IntroductionAchievement emotions have a profound impact on students' academic achievements and learning strategies, especially in online learning context where students may face great challenges in maintaining positive emotions due to physical separation and social isolation. While most studies focus on achievement emotions as predictors of academic performance, fewer have examined them as outcome variables. However, achievement emotions themselves can be seen as an important learning outcome, as experiencing positive achievement emotions is also a valuable learning goal.MethodsThis study explored key factors influencing achievement emotions among Chinese elementary and middle school students in online mathematics learning, using control-value theory as a framework. Data were collected using stratified sampling, and backward regressions were used to analyze data from 2,940 students. In addition, mediation analyses were conducted to examine whether control and value appraisals mediated the relationship between technology efficacy and achievement emotions.ResultsResults indicated that control and value appraisals were the strongest predictors of achievement emotions, positively predicting positive emotions and negatively predicting negative emotions. Notably, negative effort belief positively predicted all three negative emotions substantially, surpassing the predictive effects of control appraisal. This study also found that technology efficacy positively predicted all positive emotions and negatively predicted anxiety. Regarding demographic factors, grade level and school tier significantly influenced some achievement emotions, but gender was not a significant predictor. In addition, mediation analyses showed that control and value appraisals partially mediated the effects of technology efficacy on both positive and negative achievement emotions.ConclusionThis study emphasizes the need to optimize online learning by enhancing students' control and value appraisals, addressing negative effort beliefs. Special attention should be given to students in disadvantaged schools and boys in all schools during online mathematics learning.