Background On the basis of the integration constructs from self-determination theory (SDT) and achievement goal theory (AGT), this study aims to investigate the relationship among classroom motivational climate from four perspectives (i.e. autonomy support, relatedness support, task-involving climate and ego-involving climate), three psychological needs (i.e. autonomy, competence and relatedness), self-determined motivation and physical activity (PA) in secondary physical education (PE). Methods Participants consisted of 1186 Chinese students aged 11 to 16 years from three secondary schools in Shanghai. Accelerometers were utilized to measure moderate to vigorous physical activity (MVPA). Questionnaires were used to measure SDT variables (i.e. classroom motivational climate, perceived competence, autonomy, relatedness and self-determined motivation). Structural equation modelling (SEM) was adopted to analyse the hypothesised relationship. Results SEM analysis revealed that task-involving climate and autonomy support were positively associated with autonomy, relatedness and competence. Relatedness support was positively related with autonomy and relatedness, whereas ego-involving climate was only associated with competence. The three psychological needs positively affected self-determined motivation, and self-determined motivation positively affected the MVPA time of secondary school students in PE lessons. Conclusion These findings support a model of motivation that integrates SDT and AGT, provides new insight into understanding MVPA in Chinese PE, and establishes a solid basis for intervention research.

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This study applies self-determination theory (SDT) to test the hypothesised relationships amongst three basic psychological needs, level of self-determined motivation (i.e. self-determination index, SDI) and moderate-to-vigorous physical activity (MVPA) of Chinese elementary and secondary school students during their physical education (PE) in Shanghai, China. Gender and schoollevel differences in these relationships are also explored. The participants comprise 1829 students from three elementary and secondary schools in Shanghai, China. Accelerometers are used to measure the MVPA duration of the participants in PE. The Self-regulation Questionnaire and the Psychological Needs Satisfaction Scale are completed by the participants to assess PE motivation and the three psychological needs of students. The structural equation modelling (SEM) results show that the hypothesised model has a good fit with our data. Autonomy, competence, and relatedness are positively associated with SDI for MVPA. The SDI is positively related to the time spent by students in MVPA in PE. The multi-group path analysis results reveal that the relationship between SDI and MVPA is stronger for secondary school students than elementary students. Overall, our findings support the applicability of SDT in understanding and promoting the physical activities amongst Chinese school students in PE. Accordingly, intervention should be conducted to develop autonomy, competence and social relatedness of elementary and secondary school students. Additional efforts are required to encourage elementary school students to be more self-determinant in PE classes.: Highlights. Findings support the applicability of SDT in understanding and promoting the physical activities amongst Chinese school students in PE . SDI was positively related to school students' MVPA level. The satisfaction of autonomy, competence and relatedness towards PE was positively associated with students' SDI. . The proposed motivational sequence for adolescent MVPA in PE were similar for male and female students. . The relationship between SDI and MVPA of secondary school students was significantly stronger than elementary school students

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