The shift to online learning, particularly during the post-pandemic era, necessitates a deeper understanding of factors influencing student engagement, specifically agentic engagement—students' proactive and self-directed involvement in learning. This study focuses on agentic engagement in online college learning, recognizing its importance for effective learning outcomes. Traditional classroom settings often lack agentic engagement, a problem exacerbated in online environments due to spatial and temporal separation, reduced interaction, and inadequate supervision. Self-determination theory (SDT) suggests that teachers, as external factors, significantly impact students' learning engagement through their motivating styles. These styles can be broadly categorized as autonomy-supportive (encouraging student initiative) and controlling (imposing teacher control). Prior research shows that autonomy-supportive styles generally benefit students, while controlling styles can be detrimental. However, the online learning context presents unique challenges and opportunities, making it crucial to investigate the influence of teachers' motivating styles in this specific setting. Furthermore, students' self-regulated learning (SRL) ability—the capacity to set goals, plan, monitor, and evaluate their learning—is a crucial internal factor affecting engagement and achievement in any learning environment, including online contexts. This study aims to explore the relationships between teachers' motivating styles, students' SRL ability, and their agentic engagement in online learning, hypothesizing mediating and moderating roles for SRL ability.

The literature review examines existing research on agentic engagement, teachers' motivating styles, and self-regulated learning. Agentic engagement is defined as students' initiative, purposefulness, and constructive actions in learning. SDT highlights the role of teachers' motivating styles, emphasizing the contrasting effects of autonomy-supportive and controlling approaches. Autonomy-supportive teaching fosters intrinsic motivation and engagement, while controlling teaching can be detrimental. The literature also establishes the significance of SRL ability as a predictor of learning success across various learning contexts. SRL involves self-directed goal setting, strategy selection, monitoring, and evaluation. Studies have shown that SRL is particularly important in online learning environments, where learners require more self-management skills. The review synthesizes these findings to frame the research questions focusing on the interplay between teachers' motivating styles, students' SRL ability, and their agentic engagement in the unique context of online college learning.

This quantitative study employed random sampling to collect data from 702 college students in China who had experience with online learning, resulting in 681 valid responses. An online questionnaire, developed and validated through pilot testing, exploratory factor analysis (EFA), and confirmatory factor analysis (CFA), measured four constructs: teachers' autonomy-supportive style, teachers' controlling style, students' agentic engagement, and students' SRL ability. Each construct was measured using a 5-point Likert scale, adapted from existing validated scales. The questionnaire's reliability and validity were assessed using Cronbach's alpha and composite reliability (CR), with values exceeding 0.9 indicating high reliability. Convergent validity was confirmed through factor loadings and average variance extracted (AVE) values above 0.5. Harman's one-factor test addressed common method bias. Data analysis was conducted using SPSS 21.0 and AMOS 24.0. Pearson's correlation analysis examined the relationships between the four variables. Mediation analyses, using PROCESS model 4, explored the mediating role of SRL ability in the relationships between teachers' motivating styles and students' agentic engagement. The bootstrap method was used to assess the significance of indirect effects.

The study found significant positive correlations between teachers' autonomy-supportive style and students' agentic engagement (r = 0.777), and between students' SRL ability and agentic engagement (r = 0.832). A positive correlation existed between teachers' autonomy-supportive style and students' SRL ability (r = 0.785). Interestingly, a positive correlation was also found between teachers' controlling style and students' agentic engagement (r = -0.003). However, a negative correlation emerged between teachers' controlling style and students' SRL ability (r = -0.109). Mediation analyses revealed that SRL ability partially mediated the positive relationship between autonomy-supportive teaching and agentic engagement. Furthermore, SRL ability showed a suppressing effect on the relationship between controlling teaching and agentic engagement; the direct effect of controlling teaching was positive, but when SRL was considered, the total effect became non-significant. This suggests that while controlling teaching style might have a direct positive influence on agentic engagement, this is countered by its negative influence on SRL ability.

The findings partially support existing literature on the benefits of autonomy-supportive teaching and the importance of SRL for student engagement. The positive correlation between controlling teaching and agentic engagement, contrary to expectations, might reflect cultural norms in the Chinese context where teachers’ controlling style is sometimes considered acceptable. The mediating role of SRL highlights the importance of self-regulation skills in translating teachers' support into enhanced engagement. The suppressing effect of SRL on the relationship between controlling teaching and agentic engagement indicates a complex interaction where SRL moderates the effect of controlling teaching. Students with higher SRL ability might be less susceptible to the negative influences of controlling teaching and still achieve high levels of agentic engagement. The study's implications suggest that teachers should be mindful of their motivating styles and adjust their approach based on the specific learning context and student characteristics. Furthermore, promoting SRL abilities among students would enhance their capacity for successful online learning, regardless of the teacher's approach. The unexpected positive relationship between controlling teaching and agentic engagement warrants further investigation into the cultural and contextual nuances of teaching styles in online learning environments.

This study confirms the interconnectedness of teachers' motivating styles, students' SRL ability, and agentic engagement in online learning. Autonomy-supportive teaching positively affects engagement through its positive influence on SRL. The study's contribution lies in its demonstration of the mediating and suppressing effects of SRL ability on the relationship between teachers' styles and student engagement. Future research should expand the scope of the study by including a wider range of student populations and exploring other factors affecting online engagement. Qualitative research methods could provide richer insights into the dynamics of teaching styles and student experiences in online learning.

This study's limitations include its reliance on a single university's sample, potentially limiting the generalizability of findings. The use of self-reported measures might be susceptible to biases. The study focused on a limited set of variables, and future research could incorporate additional factors (e.g., peer interaction, technology proficiency, learning content) that influence online learning experiences. A cross-sectional design prevents causal inferences; longitudinal studies would provide stronger evidence of causal relationships.