Various findings regarding the relationship between math anxiety and engagement have been identified in the literature, with many focusing on general math anxiety and overall math engagement. Based on the control-value theory, this study examined the relationships between trait- and state-math anxiety and behavioural and cognitive engagement in math under daily practice and exam preparation conditions across math tasks of varying difficulty levels. A survey study with 449 high school students and an experimental study with 33 freshmen were conducted. Students' trait- and state-math anxiety, as well as behavioural and cognitive engagement in math, were measured under daily practice and exam preparation conditions across easy and difficult math tasks. A two-level latent variable model was built in the survey study, and two-way ANOVAs and regressions were used in the experimental study. Students exhibited greater state anxiety under exam preparation conditions in the survey study and showed differences in state-math anxiety and engagement across learning contexts and math tasks in the experimental study. Students with higher trait-math anxiety displayed less engagement in both studies, while those with higher state-math anxiety when facing difficult tasks tended to engage more cognitively in the experiment. These findings demonstrated discrepancies in the relationships between trait- and state-math anxiety and math engagement, while accounting for learning context and task difficulty.
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