Emotions: Structure and Differentiation of an Extended AEQ-ES Among Chilean Elementary School Children

Achievement emotions play a central role in mathematics learning, yet instruments suitable for young children often cover only a narrow range of emotions and have rarely been validated in Latin American contexts. This study examined the structure, differentiation, and measurement properties of mathematics-related achievement emotions using an extended Spanish-language version of the Achievement Emotions Questionnaire–Elementary School (AEQ-ES). The instrument, referred to here as the AEQ-ES-M, was extended to include anger and hope, alongside the original dimensions of enjoyment, anxiety, and boredom. Items were translated and back-translated, and semantic equivalence was assessed using Sentence-BERT embeddings (cosine similarities = 0.70–0.96). A new set of facial icons depicting a boy or a girl was developed for all five emotions, and their recognizability was examined in an independent face-matching task with 399 second-graders (overall accuracy = 79.6%). The 46-item questionnaire was administered to 514 Chilean children in Grades 2 (n = 247) and 4 (n = 267) attending nine schools. At the full-sample level, confirmatory factor analyses supported a five-factor correlated-emotions model over an alternative two-factor valence model. Reliability was high across emotion scales (ω = 0.894–0.937), and convergent validity was adequate (average variance extracted, AVE = 0.538–0.726). However, substantial overlap emerged between enjoyment and hope, particularly in Grade 2 (r = 0.983), where the five-factor solution was inadmissible. A post hoc four-factor model combining these emotions showed similar approximate fit (change in comparative fit index, ΔCFI = 0.002). Scalar invariance across sex held for both models, whereas scalar invariance across grade was supported only for the four-factor model. Girls reported higher mathematics anxiety than boys, and, in this cross-sectional comparison, fourth graders showed lower levels of the combined enjoyment–hope factor and higher anger, anxiety, and boredom than second graders. Overall, the AEQ-ES-M provides a reliable and culturally adapted measure of a broader range of achievement emotions in mathematics among Chilean primary school children. Because enjoyment and hope were less clearly differentiated in Grade 2, the four-factor specification is recommended for this grade and for cross-grade comparisons.