This study adopted a person-centered method to investigate the latent profiles of students' cognitive appraisals based on control-value theory, providing a picture of their academic emotional landscape. Students' appraisal profiles regarding academic emotions were also compared. The data were collected from 1762 students (50.7 % male; Mage = 13.88, SD = 0.84) in 68 mathematics classrooms across 11 secondary schools in Jiangsu, China. Latent profile analysis identified four patterns based on academic control and value: extrinsic value orientation (4.9 %) and low (13.4 %), medium (41.3 %), and high appraisal profiles (40.4 %). Students in the high appraisal profile showed the highest level of positive emotions and the lowest level of negative emotions, followed by those with the medium appraisal profile. Those in the extrinsic value orientation profile, however, displayed the lowest level of positive emotions and the highest level of negative emotions. The four profiles also showed significant correlations with the students' background characteristics. Educational relevance statementThis study aims to explore possible subgroups of control and value appraisals and their relationships with academic emotions in mathematics classrooms. This study suggests that students in the high appraisal profile (i.e., high academic control and value) tend to report high levels of positive emotions and low levels of negative emotions, followed by students in the medium profile (i.e., medium academic control and value). Additionally, students in the extrinsic value orientation profile (i.e., high extrinsic value but low academic control and intrinsic value) performed worse than the students in other three appraisal profiles both emotionally and academically. Therefore, it is crucial to foster students' competence beliefs and intrinsic value in mathematics to enhance their positive learning experiences.
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